Mathematics Education: Being Outwitted by Stupidity

The way we used to teach math mirrors our effective interventions for those students struggling as low achieving/learning disabled, writes Barry Garelick.

By Barry Garelick

In a well-publicized paper that addressed why some students were not learning to read, Reid Lyon (2001) concluded that children from disadvantaged backgrounds where early childhood education was not available failed to read because they did not receive effective instruction in the early grades. Many of these children then required special education services to make up for this early failure in reading instruction, which were by and large instruction in phonics as the means of decoding. Some of these students had no specific learning disability other than lack of access to effective instruction. These findings are significant because a similar dynamic is at play in math education: the effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure.

In 2010 approximately 2.4 million students were identified with learning disabilities — about three times as many as were identified in 1976-1977. (See http://nces.ed.gov/programs/digest/d10/tables/xls/tabn045.xls and http://www.ideadata.org/arc_toc12.asp#partbEX). This increase raises the question of whether the shift in instructional emphasis over the past several decades has increased the number of low achieving children because of poor or ineffective instruction who would have swum with the rest of the pack when traditional math teaching prevailed. I believe that what is offered as treatment for math learning disabilities is what we could have done—and need to be doing—in the first place. While there has been a good amount of research and effort into early interventions in reading and decoding instruction, extremely little research of equivalent quality on the learning of mathematics exists. Given the education establishment’s resistance to the idea that traditional math teaching methods are effective, this research is very much needed to draw such a definitive conclusion about the effect of instruction on the diagnosis of learning disabilities.¹

Some Background

Over the past several decades, math education in the United States has shifted from the traditional model of math instruction to “reform math”. The traditional model has been criticized for relying on rote memorization rather than conceptual understanding. Calling the traditional approach “skills based”, math reformers deride it and claim that it teaches students only how to follow the teacher’s direction in solving routine problems, but does not teach students how to think critically or to solve non-routine problems. Traditional/skills-based teaching, the argument goes, doesn’t meet the demands of our 21st century world.

As I’ve discussed elsewhere, the criticism of traditional math teaching is based largely on a mischaracterization of how it is/has been taught, and misrepresented as having failed thousands of students in math education despite evidence of its effectiveness in the 1940’s, 50’s and 60’s. Reacting to this characterization of the traditional model, math reformers promote a teaching approach in which understanding and process dominate over content. In lower grades, mental math and number sense are emphasized before students are fluent with procedures and number facts. Procedural fluency is seldom achieved. In lieu of the standard methods for adding/subtracting, multiplying and dividing, in some programs students are taught strategies and alternative methods. Whole class and teacher-led explicit instruction (and even teacher-led discovery) has given way to what the education establishment believes is superior: students working in groups in a collaborative learning environment. Classrooms have become student-centered and inquiry-based. The grouping of students by ability has almost entirely disappeared in the lower grades—full inclusion has become the norm. Reformers dismiss the possibility that understanding and discovery can be achieved by students working on sets of math problems individually and that procedural fluency is a prerequisite to understanding. Much of the education establishment now believes it is the other way around; if students have the understanding, then the need to work many problems (which they term “drill and kill”) can be avoided.

The de-emphasis on mastery of basic facts, skills and procedures has met with growing opposition, not only from parents but also from university mathematicians. At a recent conference on math education held in Winnipeg, math professor Stephen Wilson from Johns Hopkins University said, much to the consternation of the educationists on the panel, that “the way mathematicians learn is to learn how to do it first and then figure out how it works later.” This sentiment was also echoed in an article written by Keith Devlin (2006). Such opposition has had limited success, however, in turning the tide away from reform approaches.

The Growth of Learning Disabilities

Students struggling in math may not have an actual learning disability but may be in the category termed “low achieving” (LA). Recent studies have begun to distinguish between students who are LA and those who have mathematical learning disabilities (MLD). Geary (2004) states that LA students don’t have any serious cognitive deficits that would prevent them from learning math with appropriate instruction. Students with MLD, however, (about 5-6% of students) do appear to have both general (working memory) and specific (fact retrieval) deficits that result in a real learning disability. Among other reasons, ineffective instruction, may account for the subset of LA students struggling in mathematics.

The Individuals with Disabilities Education Act (IDEA) initially established the criteria by which students are designated as “learning disabled”. IDEA was reauthorized in 2004 and renamed the Individuals with Disabilities Education Improvement Act (IDEIA). The reauthorized act changed the criteria by which learning disabilities are defined and removed the requirements of the “significant discrepancy” formula. That formula identified students as learning disabled if they performed significantly worse in school than indicated by their cognitive potential as measured by IQ. IDEIA required instead that states must permit districts to adopt alternative models including the “Response to Intervention” (RtI) model in which struggling students are pulled out of class and given alternative instruction.

What type of alternative instruction is effective? A popular textbook on special education (Rosenberg, et. al, 2008), notes that up to 50% of students with learning disabilities have been shown to overcome their learning difficulties when given explicit instruction. This idea is echoed by others and has become the mainstay of RtI. What Works Clearinghouse finds strong evidence that explicit instruction is an effective intervention, stating: “Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review”. Also, the final report of the President’s National Math Advisory Panel states: “Explicit instruction with students who have mathematical difficulties has shown consistently positive effects on performance with word problems and computation. Results are consistent for students with learning disabilities, as well as other students who perform in the lowest third of a typical class.” (p. xxiii). The treatment for low achieving, learning disabled and otherwise struggling students in math thus includes some of the traditional methods for teaching math that have been decried by reformers as having failed millions of students.

The Stealth Growth of Effective Instruction

Although the number of students classified as learning disabled has grown since 1976, the number of students classified as LD since the passage of IDEIA has decreased (see Figure 1). Why the decrease has occurred is not clear. A number of factors may be at play. One may be a provision of No Child Left Behind that allows schools with low numbers of special-education students to avoid reporting the academic progress of those students. Other factors include more charter schools, expanded access to preschools, improved technologies, and greater understanding of which students need specialized services. Last but not least, the decrease may also be due to targeted RtI programs that have reduced the identification of struggling and/or low achieving students as learning disabled. .

Having seen the results of ineffective math curricula and pedagogy as well as having worked with the casualties of such educational experiments, I have no difficulty assuming that RtI plays a significant role in reducing the identification of students with learning disabilities. In my opinion it is only a matter of time before high-quality research and the best professional judgment and experience of accomplished classroom teachers verify it. Such research should include 1) the effect of collaborative/group work compared to individual work, including the effect of grouping on students who may have difficulty socially; 2) the degree to which students on the autistic spectrum (as well as those with other learning disabilities) may depend on direct, structured, systematic instruction; 3) the effect of explicit and systematic instruction of procedures, skills and problem solving, compared with inquiry-based approaches; 4) the effect of sequential and logical presentation of topics that require mastery of specific skills, compared with a spiral approaches to topics that do not lead to closure and 5) Identifying which conditions result in student-led/teacher-facilitated discovery, inquiry-based, and problem-based learning having a positive effect, compared with teacher-led discovery, inquiry-based and problem-based learning. Would such research show that the use of RtI is higher in schools that rely on programs that are low on skills and content but high on trendy unproven techniques and which promise to build critical thinking and higher order thinking skills? If so, shouldn’t we be doing more of the RtI style of teaching in the first place instead of waiting to heal reform math’s casualties?

Until any such research is in, the educational establishment will continue to resist recognizing the merits of traditional math teaching. One education professor with whom I spoke stated that the RtI model fits mathematics for the 1960s, when “skills throughout the K-8 spectrum were the main focus of instruction and is seriously out of date.” Another reformer argued that reform curricula require a good deal of conceptual understanding and that students have to do more than solve word problems. These confident statements assume that traditional methods—and the methods used in RtI—do not provide this understanding. In their view, students who respond to more explicit instruction constitute a group who may simply learn better on a superficial level. Based on these views, I fear that RtI will incorporate the pedagogical features of reform math that has resulted in the use of RtI in the first place.

While the criticism of traditional methods may have merit for those occasions when it has been taught poorly, the fact that traditional math has been taught badly doesn’t mean we should give up on teaching it properly. Without sufficient skills, critical thinking doesn’t amount to much more than a sound bite. If in fact there is an increasing trend toward effective math instruction, it will have to be stealth enough to fly underneath the radar of the dominant edu-reformers. Unless and until this happens, the thoughtworld of the well-intentioned educational establishment will prevail. Parents and professionals who benefitted from traditional teaching techniques and environments will remain on the outside — and the public will continue to be outwitted by stupidity.

Source: U.S. Department of Education, National Center for Education Statistics (2011). Digest of Education Statistics, 2010 (NCES 2011-015), Chapter 2.

Barry Garelick has written extensively about math education in various publications including Education Next, Educational Leadership, and Education News. He recently retired from the federal government and has completed his requirements for a credential to teach math (middle school/high school) in California.

¹This article focuses on math teaching and learning, but the same pedagogical issues arise in history, science, and English Language Arts (ELA), including grammar, spelling, composition, reading comprehension and literature.

References

Devlin, Keith. (2006). Math back in forefront, but debate lingers on how to teach it. San Jose Mercury News. Feb. 19.

Geary, David. (2004). Mathematics and learning disabilities. J Learn Disabil 2004; 37; 4

Lyon, Reid (2001), in “Rethinking special education for a new century” (Chapter 12) by Chester Finn, et al., Thomas B. Fordham Foundation; Progressive Policy Inst., Washington, DC.
Available via http://eric.ed.gov/PDFS/ED454636.pdf

Rosenberg, Michael S., Westling, D.L., McLeskey, J. 2008. Special Education for Today’s Teachers: An Introduction. Columbus: Pearson, Merrill Prentice Hall.

Comments

Kevin

January 30, 2012 at 3:07 pm

This is excellent, Barry, thank you! Sometimes the best solution is the simplest one. If we don’t invest in robust math education for kids early, we will be paying through the nose for that omission later.

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- Mehr
  
  March 4, 2012 at 8:05 am
  
  Excellent article! I am tired of “Everyday Math” being used in schools- its confusing and assumes that all students are on the same level of understanding. Unless you have used this curriculum since KG its impossible to implement in higher grades. Being a Special Education teacher and Math teacher its impossible for my students and the gen ed. students to be appropriately challenged by these multi-step word problems unless they have a good number sense, that they achieved through traditional math teaching!
  
  Reply
  - Barry Garelick
    
    March 4, 2012 at 8:53 am
    
    Mehr,
    
    Thanks for your comment. I would point out that even those students who have had Everyday Math since kindergarten are at no greater advantage in the higher grades than those students who did not. EM’s spiraling approach does not ensure mastery.
    
    Reply
Chris L

January 30, 2012 at 4:32 pm

Barry, Comprehensive, well conceived and well presented.
Good comparative examples help to clarify your objective.
Well done!

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SteveH

January 31, 2012 at 7:07 am

My view is that the real driving force in pedagogy is full inclusion (tracking by age) and student-centered learning in the classroom. Curricula like Everyday Math “trust the spiral”, and educators claim that kids will learn when they are ready. This allows K-6 math classes to go through the motions, enforcing little grade-by-grade mastery of the basics. The assumption is that the process works by definition. It doesn’t.

Even in the private school my son was in, many perfectly capable kids got to fifth grade and still had trouble with the times table. The teacher had to ask kids to attend after-school basic skills classes. If this happens in an urban environment, it’s too easy to blame other causes. Everybody agrees on balance, but in the current educational math world, the skills portion of balance is taken for granted. Educators see no linkage with understanding.

Skills without understanding can be fixed. Understanding without skills is meaningless. There were a number of things I didn’t like about the traditional math I had growing up, but the current pedagogical thinking went off in the wrong direction. They broke the linkage between skills and understanding.

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haberstr

January 31, 2012 at 8:15 am

Excellent article, thank you. By the way, when talking about what’s at the root of the educational establishment’s irrational embrace of spiralling, and student-centeredness, and whole language reading instruction for that matter, is that these approaches relieve teachers of accountability for student achievement of specific learning outcomes. Fundamentally, then, it’s about protection of teachers who aren’t doing their jobs well, and most teachers, the competent ones, would be on our side if they were free to choose and allowed to speak and think ideas dangerous only to poor teachers.

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Jeannette Abulafia

January 31, 2012 at 3:38 pm

‘Understanding without skills is meaningless’ ought to be an obvious truth; instead, it’s often held up as an example of a troglodytic belief.

The spiral led to by the spiral curriculum is a downwards whirl…Mastery counts: It’s a ladder leading to further achievement -as people learning to play a sport or to play a musical instrument or to speak a new language know…

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Caroline

January 31, 2012 at 6:55 pm

This is such a cogent and thoughtful discussion! I agree completely with Joe that skill-based math can and must be taught alongside what is best about what we had in years past.

I have three kids and am a veteran mom of nine Fairfax County VA public schools. The math teaching here has been uniformly abysmal, but as a parent who bought into the FCPS public relations mantra that we’re the BEST, I wasn’t sure why my kids struggled (I’m pretty sure now). They are all gifted (one went to Thomas Jefferson HS for Science and Technology).

Example: In third or fourth grade, my daughter “got” how to calculate an irregular area using multiplication, but was told she had to do the math several different ways, one of which was something to do with counting all the little lines that extended from the area on a grid. I didn’t even get it. All it did was totally confuse her, and then lay the groundwork for many cries over the years of “I HAVE to do it the TEACHER’S way, or she’ll be MAD. I can’t do it YOUR way or MY way!” What a lesson!!

Anyway, I tried to overcome what I suspected was a gaping hole in their education by making them learn the times table, to marginal good effect, because it wasn’t required in school (for reinforcement). Plus, I resented the fact that I had to teach what my taxes and principles were already supposed to be paying for. Every one of my kids suffered later in higher math. If you can’t quickly do that kind of basic math, you have a million tiny obstacles to overcome to get to anything beyond it, with every single problem you encounter.

Terrible.

I really don’t get the problem with avoiding basic drills and basic skills. I remain proud to this day of when I mastered these in the various areas and stages of my life (writing and editing, becoming an auditor, doing ceramics, now doing triathlons.) This does not have to be “kill” or slog-work if it is instilled appropriately, as Barry writes. How many of us know adults who give up at the first signs of difficulty? Just going through the process of developing the ability to stick with learn basic skills is a skill in itself. Maybe that idea could kick those soft math folks into reverse.

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Barry Garelick

January 31, 2012 at 8:09 pm

I appreciate this dialogue and thank the commenters for their interest and insights on this issue.

Caroline, I too lived in Fairfax County, VA, and know exactly what you’re talking about. Everyday Math is used in many of the schools there (as my daughter’s school did) and it is as you describe. You also bring to light the fact that kids are placed under double duty because of these math programs. They feel they have put in their work at school only to find that they have to do additional work at home–the work that their math program has left out. So there is some degree of rebellion, and it is difficult for both parents and children. The children resist the additional lessons (multiplication times table for example) and the parents feel frustrated and guilty. On one back to school night, our daughter’s fourth grade teacher told the parents that their kids didn’t know their math facts and to please work with them at home so they could learn them. The message: It isn’t the school; it’s your kids.

I want to emphasize that “skills based” math does not mean skills with no understanding. Students from previous eras learned both the skills and the understanding that go with them. Many of today’s students, by contrast, lack the basic skills. And the understanding they have obtained from the dubious programs that pass as math curricula are in many cases–ironically–learned by rote.

Traditional math is portrayed as being nothing more than rote memorization with no understanding. This may be the case for traditional math done poorly–but it was also done properly, to good effect. I addressed this in more detail in another article called “The Myth About Traditional Math Education” located here: http://www.educationnews.org/education-policy-and-politics/barry-garelick-the-myth-about-traditional-math-education/

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wintertime

February 1, 2012 at 3:00 am

After spending several years working with the cub scout and tutoring programs in our church, I am convinced that the **only** children in our county who are learning to read, and do basic arithmetic ,have parents who aggressively **”afterschool**! Honestly, in working with these kids who do **not** have parents who are literally homeschooling after school ( “afterschooling”) it is like watching a train wreck in slow motion.

Parents! Your child’s education is **your** responsibility! Absolutely take charge.

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Glynne Sutcliffe

February 1, 2012 at 4:08 am

After sweating through the argumentation around whole language for 15 years and more, and realising very early that the same arguments were occurring in the realm of math education, I can hardly believe what I read here, not that – just as predicted – math education would be next on line for the same conflict, but that it has taken so long, and appears to be still stuck in the initial early phase of actually recognising the problem. Staggering!!!

Here’s a suggestion for parents – please take note, and act, to do everything you can to develop number awareness and basic calculating skills in the under-fives . For example “Uncle Joe and Aunt Mary aren’t able to come to dinner tonight, so when you set the table for me, how many knives and forks will you need now?” OK for a three year old. Amplify and diversify in the multiplicity of opportunities provided by everyday life. Remember every number is best appreciated as an observed quantum, and “counting to 100″ without quanta is just a party trick of little value (ie count things).

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SteveH

February 1, 2012 at 5:51 am

I remember one episode with my son and Everyday Math homework booklets. I told him to stop playing and do his math homework. Five minutes later I saw him playing and told him (stern father voice) to do his homework. He said it was done. I looked at the booklet and saw 6 simple problems. All of the assignments were like that. That was when I figured out that spiraling meant repeated partial learning. One parent complained that she had three kids in different grades and they were all covering the same material.

We had a parent/teacher meeting once about Everyday Math and it ended up being a vague discussion about the benefits of balance, but it was never defined. Then, in fifth grade, the teacher had to have an after-school “club” to improve the kids’ math facts. So much for balance. I was astounded when I went to the EM website and they were admonishing teachers to keep moving and “trust the spiral”.

One parent, with a master’s degree in applied math, loved the idea of Everyday Math. (I remember thinking that he will learn.) He even started an after-school math club for problem solving. By the end of the year, he was spending most of his time on basic skills and had a completely different view of the curriculum. It’s fundamentally flawed. He didn’t want to do what the school should have been doing.

This is not just a case of Everyday Math done poorly. It’s designed around the assumption that mastery will happen. One of the authors of EM even talked about how it doesn’t require mastery at any one point in time. However, as kids move through the grades, the gaps are not fixed and the students abilities separate further, especially when parents teach at home and ensure that math does not become a circle. These are the kids who get to algebra in 8th grade. These are the kids who give EM any sort of credibility. Then again, anything would look better than the MathLand curriculum we had before that. That was so bad that it was wiped off the face of the web, except for the remaining bad reviews.

They want K-6 math to be a pump and not a filter. but what they do is to pump problems along until the kids get to the big tracking filter in 7th grade (typically). Then, it’s easier to put the blame on kids, parents, peers, and society. Worse yet, the kids believe it. The parents of those doing well in math know what is really going on.

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SteveH

February 1, 2012 at 6:13 am

After dealing with this problem for over 10 years, I’ve seen the educational defense of these curricula diminish. Their arguments don’t hold up when confronted with details. For example, I don’t see anyone coming to the defense of EM on this thread. That doesn’t mean that articles and papers are not written. It’s just that they want to keep the discussion to vague generalities. It’s their turf. They are in charge. There is no process to force debate. At best, they will throw out some vague reference to the What Works Clearinghouse even though they don’t apply their critical thinking skills to determine exactly what the data says (or not).

It reminds me of the lack of defense for the Common Core Standards. It’s going full steam ahead in our state with PARCC testing, but nobody knows exactly what that will mean in terms of ensuring mastery of the basics on a grade-by-grade basis. There is no indication that it will have any effect on increasing the number of kids who get to algebra in 8th grade without help at home. Schools could survey parents about math help at home, but they don’t want to know the results. They don’t want to see the linkage between skills and understanding. My view is that it comes down to wrapping low expectations in the cloak of understanding and critical thinking. It sounds good, but there is nothing underneath.

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Barry Garelick

February 1, 2012 at 6:21 am

Glynne,

As Steve H points out, the problem with math education has been going on for some time. Parents are not just now discovering that there is a problem; these battles started as far back as mid 9o’s . What is staggering is not that it has taken this long for people to realize what is going on, but that the problem HAS been recognized for this long and that the problem still persists.

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Rhonda Thurman

February 1, 2012 at 7:45 am

Thank you so much for a great article! I am on our county school board and have fought this “new math” being taught here for the last 12 years. FINALLY the school board has voted to go back to a more traditional method of teaching mathematics. Howeverr, the question now is-what do we do about the students who are in our system with hardly no knowledge of basic math facts-other than apologize?
I once read that the reformed way of teaching mathematics is like trying to teach a student to play water polo before they know how to swim. To me that is a perfect explanation.

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- Lorett Di Gennaro
  
  February 8, 2012 at 12:37 pm
  
  Thank you for your comments. I just by chance came across this article while researching learning disabilites and college drop out rates. I have an LD son, educated in FCPS, attempting to get through the community college. He has a lot of fortitude and drive, has taken the pre college level math four times, finally passed when the curriculum at NVCC was revised and self paced according to skill acquisiton. So now he is in college math, can’t do it, afraid he is going to fail. It is all he need to get an A.A. and it might not happen. How many learning disabled kids is this happening to? They will be part of our underemployed and/or unemployed. Because of his twelve years of dismal math teaching in FCPS, he did not have the skills for a college level course, and has had a paid tutor all this time, too. To think that his dreams of a college education and being a profession might not happend because of one college math class!
  
  It is a horrible position we put our young people in. Anything that you can do on a political level would be appreciated by all learning disabled individuals and parents.
  
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- Aycee
  
  April 13, 2012 at 1:28 am
  
  As one of the aforementioned ‘afterschooling’ parents, I can tell you that a combination of a computer program called Timez Attack (a free download) and MathScore.com remediated a rising 4th grader who didn’t seem to know any math facts by rote IN ONLY 3 MONTHS! Memorize the times 2′s using Timez Attack, then drill the times 2′s using MathScore.com. *Full Disclosure* my student spent 20 minutes per day actually working problems on MathScore, twice the recommended amount.
  
  MathScore.com seems to have been created with a mind toward school-wide implementation, lots of charts and statistics to prove it’s effectiveness for state tests, and lots of *very* thorough reports for the teachers. I suppose the same is true for Timez Attack, since they give it away free of charge
  
  Remediation is possible, and much faster than I, for one, thought! Individualized instruction is the key, and technology makes that a possibility.
  
  These are just the two programs I happened upon on the internet that I tried. There are many others. Lift up your eyes from the marketing materials of Prentice-Hall, Houghton-Mifflin, et. al., and see what the entrepreneurs are doing. MathScore.com was made by a M.I.T. graduate and a resident of California, who became motivated by the ‘Math War’ going on out there to do something. (There is a nice article on that website concerning that topic, if you’re interested.) Timez Attack, as far as I can tell, was written by a concerned parent, who also happened to be a computer programmer.
  
  I realize that computer access is not feasible for every district. I have tutored kids locked in generational poverty in rural Appalachia, and meth is a lot easier to come by than computer access. If you are working with a low-income kids, Rhonda, you really have your hands full.
  
  In the old days, a 4th grade teacher would give fact drills and somehow keep track of the exact problems a student missed. Miss it once, we would write it 10 times. Miss it twice, write it 20 times. Miss it three times, we would write it 50 times. Miss it four times…well, no one missed it four times. After we had written it 70 times we pretty much knew it cold. Those were different times, when kids did homework. Today it is not uncommon for a parent to meet with a teacher to explain that her kid plays ball, so the teacher needn’t expect any homework to be done for the next three months — one of the reasons I’m against the current philosophy of blaming the teacher for the kids’ performance. If she has the authority to choose her own curriculum and a paddle with holes drilled through it, then, yeah, go ahead and blame away. But right now a teacher’s hands are tied.
  
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John Golden

February 1, 2012 at 9:04 am

“Understanding without skills,” is a straw man, just as you complain that “skills without understanding” is a misnomer. The majority of students in this country are NOT taught in reform style, so low current achievement numbers are not an indictment of reform. Reform mathematics is not some willy-nilly experiment – curricula are tested and researched before being released, as opposed to traditional curricula that often just spring forth from the author’s mind.

Ask people whether they like math. They don’t. Ask whether they are good at math. They aren’t. Asking university professors whether they liked traditional teaching is like the following: a medical trial is performed with a new drug. 98% die from complications, but 2% are cured. Interviewing the 2% to see how they liked it is foolish.

Math teachers and university professors are the 2%. (I am one.) We’re the ones for whom it worked. Ask us about it if you wish, but don’t base policy on us. Base policy on the vast majority of people we have ruined for math, and also for many this means science, too, and the resulting lack of STEM professionals.

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- Michael Paul Goldenberg
  
  February 1, 2012 at 9:29 am
  
  Of course you are right, John, but don’t expect Barry to admit it. Look at where he starts his piece: with an analogy to reading charlatan Reid Lyon and an appeal to the notion that the ONLY problem with impoverished kids learning is “bad” instruction (the “cure” for which Mr. Lyon sold to the nation under GWB and which failed MISERABLY while Lyon laughed all the way to the bank).
  
  Is it any surprise that a like-minded educational conservative simpleton/fraud would blame poverty-related math learning issues entirely on materials and methods that don’t fit his biases and call for the narrow approach that served him and other 2% ‘mathy’ folks (an approach I see all the time in both high needs schools of poverty in Detroit and affluent suburban schools, and which leave most kids hating math like the plague)? Obviously not.
  
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Richard Bramer

February 1, 2012 at 9:36 am

I can’t believe so many people interested in Math think this article is well done. The author first uses a count of all learning disabilities and then applies the rate to Math instruction without any declared reason for supposing that it applies.

He then maintains that Math education has switched to reform-guided methods, as if the process were uniform and universal. Neither is the case. All major publishers are still publishing books that support traditional methods moreso than reform.

He also calls for a phonics-like ‘decoding’ instruction in Mathematics like has been seen in English Language Arts. With some research into that claim, one sees that the phonics movement has hardly proven its case. In fact, many schools are dropping it.

He also claims there has been very little research of quality on early learning in Mathematics, and like so many of his claims does so without reference. The notion is absurd. Math education and Reading education are the most researched areas in our field.

Then, while complaining about the mis-characterization of traditional methods, which is the one argument included which could have some merit, he repeats the error by an extremely shallow synopsis of reform methods.

He then falsely equates “explicit instruction” with “traditional” methodologies. Reformers, as their students well know, are entirely capaable of “explicit instruction”. There is nothing in being explicit that precludes teaching through discovery.

Then, if things weren’t bad enough, he provides hearsay, quite probably poorly quoted, conversations with reformer professors. No names, no means of checking if those people indeed thought RTI was the same as traditional and whether they were arguing with the latter rather than the former. Indeed, a careful reading of that paragraph strongly suggests that the author provided the RTI context entirely for this article and never occured in the conversation.

I don’t know of a serious reformer who doesn’t use, occasionally the method known as ‘drill and kill’. The author’s attempt to characterize his supposed opposition with the robotic “edu-reformers” does nothing to elucidate the issues. With the only data offered reflecting learning disabilities, and not a whit about the failures of traditional methods (which are many, but do not constitute in any classroom teacher’s mind a reason to toss it out entirely), and worse – mischaracterization and misleading, unreferenced claims to paint the worst possible picture about reform’s methods, one can only wonder how the author got published in the first place. The level of research wouldn’t pass muster in a Special Ed class in my school. And all that, presumably, without a learning disability.

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SteveH

February 1, 2012 at 10:09 am

I see that the goading caused some reaction from the old guard.

“The majority of students in this country are NOT taught in reform style, so low current achievement numbers are not an indictment of reform.”

I never made that connection to numbers, and what is the percentage for each type of curricula? What grades are you talking about? Our middle school finally (!) dumped CMP for proper Glencoe textbooks. There was a curriculum gap between 8th and 9th grades. Now it’s between Everyday Math in 6th grade and Glencoe Pre-Algebra in 7th. Our high school has not gone silly with integrated math. In K-6, however, I can’t imagine that there are many schools left using traditional curricula. That’s where all of the damage is done. It’s not just the type of curriculum, it’s the low expectations.

“Base policy on the vast majority of people we have ruined for math, and also for many this means science, too, and the resulting lack of STEM professionals.”

This is just crap. Do you really think that K-6 schools are increasing the number of STEM-ready students? What is it about reform math (say, Everyday Math) that does this? There were many things I didn’t like about my traditional math education, but at least I got to calculus in high school without any help from home. This is virtually impossible now.

Have you ever asked the parents of students who get to algebra in 8th grade what help they provided at home? I would love reform math if it worked. More understanding. Great! Where is it? Balance? Wonderful! Where is it? Everyday Math just pushes the kids along and then blames them in the end. By then, not even Math Boxes can help.

As I’ve always said, I didn’t like many things about my traditional math education, but the current K-6 reform curricula have gone in the wrong direction. They don’t provide understanding or skills. Most of all, they do not prepare kids properly for STEM careers.

Reply
SteveH

February 1, 2012 at 10:21 am

It’s interesting to see that MPG has not figured out any better arguments that his usual level of political ad hominem attacks.

Reply
Barry Garelick

February 1, 2012 at 10:32 am

“He also calls for a phonics-like ‘decoding’ instruction in Mathematics like has been seen in English Language Arts. ”

I don’t recall calling for a phonics-like decoding instruction in math. I think I would like to see more explicit systematic instruction, and also more reliance on students working individually on problems.

The shift in reform type math teaching that I refer to is in part due to certain types of texts/programs being used (e.g., Everyday Math, Investigations in Number, Data and Space, Connected Math Program, Math Trailblazers, enVision Math, IMP, Core Plus). It is also due to changes in the more traditional texts that have seen the influence of NCTM’s principles and standards. At the high school level, geometry texts de-emphasize proofs, and algebra texts contain fewer word problems of the type that reformers hold in disdain (distance/rate, mixture, work, etc) for more “real world” and sometimes open ended problems. At the K-6 level, some of the traditional texts rely on calculator use and some use a “spiralling” approach. This is not to say all, and I agree that I provided a general description of both traditional and reform math. I have gone into detail on these topics in other articles.

I openly express opinions in this article, it is true, and have used the phrase “in my opinion” in it. I also recognize in the article the need for research to make definitive what is now my opinion and I say so. As for the lack of high quality research in math education that is equivalent to that found for reading, I based that on the President’s National Math Advisory Panel’s difficulty in finding such research that met their research standards.

I do not believe that the increase in the number of students classified as LD is due solely to math instruction. I am asking whether and to what extent some portion of it is due to math instruction, and of those, how many students are low achieving, as opposed to LD. I also ask whether in a different era, whether some of the students currently classified as LD would have been able to swim along with the rest of the pack in math.

Reply
SteveH

February 1, 2012 at 10:55 am

“All major publishers are still publishing books that support traditional methods moreso than reform. ”

This is kind of an interesting new twist in the defense of reform math. Rather than defend the premise and details of reform math, the goal seems to be to claim some sort of confusion over where the problems lies.

“I don’t know of a serious reformer who doesn’t use, occasionally the method known as ‘drill and kill’. ”

I’m not sure what this means – that there are no fundamental differences in philosophy or in implementation? In a crude sense, traditional methods work up from mastery of the basic skills. The issue is that the job may not get done right and that students may not have much understanding of what it is they are doing. Reform math tries to work down from some level of understanding, with the problem that the understanding might be superficial and that skills are never mastered. I could claim that a major issue is low expectations.

Go ahead and use Socratic hands-on methods while sitting around a Harkness Table, but you better show that it works. My experience is that these methods only have a chance of working if the students are good and that there is a high level of expectations. In the real world, however, Everyday Math just pumps bright kids along without ever forcing the issue of mastery at any one point in time. At least in a traditional math format, schools bite the bullet and keep kids from moving to the next grade. They don’t pass the buck.

If our schools started to use Singapore Math in K-6, I can imagine that their full inclusion, tracking-by-age philosophy would still cause all sorts of problems. It’s just that reform methods give them more pedigogical cover for lower expectations. Kids will like math if you have more fun and use real world examples. Happy, active learning is no guarantee of success. Kids will be happy until they get to that big filter in middle school or high school.

One can also argue that kids like something if they feel comfident about their skills. Top-down real world math might be fun (like eating mathematical Twinkies) but leave the students lost and confused when pie-chart fractions turn into rational expressions. Claims of motivation and engagement are overrated.

Again, it would be nice if arguments could be made without ad hominem support.

Reply
Gary Rowe

February 1, 2012 at 10:56 am

There is a compelling solution that addresses both fluent knowledge of math facts and conceptual fluency. The software for the middle grades is iPASS and can be reviewed at my client’s website, http://www.iLearn.com. Take time to review the outcomes and you’ll find that it works effectively with all students and produces dramatic results with students with disabilities.

Reply
Richard Bramer

February 1, 2012 at 11:01 am

I’m glad to see you are willing to have a much more balanced discussion, at least in the comments section. Still to be explained is the use of stupidity, edu-reformers.

The section where you apparently call for decoding skills in Math:

“I believe that what is offered as treatment for math learning disabilities is what we could have done—and need to be doing—in the first place. While there has been a good amount of research and effort into early interventions in reading and decoding instruction, extremely little research of equivalent quality on the learning of mathematics exists. Given the education establishment’s resistance to the idea that traditional math teaching methods are effective, this research is very much needed to draw such a definitive conclusion about the effect of instruction on the diagnosis of learning disabilities.1″

Still unaddressed: your mistaken identification of traditional with RTI, and indeed, the necessity of kicking the quite dead horse of the Math Wars. Math educators have moved on. We are living in a post-NCLB world, where the shortfalls of purely “drill and kill” were highlighted and a sensible return to a middle ground represented by the new Common Core standards is upon us.

Reply
- Michael Paul Goldenberg
  
  February 1, 2012 at 3:25 pm
  
  I wouldn’t bet on the notion that the Common Core represents anyone having moved on, Richard. Have you read any of H. H. Wu’s recent articles on mathematics education, particularly those about teaching fractions? Wasn’t he a MAJOR player in the development of the math Common Core? The more I read the actual content standards, rather than the NCTM-ish sounding process standards, the more I am convinced that little is changing. The tests will be horrid, the pressure to do more of what was being done for decade after decade will increase, and only a scattering of teachers will find ways to teach meaningful mathematics in classrooms. The rest will have to resort to the underground, be it the ‘Net or local math circles or home schooling or unschooling. Those who control assessment will control content and pedagogy: last I checked, that will be Pearson, McGraw Hill, the ETS, and similar companies and organizations. And those who resist giving students a chance to think about and do mathematics in any meaningful way will continue to fight tooth and nail for a one-size fits all, Procrustean model of mathematics education. I wish I were wrong, but I’m pretty damned sure that I’m not.
  
  Reply
Laurie H. Rogers

February 1, 2012 at 11:01 am

Take a moment, if you care, to Google Mr. Goldenberg and see what he considers to be a sound argument in favor of reform math.
Also note his use here of an ad hominem argument: “…a like-minded educational conservative simpleton/fraud…”
This is what people do when logical arguments fail them.

Richard Bramer says: “All major publishers are still publishing books that support traditional methods moreso (sic) than reform.”
That is not a true statement, unless Mr. Bramer has helpfully redefined what is meant by a traditional textbook.
Bramer says: “…one sees that the phonics movement has hardly proven its case. In fact, many schools are dropping it.”
The first part of this claim is false; the second probably is true, and we will see the attendant decrease in literacy that always follows the dropping of phonics.
Bramer says: “I don’t know of a serious reformer who doesn’t use, occasionally the method known as ‘drill and kill’.”
Well, I know plenty. I don’t call it “drill and kill,” which supposedly indicates the killing of interest in math by drilling. It’s a foolish term, and Bramer’s use of it indicates his feelings about the value of practice. Children need practice, not occasionally, but all of the time. To teach them properly, they should be taught, encouraged to practice to mastery, and then given the next concept.
Only reformers refuse to understand that.

John Golden’s first paragraph is wrong, on nearly all counts. His second paragraph contains truth, however he cannot seem to connect cause with effect.

Reform math doesn’t work, not here, not there, not anywhere — not since the country first swallowed the lie whole, in the 1980s. And yet, the education establishment is married to it. They see children failing, they see the country faltering, they see economies staggering under the weight of an undereducated, frightened populace, and all they can come up with is some variation of “…a like-minded educational conservative simpleton/fraud…”

The lesson here is that parents must take back the classroom from these people. Test your children with a basic skills test like the free Saxon Placement tests or the free Singapore Math Placement tests. See what they know. Fill in the gaps. Remove yourselves from people who refuse to see the problem, and take care of it yourself. If you want any help with it, contact Barry Garelick or me or others like us.

In the end, the only thing that matters is what these children know how to do. All of the blah, blah, blah about reforming and transforming and innovation doesn’t change that simple fact. If children don’t know how to do mathematics properly (and most of them don’t), then the pseudo-intellectuals pushing reform math on us have failed. They won’t ever see it, and that’s why parents and grandparents must see it.

Thank you, Barry. I enjoyed the article.

Laurie H. Rogers
Member of the executive committee for Where’s the Math?
“Betrayed: How the Education Establishment Has Betrayed America and What You Can Do about it”
“Betrayed” – a blog on education: http://betrayed-whyeducationisfailing.blogspot.com
wlroge@comcast.net

Reply
- Michael Paul Goldenberg
  
  February 1, 2012 at 3:18 pm
  
  Right, Laurie. No good arguments for ‘reform math,’ whatever that is, exactly. So I simply have to resort to ad hominem, unlike Mr. Garelick, whose article here is just brimming with facts (or should I say “factoids”) like the fraudulent Mr. Lyon. Lyon’s failure with his ridiculous pseudo-solution to reading is well-documented in the media. Of course, that doesn’t stop certain of the usual suspects from continuing to hail him as a hero and quote his “fact-filled” call for blowing up the schools of education.
  
  Similarly, Mr. Garelick offers slanted take on the last 20 years or so of mathematics education, reducing everything to parodies of the real issues and putting WAY too much weight on textbooks. If the traditional teaching methods (i.e., lots of lecture followed by lots of seatwork practicing problems structurally identical to those done as examples. That, of course, is how the VAST majority of math textbooks, from “sensible” Glencoe to the output of every major and minor publishing house are still written/structured, though some add on various bells and whistles so as to appear to be all things to all people; however, those of us who spend our days in real classrooms in places like Detroit, Pontiac, Flint, Ypsilanti, Saginaw, and other high-needs, poverty-stricken communities – and my friends who teach in LA, NYC, Seattle, etc., report the same sorts of things – see VERY traditional teaching from VERY traditional books. As the high-stakes testing mania grows stronger, there’s less and less time spent on anything but drilling for tests, less and less content is examined, and what is examined is not looked at with any depth or thought.
  
  The red-herrings of “constructivism,” “fuzzy math,” and the rest of the rhetorical arsenal of Mathematically Correct, HOLD, and their imitators, allies, and off-shoots, continue to obfuscate the fact that there’s precious little daring, interesting mathematics instruction going on, particularly in those places most desperately in need of SOMETHING to get kids interested in mathematics and up to speed. That lack of being caught up has nothing to do with what books get used (or at least very little to do with it), and it’s not caused by the mythical influx of “fuzzy” instruction either.
  
  The problems Garelick and his ilk complain about (when not trying to make a federal case against one sort of book and in favor of Singapore or Saxon, or whatever they’re selling now) were there 20 years ago, 30 years ago, 40 years ago, 50 years ago (when I was in public school) 75 years ago (when my parents were in K-12), and before that as well. Anyone who cares to read the history of mathematics education in this country will find the real facts, not the mythology of the “Golden Age” of math when all kids knew their facts.
  
  But I very much doubt that my critics here will bother to read that history. It’s so much more convenient to claim that those facts don’t exist and blame everything on “fuzzy” reform (though now the words “educational reformers” refer to the moneyed alliance of the oligarchs (Gates, Broad, Walton, et al.) with “geniuses” like Rhee, Klein, ad nauseam). So much easier to keep pinning the blame on those who tried to shake us out of a century of drudgery (even if they erred – shock of shocks! – in one way or another with specifics), because after all, the single most important thing in a mathematics classroom is the TEXTBOOK, right? Followed closely by the expert teacher whose wisdom is unassailable and whose knowledge will be poured into the open heads of students, as long as those little critters will pay attention. Those who don’t? Well, we need not care about them. We taught our wonderful lessons: the rotten kids just refused to learn. Those who failed to learn by their own volition do not deserve success. The small percentage who do, those who are most like their teachers, will be rewarded in college and beyond.
  
  It’s a lovely self-fulfilling little prophecy and philosophy of education. The only problem is that it fails to adequately serve the VAST majority of kids. What the traditionalists figured out was that once progressive math came along, they could ignore the ’70s and ’80s that drove the reform, pretend that US math education history began in 1989 with the publication of the NCTM standards, and blame EVERYTHING on reformers. And the fools and true believers bought it then and are still buying it.
  
  Is that ad hominem? Or is it simply the truth? Well, of course, you wouldn’t resort to ad hominem yourself, any more than would Mathematically Correct or HOLD use a page or two of demeaning insults and epithets to describe anyone who isn’t part of their One True Religion. Talk about pots calling kettles “black.”
  
  What is so pathetic is that 20 years down the road, the traditionalists, like today’s GOP, ask us to ignore history, ignore the causes of progressive reform efforts, and give them have another century in which they reach the few and rationalize their disdain for the vast majority.
  
  Those who ignore history are doomed to repeat it. Those who refuse to even READ the damned history in the first place are doomed to swallow a box of thinly-disguised horse dung.
  
  Reply
Richard Bramer

February 1, 2012 at 11:23 am

@SteveH: I think, if you try that again, but this time pretend you are reading a comment from a family member, that you will find that the world has many fewer fools in it than you may believe.

In short, I don’t see the point of so blatantly misrepresenting an argument.

Reply
Barry Garelick

February 1, 2012 at 11:34 am

The treatment for math learning disabilities that I mention is explicit and systematic instruction. The reference to decoding is with respect to reading research and the interventions used there–I wasn’t calling for similar type of decoding instruction in math.

Parents continue to oppose the adoption of programs like Everyday Math and CMP in school districts and are often shut down and the school district prevails. Parents continue to be told “You like the old way of teaching math because it’s what you know” and “traditional math has failed thousands of students”. The programs come with a bill of goods that doesn’t come to fruition. While you and other commenters do not believe that reform math is used that often in the US, in the areas where it is used, it comes packaged with promises of “research-based” data. The research is questionable and the results are not all that great.

Based on these battles, I don’t see evidence that the math wars have ended. As far as Common Core standards represent a return to the middle ground, I don’t quite see that. There are many good content standards, it is true, but also many “process” type standards which reminds me of NCTM in many ways.

RtI relies on explicit and systematic instruction, as does properly executed traditional math teaching. The IES’ practice guide for Math RtI (http://ies.ed.gov/ncee/wwc/pdf/practice_guides/rti_math_pg_042109.pdf) states that “Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.” The guide provides examples of the types of instruction that should be used, and many are those used in traditional settings. The guide recommends devoting about 10 minutes to ensure fluid retrieval of math facts, and states that “Curricula may not include enough fact practice or may not have materials that lend themselves to teaching
strategies. Some contemporary curricula deemphasize fact practice,
so this is a real concern. In this case, we recommend using a supplemental program,either flash card or technology based.”

In this regard, the RtI is similar to traditional.

Reply
Danaher M. Dempsey, Jr.

February 1, 2012 at 12:37 pm

John Golden wrote:

“The majority of students in this country are NOT taught in reform style, so low current achievement numbers are not an indictment of reform. Reform mathematics is not some willy-nilly experiment – curricula are tested and researched before being released, as opposed to traditional curricula that often just spring forth from the author’s mind.”
=========

NOT TRUE in WA State… where the vast majority of k-8 students used Reform Materials

SPI Dr. Terry Bergeson pushed “Reform Math” so vigorously that 95+% of elementary schools used Reform Text books. 65% of Middle Schools used Connected Math Project.

Our state of Washington has been on the leading edge of this math disaster.

Perhaps John Golden is correct that “curricula are tested and researched before being released”

but I can assure you that when used in WA State Schools the results from using “Reform Materials” have been extremely disappointing.

The Elite Experts at the University of Washington are regular contributors to this “Reform Math” disaster.

UW Professional Development Gone Bad
A Report on some of the Damage ==>

http://mathunderground.blogspot.com/2010/09/uw-professional-development-gone-bad.html
==============
In WA State
low current achievement numbers are an indictment of reform math.

Reply
Richard Bramer

February 1, 2012 at 1:30 pm

@Barry Garelick: I see now what you intended with the decoded reference.

The direction of instructional practices is divergence of delivery – using several different modalities or methodologies in the same classroom. One method is expected to capture some students, another will work for other students. To adequately instruct a roomful, you must mix it up. I have heard this message repeated in seminars, webinars, lectures, books, articles and in hallway conversations. I can’t believe you haven’t heard the same.

About RTI, however: your description is sorely lacking. RTI is about early detection of low acheivement, re-teaching, re-measuring. Even the link you provide outlines that fact in its introductory paragraphs.

In a situation where quick, efficient practice of a small set of skills is the goal, explicit instruction is a good method. Hence, btw, the continued use of it by reformers and traditionalists alike. It is woefully inadequate to the task of encouraging problem solving where a problem is bigger than a few sentences or requires more than one algorithm.

Incidentally, RTI also calls for frequent assessments of small bits of material for this very reason. They are not only easier to measure, but are easier to address (re-teach) and hence the call for explicit methods in that context.

Reply
Barry Garelick

February 1, 2012 at 2:18 pm

Richard, I have heard about different modalities and methodologies, usually in the context of learning styles and multiple intelligences. Dan Willingham (cognitive scientist from U of VA) and others have argued that the theory of learning styles and multiple intelligences is wrong. I am not advocating for one type of delivery, and in fact my teachers used a combination of direct instruction mixed with questioning and other strategies to get us to think and lead us to the particular concept or procedure. I have heard in various hallways some disdain for such “teacher-led” inquiry and discovery. Discovery can even be effected within problem sets or exercises in which the exercises are carefully constructed, allowing for scaffolding and leaps beyond the “worked examples.”

I also am in favor of ability grouping of students, which is also held in disdain for the lower grades.

I agree that RtI is about early detection but once detected the “re-teaching” is done using techniques that are explicit and similar to if not the same as traditional methods. I do question in my article the degree of reteaching — or need for RtI — where the non-traditional or reform programs/techniques are used and suggest that this is an area of research.

You argue that explicit instruction is inadequate for problem solving, particularly where more than one algorithm is involved. Problem solving requires as a pre-requisite, mastery of various algorithms, and mastery of various methods for problem solving which can be addressed with worked examples and explicit instruction. Advancement to more complex problems comes with much practice and experience, but without the pre-requisites mentioned, it is likely not to occur. The ability to solve non-routine problems comes from a mastery of a variety of routine problem solving schemas.

Reply
Michael Paul Goldenberg

February 1, 2012 at 3:31 pm

Mr. Dempsey pretends that textbooks are the key to everything. Experience in actual classrooms in a large number of representative communities in Michigan, as well as in New York City, suggests that the pedagogy stays the same. A traditional teacher can turn any book into traditional mathematics instruction, and that is what happens most of the time. And when the traditional books are restored to prominence, the classrooms look just the same, the teaching looks just the same, the kids are just as confused and disengaged, and things continue to be awful for most students, hence the nearly-universal fear and loathing of mathematics in this country for more than a century. Lying about the imagined Golden Age is pathetic. Denying the implications of the fact that there’s never been such a time here, no matter what books were used, is, on my view, intellectually bankrupt and highly unethical. If one of you defenders of the True Faith can present real statistics and research to back the myth, by all means let’s see them. Otherwise, give the baloney a rest.

Reply
Richard Bramer

February 1, 2012 at 3:56 pm

The more these discussions continue, the more my point is made, I think. There is a lot less space between the two sides than is often imagined.

The simple facts: economies of time and effort suggest traditional methods but these don’t handle higher order thinking and complex problem solving as well. Depth of understanding and creative solutions, (and all polls of private businesses suggest that these are much sought-for skills) suggest reform methods but these don’t handle standardized tests as well.

Reply
Raza usman

February 1, 2012 at 10:29 pm

To know math you have to do math. To do math you need skills.

The high IQ need to work problems once, repeatedly solving problems work for the rest of us. Its as simple as that…

Reply
David Roth

February 1, 2012 at 10:32 pm

The politics of reform v traditional math are absurd. Students clearly need both, just as in reading they need real books with real content as well as phonics instruction and in history they need facts and big think.

We need more time on task more than anything else. We need the hybrid of teaching skills and routines along with out-of-the-box problem solving and deep thinking problems.

The reform curricula generally provide neither solid algorithms nor do they give intellectually interesting or challenging word problems that can be built upon for skill or intuition. They instead are in love with their own favorite approaches, and force idiotic algorithms down students’ throats even worse than traditional math does.

I do tons of extra intuitive and structured math with my kids and their friends because school is so inadequate, as much for the limited time on math as for poor approaches.

Reply
SteveH

February 2, 2012 at 5:45 am

“economies of time and effort suggest traditional methods but these don’t handle higher order thinking and complex problem solving as well. Depth of understanding and creative solutions, (and all polls of private businesses suggest that these are much sought-for skills) suggest reform methods but these don’t handle standardized tests as well.”

It’s not only the tests that it doesn’t handle well, it’s the skills. Even with our state tests that match the critical thinking and understanding taught by reform methods, kids don’t do well. There is not some magic sort of understanding that makes it OK not to do well on tests. All you have to do is to look at the questions on the tests and the raw percent correct scores. Kids might appreciate math, but many will be off the STEM career path by 7th grade unless they get help with skills outside of school. I have received notes from our schools telling us parents to work on math facts with our kids. What if parents won’t or aren’t able to help?

You don’t get something for nothing. If you start from the top and work down with real world problems and understanding, you might see a lot of active learning, but the time taken up in class for this leaves little room for ensuring mastery of the basics. This even causes problems with kids in affluent towns, so how can one expect that it will magically work in urban areas? Everyday Math tells teachers not to slow down – to “trust the spiral”. My son’s 5th grade teacher realized that basic skills were not getting done and spent more time on them. She didn’t get to 35% of the material. You don’t get something for nothing. Engagement is not some magic elixir that will make mastery easy or automatic.

Nothing stops tradidional approaches from doing real world problems – my son did these things while proceeding through a Glencoe Pre-Algebra textbook, but these problems were added on after basic skills were mastered. They were not the vehicles for learning basic skills.

There IS a fundamental difference in philosophy. This article talks about the critical importance of skills – about how they have to be addressed and mastered first. You cannot rely on going through the motions of a spiral and trusting that skills will be achieved. It doesn’t happen.

A top-down approach that uses up a lot of class time with student-centered learning requires much higher expectations for homework. I’ve seen this work only in schools (usually high schools) that set much higher expectations. Phillips Exeter with it’s Harkness Table is one of them. There is a high school academy in our area that also uses that approach. However, there are other high schools (like Phillips Andover) that use a more traditional approach. They also set high standards and expectations.

I don’t see this top-down philosophy working well in K-6, especially in urban areas. I haven’t even seen this work well in affluent towns. A top down approach requires higher expectations, but I don’t see that at all with K-6 reform math curricula. I just see lower expectations. Schools want full inclusion and tracking by age. Curricula like Everyday Math allow schools to do this by spiraling through the material, trusting the spiral, and putting the onus on the students.

This is all about ensuring mastery of skills in a timely fashion. To get on a STEM career, you need to start ensuring these skills in first grade. You cannot trust the spiral.

Reply
If it works for struggling math students … — Joanne Jacobs

February 2, 2012 at 6:08 am

[...] Explicit instruction in math — once the traditional way to teach — works for struggling …. It would work for all students, argues Barry Garelick on Education News. What Works Clearinghouse finds strong evidence that explicit instruction is an effective intervention, stating: “Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.”. [...]

Reply
Richard Bramer

February 2, 2012 at 10:29 am

Circles in geometry are interesting. In adult conversation, less so.

If you have decided that traditional math ed is the only (or even simply superior) way to go, I’m quite certain no amount of common sense or data will change your mind. For that reason, I am not attempting to do so.

Pointing to basic skills does nothing to support the argument. Traditional math ed does a poor job of attracting students to the task. Thus, like junkies, they need the quick, economical approach, the ‘quick fix’ afforded by explicit instruction. Relying overly on it creates the need for more of it. This is not a point in it’s favor.

In-depth problems are simply not handled well by explicit instruction. It doesn’t work that way in any field, much less in math.

Does that mean teaching basics is an optional activity? Of course not. Think of the professional football coach who showed up at practice and announced to his millionaire players, “This is a football.” Rehearsing the basics is a good idea. But it will not, by itself, create deep thinking or creativity.

Reply
Michael Paul Goldenberg

February 2, 2012 at 10:45 am

The continued lie propagated by Garelick and the Mathematically Correct/HOLD crowd is that progressive mathematics educators believe in a dichotomy where one must choose between content and understanding. I have yet to read, in more than 20 years in the field, a single research or journal article that advocates for that dichotomy, let alone that we should teach understanding rather than content.

What makes that lie so specious and insidious is that in fact what progressive mathematics educators have posited is that the majority of mathematics instruction in this country places computation over thinking. Not the ludicrous notion that one can think about mathematics without being able to do computation (though HOW that computation is accomplished is a point of contention), but rather that making mathematics little more or nothing more than computation in K-12 has killed the subject for most Americans, making it as dead as a music class that insists that we best learn music and its pleasures by memorizing the names and dates of composers and their works, rather than listening to music, analyzing it, perhaps even trying to do a little elementary composition of our own (perish the thought!)

The fraudulent claim that progressive approaches to math are “content free” is repeated so often that those who aren’t familiar with what’s actually going on become convinced in advance that the choices are “real mathematics with real content taught in the traditional manner” and “content-free math ‘appreciation’ that encourages kids to describe math in poetic terms but never actually learn any mathematics.”

It’s a lovely bit of sophistry on the part of the anti-progressive crowd, but it’s also an utter lie. And Garelick’s latest bit of sneering rhetoric, with a predictably insulting title meant to utterly dismiss any approach (and person) not dreamed of in Barry’s philosophy as ‘stupidity.’

If I were to publish something like that, merely turning everything around, my critics here and elsewhere would attack me for my shameless and shameful ad hominem attacks. But Barry Garelick, a heroic Math Warrior, gets a free pass from these same folks, merely making crystal clear to any neutral observer that the anti-progressives never play by the same rules those who oppose or question them are expected to follow. And it is precisely that hypocrisy that long ago convinced me that I need not be bound by decorum in dealing with these very dirty players. I neither apologize for nor regret anything I’ve said about them, and with very good cause.

Reply
Katharine Beals

February 2, 2012 at 12:08 pm

Progressive approaches to math aren’t content-free. They just have a lot less math content, and more heretofore unheard-of problems that involve much less math (and a higher ratio of non-math to math), like “How did you practice your multiplication combinations? Who helped you?” (4th Grade TERC/Investigations); “Work with a partner to find out how exercise affects your heart rate” (5th grade Everyday Math), and “Try to remember a time when you or someone in a group you were in was left out of a discussion. Describe the situation, Did anyone try to include that person? If not, why not? If yes, then how?” (Interactive Math Program).
In 4th grade TERC/Investigations, an entire assignment consists of problems like 399 + 1 = ___. In the dozen Reform high school math texts I’ve reviewed, I have yet to see simultaneous equations with more than two unknowns, or many (if any) problems involving polynomials of degree greater than 2. Assignments requiring formal proofs, which for many of us were the highlight of geometry, are practically nonexistent.

These are just a few ways in which, compared with traditional math, and, indeed, with math used in Continental Europe (including Russia), the Indian subcontinent, China, Japan, Singapore, and Taiwan, American Reform Math has much less mathematical content.

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Kim Simons

February 2, 2012 at 1:20 pm

Actually, there’s a very simple solution to the myriad of problems that plague our education system – get rid of it. Forget the back and forth debates because no one will ever win, and frankly, both sides are wrong. Give schools the power to decide for themselves which instructional practices and program they want to employ and give parents the right to choose where to enroll their children.

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SteveH

February 2, 2012 at 1:49 pm

“If you have decided that traditional math ed is the only (or even simply superior) way to go, I’m quite certain no amount of common sense or data will change your mind. For that reason, I am not attempting to do so.”

I’m open to new approaches if they work. Do you have one of those?

“Pointing to basic skills does nothing to support the argument. Traditional math ed does a poor job of attracting students to the task.”

Reform math does a better job? Maybe it attracts them to the task, but is the goal accomplished?

“In-depth problems are simply not handled well by explicit instruction. It doesn’t work that way in any field, much less in math.”

Explicit instruction doesn’t work on “in-depth” problems? Wow! Do you have proof of that? It doesn’t just do a poor job of attacting students to the task, it apparently doesn’t work? How does reform math do a better job? It attracts students but doesn’t work?

“Think of the professional football coach who showed up at practice and announced to his millionaire players, “This is a football.” Rehearsing the basics is a good idea. But it will not, by itself, create deep thinking or creativity.”

Professional football players do a lot more than rehearse. There is a lot of direct instruction and high expectations. So what does rehearsing consist of in reform math? How do you know it gets done if you denigrate standardized tests? This is the key criticism of reform math. The rehearsal doesn’t even prepare kids for any sort of meaningful “deep thinking and creativity.”

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SteveH

February 2, 2012 at 2:06 pm

“I have yet to read, in more than 20 years in the field, a single research or journal article that advocates for that dichotomy…”

The charge is leveled at the reformists. If you don’t believe in the dichotomy, then show how mastery of the basics are ensured on a grade-by-grade level. Clearly, Everyday Math is not designed to ensure mastery. Of course all curricula work on skills. The real question is whether the job gets done. Things might not have been so great in the “Golden Age”, but they are worse now. Skills are worse and understanding and critical thinking are illusory.

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SteveH

February 2, 2012 at 2:27 pm

“Give schools the power to decide for themselves which instructional practices and program they want to employ and give parents the right to choose where to enroll their children.”

In our area, the regular public schools are fighting against letting parents do that. They are telling urban parents that they can’t find their own solution. The affluent get choice, but not the urban poor.

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- Kim Simons
  
  February 4, 2012 at 6:59 am
  
  That is tragic Steve. More people need to wake up a realize that our public schools are failing because of political forces that are too powerful for mere parents to change. We had a petition requesting a change in instructional practices in our school district that was signed by more than 1600 parents, and continues to gather signatures to this day. We were ridiculed and belittled and attacked by school officials who found the idea of parental choice too frightening to consider.
  
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EB

February 3, 2012 at 5:32 am

STudents who made it through high school in the ’60′s and ’70′s had all-explicit instruction. What data do reform math proponents use to prove that “it didn’t work?” It’s been my experience that most of those folks attained the ability to handle all of the mathematical challenges that typically come their way — interest rates, fractions, quick computation, ratios, simple stats, simple “find the unknown.” What else are we expecting from our K-8 curriculum? and, we’re certainly not getting that from students who are using the “inquiry” and ” problem-based” curricula.

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SteveH

February 3, 2012 at 6:49 am

Anything of importance requires hard work that is not necessarily fun. You can try to make it fun, but that only goes so far. My son started playing the piano at an early age. Private lesson teachers tend to fall into a range between two extremes. At one end you have those following a strict pedagogy that includes specific books, levels, memorization, and recitals. At the other end, you have teachers with no particular goal other than to make sure that the students enjoy themselves. There are risks at both ends.

At the low end, students may like to play the piano, but they will never progress at a level required to get to a conservatory. At the upper end, the students could be exceptional, but burnt out or end up not liking to play. In between the two extremes lies a wide range of approaches, some of which might work with some students and not others. However, there is some level that you have to achieve to keep all doors open. Those doors are defined not by primary or elementary teachers. They are defined by career, competition, and college requirements. Starting on a learning slope below these standards might not mean much for sports or playing a musical instrument, but it matters a great deal in math.

Reform math’s slope is angled towards the fun and engagement end of the spectrum. On a statistical basis, that might help at the lower end, but the level of expectations and skills is below the cut-off point for STEM careers. They might get more students who “like” math and are better prepared to be good citizens, but the result is that doors will close early, usually by 7th grade. Few students can handle the change in slope without help at home or with tutors. Even for kids not on a STEM track, they will have to start working a lot harder on skills to get through the required math in high school.

With a musical instrument or with sports, kids can stop any time they want. There are no requirements. Students can have a more relaxed or fun approach. Fewer will be competitive, but it will make some feel better about not having a pushy educational process. When you get to the typical competitive cut-off in sports at age 10-12, it doesn’t matter much for those left behind. With math, however, most high schools require 4 years of math. That fun, engagement liking of math quickly disappears when you have big gaps in basic skills.

The reason students get to STEM careers is not because of engagement or some reform math version of understanding or critical thinking. It will be because schools or parents or tutors made sure that the required slope of learning and the required mastery of skills was achieved every year along the way.

Unfortunately, individual urban kids get treated as an average statistic. They are not even allowed to choose to go to another school that sets a higher slope or higher expectations. They are doomed from the start by low expectations. Educators might rejoice that little urban Suzie got to the community college even though she had the ability to get to Harvard. Individual kids are not statistics. Even in our affluent community, I had to spend a lot of time helping my son with the basics. Most high schools, and some middle schools, offer proper math tracks. I help my son very little now. The major problem is low expectations and no choice K-6 math.

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NikS

February 3, 2012 at 9:07 am

Barry, I couldn’t agree with you more that children need more explicit systematic instruction, and more reliance on students working individually on problems.

It is a misnomer that traditional methods did not work. Children came out of school proficient in math facts and algorithms. The traditional methods could have focused more on word problems, that is where it was failing. However, today’s education is now failing on simple math facts, simple calculations and algorithms. In fact, when I was in school, I do not remember one child in K-5 with a tutor and now it is the norm.

I’m not sure what makes anyone think that a child doesn’t need explicit systematic instruction. If you spend your day with children this should be obvious. Also, Children don’t consistently stay focused when in a group setting because attention span is developmental. Children are not small adults and they do not learn like adults.

The people who are a fan of reform math can say over and over again that it is working, but repeating yourself doesn’t make it true. Its better to open your eyes and look at the realities of the classroom and the children who are in it.

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E. Berg

February 3, 2012 at 11:01 am

Barry, we totally agree with the value of explicit instruction in math. At our school we use a standard, “meat-and-potatoes” text book, including a strong math facts curriculum K-5, and our students are scoring with the top schools in our area in our state tests. However, we (a charter school) have much higher diversity than they for minority, ELL, and FRL populations. Interestingly enough, the state tests include a lot of process oriented questions. If taught to mastery, our students have no problem extending their thinking and responses to a very different kind of problem or question. Almost half of our 5th graders, and at times more than one half, achieve scores of “Advanced” on the state tests. Our disaggregate data is very even.
True that some of our teachers are extremely skilled and experienced in delivering explicit, “slice it thin/teach it fast” instruction, embedding artful higher-order questions and providing careful cueing for reasoning processes. However, even our newest instructors or average teachers are getting very decent results because they are not confusing students with murky, opaque methods and curriculum. When I’ve seen other schools doing process-oriented instruction in math, I’ve seen a lot of unengaged students not doing much math. It is not just the students who have more success with explicit instruction!
I remember in 5th grade when I had the epiphany of how long division truly made sense; I was using a piece of charcoal on our back yard wooden fence, playing “teacher” with a friend – much to my father’s ire when the marks would not come off. As I was explaining it to my (less than enthusiastic) friend, long division suddenly became more than a rote series of steps: all the processes came together as logical, reasonable steps that made perfect sense to me. I had been successfully using long division in math for several years, but I didn’t know why it worked. I believe this illumination came because I knew the procedures very well, and because I had fluency in executing the steps, I could finally see the mathematical sense of it all. First we do it, then we understand it – maybe after years of doing it.

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Richard Bramer

February 3, 2012 at 3:23 pm

I was educated in the 60s and 70s and did not have the honor of being taught solely through explicit instruction.

I suspect, once again, (the suspicion was first born when the Math Wars were raging) that devout traditionalists either have never worked on an honest to god open ended real world problem, or have never seen a reformed classroom.

Anyone can cherry pick phrases out of a text or program and find oddities. The Constitution of the United States has some regrettable phrases in it, but overall it’s a pretty good document. The Bible has its share of contradiction, but is accepted as having eternal truths as well by many. A traditional textbook, as purely traditional as the ideas espoused herein, is a myth; nonetheless, on the whole books that are largely of that approach will have fewer projects, fewer inter-topic connections, fewer intrincially high interest questions to answer. Even if a reform book has fewer opportunities to ‘get’ the basics, one has to ask which is the more aggregious error?

Business has been asking educators to try and produce people with creativity, problem solving ability, team work ability, and dedication/confidence to pursue a difficult task to completion. Doing heavy repititions of similar problems with relatively quick solutions does not nurture any of these skills.

The idea that the rest of the world is teaching ‘traditionally’ is also nonsense. Please, if you believe this, travel abroad and check for yourself. I have. It’s not what is happening in India, Taiwan, Japan, England, France or Spain as far as I can tell.

Ultimately, the outsider (namely politicians and parents) to this argument has to ask this question: is it better to practice minutiae repeatedly and hope interest and dedication springs into the hearts of sufficient numbers of students, or is it better to nurture interest and confidence – and enough skill to insure that students can/will find out for themselves that which they haven’t previously seen?

One could make reference to learning to fish and being handed a fish, but that analogy and many others have been used in this argument ad nauseum before.

Personally, my co-authors and I chose to create a text that hewed to a fairly middling position, thus hoping to get the best of both (and temper the ideological storm such as is seen here).

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- Katharine Beals
  
  February 3, 2012 at 6:19 pm
  
  To establish as “nonsense” my claim that Eurasian math programs have more mathematical content than American math programs do, you would have to look in detail at their actual curricula, which I have done (French, Russian, and Singapore Math in particular).
  
  You might also talk to Eurasian visitors in this country whose children attend American schools. Ask them how the math their children are doing compares here with the math they were doing in their Eurasian schools. Their answers should disconcert you.
  
  I’m also curious whether you can cite specific examples from Reform Algebra, say, of simultaneous equations with three or more unknowns, or of factoring involving polynomials of degree greater than 2 or with two or more variables. Or evidence in American Reform Geometry of myriad, multi-step formal proofs. Please share what you have in the way of evidence, if it exists.
  
  I’m also curious whether you can cherry pick for me any examples from pre-Reform texts of problems with the high-ratio-of-non-math to math problems seen in the ones I’ve “cherry picked” from Reform Math.
  
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- Kim Simons
  
  February 4, 2012 at 7:05 am
  
  Parents as outsiders? Excuse me, but if the programs the school employ are complete and utter failures it’s ME, the outsider parent, who will have to pay for tutors so that my child can go to college. It’s me, the outsider parent, who will have to live with the reality that those programs have closed doors that should have been open to my child.
  
  Teachers have my child for 10 months. I have them for their entire lives. So please, don’t call me an outsider.
  
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NikS

February 3, 2012 at 6:59 pm

I’m an educator and a parent and I can tell you specifically what is egregious, 1/2 of my township pays for tutoring children in K-6. If I had a choice, I’d go back to the traditional math of the 80s even though it was not optimal, at least parents could help with the homework. Something is wrong when the only mathematician in town is the only one that can help their child with grade 2 homework.

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SteveH

February 4, 2012 at 5:05 am

“…, or have never seen a reformed classroom.”

This isn’t just a problem with philosophy. Most of the people complaining have or had kids pass through a reform math curricula. We can cite very specific problems both in the assumptions and the details of implementation. I have been struggling for years to get the discussion away from Math War platitudes down to the details. When I raise these detailed issues on threads, reformers fall right back to generalitites and ad hominem attacks. I even talk about the higher expectations it takes to make a child-centered, thematic, real world curriculum work. K-8 reform math curricula don’t require them. They go through the motions and “trust the spiral”. It doesn’t work. This isn’t a guess. I’ve seen it in action. I’ve been to school/parent meetings about it. It always fallls back to generalities and talk of balance without any details or proof that it works, in spite of the evidence that bright kids were getting to 5th grade still figuring out 7+8 using their fingers; in spite of the fact that the teacher had to drop the Everyday Math format to ensure mastery of basic skills that fall under anyone’s definition of balance.

“Even if a reform book has fewer opportunities to ‘get’ the basics, one has to ask which is the more aggregious error?”

Once again we have vague generalities. What does understanding mean when kids don’t know the times table? How does a pie chart understanding of fractions translate into an understanding of how rational expressions can be manipulated. There IS linkage between skills and understanding. The more egregious error is understanding without skills. That is meaningless. Rote skills cause failing grades. Skills that consistently work are filled with understanding. Those are the building blocks of true mathematical understanding.

Back when I taught college algebra, nobody could pass with just rote methods, and nobody could pass with vague understandings that didn’t show up in the skills. Math is not some vague thinking process as pushed by Professor Hill in The Music Man. Math is about specific techniques that require mastery of specific skills. There is no way to fake it with some sort of rote knowledge. Even on our standardized state test that reflects the current problem solving ideas of math, those with the best skills get the best grades. As I said before, there is no magic understanding that makes it OK to do poorly on any test.

When you get to complex, in-depth math problems, one of the first things you have to know is whether the problem has been done before. You have to know if there are certain governing equations that apply, like D=RT. You have to have practiced a lot to know the subtleties of things like not averaging rates. A proper understanding can only be tested by showing that you can do a variety of problems. Reform math gives up after a simple, conceptual level of understanding. It’s not enough.

“It’s not what is happening in India, Taiwan, Japan, England, France or Spain as far as I can tell.”

More generalities. Are they using Everyday Math or Investigations? What are their scores on international tests? If the results are so good while using the same curricula, then what is going wrong in the US? Please get to the details.

“… is it better to practice minutiae repeatedly and hope interest and dedication springs into the hearts of sufficient numbers of students, or is it better to nurture interest and confidence – and enough skill to insure that students can/will find out for themselves that which they haven’t previously seen?”

More generalities. Does it work? Reform math has been around long enough to give you enough data. Parents might like the idea, but they see that it doesn’t work. Kids struggle with the basics. They are confused and unhappy. I don’t call this “nurture”. Kids love it when they have skills. Besides, what does “enough” skill really mean? This view is coated with low expectations and a vague hope that engagement will work. “Enough” is not good enough for a STEM career. I can hear the doors slamming shut.

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SteveH

February 4, 2012 at 7:06 am

“Depth of understanding and creative solutions, (and all polls of private businesses suggest that these are much sought-for skills) suggest reform methods but these don’t handle standardized tests as well.”

Those darn pesky standardized tests. Shoot the messenger.

An article in the NY Times on Jan 28 talked about unemployed techies in Silicon Valley.

“While Web-based companies like Facebook and Google are scouring the world for new talent to hire, older technology workers often find that their skills are no longer valued.”

Did these old techies suddenly lose their depth of knowledge and creativity? No, it’s about specific skills in specific areas. I remember putting together my first resume (long ago). I filled it up with all sorts of things that tried to show my general experience and depth of knowledge. I quickly found out that they wanted to know my skill set and how good I was in those areas. They wanted to know whether I knew FORTRAN or Pascal. They wanted to know details about how good I was at those skills. The depth of ability and results in those skills showed them my ability and potential. It also told them whether or not I would be productive right away or whether I would require training.

You can tell what companies want by going to job interviews. They want specific skills in specific areas, and they won’t accept generalities and talk of creativity. Too bad if you were really good with DEC’s Vax VMS when it disappeared off the face of the earth. Nobody wants to hire you (no matter your experience and creativity) and then retrain you in new technology. Companies can find a cheaper person a few years out of college who knows the new technology. So much for your critical thinking capabilities.

The key to the tech field is skills. Experience and creativity might give you an advantage once you are in a job, but it’s skills that get you the job in the first place. However, you have to keep up on the latest changes and that requires an ability to absorb new technology quickly. You have to be able to do a lot of work that is not really much fun. What have I gone through over the last 30+ years? FORTRAN, Algol, Pascal, C, C++, all sorts of system analysis tools, MFC classes, Qt apps, UML, and on and on. You can now cross off Unix and even Linux. The signs are on the wall that these are disappearing. The cost models are too expensive, even for Linux. You better start learning about new technology and positioning yourself onto a better technology track or you will end up on legacy technology and then finally laid off. Once laid off, you can’t get a new job because you don’t have the new skills. You can’t go to another technology area and take less pay. They think you will leave as soon as you can find something closer to your skill set.

Educators need to get out and see what the real world is really like. Vague notions of deep understanding and creativity are just so much fluff.

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Good/ Bad Teacher « acburt

February 5, 2012 at 2:41 pm

[...] Current Event: This article talks about how the number of childred diagnosed with a learning disability has increased drastically over the past years. They do not think it is truly a learning disability but that teacher are not doing what they should be doing to teach the material. One of the hardest subjects for most kids is math. http://www.educationnews.org/education-policy-and-politics/barry-garelick-math-education-being-outwi... [...]

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EANelson

February 6, 2012 at 7:21 am

The goal of learning is to be able to solve problems. Research by Tom Loveless at Brookings and others has found that even though student test scores in math reasoning have gone up since 48 states adopted the NCTM 1989 standards as their state standards, the ability of students to solve math calculations, especially the type encountered in the sciences, has plummeted.

One result: according to the NSF document (NSF InfoBrief 08-301) , in 2006, the only 23% of the Electrical Engineering Ph. D.’s awarded by US universities went to children of our own citizens. And the EE doctorates in a nation’s population are probably the best measure of the nation’s competitiveness in the world economy.

For all US engineering doctorates, 32% went to the children of the US parents whose taxes built those universities, while 44% went to children whose parents were citizens of China, India, and Korea (same page).

Certainly, our nation benefits because so many of these best and brightest stay here after graduation. However, how long will they stay when they find out that their children attending US schools have such a low chance of following in their footsteps? And how long will US citizens support universities that disproportionately educate foreign children in the best- paying careers (because our own children are not being prepared for scientific majors)?

Check out the data on math achievement since 1978 at http://www.ChemReview.Net/BCCEpost.pdf

For the cognitive science of learning (and teaching) math, see http://www.ams.org/notices/201010/rtx101001303p.pdf

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SteveH

February 7, 2012 at 7:20 am

The second link on learning is good, but it doesn’t go far enough. Rather than study the problem from a generic cognitive science point of view, why not ask practicing engineers and scientists for specific examples?

Math is not some generic thinking process, but the chess example is not really appropriate. The goal of math is to allow you to think less. If you master the techniques, many problems become exercises – just turn the crank. That is the benefit of math. However, mastery of the skills allow you to apply them to solve new classes and types of problems. Mastering existing mathematical techniques allow you to incrementally come up with new and improved approaches. These new approachs do not flow from some general thinking process.

For example, I once had to (as part of a larger program) create a fast way to find the intersection segment between two triangles that were defined by three points in space. To solve this problem, one has to know the literature and see if the problem has already been done. I have lots of books on my shelf behind me, including the 5 volume set called Graphic Gems. I couldn’t even begin to find a solution without a skill-based understanding of vectors, matrices, and parametric equations. If a solution existed, then I’m done. Since I wanted a very fast way to do this (one triangle could be checked against millions of others), I had to come up with my own solution. I didn’t start from scratch using some general thinking process. I studied the existing methods to see what I could use and what I had to create myself. The creative solution (actually, I never think of it as creative) I ended up with was not possible without a lot of basic mathematical skills, and I’m not talking about percents and decimals. I’m talking about vector and matrix techniques.

Reformists vaguely refer to “enough” skills, but their approach still focuses on some general problem solving skills. This is an illusion. Problem solving comes from a high level of mastery of many layers of specific mathematical techniques.

I know that if I have three non-colinear points that define a triangle, I can use a cross product to find a normal vector. I can use that normal to define an impicit plane equation. I know that the normalized plane equation can be used to find the signed distance of any point in space to that plane. I know that if two points of another triangle have different signs for the distance to the plane, then the triangle crosses the plane. I can find the line segment of the plane and the triangle and then I can find the intersection of the line and the triangle that defined the plane. This problem solving based on mastery of skills.

I can’t possibly do this with rote knowledge, and a general problem solving process offers me very little to nothing. There IS linkage between proper mastery of math skills and understanding. This understanding is created from mastery of mathematical skills, not from a general thinking process.

Reformists think they can get something for nothing – that engagement and real-world problems will get the job done with “enough” skills. It dosn’t work unless you set high expectations and skill mastery for homework. That’s not happening.

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T M Widdershins

February 7, 2012 at 10:53 am

Amazing how full of crap all of us parents are. Sorry, but I’ve spent years filling in the holes left by the “work in groups” “deep thinking” crap peddled in our district by textbook salesmen and administrators who assured us we just didn’t understand the modern world. If we complained about the curriculum, we were told that the curriculum isn’t everything, the teaching is the most important thing. When things started to go downhill, it wasn’t the curriculum that was failing to teach — the teachers weren’t implementing it correctly (and god forbid they teach the times table on the side). I have two “gifted” children subjected to years of horrible math instruction by teachers many of whom hated the curriculum, but were forced to put their teaching experience to the side and do what the bozo in the central office told them to. Never mind that the teacher had 20+ years in the classroom and the central office employee and the consultants they worshipped spent maybe two years total in the classroom.
My kids have experienced the “wander around and discover it for yourself” stuff, and explain it to me and show me how it works more “traditional stuff.” They prefer that I explain how it works. My daughter knows that the “groups” she ended up working in were a pain in the butt because the other kids would just copy off her. And she knew what she was doing because of the entirely different instruction she got at home.
Stop treating us parents like we know nothing. We know what is happening with our kids and it makes us angry. Especially as most of us barely have the time and resources to save our own kids from this mess. We can only look on at the horror being created by the mixture of poverty and poor instructional practices. Walk into a sixth grade classroom of urban kids and tell them that they have been served well when they multiply by bundling sticks and it’s ok because we’re going to shove them all into Algebra by 8th grade, and it’s their fault if they fail. Or maybe it’s the teacher’s fault because they didn’t follow the curriculum. There’s always someone else for you all to blame.
My kids will be successful because I taught them math — funny how the administrators at my kid’s schools always wanted to be sure I had them there on math testing day — my kids helped save their stats.

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wintertime

February 8, 2012 at 2:12 am

TM Windershins states, “My kids will be successful because I taught them math — funny how the administrators at my kid’s schools always wanted to be sure I had them there on math testing day — my kids helped save their stats.”

After working with the scouting and tutoring programs with our church, I am convinced that the **only** children learning to read and do arithmetic in our county have parents who are doing tons of afterschooling! Who takes the credit for all the hard work done in the home? The government school administrators, of course!

Parents beware. If you are considering making the financial sacrifice to move to a “good” government school district, it may not be the school that is “good”. The testing results of the school are likely merely a reflection of the hard work of “after-schooling” and” after-tuitoring” done by the parents in the district. Those high scores likely have nothing to do with what is going on in the government classroom.

By the way, I homeschooled three children. All three were admitted to college by the ages of 13, 12, and 13. All finished all general college requirements and Calculus III by the age of 15. The two younger children earned B.S. degrees in math by the age of 18. One of these earned a masters in math by the age of 20. We used Saxon Math.

It is interesting that even though my children’ achievements were reported in the local newspaper and even given a full-page article in the university paper, no “educator” has ever contacted my children or my husband and me, to inquire about our methods. I find that surprising since in my profession, when there is a success, researchers are all over it like white on rice. I suppose “educators” lack curiosity.

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- Texas Middle School Math Teacher
  
  March 9, 2012 at 2:04 pm
  
  Are there any general ideas or tips you can inform me of that you think made your children so succesful? I am currently in my second year of teaching middle school math in Texas and I have much to learn! Thank you for any help you can provide.
  
  Reply
  - wintertime
    
    March 11, 2012 at 11:20 pm
    
    Texas Middle School Math Teacher…..You are the first teacher or professor of education to ever ask me, or the children, and they are now adults. Amazing! I will respond in the morning.
    
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  - wintertime
    
    March 14, 2012 at 6:08 pm
    
    Texas Middle School Math Teacher,
    
    We used Saxon Math. I required that the children have mastery of the material before they were permitted to move on to the next level. Concepts were introduced using concrete materials that they could manipulate with their hands ( beans, pennies, pebbles, etc.) But mastery was required before moving forward. For example, they had to be able to answer each math fact ( addition, subtraction, multiplication, and division) in less than 3 seconds. Once past these early foundational years it was simply a question of doing every example and every question in every chapter of the Saxon Math books.
    
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Leslie

February 24, 2012 at 8:14 am

I also provide a great deal of home instruction, although my children are in what is considered one of the best schools in the district.

When I learned they hadn’t been required to learn (hadn’t been taught) the multiplication tables by third grade, we worked on them as we walked to and from school every day until the girls were proficient.

But my instruction isn’t limited to math–I am actually teaching them in every content area. Instead of providing actual instruction, some teachers simply play audio of the textbook. Others distribute worksheets without first offering the instructions the students need in order to do the work. Almost all assign excessive amounts of homework, homework that seems clearly intended to shore up the weaknesses of what should be happening (but is not) in the classroom.

I worry about the students who don’t have this level of support at home.

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Bookworm Room » Clearing off the spindle, which creates an awesome series of links to cool stuff

March 16, 2012 at 6:20 am

[...] a good example of Education News fare, with this one focusing on the virtues of old-fashioned approaches to math. I didn’t learn math the old way, and I’m perfectly certain I wouldn’t learn it [...]

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ihor

April 14, 2012 at 1:32 pm

Barry ends with: “Parents and professionals who benefitted from traditional teaching techniques and environments will remain on the outside — and the public will continue to be outwitted by stupidity.” The dung gets thrown from both sides of the isle, but I find Barry’s the most egregious. Why? Because he hates the reformers and is blind to everything except what he believes about the good old days which is based mostly on myth. It’s my way or the highway! Get a life, Barry.

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- Barry Garelick
  
  April 14, 2012 at 5:23 pm
  
  There is a wealth of data suggesting deteriorating skills in math, however, fewer advanced degrees in STEM fields, more difficulty in hiring mathematically skilled graduates, increased STEM hiring from oversees, higher remedial rates in college in mathematics, lower pass rates in math in college, and problems hiring from the 18-25-year-old group because of low levels of skills in math and grammar and also self-initiative.
  
  If someone claims that math is being taught better now than it was in the 1960s, I would say that person is ignorant, perhaps willfully so, of the stark and shockingly bleak reality all around.
  
  As far as the “myth” of traditional math, see http://www.educationnews.org/education-policy-and-politics/barry-garelick-the-myth-about-traditional-math-education/
  
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Barry Garelick

April 15, 2012 at 6:18 am

Note: I posted the above comment before adding the following: The first two paragraphs were quotes from a paper written by Laurie Rogers, author of “Betrayed: How the Education Establishment Has Betrayed America”.

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See it my way.

April 25, 2012 at 11:47 am

[...] In a well-publicized paper that addressed why some students were not learning to read, Reid Lyon (2001) concluded that children from disadvantaged backgrounds where early childhood education was not available failed to read because they did not receive effective instruction in the early grades. Many of these children then required special education services to make up for this early failure in reading instruction, which were by and large instruction in phonics as the means of decoding. Some of these students had no specific learning disability other than lack of access to effective instruction. These findings are significant because a similar dynamic is at play in math education: the effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure. … http://www.educationnews.org/education-policy-and-politics/barry-garelick-math-education-being-outwi… [...]

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Math Education Article « Mr. Crader's Blog

May 2, 2012 at 8:59 am

[...] out this link: http://www.educationnews.org/education-policy-and-politics/barry-garelick-math-education-being-outwi…. It will take you to an interesting article about one man’s thought on math education today. [...]

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Barry Garelick

May 2, 2012 at 1:38 pm

Interesting article in the Atlantic proposed reforms for special ed. One recommendation underscores the main idea in my article “Outwitted by Stupidity”:

.:•Focus on improving regular education for all students. The better that regular education is, the fewer students need to be identified for special education services. When developing inclusive programs, schools should base them on effective teaching practices that improve educational outcomes for both students with disabilities and regular education students. As part of this mission, align IDEA and NCLB to end confusion.”

Found here: http://www.theatlantic.com/national/archive/2012/04/4-common-sense-proposals-for-special-education-reform/256435/

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» Post Topic » Mathematics Education: perhaps going back to old and tried approaches will solve most of our current problems?

May 15, 2012 at 4:37 pm

[...] Read the whole article here. [...]

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Julie Krammer

May 16, 2012 at 11:32 am

Barry, this article is great! As a mother, I am constantly seeking new ways to teach my kids math. I recently started my kids on a program called Brainetics (www.brainetics.com) – and have found so many different ways to make math fun and, more importantly, keep contributing to my children’s education. Keep up the good work!

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Sheila Gromer

May 29, 2012 at 8:15 am

While the opinions expressed in the article do have merit, some of these comments are disturbing. A connection between understanding and skills is vital to mathematics education. Learning the processes and then understanding why the processes are being completed is the way I would teach.

I don’t agree with the comments suggesting that parents should not have to/need to help their children with any skills in math or other academics. I have heard before that reading to your child is the number one activity you can do to further a young child’s reading ability. Should we not engage in the same practices for math? Plenty of parents count with their children. Can we not continue by adding, subtracting, multiplying, and dividing with our children?

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suraj poudel

June 4, 2012 at 6:56 pm

when i was in grade 1, 2, 3 I like maths very much because it was very easiest subject at that time but when go up slowly and slowly maths subject became harder and harder. so, math subject become boring subject and i give interest in economics now i like economics very much.

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Donna

June 6, 2012 at 9:02 pm

WOW! So glad to see the awakening to this failing math. Four years ago I approached the principal about my concerns regarding Everyday Math. I was given the sales pitch on how wonderful it is. When my daughter received an A- on her 5th grade report card, I was elated. A few weeks later we started homeschooling ( due to medical issues). Boy was I surprised to find out she couldn’t do 3rd grade math. We are now into our 3rd yr of homeschooling, using traditional math lessons. Her math comprehension has greatly improved. Barry, not sure if your aware of this, but Everyday Math was developed as an experimental math out of Chicago University by “educational specialists”, not math specialists. Furthermore, over 200 math experts across the nation petitioned then Sec. of Education Riley, stating that this method of math would be detrimental to teach. The Sec. ignored this petition and endorsed this confusing curriculum.www.mathmaticallycorrect.com/riley/ht

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- Barry Garelick
  
  June 7, 2012 at 3:14 pm
  
  Donna,
  
  Thanks for your comment. I am aware of the history of Everyday math as well as the petition by the 200 math experts. I had similar problems with my daughter. See http://educationnext.org/anamazeingapproachtomath/
  
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