The State of the Art of Math Education: Let's Move On

9.9.10 – Barry Garelick – I recently took a math teaching methods class in education school–a remarkable class for its embrace of every educational fad I detest. One book we had to read in the class was "Integrating Differentiated Instruction and Understanding by Design" by Carol Ann Tomlinson and Jay McTighe.

This book is  popular in the education school and professional development circuit.  It also hit every hot button I had as evidenced by my copy of the book: it is missing the front cover, which tore off when I hurled it across my bedroom. 

Even worse than the book itself were the discussions in class that came out of it.  One event in particular stands out.  In a chapter that discussed the difference between “knowing” and “understanding”, a chart presents examples of “Inauthentic versus Authentic Work”.   In this chart “Practice decontextualized skills is listed as inauthentic and “Interpret literature” as authentic.  The black and white nature of the distinctions on the chart bothered me, so when the teacher asked if we had any comments, I said that calling certain practices “inauthentic” is not only pejorative but misleading.  I asked the teacher “Do you really think that learning to read is an inauthentic skill?”

She replied that she didn’t really know about issues related to reading.  Keeping it on the math level, I then referred to the chart’s characterization of “Solve contrived problems” as inauthentic and “Solve ‘real world’ problems” as authentic and asked why the authors automatically assumed that a word problem that might be contrived didn’t involve “authentic” mathematical concepts.  “Let’s move on,” she said.

Both this incident and this book remain in my mind because they are emblematic of the educational doctrine that pervades schools of education.  This doctrine holds that mastery of facts and attaining procedural fluency in subjects like mathematics amounts to mind-numbing “drill and kill” exercises which ultimately stifle creativity and critical thinking.  It also embodies the belief that critical thinking skills can be taught. 

In their discussion of what constitutes “understanding” the authors state that a student being able to apply what he or she has learned does not necessarily represent understanding.  “When we call for an application we do not mean a mechanical response or mindless ‘plug-in’ of a memorized formula.  Rather, we ask students to transfer—to use what they know in a new situation”. In terms of math and other subjects that involve attaining procedural fluency, employing worked examples as scaffolding for tackling more complex problems is not something that these authors see as leading to any kind of understanding.  They blur the distinction between learning a discipline (pedagogy) and practicing it (epistemology).  That a mastery of fundamentals provides the foundation for the creativity they seek is lost in their quest to get students doing authentic work from the start.

The authors’ approach to how one teaches for understanding is through a process that they call “backward design”, in which educators plan their courses, units and lessons by starting from what they want the end result to be.  That is, what should students know, understand and be able to do?  The planning process then entails working backwards from there, identifying the content that goes into this, the big ideas, the questions to be explored and so on. 

As the authors state, backward planning is not a new idea.  In fact, I was a bit confused as to why it is even needed, given that such work has essentially been done in the writing of the textbooks that cover the course material.  Teachers who have had fairly good success using the structure and sequence of a well organized textbook may question why they need to reinvent the wheel.  But this brings us to another axiom which I have heard repeated in education school, which states that textbooks are a resource and not a curriculum.  The authors pick up on this as well and regard using the textbook for planning as a “sin”, stating that “The textbook may very well provide an important resource but it should not constitute the syllabus.”   By using the method of backward planning, the authors believe that teachers are less likely to rely on “coverage-oriented” teaching.  They believe this is so because the backward planning process allows the teacher to address the big ideas, enduring understandings, and skills to be acquired in any order that works, thus freeing them from the burden of highly structured, rigid, and largely inauthentic textbooks.

In a paean to constructivism and the abandonment of textbooks, Tomlinson and McTighe, dispose of the notion that sequence of topics and mastery of skills is important, calling such beliefs the “climbing the ladder” model of cognition. “Subscribers to this belief assume that students must learn the important facts before they can address the more abstract concepts of a subject,” the authors state, and then quote Lori Shepherd, a University of Colorado education professor to make their point:

“The notion that learning comes about by the accretion of little bits is outmoded learning theory.  Current models of learning based on cognitive psychology contend that learners gain understanding when they construct their own knowledge and develop their own cognitive maps of the interconnections among facts and concepts.”

In fact, this is the crux of how they approach differentiated instruction. Sequence doesn’t matter. Each student constructs his or her own meaning at their own pace, by being immersed in what the authors term “contextualized grappling with ideas and processes”.  What does this mean? There are many examples, but the prevalent pattern of instruction to emerge from the book seems to be one of giving students an assignment or problem which forces them to learn what they need to know in order to complete the task. Say it is quadratic equations.  Rather than teach them the various methods of factoring first, with the attendant drills, they might start with a problem such as x2 + 5x + 6 = 0. The teacher may then provide some activities that illustrate what factoring is, and then provide some exercises.  The goal would be to factor the above equation into (x+3)(x+2) = 0 and, from there, lead the students to see that there are two values that satisfy the equation. This is what they mean by “contextualized grappling” as opposed to “decontextualized drill and practice”.  It is a “just in time” approach to learning, (my choice of phrase, not theirs) in which the tools that students need to master are dictated by the problem itself by not burdening the student’s mental inventory with “mind numbing” drills for mastery of a concept or skill until it is actually needed.  In the example above, the teacher may differentiate instruction by assigning extra factoring problems for students having difficulty, and provide instruction to the more capable students on how to solve quadratic equations by “completing the square” for expressions that cannot be factored.

While the authors are advocates for constructivism, they lean toward another ideal talked about often in education school classes: the balanced approach.  They admit that there are times when direct instruction or ‘teaching by telling’ might work extremely well. “There is a need for balance between student construction of meaning and teacher guidance”, they proclaim. That direct instruction would work even better if topics were presented in a logical sequence is not the message of this particular book, however.  Nor are the authors concerned over how many students will learn to hate math and other subjects because worked examples are “inauthentic”.   “Just in time” approaches that work as a model for business inventory work just as well in education, they believe.  The result is an approach that is like teaching someone to swim by throwing them in the deep end of a pool and telling them to swim to the other side.  For the students who may already know a bit about swimming, they may choose to take that opportunity to learn the butterfly.  The teacher might advise the weaker students to learn the breast stroke and provide the much needed direct instruction which they may now choose to learn.  Or not. 

Let’s move on.


This article was published in slightly different form in Educational Horizons, Vol. 88 Number 4; Summer 2010; p. 199


Barry Garelick is an analyst for the Environmental Protection Agency.  He is a cofounder of the U.S. Coalition for World Class Math ( .


  1. Danaher M. Dempsey, Jr.

    Many thanks to Mr. Garelick. He has demystified why when the University of Washington "helps" Seattle high schools with "Professional Development" for math teachers the results are significantly worse.

    Over the last three years, Seattle’s Southeast Education Initiative poured added funds into Rainier Beach and Cleveland High Schools. Since 2004, the University of Washington has been guiding with National Science Foundation funding the professional development of math teachers at Garfield and Cleveland. Two years ago, Rainier Beach joined the UW’s professional development for math teachers and a collaborative planning period was added. OSPI annual test results show that these programs netted progressively lower passing rates for Black and Limited English students at these three schools. The students needed effective interventions but the money went elsewhere.

    Washington State grade 10 annual testing.

    2008 (2009) 2010 for Black students’ pass rates:

    Cleveland HS: *6.3 (*12.7) *5.7`~
    Garfield HS**: *22.5 (*29.8) *16.7`~
    Rainier Beach : 21.6 (*15.6) *3.9`~

    Seattle avg.: 16.0 ( 16.3) 12.4`~
    WA State avg: 22.2 ( 20.9) 19.0

    2008 (2009) 2010 for Limited English Speaking students’ pass rates:

    Cleveland HS: *4.8 ( *0.0) *3.3`~
    Garfield HS**: *0.0 (*16.7) *0.0`~
    Rainier Beach HS : none*

    Seattle avg.: 19.5 ( 11.2) 6.7`~
    WA State avg: 12.7 ( 8.1) 9.3

    ** AP Magnet
    * UW NSF project assisted year

    `~ first year of "Discovering Math"
    series from Key Curriculum Press

    In 2006, 2007, 2009 years tested Cleveland and Garfield used Interactive Math Program materials while most Seattle High schools did not.

    In 2010 test year all Seattle High Schools used "Discovering" that textbook adoption is still in litigation .. now in WA Appeals court.

    The UW math gurus supported the "Discovering" Math textbook adoption. The Seattle Math Program Manager was hired away from UW.

    A year ago, Seattle adopted OSPI non-recommended and State Board of Education rated "mathematically unsound" “Discovering Mathematics” for high school and OSPI pass rates plummeted from 24.2 percent to 12.4 percent for Seattle’s Black students and from 11.2 percent to 6.7 percent for Limited English students.

    In the prior year (2009), Seattle Black students’ 10th grade pass rate was 85 percent of their middle school cohort rate, Limited English speakers passed at 94 percent of cohort rate. In 2010 the corresponding rates are 51 percent and 57 percent.

    I thank Mr. Garelick for his fine explanation of why these extremely poor results occur when the University of Washington Math education experts "Help". Why are National Science Foundation funds being spent to mathematically disable students?

  2. Katharine Beals

    I think we should take the same approach in driver's ed classes. The state driver's manual should only be used as an occasional resource. The students should spend most of their time in driver's seats in authentic traffic situations. What better way to inspire them to figure what needs to be done in order to get back safely. Automobiles and traffic rules, just like mathematics and literacies, are social constructs, and, as such, should be grappled with and (de)(re)constructed by individual students according to their distinct learning styles and points of entry.

  3. Fredricka Reisman

    Too bad Mr. Garelick isn't going into teaching as we need more critical and creative ed students alah his model to offset the mindless textbooks and profs in too many jargon indundated education classes. Harmful bandwagons can be and are limited by many scholarly and reasoned ed profs–but too bad that they need to waste their creativity, energy and talents offsetting illogical pedagogies.

  4. Barry Garelick

    Fredericka, Thanks for your comment. I am in fact going into teaching. I plan to teach math. Whether I'm allowed to teach it properly will depend on whether there are any schools that allow such teaching to occur.

  5. Krista English

    I highly recommend the Mathematician's Lament – a wonderful essay from a mathematician on the way math is taught in schools today and how the fascination of math is lost. It's a great read and highly respected among math educators. It's available online for free, or in book form via the most popular online bookseller named after a jungle river. After reading your article though, I had a question lingering – do you expect every child to be able to display their understanding of math through speed of computation and testing? I would think if a child has a real aptitude for math, a high interest in math or both, they're going to excel no matter how you teach them, but your traditional method works well for them. And those who don't have those qualities probably aren't going to choose a path that requires mastery anyway. Teaching these kids in another way would be appropriate – not killing their spirit or making them feel inferior to a math-talented folk because in truth, they are quite capable and talented in other areas.

  6. Ann Marie Banfield

    Once again, Barry spells out the lunacy that prevails in the land of education.
    Great Job Barry!

  7. Barry Garelick

    "And those who don't have those qualities probably aren't going to choose a path that requires mastery anyway. Teaching these kids in another way would be appropriate – not killing their spirit or making them feel inferior to a math-talented folk because in truth, they are quite capable and talented in other areas. "

    Actually, they are more capable and talented in math than people think, but the trend in the US is to think that gifted kids will "get it" no matter how it is taught, and those who aren't gifted are not going to benefit from the very instruction that they need to excel. In fact, both types of student need mastery and understanding of the basics. Vern Williams, a former member of the National Math Advisory Panel has taught middle school math for over 30 years and for most of that time has taught gifted and talented students. He was recently assigned to a class of students who were in the "regular" math class; i.e., not gifted and talented. He was amazed at the lack of instruction and concepts they had received. He began instructing them in the traditional manner that you have stated above that you feel is not effective. He found that the students enjoyed not being "treated like babies" and given real instruction and taken seriously.

    Lockhart laments how kids need to know what math is "really" about. Nothing wrong with these kind of problems, but without the instructional and mastery basis, such talk amounts to math appreciation. One criticism of traditional math is that it consists of word problems and other problems that students find "irrelevant". Some of these problems involve numbers, such as one number is twice the amount of 5 more than the first number, etc etc. And yet, Lockhart encourages exposing students to "real" math which are very much like the number problems derided as irrelevant. Students enjoy challenges, but must be given the tools to be able to take the challenges on. Giving them the tools in a haphazard "just in time" manner is not doing students any favors–gifted or otherwise.

  8. Joye Walker

    I disagree with Krista’s words, “I would think if a child has a real aptitude for math, a high interest in math or both, they’re going to excel no matter how you teach them.” I teach honors students, struggling students, and students who fall somewhere in between, so I have wide experience with all kinds of learners. Students who have real aptitude are often either bored by the slow-paced and insufficient kinds of instruction that occur at the elementary level, particularly those that require invented strategies for computation, or they are left underprepared for learning algebra and higher math by learning processes for computation that do not carry forward and do not require solid understanding of such concepts as place value (check out lattice multiplication to see what I mean). The structure of using least common denominators in working with fractions, for example, is directly related to the use of algebraic fractions at the algebra two level and beyond. Failure to achieve mastery in this skill, for example, can lead to struggles at the precalculus and calculus levels as students work to solve rational equations and inequalities and analyze the behaviors of rational functions. If you don’t know and understand the content to which I am referring, then you have no basis to comment on how operations with real numbers should be taught in order to prepare students for algebra and ultimately for college, regardless of intended major. It is my professional opinion that literally hundreds of students who have passed through my classroom in recent years could have studied math at much higher levels, both in high school and in post-secondary institutions if they had been expected to master all standard algorithms for computation and if they had been expected to master all operations with rational numbers. When Krista mentions “killing their spirit,” nothing pains me more than to see a student’s spirit “killed” because (s)he cannot learn to solve the simplest linear equation like 6x – 5 = 8x – 9 because of lack of expectation of proficiency in operations with integers. Such students feel that attending college is a futile dream because they are not able to learn and pass basic algebra one. Often, those students who are proficient with computation (and get into the higher level, or honors classes) are proficient because their parents/relatives/friends are teaching them outside of the classroom. They often are children of parents with resources who can provide tutoring or whatever is necessary to fill in the gaps in learning. This becomes an equity issue as those children of parents without such resources are left with insufficient mental structures to move forward to higher levels in math and ultimately, are shut out of the possibility of going to college. When are Americans going to wake up and realize this?

  9. Niki Hayes

    I confess I continue to be amazed by the beliefs that learning math can be like learning to play the piano by ear; i.e., you either have a natural gift for it or you can discover and tinker with the keys until you learn how to "create" your own music, and that is the only reason for studying the instrument.

    I suppose everyone could finally learn to create some sort of elementary tune by ear, given enough time and energy and dedication. Unfortunately, schools have a finite time to teach students and, in truth, the cognitive "windows" are fairly demanding in their timeframe for learning certain subjects.

    Meantime, there are those of us who think piano students should learn the sounds of the notes and their names and functions, and practice that new base of knowledge, even repetitiously(including those boring finger drills). Once those notes and their related strategies of being put together for certain sounds are recalled with automaticity, new creations with those notes can be understood and extended into more complicated performances. The students can even advance into their own "discovery" of new, true creativity made relevant in their lives.

    These students will also be able to teach others the common foundational elements and strategies for playing the piano. The least capable students even have some appreciation for music and its impact on their lives. The most gifted may choose (CHOOSE) to become great pianists. Their firm knowledge base gives them the power of CHOICE in a variety of musical careers.

    The "discovery" learner, who doesn't have that natural intuitive ability for playing by ear (and that's only 5% of the learning population), cannot teach or explain his personal methods because they are unique to him and not easily transferable to another's "learning style."

    In summary, there is a math author and publisher who proved with irrefutable evidence that what I've said is true. As he used to say, "Even Van Cliburn, the great pianist, practiced his scales everyday because that helped remind him of the nuances of his musical selections."

    In fact, it was from him and his books that I learned I could teach Indian kids on a reservation to love and succeed in math as well as my gifted kids in a Seattle all-white elementary school. His curriculum gave solid instruction in the fundamentals, which made my life easier as a teacher. In both cases, my students and I learned that resulting "creativity springs unsolicited from a well-prepared mind." I wrote his biography after my retirement. Check it out on or my website, The book's title is John Saxon's Story, a genius of common sense in math education.

  10. Laurie Rogers

    Thank you, Barry, for an excellent article.

    It’s wrong to think gifted and talented (GAT) students will learn regardless of how they’re taught. GAT students tend to process information differently, faster, or with better retention, but they still need logically ordered information, instruction, and practice. Somehow, the reform argument goes, GAT students will be able to pick up math from curricula that don’t provide it. It’s ridiculous. Instead of becoming engineers, doctors, scientists, architects, carpenters, and pharmacists, GAT students join all other students in eking their way out of high school without the math skills they need to go to college or begin a trade.

    I have tutored gifted 6th and 7th graders who came to me not knowing long division or the number line, and who were unable to add fractions together, subtract a negative, reliably multiply, or isolate a variable. They didn’t have these skills because they were not taught them for sufficient lengths of time or allowed to practice them to mastery. They might have had a few teachers who went outside of the district curriculum to provide them with actual mathematics, but that instruction – while dedicated and honorable – could not overcome the several years of miseducation the students had already received via the district’s reform curricula and constructivist teaching approaches.

    Krista English said: “And those who don't have those qualities probably aren't going to choose a path that requires mastery anyway.”
    Boy, that just irritates the heck out of me. Which of us is so prescient that we know which of these students “have those qualities”? How arrogant to refuse to teach the students properly and then to decide they are incapable of learning.

    All students need instruction, practice and reinforcement. America’s math problem begins and ends with the persistently idiotic teaching approaches school administrators force on their teaching staff.

    Reform administrators say GAT students will learn capably from any methodology yet are adamantly opposed to traditional instruction. So they really mean “any methodology that is a reform methodology.” When teachers really want a student to understand something, they tend to go back to a traditional approach. Meanwhile, districts persist in dragging teachers through constant “professional development” that forces them to use – not any methodology – but reform methodology.

    If Krista English is correct, that any methodology will work, then teachers should be allowed to use a traditional approach. In Spokane, WA, teachers, parents and students have asked for that, and the district refuses to allow it. Why?

    Laurie Rogers

  11. concerned

    Great Read!! Thanks!!
    [The claims of the]“just in time” approach to learning, in which the tools that students need to master are dictated by the problem itself by not burdening the student's mental inventory with “mind numbing” drills for mastery of a concept or skill until it is actually needed [are not consistent with research in cognitive science]

  12. SteveH

    "Which of us is so prescient that we know which of these students “have those qualities”? How arrogant to refuse to teach the students properly and then to decide they are incapable of learning."


    But that's why they use curricula like Everyday Math. It presumes that it separates those kids properly. All they have to do is "trust the spiral". It works by definition. All they have to do is point to the kids who are able to get to algebra in 8th grade. As I have always said, if you wait long enough, you can blame it on the kids, parents, society, poverty, or whatever. They even get the kids to believe that it's their own problem. It must be nice to have a philosophy that puts all of the onus on the child and hides incompetence with pedagogy.

    For the "Mathemetician's Lament", we are told:

    "… a wonderful essay from a mathematician on the way math is taught in schools today and how the fascination of math is lost. It's a great read and highly respected among math educators."

    First, what is taught in schools today are things like Everyday Math. Before that, it was things like MathLand. These curricula have been around for a long time. Where are the results? Oh, I forgot, it works by definition.

    "the fascination of math is lost"

    I remeber a parent who had a daughter in my son's 5th grade Everyday Math class. He had a masters degree in applied math. He thought that EM sounded pretty good and even ran an after-school math club to work on "fascinating" math problems. By the end of the year, his tune changed and his after-school club turned into a remedial mastery class.

    Educators love the "Mathematician's Lament" because it tells them what they want to hear, not because it comes from a mathematician. They routinely ignore masses of complaints from other matematicians, engineers, scientists, and effective math teachers.

    I see it as an academic turf issue. Damn the torpedoes, full-inclusion discovery ahead. If you take away their pedagogy, they have nothing.

  13. Krista English

    Lots of assumptions were made because we live in such a label-filled society. I didn't realize that I had the leeway to write so much more or I guess I might have defined every word I used that can be taken the wrong way.

    When I spoke to chilren's natural gifts or talents I was NOT referring to GATE programs. It was simply those who see the patterns and can put numbers together easily, without hindrance. I never said you don't need to teach them. I am saying that the traditional model works very well with them. I never said you shouldn't teach the traditional model. So much name calling and labeling, all that anger you possess hinders coming to find true solutions for the few students that find the traditional-style of learning NOT working for them. Are you saying they are not worthy of trying something new and if that new idea works for them they shouldn't go for it?

    And you are right, I am not a mathematician, but I love math and am good at it at the level I need it. An interesting pattern I see in my own family is that those who are super good at basic math seem to have trouble with complex math beyond Algebra while those who excel at all the higher level maths have a hard time computing basic stuff. I just find the topic interesting and don't have much anger about how people choose to get their knowledge. But I am also not involved with educating the masses. I enjoy the freedom to customize education and help others to do so, even working with their school teacher to present the information in individualized ways. (I'm not talking about math though in that case.) You mentioned how you would tell who has a talent for math – it's quite observable, but really can only be done in a context of relationship. Large-classrooms don't allow for much in the way of relationship between individual student and teacher, but it's not impossible.

    For the kids I work with who were once in tears, whose parents were in tears, whose teachers had had it, education is fun again, the dead have come alive, the parents/teachers are thrilled, the motivation and eagerness their student once possessed as younger child has returned and a sense of purpose and passion for life leads them to success. What is your definition of success?

  14. SteveH

    Fun. Eagerness. Motivation. Success. Of course, you never say what success is in terms of how far they get in math. How do you know they couldn't get further? What makes you think that the problem is the "traditional model", whatever that is? Nothing is stopping schools from having kids follow different speed tracks. Of course, with full inclusion and social promotion, this is pedagogically impossible. What's left to do? Dumb down and slow down the material for all. Only those kids with help at home will get a chance at STEM careers.

    Although you say that this model works well for some kids, how does this work in practice. Do you start with a traditional model and wait for the tears? Do your schools offer two separate math tracks in K-6? How does speed of coverage tie in with a pedagogical approach? Does a discovery approach magically allow all students to move at the same speed with mastery for all and no tears?

    Virtually all school systems separate kids in math at some point. They usually give a math test in 6th grade and the best students get to pre-algebra in 7th grade. It is a reasonable argument to claim that students should be tracked in earlier grades. However, there are two issues; the pedagogical approach to the material and the speed of coverage. You can't grasp at a problem with speed and claim that it justifies whatever silly, hands-on, engaging approach to the material you want. Happiness and motivation are not good enough criteria for success.

    You can't talk about how things could be different or customized on a one-to-one basis. That's not what this is all about. We're talking about peagogical ideas that are forced on all in K-6. The modern claim is that the material can be differentiated, but that is all just smoke and mirrors. Enrichment is silly and acceleration is impossible.

  15. Algebra

    As usual, Garelick's over the top hate of constructivism shines through and his few usual followers hail him. But the fact is that if he ever does become a teacher, he will find that the overwhelming majority of math teachers (especially in high schools) are traditionalists like himself and hate constructivism just like he does. The irony is too much. But, alas, from afar Barry can continue to make false claims – although he does it well – the data will not support him. Over 90% of high schools teach from traditional texts with lecture style approaches.

  16. MT

    The constructivist based practices described in the article and addressed in the book are practice in elementary and middle schools. So while it may be true that high schools tend to teach math in a more traditional manner, they must contend with students who have not mastered basic arithmetic due to these practices. The quadratic equation example in the article actually is the approach used in Connected Math, a program seen in middle schools. In fact, the Connected Math algebra sequence in 8th grade is used as an algebra course.

  17. Danaher M. Dempsey, Jr.

    Dear Algebra,

    In WA State over 90% of k-5 math programs in 2008 were "Constructivist" programs. You are correct that there were more traditional Math programs being taught in WA high schools than "Constructivist" ones. But it was not 90% more like around 65% is my recollection from OSPI stats.

    The huge problem is in k-3 as this is where the huge gap between low income and non low income students originates and it never closes in math.

    The shortage of effective and efficient instructional materials is devastating in k-3 to those without lots of help outside the classroom. [See project Follow Through data]

    I am not against all exploration. I like some balance. I am against minimally guided lessons that pointlessly wander. The UW is a great advocate for this "minimal guidance" and has clearly proven on multiple occasions that this DOES NOT work. The UW seems not to care about the no positive results part.

    Check the Seattle student performance by Income level here:

    The UW has precisely the approach you apparently like for high school. Check the results of their Math Education Project (MEP) here:

    Seattle now has:
    (1) Everyday Math (k-5) at all elementary schools except two.
    (2) Connected Math Project 2 (6, 7, 8) (3) Key Press' Discovering at High School. (under appeal in WA appellate court – after HS math adoption rejection in Superior Court)

    Note check results for Singapore Math used at Schmitz Park Elementary School.
    SM has been used for two years. Check grade 5 scores Here:

    and Here:
    Math – Grade 5

    …Percent Meeting Standard 94.5%

    Level 4 (exceeds standard) 65.5%

    Level 3 (met standard) 29.1%

    …Not Meeting Standard 5.5%

    Level 2 (below standard) 1.8

    Level 1 (well below standard) 3.6%

    You slammed Mr. Garelick with "the data will not support him."

    It seems the data that counts "Student performance" does support him.

    The data certainly does not support the "Expensive University of Washington Approach" of discovery/inquiry for which you apparently advocate.

  18. SteveH

    I'm not sure what "Algebra" is reading, but does Barry need to state what is obvious to him and (almost) everyone else? The constructivist spiraling damage is completed by 7th grade. It's all over. The real irony is that schools dump these kids right into classrooms that use textbooks and problem sets. Only those with help at home or with tutoring can make the nonlinear jump (As Wu describes it) to a real algebra course and a chance at a STEM career. The rest head towards high school integrated, (or remedial) hands-on math classes where educators blame poor results on students' lack of engagement and motivatiton, not the fact that they don't know 6*7.

    However, if you look closely, the problem is not discovery. All kids discover things, … preferably with homework sets. The real problem is that educators hide low expectations and lack of mastery behind the veil of discovery and conceptual understanding. Somehow, they expect us to believe that less is more.

  19. SteveH

    "In fact, the Connected Math algebra sequence in 8th grade is used as an algebra course."

    This is another example of where discovery is less, not more. Our middle school used CMP until enough parents complained that there was a clear content/skill/curriculum gap between 8th and 9th grades. Now that the middle school is using proper pre-algebra and algebra textbooks, the big math filter is at the end of 6th grade, where Everyday Math spirals them off into the deep end of the pool. Trust the spiral, then blame the kids.

  20. algebra2

    Dempsey is always ready with her Washington state data. If she toned down her anger attack rhetoric, she would be taken more seriously. Washington state is an outlier in the nation, where no more than 10% of the nation uses Connected Math. And for Everyday Math, I am sure the recently released WWC findings of over 3,000 students in Texas that found positive effects for Everyday Math will be ignored by the Garelicks and Dempseys.
    They would much rather attack than find solutions.

  21. SteveH

    "I am sure the recently released WWC findings of over 3,000 students in Texas that found positive effects for Everyday Math will be ignored by the Garelicks and Dempseys."

    3000 students. "Positive Effects".

    Wow! I'm convinced. What were they using before? MathLand?

    "They would much rather attack than find solutions."

    Singapore Math. Forgot about that, did you?

  22. algebra3

    As usual the ridiculous attacks continue. Very typical. Singapore Math is loved by your type? But why? There is no research supporting it at WWC, is there? In fact, Singapore math does so many things that you all hate. It has alternative computational algorithms. It has constructivist lessons. And it has a much narrower content per grade like the Common Core Standards which Garelick hates. (Note that Wu and Wilson support the Common Core – so even the anti reformists cant agree among themselves anymore.)

  23. SteveH

    "But why? There is no research supporting it at WWC, is there?"

    As you well know, WWC reviews only existing research. It makes no claim about whether there is enough information to make any judgment about any curriculum. That doesn't stop EM supporters.

    "And it has a much narrower content per grade like the Common Core Standards …"

    This is false. And it's worse once you get to pre-algebra and up.

    However, if you view Singapore Math as not so different from the Common Core standards, then there is no disagreement. Let everyone dump Everyday Math and go with Singapore Math. You can't argue it both ways.

    Some like the Common Core because it at least goes in the right direction … barely. This issue is not about traditional versus constructive approaches to math. It's about low versus high expectation.

  24. Sigapore

  25. Barry Garelick

    Contrary to the assertion from "algebra3" above, I do not believe that Singapore does things that I hate. Proper scaffolding of material in a logical sequence that builds upon itself is not the same as a helter skelter discovery and "just in time" approach to math. Discovery can be done well and can be done poorly. When it is done well, there is proper sequencing of key information and room for students to make inferential leaps via scaffolded material.

    I'm not sure what "Singapore's" message was in providing the link to Achieve's comparison of the Common Core standards (CCSS) with Singapore's since their report can be read in a number of ways. Achieve's comparison of the CCSS with Singapore's standards results in their concluding the following:

    "Overall, the CCSS are well aligned to Singapore’s Mathematics Syllabus. Policymakers can be assured that in adopting the CCSS, they will be setting learning expectations for students that are similar to those set by Singapore in terms of rigor, coherence and focus."

    While one could read this as a major endorsement of the CCSS standards (of which Achieve had no small part in crafting), it could also be read as a major endorsement of the Singapore standards and thus the Singapore program. As such, Achieve's report can also be read as a major "green light" to schools to adopt Singapore's math books.

  26. SteveH

    Interesting link.

    "The CCSS and Singapore Mathematics Syllabus describe similar levels of rigor. Where grade placement discrepancies occur between the two documents, they are usually within one year of each other."

    What difference does one year make? Actually, it makes the difference between whether the student gets on the high school math track to a STEM career, or whether they struggle to "Achieve" a pseudo algebra II level of math capability that meets some meaningless "workplace analysis".

    Where's the analysis of Everyday Math? Where's the analysis of whether schools actually cover the material, let alone ensure mastery? Everyday Math throws in everything but the kitchen sink and tells teachers to just "trust the spiral". If kids don't learn, then it must be their own fault.

    I'm realistic. If my son's school used Singapore Math, they would screw that up too. They don't value mastery. They assume that mastery is just about speed, not understanding. Math must be some sort of magical Zen-like problem solving skill that flows from discovery learning and conceptual understanding. Right. What's 6*7? What's -2(3x-5)?

    The CCSS standards might move the goalposts a little further away, but they won't change K-6 teachers' silly constructivist ideas about math. On top of this is the idea that proper math preparation can be done with very wide mixed-ability classrooms using differentiated instruction. Our lower schools are based on differentiated instruction. It doesn't work. In fact, they now call it differentiated learning. Nothing like placing the entire onus on the child.

  27. Education School and Data on Effective Teaching « Grantcoulson's Blog

    [...] The State of the Art of Math Education: Let’s Move On [...]

  28. candy toy

    However, if you view Singapore Math as not so different from the Common Core standards, then there is no disagreement. Let everyone dump Everyday Math and go with Singapore Math. You can’t argue it both ways.

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September 9th, 2010

Barry Garelick Contributor

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