## Protecting Students from Learning

Barry Garelick – I attended Mumford High School in Detroit, from the fall of 1964 through June of 1967, the end of a period known to some as the golden age of education, and to others as an utter failure.

**Raymond **

I attended Mumford High School in Detroit, from the fall of 1964 through June of 1967, the end of a period known to some as the golden age of education, and to others as an utter failure. For the record I am in the former camp, a product of an era which in my opinion well-prepared me to major in mathematics. I am soon retiring from a career in environmental protection and will be entering the teaching profession where I will teach math in a manner that has served many others well over many years and which I hope will be tolerated by the people who hire me.

I was in 10th grade, taking Algebra 2. In the study hall period that followed my algebra class I worked the 20 or so homework problems at a double desk which I shared with Raymond, a black student. He would watch me do the day’s homework problems which I worked with the ease and alacrity of an expert pinball player.

While I worked, he would ask questions about what I was doing, and I would explain as best I could, after which he would always say “Pretty good, pretty good”—which served both as an expression of appreciation and a signal that he didn’t really know much about algebra but wanted to find out more. He said he had taken a class in it. In one assignment the page of my book was open to a diagram entitled “Four ways to express a function”. The first was a box with a statement: “To find average blood pressure, add 10 to your age and divide by 2.” The second was an equation P = (A+10)/2. The third was a table of values, and the last was a graph. Raymond asked me why you needed different ways to say what was in the box. I wasn’t entirely sure myself, but explained that the different ways enabled you to see the how things like blood pressure changed with respect to age. Sometimes a graph was better than a table to see this; sometimes it wasn’t. Not a very good explanation, I realized, and over the years I would come back to that question—and Raymond’s curiosity about it—as I would analyze equations, graphs, and tables of values.

The study hall was presided over by a high school counselor whose office was in the corner of the great room. The day came when we were to sign up for next semester’s courses, and she called out the names of the students in her custody. Raymond went in for his appointment. There was some discussion going on inside and suddenly the counselor, not given to sensitivity nor controlling the volume of her speech, blared out in unrelenting anger for all the study hall to hear: “You want to take algebra 2? You didn’t finish Algebra 1, and you got a “D” in the part you did finish! You will take ‘General Arithmetic’, young man!”

Raymond walked back and took his seat next to me. I said I was sorry about what happened, but he didn’t look in my direction. I was 15 and didn’t quite know what to do, so I didn’t do or say anything else to him. He didn’t speak to me for the remainder of the semester, and when I worked my algebra problems he found something else to do.

I never saw him again after that semester though I do know he graduated when I did. I suspect that he didn’t take any more math classes, arithmetic or otherwise. I don’t know whether his interest in math was based on my making it look easy, or whether he would have made a serious effort to get up to speed. I also don’t know whether his poor performance in the algebra course he took was because of poor teaching, lack of ability, or because he was a victim of neglect who had been passed on and promoted to the next grade as many students had been. I doubt his counselor knew either. Whether his counselor would have reacted differently had Raymond been white is also something I don’t know. What I do know is that his interest was strong enough to want to enroll in an algebra course, and the question “Why do you need to learn that stuff?” did not seem to be on his mind.

**The Exchange of One Inequity for Another **

I have written previously and extensively about math as it was “traditionally taught” because I feel strongly about it and it is what I know best. Two of the main criticisms about traditional math – which have also been levied against education in general for the era — are that 1) it relied on memorization and rote problem solving, and 2) it failed thousands of students.

This last criticism refers to the low numbers of students taking algebra and other math classes in the 50’s and 60’s and is taken as evidence that the techniques of traditional math—drills, memorization and word problems that were not necessarily related to the “real world”—worked only for bright students who learned math no matter how it was taught. Another side to this argument, however, is that the low numbers of students who took algebra and other math classes during this period was because of the tracking practices that were in force at the time.

The history of tracking students in public education goes back to the early part of the 1900′s. By the 20′s and 30′s, curricula in high schools had evolved into four different types: college-preparatory, vocational (e.g., plumbing, metal work, electrical, auto), trade-oriented (e.g., accounting, secretarial), and general. Students were tracked into the various curricula based on IQ and other standardized test scores as well as other criteria. By the mid-60’s, Mirel (1993) documents that most of the predominantly black high schools in Detroit had become “general track” institutions that consisted of watered down curricula and “needs based” courses that catered to student interests and life relevance. Social promotion had become the norm within the general track, in which the philosophy was to demand as little as possible of the students. The educational system in the U.S. pitted many groups against each other— skin color was not the only determinant. Children from farms rather than from cities, and children of immigrants, for example, were often assumed to be inferior in cognitive ability and treated accordingly.

During the 60’s and 70’s, radical critics of schools such as Jonathan Kozol, brought accusations of sadistic and racist teachers, said to be hostile to children and who lacked innovation in pedagogy. “Traditional” schooling was seen as an instrument of oppression and schools were recast in a new, “hipper” interpretation of what progressivism was supposed to be about. In moving away from the way things were, the education establishment’s goal was to restore equity to students rather than maintaining the tracking that created dividing lines between social class and race. The end product however was a merging of general track with college prep with the result that college prep was becoming student-centered and needs-based with lower standards, and less homework assigned. Classes such as Film Making and Cooking for Singles were offered, and requirements for English and History courses were reduced if not dropped. Social class and race was no longer a barrier for such classes as evidenced by the increasing numbers of white students began taking them.

By the early 80’s, the “Back to Basics” movement formed to turn back the educational fads and extremes of the late 60’s and the 70’s and reinstitute traditional subjects and curricula. The underlying ideas of the progressives did not go away, however, and the watchword has continued to be equal education for all. While such a goal is laudable, the attempt to bring equity to education by eliminating tracking had the unintended consequence of replacing it with another form of inequity: the elimination of grouping of students according to ability. Thus, students who were poor at reading were placed in classes with students who were advanced readers; students who were not proficient in basic arithmetic were placed in algebra classes. Ability grouping was viewed as a vestige of tracking and many in the education establishment consider the two concepts to be synonymous.

The elimination of ability grouping occurs mostly in the lower grades but also extends to early courses in high school. The practice of such full inclusion is now so commonplace that theories have emerged to justify its practice and to address the problems it brings. “Learning styles” and “multiple intelligences” are now commonplace terms that are taught in schools of education, along with the technique known as “differentiated instruction” to address how to teach students with diverse backgrounds and ability in the subject matter. Teachers are expected to “differentiate instruction” to each student, and to keep whole-group instruction to a minimum. To do this, the teacher gives a “mini-lesson” that lasts 10 to 15 minutes; then students work in small groups and told to work together. The prevailing belief is that by forcing students to solve problems in groups, to rely on each other rather than the teacher, the techniques and concepts needed to solve the problem will emerge through discovery, and students will be forced to learn what is needed in a “just in time” basis This amounts to giving students easy problems, but with hard and sometimes impossible approaches since they have been given little to no effective instruction to the mathematics that results in effective mathematics problem solvers.

The limitations of differentiated instruction work hand-in-hand with other aspects of the educational beliefs that shun “traditional” modes of instruction. (Beals (2009) describes the current trends in very accurate detail.) It is not unusual to hear parents concerned over art-based projects in English classes that call for students writing book reports in the form of a book jacket or poster—in which the artistic merits of the poster or book jacket may count as much as the actual composition. Exercises in grammar have declined to the point that they are almost extinct. Essays now are “student-centered” which is to say that students write about how they feel about certain events that occur in a story, relating it to themselves—this extends to history classes as well. They may be asked how Hester Prynne would write a profile about herself on Facebook, or George Washington on the eve of battle. Objective analysis, along with grammatical drill, sentence and paragraph structure and other tenets of a basic education are considered passé and not in keeping with the current watchword of 21st century education.

Brighter students are seated with students of lower ability in the belief that the brighter students will teach the slower ones what is needed. And frequently this occurs, though the fact that the brighter students are often obtaining their knowledge via parents, tutors or learning centers is an inconvenient truth that is rarely if ever acknowledged. The result is that brighter students are bored, and slower students are either lost, or seek explanations from those students in the know. Another inconvenient truth is that in lower income communities, there are unlikely to be students who have obtained their knowledge through outside sources; they are entirely dependent on their schools.

Students forced to endure this form of education do not progress as rapidly and do not master the essentials necessary to be successful in high school math courses. Even many of the classes for gifted and talented students are conducted in this manner. For example, one gifted class for seventh graders designed a new playground to a budget. The parent who told me this was quite proud to add that the playground was built with minor changes. The project took the bulk of the semester and there wasn’t much else in the way of geometry, proportions, rates, and pre-algebra concepts such as negative numbers, exponents and radicals—unless such concepts were visited on a “just in time” basis as discussed above.

In lower grade math classes, teaching mathematical procedures and algorithms has given way to more pictorial explanations, using alternative methods of adding, subtracting, multiplying and dividing in the name of providing students with “deep understanding”. Process trumps content. The results are that such students are passed on into algebra courses in high school with little to no mastery of the arithmetic procedures that are essential to move on to more abstract versions of the same. As such, they do not qualify for the honors track courses, nor—ultimately—AP calculus.

Many who make it to the honors have received the instruction and knowledge they need through tutoring/learning centers or their parents. In some cases, there are schools whose gifted and talented program consists of a traditional approach for math and other subjects. Thus, students who qualify for such programs are exempted from the one-size-fits-all, student-centered classes. In either case, students entering high school have been unintentionally split into groups of students, some of whom will qualify for honors classes and those who will not. Depending on the high school, the non-honors courses may be watered down versions often by necessity. These students are passed on through the system in some schools; in others they receive failing grades. Students, through circumstances beyond their control, may end up “tracked” in sub-standard courses and will be ill-prepared to take math courses in college, thus shutting out possibilities of a career in the sciences or engineering.

A recent study by William Schmidt of Michigan State University (Schmidt, et al., 2011) also observes the differences in learning opportunities and concludes that the differences are a function of the education system structure. Thus, there are differences in content depending on the area of the school district and that there is a fundamental relationship between content coverage and achievement. Schmidt states that with respect to mathematics, if the districts examined in his study were to hold generally for the U.S. then “any student can be disadvantaged simply due to differences in the rigor of the mathematics taught in the district in which they happen to attend school.” While a variety of factors contribute to the disadvantaging of students as discussed above, eliminating ability grouping is a big one. Through the efforts and philosophies of otherwise well-meaning individuals, full inclusion and equality for all has served as a form of tracking.

**Not Good Enough for Traditional**

Critics of the traditional model of education–particularly math–argue that traditional methods worked only for the gifted kids (for whom it is assumed they will learn what they need to know no matter how it is taught). And the corollary to such thinking is that students not gifted are not good enough for the traditional method. The move to homogenize skill levels in the classrooms has been entrenched now for several decades. It has come to the point now that students who have been forced through circumstances into non-honors tracks, and judged to not be able to handle the “traditional mode” of education and are thus “protected” from it. And in being protected from learning they are therefore not presented with the choice to work hard—and many happily comply in a system that caters to it.

Which raises the question of whether higher expectations and more teacher-centered instruction yield better results. Vern Williams is a middle school math teacher in Virginia, who teaches gifted students and served as a member of the President’s National Math Advisory Panel. He relates a story about how he was recently assigned a tutorial class made up of students who had failed and barely passed Virginia’s sixth grade math exams. When he first started teaching the class they wanted to play games, but Williams challenged them and included material that he was teaching to his seventh grade (gifted) algebra classes. He reports “Many of the students wanted to ditch their regular ‘baby’ classes and just attend mine. They viewed my class as not only interesting but serious.”

But students who have been put on the protection-from-learning track fulfill the low expectations that have been conferred upon them. The education establishment’s view of this situation is a shrug, and—despite their justifications for the inquiry-based and student-centered approach that brings out all children’s’ “innate” knowledge of math—respond with “Maybe your child just isn’t good in math”. The admonition carries to subjects beyond math and is extended to “Maybe your child isn’t college material.” And while it is true that a “college for all” goal is unrealistic, the view that so many students somehow are lacking in cognitive ability raises serious questions. Simply put, you no longer have to be a minority to be told you may not have cognitive ability. As Schmidt (2011) states in his paper: “To attribute achievement differences solely to differences in student efforts and abilities is grossly unfair and simpleminded and ignores the fundamental relationship between content coverage and achievement.”

There is now an in-bred resistance against ability grouping using explicit instruction. That such approaches may result in higher achievement, with more students qualifying for gifted and honors programs, is something that the education establishment has come to deny by default. What they have chosen instead is an inherent and insidious tracking system that leaves many students behind. They have eliminated the achievement gap by eliminating achievement. And many of those left behind disdain and despise education and the people who managed to achieve what they could not—just as I imagine Raymond must have many years ago.

*Barry Garelick is an analyst for a federal agency. He is cofounder of the U.S. Coalition for World Class Math. (http://usworldclassmath.webs.com/) He plans to teach math starting this fall, after his retirement.*

**References **

Beals, Katharine. 2009. “Raising a Left-Brain Child in a Right-Brain World”. Trumpeter. (Chapter 3).

Mirel, Jeffrey; David L. Angus. *Equality, Curriculum, and the Decline of the Academic Ideal: Detroit, 1930-68*; History of Education Quarterly, Vol. 33, No. 2 (Summer, 1993), pp. 177-207

Schmidt, W., et al. 2011. Content Coverage Differences across Districts/States: A Persisting Challenge for U.S. Education Policy, *American Journal of Education*, Vol. 117, No. 3; University of Chicago Press; (May 2011), p. 422

# Subscribe

Enter your email to subscribe to daily Education News!

# Hot Topics

- Education Technology
- Online Education
- California Education
- Charter Schools
- Teachers Unions
- Education Research
- New York Education
- School Choice
- Education Funding
- UK Education
- STEM Education
- Parent Involvement
- Common Core
- Cost of College
- New York City Schools
- Florida Education
- Julia Steiny
- School Health
- Texas Education
- Testing
- Math Education
- MOOCs
- Los Angeles Schools
- Pennsylvania Education
- Louisiana Education
- Education Reform
- Obama Administration
- New Jersey Education
- Chicago Schools
- College Admissions
- Online Courses
- Teacher Training
- Vouchers
- Health Education
- Tennessee Education
- Teaching
- Early Childhood Education
- Ohio Education
- Massachusetts Education
- C. M. Rubin
- Illinois Education
- UK Higher Education
- School Nutrition
- Arne Duncan
- iPads in the Classroom

# Career Index

Plan your career as an educator using our free online datacase of useful information.

- Select a City Subject
- Math Schools in Abilene
- Math Schools in Alvin
- Math Schools in Amarillo
- Math Schools in Beaumont
- Math Schools in Beeville
- Math Schools in Brenham
- Math Schools in Clarendon
- Math Schools in Commerce
- Math Schools in Corsicana
- Math Schools in Dallas
- Math Schools in Denison
- Math Schools in Georgetown
- Math Schools in Houston
- Math Schools in Huntsville
- Math Schools in Irving
- Math Schools in Keene
- Math Schools in Kingsville
- Math Schools in Levelland
- Math Schools in Longview
- Math Schools in Marshall
- Math Schools in Midland
- Math Schools in Nacogdoches
- Math Schools in Paris
- Math Schools in Pasadena
- Math Schools in Prairie View
- Math Schools in Sherman
- Math Schools in Snyder
- Math Schools in Temple
- Math Schools in Texarkana
- Math Schools in Tyler

## Comments

I agree with you Barry.

Differentiated instruction is a myth foisted upon parents and politicians to entice them into compliance. Reality is that course work and instruction is one size fits all. If your child has already mastered the objective of this week or month’s lesson, he / she will be used as a co-teacher, sent to the library, of just twiddle his / her thumbs during math. The classroom teacher, with 26 – 28 other students she’s responsible for, simply doesn’t have the time to customize instruction for one child or one group of children. Worse, with so many admittedly math-phobic teachers in elementary education, she very likely lacks the knowledge necessary to understand what comes next so that she can provide that one “above average” learner with the “more advanced” instruction he / she deserves.

My oldest child mastered the coursework necessary for his grade level before Christmas. He’s asked his teacher repeatedly for more challenging work and has demonstrated that he knows the math. He’s never gotten one bit of more challenging work. He has, however, helped the classroom teacher by moving around the room assisting his classmates who were struggling to grasp the concepts being taught (this was at her suggestion, BTW). He’s also read a great number of books during math and because quite adept at drawing his favorite video game characters. What he hasn’t learned is any math he didn’t already know.

His experience is repeated over and over again in every classroom and every school.

Worse, if that’s even possible, is what happens to a child who is bright but truly struggling in math. My son’s best friend hasn’t scored above 60% on a math test this year. He failed his state math exam last year and may well fail it again this year. He spends one day a week being tutored after school for “state exam preparation”. But contrary to what his parents expected, that preparation isn’t additional instruction on topics he’s struggling to grasp, it’s drill on old exam questions over and over again. The objective of this course is apparently to get him a passing score on the state exam, not ensure that he has the necessary knowledge and skills to move to the next level.

Vern’s experience echos what I see every time I visit my son for lunch. One time I happened to have some paper and gave the kids a challenging math problem I’d read earlier in the day (at Katherine Beals’ blog). When they were stumped I walked through the solution and explained how it worked. The kids wanted more paper and more problems. Now whenever I got to lunch they want me to bring paper and pencils so that they can do what they call real math.

Contrary to what we’re told, kids don’t want to be coddled, especially in upper elementary and secondary school. Yes they want a break occasionally, by they want to be challenged. They want to put their minds to work and want to really push the limits of what they understand.

But they’re not getting that and we are failing them.

I wonder why all the problems with inequity in our education system haven’t succeeded in leaving Asian American students behind?

Will Fitzhugh

fitzhugh@tcr.org

http://www.tcr.org

Asian Americans are not a monolithic demographic of math nerds. There are many Asian immigrant groups, in many different immigrant and American-born generations, from many different class backgrounds from very privileged to poor and refugee and working class. Some Asian American students have language issues and struggle. Some have learning disabilities. Some live in urban areas and attend under-funded, low-achieving schools while others attend well-funded suburban schools where parents routinely pony-up thousands of dollars of donations for their free public education. Some Asian American students are stellar at school and some are falling behind.

Asian American students frequently receive extra help outside the school day. Kumon. Russian School of Math. Tutoring with a parent. Paid tutors.

Other students avail themselves of these resources as well. It is also a great help to have a parent who understands math. As math may be a universal language, even parents new to the US can tutor their children in math.

Mr. Fitzhugh’s question is well taken. As stated in the article: “The fact that the brighter students are often obtaining their knowledge via parents, tutors or learning centers is an inconvenient truth that is rarely if ever acknowledged.”

The students who are not left behind are those who get the knowledge they need through various means.

Great article.

Let’s play “What if”.

How would the story play out if Raymond had been allowed to take algebra 2?

Let’s ask a few more “What ifs”.

What if Raymond’s difficulties with math were because he’d never been properly taught it in school and his parents were too afraid or insecure in their own mathematical abilities to challenge the teacher so they just kept quiet and hoped he’d learn what he needed? What if Raymond was just passed along from grade to grade without ever mastering the skills he needed to proceed to the next level? When would he finally hit that brick wall and be told he couldn’t proceed? What if no one ever took the time to figure out why Raymond struggled with math and his teachers and administrators just assumed he was mathematically inept?

Far too often in today’s schools parents play the role of spectator, sitting idly by as their child struggles or skates through work with little to no effort because they assume the teachers know best. Then, years later when their child can’t complete a basic Algebra course or can’t properly construct a sentence, some wonder if they should have paid attention to those warning signs so may years ago while others just assume their child isn’t book smart.

Far too often in today’s schools struggling students aren’t given additional instructional support on the topics they have difficulty with; instead they’re given test taking training where they study questions from old state mandated exams in the hopes that they’ll pass the state exams and then they’re passed along to the next grade level despite having never really grasped the concepts they need to move to the next level.

Far too often in today’s schools kids who are capable of doing well, fail. Not get failing grades, they fail to develop the skills and knowledge they need to be successful in life. After years of struggling with basic stuff those kids begin to believe that they’re stupid or incapable. They figure they’re too stupid for college so they don’t bother trying anymore. Why bother trying when you know you won’t get any help and don’t know what the heck is going on anyway?

Rory,

I state in the article that I don’t know the story behind him; i.e., why he did poorly in math, whether his interest in algebra was because of a passing fancy. I suspect he definitely needed additional help in math to be able to succeed in algebra 2. Though the counselor’s decision was a correct one, there was no effort made to follow up on what appeared to be an interest that he had. As such, for Raymond like many others, math was a subject that was off limits. Ironically, many of today’s students who are similarly unprepared for algebra, are passed on to those courses. Teachers who have to teach algebra 1 and 2 have students whose basic arithmetic skills are lacking.

Beautifully written!

A few observations. First, you write that the uncritical belief in “differentiated instruction” leads to:

“Since the teacher only gives mini-lessons, students have limited opportunity to learn as part of the whole class.”Indeed. And it is fascinating to observe the differences between what is happening in Finnish classroom (a celebrity state du jour) and in an Icelandic one:

Comparison of the Classroom Practices of Finnish and Icelandic Mathematics Teachersat http://journal.tc-library.org/ojs/index.php/matheducation/article/view/575/355 . Surprise surprise — the Finns mostly use whole class instruction, same as observed in the celebrated Japanese TIMSS video from 1995 (http://www.cs.nyu.edu/faculty/siegel/ST11.pdf )You already commented on another point, that

“Another inconvenient truth is that in lower income communities, there are unlikely to be students who have obtained their knowledge through outside sources; they are entirely dependent on their schools.”It is also worth noting that reform-oriented “textbooks” such as TERC tend to rely on class-based activities, cutting off yet another traditional avenue to self learning — textbooks. There is nothing one can learn on one’s own in those “textbooks” when school or teacher fails to instruct.But your statement that

“Through the efforts and philosophies of otherwise well-meaning individuals, full inclusion and equality for all has served as a form of tracking.”is your most powerful accusation. May it reverberate long and loud.Please check out Khan Academy on Youtube. This comprehensive series of very short math instruction videos will change the way math is mastered throughout the world. It will also change how math is taught in our classrooms by freeing the teachers time to direct their attention to the students who are stuck on a concept and cannot move forward. If you have not seen these videos or the TED videos on Khan Academy you are missing out. He’s definitely on to something here.

Great article — I taught at Southfield High School from the fall of 1968 to the Spring of 1974. During this time I attended Wayne State and received my Masters’ Degree. Your memories are my memories as I experienced living in that area and spending a lot of time with Detroit Teachers also enrolled in the Masters’ Program.

The experiences you had are being repeated today and need to be addressed. Thank you for your dedication and how you have learned from your past. I predict a great learning experience for your students.

I’ve seen classes in which elementary-school students ‘are given minimal instructional background on procedures’ and in which, as you point out about that sort of teaching, alternative methods of basic computation are touted as providers of deep understanding. My question is, understanding of what? Certainly not the concept of place-value, for one essential -particularly in classes where students are literally forbidden to use traditional algorithms; and certainly not mental preparation for algebra, if students are taught to believe that any method they derive that produces a correct answer is as good as any other method that produces the same answer. -Is the teacher checking these student-derived methods to see whether they’re universally valid? Not in my observations: I saw any and every attempt praised.

On the subject of tutoring: I, too, have seen school-sponsored tutoring in particular be no more than either naked standardised-test preparation or repetition of the same teaching-methods that failed to work the first time.-I’ve seen good tutoring, too: That sort of tutoring uncovers the student’s weaknesses or misconceptions so that the student can be instructed and given practice in what he or she needs to learn.

-One topic that I believe deserves mention is the language of mathematics. Why not teach the formal language of arithmetic -addend, minuend, subtrahend, multiplier, multiplicand, etc.- as soon as possible? (Three mnemonics my students really liked use ‘SUBmarine’ as the aid to remember that the SUBtrahend goes UNDER the minuend, and ‘baker’ and ‘actor’ to differentiate between ‘multiplier-multiplicand’ and ‘divisor-dividend’: a bakER does the work of baking and a multipliER does the work of multiplying; an actOR does the job of acting and a divisOR does the job of dividing.) And, using accurate but clear definitions, why not define words like ‘operation’ when order of operations is introduced? ‘Think like a mathematician’ was the teachers’ cant and chant in the non-traditional

classes I observed. As I see it, ‘thinking like a mathematician’ means first defining your terms…

Great article Barry.

“Maybe your child isn’t college material.”

They don’t want math to be a filter, so they just pump kids along. “They will learn when they are ready” is a common refrain. The corollary, however, is that if they don’t learn, then it’s their own fault. The filter will come, and when it does, it will be too late to fix anything.

What bothers me is that schools make no attempt to test the learning-when-ready (“trust the spiral”) theory. Even when kids get to 5th grade not knowing the times table, schools don’t question themselves. If you look at sample 4th grade NAEP math questions and results, it’s amazing to see such bad results for such easy questions. You don’t need homework. How simple do questions have to get before anyone notices that something is fundamentally wrong.

I remember an open house our K-8 schools gave about our state NCLB test. Teachers talked about understanding and looked at the (relative) scores for math, broken down into vague groups like problem solving and numeracy. They compared our numbers with those from other towns. I was the only one who asked to see the actual questions and compare them with the raw percent correct scores. They were assuming that they were close and that there were no fundamental educational problems. Educators are stuck in a relative statistical world. They don’t have to get a job done; they just have to make the needle move in the right direction. A rising tide will float all boats, but nobody will learn to fly, unless, that is, they get help at home. Then, schools will point to all of the flying students but fail to ask how that could happen. Their parents will be glad to tell them.

“The fact that the brighter students are often obtaining their knowledge via parents, tutors or learning centers is an inconvenient truth that is rarely if ever acknowledged.”

“Through the efforts and philosophies of otherwise well-meaning individuals, full inclusion and equality for all has served as a form of tracking.”

These are really key points, very well made here, and in need of constant repetition.

Working with an immigrant community in West Philadelphia, I’ve noticed that it’s not just students from certain socio-economic groups that aren’t getting outside help and are ending up at the worst schools, but also students whose parents come from countries where one *can* rely on schools in general to educate students in mathematics. These parents may value education highly, but not realize that they shouldn’t be relying on U.S. schools to provide it–or that their local school may be downright atrocious. Language barriers may keep them in the dark about this until it’s too late.

Beautiful article —-

I want to register a concern about the idea that the Khan Academy videos (which I use myself) will “change how math is taught in our classrooms by freeing the teachers time to direct their attention to the students who are stuck on a concept and cannot move forward.” It seems obvious to me that there’s a lot of enthusiasm for the ‘flipped’ classroom in public education, possibly because people are thinking that the teacher can become a full-time ‘guide on the side’ with no need to deliver even a mini-lesson.

As far as I can tell, under this model – at least as described above – classroom instruction becomes essentially a form of “extra help,” which is not good instruction. (See Richard Elmore & Richard DuFour on this subject, for example).

Good instruction should keep the number of students who get stuck and can’t move forward to an absolute minimum.

The Khan videos aren’t interactive; they don’t stop to check whether students are following the content; they don’t ask or answer questions. When I watch a Khan video, I do get stuck, and when I’m stuck there’s no one to explain or demonstrate the concept a different way.

If students watching a Khan video at home get stuck, they’ll have to wait until the next day to get help from the teacher, by which time they will likely have forgotten what they were confused about in the first place. It’s quite difficult to remember clearly something you’re confused about and don’t understand.

Differentiated instruction is a total scam. You MUST teach in order for students to learn, and you must offer practice time during which you are available to lend assistance. No superteacher can do both at multiple levels and through multiple modalities daily in the course of a single 55 minute period class, and do it well.

Teachers are not the folks who have perpetrated this myth. Teachers have had this myth forced upon them by administrators, and as far as I know, colleges have promoted this nonsense.

“Teachers are not the folks who have perpetrated this myth.”

Join the club. Schools force lots of myths on parents and kids, but I don’t look to teachers (as a group trained by ed schools) to have a better pedagogical solution.

All administrators I know used to be teachers, and I never think of all or most teachers (or administrators) as being in pedagogical agreement. Most parents I know don’t blame the teachers or blame the administration. They blame the schools. The implication is that if we fix the administration, then teachers will be happy and we will have more rigorous schools that ensure mastery of basic facts and skills. I don’t see that. If our schools dropped their strong differentiated instruction approach for a Core Knowledge approach, I expect that many of our K-6 teachers would yell and scream. Happy teachers won’t mean that the myths will go away.

The solution may have to be a top-down one, but will we be exchanging one set of myths for another? Who gets to decide. It should be the customer.

Thank you for clarifying the difference between “tracking” and “ability grouping.” Too often, the two are used interchangeably, with the damaging results you note. Gifted programs have been eliminated in recent years as being “elitist.” Kids that have mastered the material are expected to help the teacher, not learn new math.

Another discouraging development is the push for algebra in 8th grade, regardless of preparation of the student. The algebra class offered is not like anything recognizable as algebra — lots of time spent on the graphing calculator learning how to graph a single complicated “real world” problem — but little time learning the fundamentals of balancing equations and working in the abstract.

Barry, Great article. My high school has 39:1 in core classes and 30:1 in electives. I am as concerned with the delivery model as the size of the classes. However, paired together, the delivery model foisted on a classes of that size, means almost 200 kids a day and getting a watered down education. I think my fellow teachers also lump tracking and ability grouping into the same concept. Thanks for the clarification. Jesse

Thanks for a great article. In my opinion, pretty much the entire field of elementary pedagogy as taught and practiced in the late 20th century was a total crock. The problem is, no matter how many people like you keep pointing this out, the general public remains clueless. And given that instructional practice determines to a great degree the cluelessness of future generations, it would appear that we are moving in the wrong direction.

One of my favorite movies of all time, “Idiocracy”, gives a glimpse of where we’re probably headed.

Thanks for sending me this article, man. I agree wholeheartedly with the differentiation pieces. Lots of that mess just doesn’t work. As far as tracking and ability grouping, I agree with that as well. I think there’s a difference between saying we’re offering two different curricula and two different curricula that are varied in rigor and intellect. For instance, I don’t think calculus is for every one, but every senior in high school should take some sort of math that’s challenging on some level, whether it be pre-calc or stats. Make them all challenging and go from there.

I noticed with your friend Raymond that he probably didn’t know what you knew with regards to math, but if we could get a group of kids like him all in one class, find out where they are, and push them to where they need to be to really have a good understanding of the math, then I’m for that.

It’s what I try to do with my students now. We have two different sets of 8th grade classes, one taking Regents 9th grade Integrated Algebra and one taking the regular 8th grade. As far as how tough the classes are, I wouldn’t say there’s much difference between the two. One just covers a little more because of where the kids came in.

Thanks again for this, and good talking to you.