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The 'reform math' problem

By Katharine Beals

Recent reports put the number of children with autism spectrum disorders at one in 100. Also in the news, following the latest national and state test results, is math education. What has escaped the media's attention is that these two topics are connected.

Their connection begins in the classrooms into which an ever higher proportion of children with autism spectrum disorders are being mainstreamed. More and more of these regular K-12 classrooms are using new "reform math" programs such as Everyday Math, Investigations, and Connected Mathematics. In the Philadelphia area in particular, it's hard to find a public, private, or charter school that doesn't use reform math.

The prevalence of this curriculum is coinciding with widespread special needs. Students on the autism spectrum, however much they vary, share several basic traits. They don't perform well in unsupervised groups of peers. Many have trouble putting words together, and nearly all struggle with verbal comprehension to some extent.

To make progress socially, linguistically, and academically, these children require structure; direct instruction; an incremental, step-by-step curriculum; and specific, well-defined tasks. Indeed, these are the ingredients of the most promising and commonly used autism therapies.

Reform math gives them the exact opposite. Instead of direct, structured instruction by teachers (for example, on how to add large numbers), it offers child-centered learning through incidental discovery (for example, of ad hoc ways to add particular numbers). Instead of a curriculum organized incrementally around math concepts (such as borrowing from the tens place), it favors a sequence of themes ("Sticker problems," "How many pockets?").

Students spend large chunks of class time working in unsupervised groups. Assignments are open-ended and language-intensive: "Create a riddle about your favorite number"; "Write a letter to a second grader convincing them that 1/3 is less than 1/2." Even correct answers earn only partial credit if they lack verbal explanations.

Ironically, children with autism, especially those with high-functioning autism or Asperger's syndrome, have the potential to do well in math - often extremely well. Indeed, a number of accomplished mathematicians, including one recipient of the Fields Medal (the mathematics equivalent of the Nobel Prize) have Asperger's syndrome. Among engineers and computer scientists, rates of autistic spectrum disorders are even higher.

Under reform math, the next generation of autistic math, computer, and engineering buffs is languishing. They lose points for failing to cooperate in groups, explain their answers, and comprehend language-intensive problems, often getting lower grades than their peers. Worse, reform math holds them back mathematically - often way back. By the time they reach fifth grade, mathematicians have estimated, students of reform math can be up to two years behind their non-reform peers.

All this drastically diminishes the opportunities for students with autism spectrum disorders to develop their natural talents; gain recognition not just for their weaknesses, but also for their strengths; and ultimately pursue what were once their most promising careers.

We've gotten quite good at recognizing autism in young children. We're also quite good at recognizing how important it is to embrace the learning needs of all students. The crucial and overdue next step is undoing the stranglehold that programs like Everyday Math, Investigations, and Connected Math have on our schools - and on the futures of so many of our most vulnerable yet promising students.


Katharine Beals is a lecturer at the University of Pennsylvania's Graduate School of Education and the author of "Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School." She can be reached at katie.beals@comcast.net.

Comments   
Posted 11:17 PM, 11/09/2009
Pat Murray
As a concerned parent of two boys in school, one being taught Investigations in Data and Space and the other Connected Math, I contacted 22 other elementary schools in Maine to see what programs they were using. I was surprised to find out that most of them are using the new "reform math" programs but are using Saxon Math for special ed students. One is using SRA Direct Instruction. There must be a logical reason, right? If you are one of those parents who are confused and concerned check out: meworldclassmath.webs.com
Posted 07:52 AM, 11/10/2009
Judy T
While the deficits of the reform math program for students on the autism spectrum is certainly a problem, and my son with Asperger's was revolting against the "explain your answer" demands in elementary school when these pieces of the program started to make their way into his math course, its failure for ASD students is only one small part of its failure as a math program in general. It is absurd for schools to be using a math program that holds back the mathematical skills of students, as demonstrated by the fact that students using "reform math" are two years behind their non "reform math" counterparts. Furthermore, by using what is essentially a language arts approach to math, the program takes students for whom math might otherwise be the one bright spot in their academic day and turns it into misery! Math is not about persuasive writing or verbal explanations. Students who understand math concepts should not be made to feel incompetent because their brains function like ... mathematicians ... instead of like English majors. This is the ultimate absurdity in education.
Posted 09:59 AM, 11/10/2009
BarryGarelick
I've tried posting my comment twice before with no success. Let's hope that the third time is the charm. This article is most welcome. Over the past two decades, the number of students with learning disabilities has increased. In 2006, approximately 2.6 million students were identified with learning disabilities, more than three times as many as were identified in 1976-1977. One reason for this growth might be better means of diagnoses of specific disorders, (including autism). Nevertheless, the increase in the number of students with learning disabilities raises the interesting and inconvenient question, of whether the older way of teaching (direct instruction and mastery learning, less group work, and ability grouping) may have had unintended benefits. There are many in the education establishment who maintain that direct instruction and methods fits a mathematics for the 1960s, when skills throughout the K-8 spectrum were the main focus of instruction. This of course ignores that procedural fluency and skills lead to conceptual understanding. I hope that Katharine's article will be a wake-up call to those who believe that mastery of basic skills is not part of the problem—but in fact is a solution to the failure of reform-based math.
Posted 04:35 PM, 11/10/2009
JohnCarr
I am an education consultant and my 8th grade son is high functioning autistic with language receptive/expressive challenge, and dyscalculia and an English language learner. I want my son to understand explain how he thinks, so his teachers and I can get a better idea how to tailor math instruction to the way he thinks (see Getting to "Got It" by Garner). I want him to be able to speak and listen like a mathematician, or a math literate person. I want him to learn from peers in a very small group when he didn't understand what the teacher said. I want his teacher to strengthen his weak areas of learning and communicating that learning. Reform math is about understanding and conceptualizing math within real world problem solving situations. I want my son to go to the supermarket and pick the cereal with the best price. Traditional math only taught him to add, subtract, multiply, and divide, but not how to apply them. I propose a balanced approach of mini-step direct instruction with visuals, reinforced with guided pair or trio small group work on real situations requiring application of mathematical thinking. My books (Making Mathematics/Science Accessible to English Learners) explain my stance, but would need another chapter to go deeper into emphasizing and adjusting certain strategies for high functioning autistic students.
Posted 05:17 PM, 11/10/2009
Magistra
All these comments are articulate and helpful. I supervise a mathematics/science practicum which is directed partly by the Everyday Math reform curriculum used in Philadelphia public schools. The program depends upon a cyclical approach so that the same topic is revisited once a week for a period of time instead of indepth instruction for mastery over days or weeks. Obviously, it depends on students getting a concept from bits and pieces spread out over a long period. Not good. I agree that we need a combination of approaches with mastery as the goal. Students need to be exposed to methods that meet their individual needs not the needs of publishers or test designers. In the primary grades it is most important to establish basic concepts and facts sequentially. Later the children can learn to apply those concepts to real world problems and cross curricular situations. For example, all children need to learn the meaning of more and less before they can understand subtraction. They must learn patterned addition before they can grasp multiplication. Each step in the sequence must be solidly mastered if the next step is to be understood. This can all be learned in real world situations (like cooking) without sacrificing accuracy.
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