kitchen table math, the sequel

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Kitchen Table Math hasn't previously addressed the work of Asha K. Jitendra or the "Schema-Based Instruction" approach

Adrienne Edwards wrote a precis of Jitendra's recent article. What follows is her introduction:

In the Spring 2008 Issue of Perspectives, the quarterly publication of IDA, Asha K Jitendra describes a workable way to teach math to LD (indeed all) students. This post is adapted from it.

Since problem solving is not well addressed in many mathematics textbooks, Jitendra and colleagues have developed a conceptual teaching approach that integrates mathematical problem solving and reading comprehension strategies (e.g., reading aloud, paraphrasing, questioning, clarifying and summarizing).

Called “Schema-Based Instruction” (SBI), the system was tested and perfected for a decade. The goal: to improve student learning of word problems, especially students with LD and those at risk for math failure.

I recommend that you read Edwards' whole summary and the journal article reprinted at LD online before commenting here (Edwards doesn't allow comments on her blog, but I've emailed her a link to this post -- perhaps she will come over and comment).

Elsewhere on Schema-Based Instruction for Mathematics

Schema-based instruction improves math skills (APA Monitor Online, Monitor on Psychology Volume 38, No. 4 April 2007

Students who learn to identify three different kinds of word problems—and what strategies to use for each—do better on math tests than students who learn only one general-purpose model, finds a study in the February Journal of Educational Psychology (Vol. 99, No. 1, pages 115–127). Stopping to categorize a word problem before picking a plan to solve it may be especially effective for low-achieving students, says study author Asha Jitendra, PhD, a special education professor at Lehigh University.

LD Online: An Exploratory Study of Schema-Based Word-Problem-Solving Instruction for Middle School Students with Learning Disabilities: An Emphasis on Conceptual and Procedural Understanding (reprint of article in The Journal of Special Education (2003): Vol. 36/NO. 1/2002/pp. 23-38)

Implications for practice: The findings from this study have several implications for practice. First, the schema-based intervention, with its emphasis on conceptual understanding, helped students with learning disabilities not only acquire word-problem-solving skills but also maintain the taught skills. Therefore, results of the study highlight the effectiveness of strategy instruction for addressing mathematical difficulties evidenced by students with learning disabilities (Montague, 1995, 1997b). Second, the results of this study suggest that teaching students to identify the relationships present in each word problem promotes generalization to other, untaught skills (e.g., multistep problems). Students with learning disabilities should receive instruction that teaches them to understand the key features of problems prior to solving them. Third, the effectiveness of the strategy when implemented by the classroom teacher may indicate the importance of researchers' collaborating with practitioners to adapt instruction to meet students' individual needs. Involving the classroom teacher in the implementation of this study was important because the teacher is now more likely to invest effort in continuing to use a strategy that had beneficial effects for her students.

Journal of Learning Disabilities, v29 n4 p422-31 Jul 1996 (ERIC digest)

Paper presented at the Annual International Convention of the Council for Exceptional Children (73rd, Indianapolis, IN, April 5-9, 1995). (ERIC digest)

A comparison of single and multiple strategy instruction on third-grade students' mathematical problem solving Journal of educational psychology (2007), vol. 99, no1, pp. 115-127 [13 page(s) (article)]
Abstract

The purposes of this study were to assess the differential effects of a single strategy (schema-based instruction; SBI) versus multiple strategies (general strategy instruction, GSI) in promoting mathematical problem solving and mathematics achievement as well as to examine the influence of word problem-solving instruction on the development of computational skills. Eighty-eight 3rd graders and their teachers were assigned randomly to conditions (SBI and GSI). Students were pre- and posttested on mathematical problem-solving and computation tests and were posttested on the Pennsylvania System of School Assessment Mathematics test, a criterion-referenced test that measures student attainment of academic standards. Results revealed SBI to be more effective than GSI in enhancing students' mathematical word problem-solving skills at posttest and maintenance. Further, results indicate that the SBI groups' performance exceeded that of the GSI group on the Pennsylvania System of School Assessment measure. On the computation test, both groups made gains over time.

Google Books: Teaching Mathematics to Middle School Students with Learning Disabilities ;
here's the link to the Amazon page

Curricula:
Solving Math Word Problems: Teaching Students with Learning Disabilities Using Schema-Based Instruction
(12452) ISBN: 9781416402459 (53ドル.00)

This is a detailed-scripted program using Schema-Based Instruction (SBI), designed as a framework for instructional implementation. It is primarily for school practitioners (e.g., special and general education teachers, school psychologists, etc.) teaching critical word problem solving skills to students with disabilities, grades 1-8.

I can see that I will really need to wrap my brain around this approach.

From what I've seen so far, Everyday Math (EM) has few redeeming qualities as a primary source of elementary math instruction. I have heard that it works well as a supplemental source of instruction. I suppose the idea is 1. to use EM as a source of somewhat atypical practice problems and 2. that students will get more out of EM's conceptual oriented pedagogy if they have a firm prior understanding of the underlying procedures.

I remain somewhat dubious of the efficacy of both of these rationales. From my experience with the first and second grade EM materials, a large percentage of EM's practice problems are simplistic, dopey (that's a technical term), or both. Usually both. And, the amount of practice problems is woefully inadequate even for students who don't require as much practice (i.e., the students who typically excelled under the traditional curriculum). Moreover, EM's "conceptual understanding" is wildly overrated. Conceptual understanding does not begin and end with pattern matching as the authors of EM seem to think. A much better supplemental curriculum for teaching conceptual understanding is Singapore Math, but I digress.

Nonetheless, the best way to get through EM without befuddlement and tears is to treat EM as a supplemental curriculum. This implies that some other curriculum needs to be used as the primary curriculum. It also implies that the primary curriculum needs to stay ahead of the rather steep spiral employed in EM. This won't be easy because teaching to mastery takes longer that teaching to exposure which is how EM accomplishes its brisk pace and steep spiral.

Step One: Identify the Enemy. Beginning no later than kindergarten, you need to identify the math curriculum used in your school. If it is EM or some other fuzzy curriculum you need to select, secure and begin using a primary math curriculum in order to not only get a jump on first grade but to also take advantage of the light homework load of kindergarten and (hopefully) first grade.

Step Two: Select Your Weapon. I'm going to cut right to the chase here and tell you that my weapon of choice is Connecting Math Concepts (CMC). Other popular choices are Saxon and Singapore Math, but I picked CMC primarily because I thought it would minimize the amount of work I'd have to do. So far it has and I don't expect that to change. There are other reasons to select CMC:

1. It is fully scripted. This is key because while I fancy myself as an expert of elementary math, I am smart enough to know I am no expert in teaching elementary math. And, quite frankly, I don't want to become one. All I know is that when I try to teach a concept using my own words, I get a blank stare at least 50% of the time. When I use the script, I've never gotten a blank stare in over 200 lessons. You can't argue with that kind of success and I don't plan to.
2. The scripts are short. The teacher-led parts of each lesson take about 15 minutes to get through. The rest of the lesson involves the student working problems he's just learned or working distributed practice problems. I spend this part of the lesson in the teacher lounge, i.e., on my couch. I only emerge at the end to do a work check and to say "good job." Now, that's what I call teaching.
3. Zero prep time. My prep time consists of opening up the teacher's manual and doing some pre-reading as the student works some problems. I suppose if I was presenting to a class of lower-performers, I'd want to home my performance. But one non-low-performing student can tolerate an unpolished performance.
4. The scripts use simple language. Simple language is good because since you're going to be pre-teaching a student who is on the younger side of the expected student level.
5. Ample distributed practice. Distributed practice is built into the curriculum. This means you don't have to make-up your own practice sets. This means less work for you.
6. More is more. The curriculum is designed so that lower-performers can succeed. This means that your average or high performer will succeed as well. The only trick is to know when to cut back on practice problems, when to skip lessons, and when to convert teacher-led sections to independent work (this is a classroom curriculum in which some students will likely be absent, so teacher-led portions are repeated for absent students. My student, by definition, is never absent.) The general rule is that it is easier to cut than it is to supplement.
7. Relatively cheap. You can pick up used materials for about 100ドル from EBay. Textbooks and workbooks are easy to come by. Teacher presentation books not so much. The presentation books are the script. There is supplemental materials, but you can generally skip those unless the student needs extra practice, which is unlikely.
8. Aligns well with EM. Almost everything taught in EM has been covered in CMC, at least so far. Concepts that have not been covered are generally concepts that most consider outside or tangential to traditional elementary math anyway, so relying on EM to teach these concepts is largely inconsequential. These are inert concepts anyway, nothing builds on them and they are not important to future learning, so not learning them to mastery now isn't critical.
9. CMC is aligned with Math Mastery. Math mastery is a dvd/online review course for elementary math. It was designed to remediate struggling students, but that doesn't mean you can't use it for review or for teaching some topics for the first time. The lesson presentation is very similar to CMC, except that it's multimedia. Kids like that kind of stuff. Go check out a sample lesson. My son wanted me to teach him multi-digit division. That's a topic that doesn't get covered until CMC level D where it is spread out over the course of the year. he didn't want to wait that long, so I just put in the division mastery dvd and he was introduced to division problems. He needs a lot more practice before I'll claim that he's learned it. But it's a good start.

Step Three: Calibrate your weapon. I've done the hard work for you here. No later than midway through kindergarten begin level B and strive to finish one level every 12 months. That's about three lessons a week at most. Remember weekends are your friend. So is summer vacation. And winter/spring breaks. Just don't go too long between lessons since the student is likely to partially forget newly taught topics if they've lain dormant too long. Why cause more work for yourself? Plus, one of the reasons why you're not relying on EM as the primary curriculum is to avoid this deficiency in the first place.

At this point you may be asking: what happened to level A? You can skip level A if you've taught your child how to count to twenty and how to recognize and write numbers, i.e., the knowledge that most middle-class families send their children to school with. plus, for some reason level A is difficult to find second hand. Also, level B reviews much of level A for the first few lessons anyway.

Step Four: Fire. Right now my son is in second grade and we are just finishing up level C of CMC and we have really slacked off this year since he has quite the busy social calendar this year and the amount of homework he's getting has increased. Nonetheless, we are way ahead of the EM curve by quite a bit. He can typically complete his EM homework in about 5 minutes with minimal parental involvement or explanation. I never have to re-explain an EM lesson to him because he already understands the underlying concept. And, he scores well on his tests. In short, I don't have to worry about what he's learning in EM or whether EM is adequately preparing him for higher level math.

The only problems we have are primarily related to bookkeeping. He is fluent with his math facts and can do quite a bit of arithmetic mentally. As a result, he doesn't like to show his work for work he can do mentally, especially when "show his work" means drawing a 7 x 8 array of dots or any of the other superfluous crutches EM relies on to excuse itself from teaching to mastery.

This is not exactly a bad problem to have.

I would have preferred that his school teach him properly in the first place for the same reason that I don't like having to re-bake bread I've bought from a bakery (especailly an expensive bakery).

So if you find yourself in the same situation, this is one proactive way to survive Everyday Math. And, it surely is less painful than going the reactive route which I do not recommend. Motivation is a difficult thing to win back once you've lost it.