I have a few comments about the two articles:
1. I appreciated the specificity contained in the Woodward and Montague article. For example in the Instructions in Computations (pg 95) section they use specific questions to illustrate why learning a complex algorithm and then constantly attempting to master the algorithm is not beneficial to some students. With respect to the point made by the author, during my experience I have found that many learning disabled students that I have encountered will be asked to work on 100’s of complex algorithms, none of which they understand and it appears to be more to keep them busy as opposed to anything else. This is something that they can do and master, but it is essentially a waste of time, because they have no concept of how the algorithm is working. With regards to creating more contextually based problems for students, as advocated in the NCTM document, for some students unless an EA or teacher spends a great amount of time working with the student on a problem, the student will not be able to work through the question alone and will quickly become frustrated. There is a need for a balance between questions that involve practicing skills with questions of a type that are more problem solving based.
2. A line in the Woodward and Montague article that resonated with me involved his reference to Asian countries compared to North American countries:
“More successful approaches, found particularly in Asian countries, tend to focus on fewer topics.” (pg 91)
We try to accomplish too much, and as a result do many things poorly. I believe this is still a legitimate criticism of Ontario’s math curriculum.
3. Finally, the section in the Woodward and Montague article regarding the “emotional” dimensions of problem-solving instruction (pg 97 right side of the page 2nd paragraph) brought back the memories of one student (Rex) that I worked with (real name changed). Rex, had difficulty with math and was a student with special needs. He was working in a grade 11 course with an alternative program. A re-occurring issue with Rex, would arise when Rex had to work through any type of problem type question. Rex had an EA but liked to do things by himself. He was fine with any type of question so long as it was of a fairly basic nature. For any questions that were contextually based such as find the total price (including tax) of a jacket on sale for 30% off, Rex wanted to know a quick calculation to get the answer. This was fine when the questions were of a type similar to the aforementioned but not so fine when Rex was asked to determine the better deal between two sale items. For a question that involved making a choice between two sale items, Rex would quickly become frustrated and either become belligerent and angry or cry. He would not accept any aid from an EA or a teacher but he would not be able to get over the emotional frustration he experienced with the question. The questions/work given to Rex had to be closely monitored because once he started a question he needed to finish it.
4. Teaching as a Profession – With regards to the issue of professional development as discussed in the Schoenfield article, I have found that there is never enough time to get together with colleagues. There used to be professional development days, but they have been taken away or used to make the school year slightly shorter. I believe many issues related to the lack of professional development have arisen because of the inharmonious union/board relationship present within many school boards.
What Does Equitible Instruction look like for Students with LD
ReplyDeleteI have struggled with how best to teach students with learning disabilities, and students with little commitment to mathematics. Like MP, I have students like Rex, who get emotionally upset if a problem is too challenging (or if it is too easy which the students take as insulting). A couple of years ago I audited a class in Mathematical learning disabilities and really saw two camps: those researchers who are all about the basics and those researchers who are trying to implement NCTM principles for all students. All last summer I read about teaching mathematics to students with special needs and was more confused at the end than when I started.
I found the Woodward and Montegue paper helped me reconcile the concerns of the special education community with the NCTM principles and learning theory. Page 90 describes how many in the special education community found the open vision of the NCTM standards too ill-defined and many attacks on the NCTM principles attack extreme versions - or Straw men. This reminded me of something Joan Peskin (HDP 1237 Cognitive Development and Learning- a great course) used to say: constructivism is widely accepted as a theory of learning- people construct their own ideas based on their experiences. However this does not necessary imply a single way of teaching or even necessarily a constructionist model.
Much of the published material for students with learning disabilities focus on basic skills with lots of repetition of operations (which the students promptly forget when the unit is over). I think because it’s easier on the teacher- because of students like Rex how get upset when the material is too challenging. There is increasing material, supported by good research, that works at teaching problem-solving through strategy instruction and heuristics. Last semester, I started to teach do some problem solving strategy instruction but ran into logistical problems (trying to team teach with a new teacher that was struggling in the basis), but I found with the my own experiences as a learner of mathematics, time constraints and the lack of good material for fact and computations, this strategy instruction often got forgotten.
The phrase “what we value” is repeated throughout the article and I hope the phrase will become ingrained into my lesson planning instead of falling into old habits. I think finding videos of strategy instruction will help me feel more comfortable with this technique, so it is more easily incorporated into my repertoire. I also need to explore anchored instruction, and look at the cited reference (Greeno Collins and Resnick 1996) investigating scaffolding , and situated cognition in the context of different theories of learning .