Response to A Research
Programme for Mathematics Education
The Author, David Wheeler sent a callout to a number of
Mathematics Educators asking how they would envision a research program for
Mathematics Education. Three responses are published. After reading the
introduction, I assumed the respondents would suggest quantitative studies
which contrasted student results being taught math concepts through traditional
rote learning as compared to being taught using manipulatives and a more
problem solving approach. I was not too
far off. Nesher responds with a suggestion that Math research should focus on
the processes involved in the acquisition of math as a language system. Ball
would like to instill a “programme of teaching experiments where the aim is to
achieve a discrete permanent change in the level of understanding of individuals
in a key conceptual task” He suggests research using manipulatives and
meaningful examples to create meaningful understanding would provide us more
evidence of how students learn math. Finally, Gattegno suggests a research
program that starts from the recognition that mental structures required by
math are the ‘endowments’ of perceptive people being becoming aware of their
own surroundings.
Ball and Gattegno’s responses seem to support each other in
that they believe an effective math education system should start with
meaningful problems, and provide students with the motivation to find ways to
reconcile these problems. Nesher’s reponse implies that she believes the main
stumbling block for math understanding comes from students not understanding the
‘language’ of mathematics – not only the syntax but also ‘conceptual frameworks’
required for math understanding. I particularly liked Ball’s quote that “we
know that most of what is taught is not learned” and that math research should
focus on ways to identify what is learned
and how we can learn from what is learned. It is interesting to me that this
article, published in 1981 identifies the same issues and stumbling blocks to
math education which we still struggle with today, 34 years later. It will be
interesting in this course to examine how researcher’s work has progressed into
curriculum changes, and what the results are of these changes as far as
students’ math understanding in the last 30 years.
I am very interested in the part about researching the use of manipulatives and how they effect learning of math concepts. At the elementary level, manipulatives are used quite a bit, but at the secondary level they are hardly used at all. I think finding a way to still incorporate some hands-on aspect into the higher level maths would greatly help in raising conceptual understanding of math concepts that students have. The part you mentioned about "we know that most of what is taught is not learned" is so true and it is so sad that it is so true. However, I think this is a result of how school systems are set up in general and not necessarily the math educators fault. Some students just do not understand math very easily, and adding things like a time limit or grades only makes it that much more difficult for these students to succeed.
ReplyDeleteRight- but I also think part of the challenge of secondary math is to get students to be able to think abstractly. Sometimes manipulatives like algebra tiles can help with a concept, but they usually fall apart as a concept (or get unnecessarily complicated) as you try to expand that concept (like to multiply negatives or to larger numbers). While it's great to use manipulatives, it's important to also recognize their limitations and realize that we still need to encourage students to think abstractly even if using concrete items
DeleteIt seems as though the line of your article was what I initially expected from mine. I agree with you that it is interesting to see that a subject of concern in the 1980's, is still a major problem today. Although I agree that the ability to explain mathematics using outside materials and manipulatives is extremely valuable, there is value in being technically proficient. If we relate mathematics to salsa dancing, we know that an experienced salsa dancer is not only technically proficient, but has a great sense of rhythm in their movement. Why is it so hard to find this balance in the school system and why are education researchers stuck on one side of the fence or the other?
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