Math 629 Project Update - Improving Transfer

For my Math 629 project, I am doing some work that will hopefully contribute to my master's project.  What I am hoping to produce is a working draft of the literature review portion for my project.  In my foundations and curriculum development courses at Grand Valley, I have done some work addressing the problem of poor transfer ability in mathematics students, and higher order thinking skills in general.  I am planning to do the same for my master's project.

To transfer learning is to take what you have learned and apply it to something new or different.  I am often surprised at the difficulty my students have with math problems that are only slightly different than ones they have encountered previously.  It's an issue that is very disconcerting to me, too, because I want their learning to have value.  If they can't do anything with it beyond a narrow set of examples, it's not very valuable.  Another immediate concern is the Smarter Balanced Assessment, which will (likely) replace the Michigan Merit Exam.  It will demand a lot more flexibility and transfer ability from students.

To address this problem in my master's project, I have in mind a capstone unit that would fit at the conclusion of an algebra II course.  The unit would engage students in problem-based learning and cooperative group work, with a lot of metacognitive reasoning structured into the activities.  I do think that all of these things would be best applied throughout a course, but for my project a capstone unit seemed appealing to me, since it offers more opportunities to build connections between a variety of algebra II topics.

I have found a number of good primary research articles to support those three elements (problem-based learning, cooperative group work, and metacognitive reasoning) as a means of addressing the problem of low transfer ability.  One in particular has shaped my approach to the problem more than any other one article.  It addresses the problem, and ties together most of the ingredients I am applying in my proposed solution.  Kramarski and Mevarech (2003) studied the effects of cooperative group work and metacognitive instruction on secondary students' mathematics reasoning and ability.  Their study compared a control group to three other treatment groups, one of which underwent cooperative learning, another received metacognitive instruction, and another underwent a combination of the two.  The results showed better outcomes in the group that received both treatments than in any other group.  This group provided more correct explanations for their reasoning, and they outperformed their peers on tasks designed to assess transfer ability.  In an earlier study, Kramarski, Mevarech, and Arami (2002) found that metacognitive instruction improved student performance on both standard mathematics tasks and authentic tasks.

Both of these studies are well designed with decent sample sizes, and they look at secondary math students, which is my focus.  Their main drawback with respect to my project is that they are Israeli studies, which raises the question of external validity.  But they are more robust than most of the other studies I have found on cooperative learning and/or metacognitive instruction, and their control-group design also makes me more confident that I could extend their results to my own setting.  As I look for and gather more sources, though, I am hopeful that I can find a few more domestic studies touch on the same topics.


Referenced Sources:

Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom:  The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281-310.

Kramarski, B., Mevarech, Z.M., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49, 225-250.