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.
Good lit search! Very nice summary and then connection with you purposes and plans.

ReplyDeleteThis could be more of the same, but sounds relevant:

Using Errors as Springboards for Enhancing Mathematical Reasoning With Three Metacognitive Approaches

Kramarski, Bracha; Zoldan, Sarit. The Journal of Educational Research102.2 (Nov/Dec 2008): 137-151,160.

And did you see these two MTMS articles that use this research?

I-THINK I Can Problem Solve, Sararose D. Lynch, Jeremy M. Lynch and Johnna Bolyard, Mathematics Teaching in the Middle School, Vol. 19, No. 1 (August 2013) pp. 10-14

Putting Mathematical Discourse in Writing Sararose D. Lynch and Johnna J. Bolyard, Mathematics Teaching in the Middle School, Vol. 17, No. 8 (April 2012) pp. 486-492

From the research it looks like you'd want the meta-unit at the beginning of a course. Unless you're trying to use the stus previous work as a sort of control?