March 19, 2007
The focus on metacognitive skills: Writing in PBL
Posted by emmapbl under Transition to PBL Entries | Tags: Writing in Mathematics |[2] Comments
I’ve recently read an article that discussed a study relating writing-to-learn programs and their effectiveness on academic achievement. This article (Bangert-Drowns, et al, 2004) states that using a writing-to-learn program has a small positive impact on students learning (measured by testing) in a specific class. I should mention here, that we have been using an informal writing-to-learn program in our Problem-Based Curriculum this year in the form of journal writing. We have required every geometry student to keep a journal which has become a compilation of their questions, ideas and problem-solving processes that the students use for reflection. Since this was the first year that all of us geometry teachers were trying this, we decided to do it very casually and not require certain entries on specific topics. We left it up to the students what problems they would write about and how detailed they would be about their solution methods.
However, we graded the entries on the depth of understanding shown in the entry. Not only understanding of the problem’s solution, but of the context of the problem, how it relates to other problems, how it would be categorized, what relevant new material was explored, etc. Students’ journal entries have ranged a great deal in quality and quantity. As the year progressed, practically every single student has improved in their ability to write clear, concise and thoughtful explanations and sometimes even made connections to other problems. We felt that this part of the curriculum was very successful.
- Until I read more into this article I received. It seems that the authors who were writing a meta-analysis (a study of studies concerning writing-to-learn programs’ effectiveness) across disciplines. It seems that in order to be most effective, these programs needed to be used over a long treatment length. Well, this is good, I thought to myself. We’ve been doing it all year, generally one or two entries a week, this must mean that it’s being effective right? Hmmm, well some of the factors that created negative effects were introducing the writing in middle school (phew!) and having longer individual writing assignments. OK, well also didn’t do either of those. However, the other factor that enhanced the positive effects was the introduction of metacognitive prompts. This we were not doing (well, 3 out of 4 ain’t bad, right?)
Well, let’s think about it. The role of the metacognitive prompts would be to get the students to begin to think about how they were learning the material they learned in each problem. These prompts would be questions such as “Describe your thought process when you first attempted this problem and comment on your misunderstandings or misconceptions” or even “How does the theorem discovered in this problem relate to a previous problem on a procedural level?” I think I could come up with some of these prompts and actually make them more a part of the journal writing process next year. If it has shown to help students’ academic achievement it is hard to argue with.
It does take a lot of effort to put all the pieces in place, so why would it be worth it to me? It seems to me that one of the premises in which PBL is rooted, is the value of procedural and conceptual thinking. Writing on the metacognitive skills needed for the problem solving processes seems to be one way in which to focus the students’ attention in a reflective mode of thinking. This reinforces their responsibility in their own learning, creates authorship of their own ideas and invests them in the processes of which they write. For example, one student wrote this about learning an algorithm to use to find the coordinates of a point reflected over a line.
“What did we just do? – We know that the perpendicular bisector of a segment is the mirror of a reflection. In order to reflect point K over the mirror line we made a perpendicular line going through point K. Then by finding the intersection point we were finding the midpoint of the segment KN and then adding the vector of K to the midpoint to the midpoint, was finding the actual point B which was the image of K by reflection”
OK, so it’s not Pulitzer Prize writing, but this high school freshman was able to articulate a very complex process. Here’s an added comment she wrote below her more “algorithmic” message:
“On the homework, when adding the vector to the original point, I was so used to finding vectors from the origin that I just doubled [the vector] instead of thinking I had to put the actual coordinates of the point into perspective. It wasn’t until class that I realized the actual vector from point K to the intersection was [half of it].”
This was quite an a-ha moment for this student who made a very conceptual jump in her head from the process she wrote about before. She realized that the vector she found from the point K to the mirror line would be half the vector from K to its image – something she came to because of the practice of thinking metacognitively about her work.
My plan for next year is to have a list of metacognitive prompts to help enhance this program. I know the work of providing these prompts will take some time over the summer, but at this point, I’m so invested I can only hope to improve on what we’ve created this year.
Bangert-Drowns, R, et al (2004). The Effects of School-Based Writing-to-Learn Interventions on Academic Achievement: A Meta-Analysis. Review of Educational Research, 74(1), 29-58.
August 26th, 2007 at 12:53 am
Dear Mrs. Schettino,
Hi. I caught your session at the Exeter Conference earlier this year. Wow. Your explanations of how PBL works and how it worked for you were great. I loved seeing the journals and your comments in them. In this article on metacognitive analysis, I can see how generating the questions is a key role of teacher as facilitator.
I will be using the problem sets from Exeter this year with my honors geometry class. It will be a first with PBL for our school. I am honored to be the one introducing it. I even started a blog. Let me know if you’re interested.
My question today is, were you able to come up with more meta-analysis questions you plan on using this year? Would you be willing to share those with me?
Thanks again, for all you’ve done in furthering this work. I think it’s great you share your teaching experiences. There is soooo much to learn.
Mark
August 26th, 2007 at 7:32 pm
Hi Mark,
Thanks for coming to my session and thanks so much for taking the time to visit and read my blog! I am very excited for you (being your own school’s math maverick) in starting the PBL at your school. I’d love to hear how it goes for you. I hope you can learn from my experiences too.
If you go to my website which you can find at http://community.emmawillard.org/Math/SchettiEmmaWebsite/index.htm
I have added a new rubric for grading journal entries which my colleagues and I have come up with this summer. I will be updating my Math 225 Algebraic Geometry class calendar with journal-writing prompts every other week. I’ve made a committment to myself this year to do that. So keep checking that as well. if you’d like to check out the pdf files that are the materials that we use for our courses, they are also posted at my website. They are pretty much the Exeter materials rewritten specifically for our kids.
Well, good luck and please keep in touch!
All the best, Carmel