I'm shelving the Hattie post for now. I can't do it without it turning into a 3-part series on meta-analysis. I'm hoping if I walk away from it for a little bit I'll be able to turn it into something more concise (and coherent).
Until then, I'm changing it up. I read a lot of educational research. At least, a lot for a teacher who isn't enrolled in any grad school program. I'm going to start sharing some research I've already been incorporating and later move on to just things I've found interesting but haven't figured out how to implement.
First up: IMPROVE: A Multidimensional Method for Teaching Mathematics in Heterogeneous Classrooms
IMPROVE is an acronym created by Zemira Mevarech and Bracha Kramarski out of Bar-Ilan University in Israel and describes the method they devised for mathematics instruction. It's based on three principles: metacognitive training, learning in heterogeneous cooperative grouping, and provision of feedback-corrective enrichment.
IMPROVE stands for:
Introducing the new concepts
Reviewing and reducing difficulties
Sounds cheesy. I know. But I'm only going to focus on one part—metacognitive questioning. The authors drew from Polya for these but I like this structure a bit more .
For the study, Mevarech and Kramarski designed a series of questioning cards. I picture them as index cards with questions written on them but I don't have any actual examples. The questions were first used when the teacher was modeling problem solving for the class. In groups, students then took turns solving problems while answering the questions. The teacher would also circulate the class and take a turn at each group (solving problem and answering the questions along the way). Students wouldn't move on to the next problem until they reached a consensus based on discussion.
There were three categories.
Comprehension Questions - Students were asked to reflect on the problem first. They read it out loud, described the concept in their own words, and what type of problem it was.
Examples: What's the problem asking? What is it giving you? What type of problem is it? What are the essential features?
Connection Questions - Students focus on the similarities and differences between the current problem and the previous problem or problem set.
Examples: How are....and....similar? How are....and....different?
Strategic Questions - Students were asked what strategy they selected to solve the problem and for what reason.
Examples: What strategy is most appropriate? Why is this strategy most appropriate? How can the suggested plan be carried out?
The authors state that, "...students were introduced during the year to a large repertoire of strategies from which they had to select the appropriate one...." Examples given were constructing a table, drawing a diagram, and selecting the appropriate formula.
I'd love to see the selection of strategies but unfortunately they were not included.
I also have Reflection Questions (How do you know it's right? How could you have solved it differently?). I'm pretty sure the authors added this in future versions of IMPROVE but I could just be making it up.
I've been using these questions for three years now. I like having frameworks for my students to work within and if I just said, "Talk about science," I'd get many conversations about the last Chivas game and very little actual science. I don't use cards. I just put problems on the left side of a paper and leave a column on the right side for students to fill in with the answers to the metacognitive questions. They don't do them every time, just when they're working on something new. I also use them when students are planning labs.
On my part, I model them when demonstrating something and try to reference them as explicitly as possible when I'm prompting students who are stuck.
I've been happy with it although I need to work harder at having the students generate and refer back to a list of strategies.
Addendum: Talking with @park_star on Twitter she mentioned that this is how teachers in her ed program taught problem solving. So if you're in Canada, nothing new I guess. Also, I forgot to mention is that after I've worked a bit at building the habit, I've found that it's something I should only push when it's truly problem solving. The students need to be working on something difficult so that these metacognitive questions are actually useful. Otherwise it becomes just another task that's forced on them and is the metacognitive equivalent of showing your work.