An article written about using “math talks” to analyze student thinking and allow students to problem solve.
Metacognition is the awareness and understanding of one’s own thinking or simply “thinking about thinking”. As adults we have a tendency to already know our processes for problem solving, but young students today have a very hard time being problem-solvers. Students expect the teachers to tell them where to start or what to think. This is very true of our curriculum now, especially in math. We overload them with strategies and processes that they may not connect with. Let me preface: by no means am I saying throw out your curriculum (but that would be cool wouldn’t it?). I am so however that we need to aide students in recognizing their own thinking! But how do you do this you ask? Especially with a room full of blank stares during math time…
I recently attended a math training for CGI (Cognitively Guided Instruction) and it really changed my perspective on my math instruction. What I took from this training is the importance of understanding your students’ thinking as well as helping them understand their own thinking. Although it doesn’t seem like it by 2nd grade, we ARE innately build with problem solving skills. We need to get to know how are students are thinking to help drive our instruction.
Something simple I’ve added into my math instruction is a “number talk” of sorts. I use the term lightly because I am under the impression that “number talks” are strictly mental math. During my “math talk” my students are allowed to use any means necessary (any manipulatives/drawings) to solve the problem. The purpose of our “math talk” is not to make math abstract (by doing it in our brains), but to make math concrete and tangible.
Here is an example of a simple “math talk” we did in my class (excuse the messy handwriting, these are REAL life photos, hehe):
I proposed a simple multiplication problem and told my students to find the answer, but SHOW how they got there. That was quite the challenge because so many students just memorize their multiplication facts (which is dandy, but some students just can’t and need additional ways to do it).
This student skip-counted to get his answer.
Another student found a multiplication fact she was most comfortable with (7 X 5) and then added on.
This student invented her own method of a bubble map (as she told me) of six 7’s, then added them together.
Lastly, this student had an invented algorithm. She explained to me that she knew 6 X 6 then knew she needed one more 6, but she broke the 6 apart into 2 and 4. She added those to the total. MIND BLOWN!
If you’re not into reading all that, here’s the Facebook live video that explains it!
I was thoroughly impressed by all the strategies and invented ways I came across in one classroom! There were only a few students who had the same strategy, which is WILD to me!
I also love asking students to make sense of OTHER students’ work. “What did Jill do?” “Do you notice anything?” “What do you wonder?” “Why did he do this?”. Questioning is a BIG part of getting students to think. Remember your job as a teacher is not to work harder than your students!
Why is all this so important? When I ask about and analyze my students’ work, I am getting a better understanding of how they are thinking. Then I can plan my lessons accordingly.
I also like to leave some of our “math talks” up in the classroom. Then students can use that as a reference for further problem solving. I always make sure to label it with the student name instead of “skip counting” because I notice when students have ownership of strategies, they have more investment in the work.
Interested in more CGI-inspired activities? Check out this blog post on Counting Collections by Holly over at Research and Play. It is an amazing activity to check out your students’ thinking in what ways they can and cannot count, analyzing their strategies for counting large numbers of objects!
Disclaimer: CGI is research. It is not a program. This article and the activities in it are only inspired by CGI and not directly related to it.