On Teaching Math: Part Seven
Welcome to A Mother’s Thinking Love: Living Ideas, Lovingly Shared! I ended my last post with some ideas for math journals. In this post, I want to go a bit more in-depth with the idea of math journals. I believe they can be an important part of math study in most years. Join me for: “On Teaching Math: Part Seven”!
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LINK TO REST OF THE POSTS IN THE SERIES
The Purpose of Math Journals
Since I started teaching math with no student textbooks or workbooks, I had to get creative with how students would record what they were learning. This ended up being a blessing because, I think, the result was even more successful. Math Journals became a space for students to memorialize their math journey. While most problems were not solved in these journals, some were. By recording the solving in their journals, students could go back and reference their work.
Math journals were also a form of narration. While I didn’t know this term and had never been told of this beneficial practice, I clearly observed that students understood their work better if they could talk or write about it. I noticed this very early on, so narration, oral and written, became a cornerstone of our math time.
Vocabulary
I did not spend much time teaching math vocabulary directily. I still don’t. I was not interested in quizzing students over their abilities to memorize definitions. I thought it was pointless. Let’s say I wanted to introduce students to the idea of the associative property of multiplication. I would begin the lesson with a story problem. After our problem solving discussion, see previous posts in this series, I would make a suggestion.
Let’s say the word problem dealt with three groups of five. By the end of our math discussion, 3×5=15 would be written on the board, of course. So, I would say, “Hmm. I wonder. We know that 3×5=15. I wonder what 5×3 equals?” Before I could direct them to do so, students would begin working on solutions. All across the room, “Eureka!” moments would be happening. Excitement filled the air.
Then, I took it a step further. I would say, “Well, that’s interesting. I wonder what would happen if we solved 4×5 and 5×4?” Again, students would begin working. At this point, students would be trying more and more options. They would begin looking for exceptions to our discovery. Eventually, we would need to end our lesson, so I would close with a very brief commentary. It might go something like this.
“Well, class, what did we find today?” Inevitably, a student would raise a hand and say, “We can put the numbers in any order. The answer stays the same!” I would write “Associative Property of Multiplication” on the board. I would direct students to open their journals and write this term at the top of the page. Then, I would have them write down the examples we discovered as a class or ones they discovered on their own.
What Does it Look Like to Know?
I would not use the term “Associative Property of Multiplication” often in class discussion. Number one, it is a long term. By the end of saying it, students would often check out. I just never found that students needed to be able to recall that precise term. Later, I began to think through that a bit more thoroughly. Doing so strengthened my convictions in this area.
After all, what does it look like to “know” the Associative Property of Multiplication? Is knowing epitomized in the student who can memorize the definition and match it to the term on a test? Or does knowing look like a student who can use the concept of the property in solving a problem? In my humble opinion, the latter is what it truly looks like to “know”.
Practicalities: Table of Contents
One practice that I developed later was saving space for a table of contents at the beginning. This worked well with my third graders. Students in younger years may need a bit more help. Students would title and number each journal page, then add it to their table of contents. For example:
“Associative Property of Multiplication” pg. 5
Students may write it like this, but they might also write 2×5=5×2 in the table of contents. I left that up to the student’s discretion.
Closing
I hope you have enjoyed “On Teaching Math: Part Seven”! I think this post, in particular, was a good mix of ideas and practical suggestions. I hope to do the next in the same post. Also, I want to make sure to emphasize that I hope you don’t feel burdened by any of these ideas. They are just ideas. My goal is to bring freedom to the mother-teacher, and her children, not to add more to her plate. Feel free to share comments and questions below!
