Math Journal

In my math group students often use their journals to work through and show math solutions. I base many of the problems we use on  Cognitively Guided Instruction (CGI) . CGI is a process developed by Elizabeth Fennema, Thomas Carpenter, Penelope Peterson, and Megan Franke and outlined in their book Children's Mathematics: Cognitively Guided Instruction.

It works to build on the math knowledge that students have. A part of the process is for students to solve a variety of types of problems using strategies that make sense to them: modeling and manipulatives, counting strategies, and combining numbers in different ways. Students work to communicate these strategies in their journals. We then share strategies together, so students can learn from their classmates’ process. 

I often work to use the students' names in the problems we solve. That adds to their enjoyment of the process. For some the problems are challenging, and they work hard to come up with their solutions and record them. Other times students easily come up with answers in their heads. Then the challenge is to understand the process they used and represent it in their journals.

Math Journals and the 0-99 chart

I use math journals in a lot of ways. Often I ask children to record their math thinking about a group problem solving session in their journals. They also record math explorations and math game results. Recently we have been working to place numbers on the 0-99 chart.

The first day I presented the chart, I had already placed 0-16. I asked how many number cards were placed on the chart. Some students thought 16, but then someone pointed out that 0 was a number, too, so there were 17 cards on the chart. That day we placed 17 more numbers. At our next math group I turned the chart around so that they could not see it. I reminded them that there had been 17 cards on the chart to start with and that we had then added 17 more cards. How many cards were on the chart now? I asked each student to figure out the answer to the question and to show how they figured it out in their journal. Some students found a way to represent the cards in a drawing or by marks and added them up. Some used grouping by tens to help with that. Others worked with equations. Some needed a little help to talk through their process before writing it down. Some came up with the correct answer and some did not, but all were able in the end to represent the math process. The next math group we counted the cards to check our work. Those who came up with an incorrect answer were able to see what tripped them up. I told them that my goal was that everyone be able to show their math process in their journal. Everyone met that goal.

"But it doesn't come out even!"

This is another journal problem that can puzzle the kids because it doesn't come out even. Today I asked my students to consider this problem:
You invite 10 friends over for a party. You want to serve juice. You want enough for each person to have 1 cup. The extra special juice you want to buy (raspberry razzle-dazzle kiwi!) only comes in quarts. (At this point I asked the students to remember how many cups are in a quart and one of the students supplied 4.) How many quarts do you need to buy? Prove your answer.

Quite a few asked for help. For each I asked leading questions until they came up with an answer and a way to express their understanding of it. Some included themselves in the planning and some did not. One kept trying to adjust the number of people so that every cup was accounted for: "well my parents could come, or maybe I'll have one go out and one stay." That extra cup tends to bother them a lot and I don't think it is in the name of "waste not want not." For them division should be neat and tidy. We'll share our solutions soon. I hope problems like this help them reach some peace with the idea that math can be messy!