Math Discussions – Educational Aspirations

Better Quality Math Discussions

This year my district decided to switch to a new math resource. After using Origo for more than a decade we are now using Illustrative Mathematics. Besides the change in materials, teachers have had to navigate a new platform and instructional approaches that are significantly different compared to the last adopted resource. This change in expectations has been a challenge. The shift in a different math instruction approach was discussed during curriculum night earlier in the year. One of the larger foundational shifts involves the increased amount of math discussions that are expected to occur throughout a lesson. This year students are asked to engage in quality math discussions at least a few times every lesson. There are many “what do you notice, what do you wonder”type of prompts as well as others. The conversations are usually around 3-5 minutes and then students share their discussions with the whole class.

Along with other teachers, I observed that the math conversation opportunities were far from perfect. Some groups had one particular student that spoke for the entire time. Other groups didn’t stick to the prompt or jumped into the conversation before the partner was ready to discuss. After reflecting a bit I felt that students needed a routine for math discussions. That structure, just like many of the routines at the beginning of the year, would hopefully pay dividends as the year progressed. My goal was and still is to improve the quality of the math discussions happening in the classroom. I re-read this book to get a few ideas bout the process. Then I started to build a Desmos deck to help communicate the process that the classes were going to use moving forward.

The deck started off by asking students about past math conversations.

Students picked an option and we discussed it as a class. The consensus was that the class should analyze the picture or problem first. That led to the next slide related to what happens after we analyze the prompt.

Moving on the next slide gets the students talking about the process after analysis. Students will give a non-verbal signal showing that they’re reading to discuss. The class had a fun time creating their non-verbal signals, although I had to repeat more than once to make sure they were appropriate (ah fifth graders!). As students progressed through the deck we reviewed who should go first in the group and why.

We went with the alphabetical approach since the groups will change throughout the year. The class also discussed how to non-verbally show that you agree with the statement from your partner to make sure the conversation continues without interruption. We also discussed sentence stems that can be used to help start the conversation.

The next few slides reviewed the process discussed earlier in the deck.

The class went through a review of the process and tried out a practice round with their current partner. The entire class deck took about 25-30 minutes including the practice round. Feel free to use the Desmos activity by clicking here. The class completed this activity on Tuesday and we used the process daily since then. So far I’m seeing positive results and better quality math conversations. Of course there are hiccups, such as students still using more time than anticipated and/or students finishing too early, but I’m glad to see the conversations moving in the right direction. Later in the week the classes reinforced the math conversations procedure with this quiz.

I’m curious to see what others use to emphasis quality math conversations in the classroom.

Feedback and Reflection Opportunities

Screen Shot 2019-10-19 at 8.48.12 AM

Over the past few years I’ve emphasized the use of student feedback, reflection and goal setting in my classroom. Trying to find an adequate balance for this has been a challenge. This school year I’m looking at different mediums in which students can reflect on their math progress. Reflecting on individual progress and determining where students are at in the progression can lead to powerful outcomes. This year I’m looking at different ways to encourage students to make more meaningful reflections that lead to actionable goals.

Math journals

Each student has a math journal. These journals take the form of a 70 count spiral notebooks. The journals are primarily used to reflect on assessment performance. My class has eight unit assessments per grade level and there’s a reflection sheet designated for each one. I’ve written about the different sheets and journals: (1)(2)(3). Students then complete the sheet and bring their test along with their reflection to the teacher to review. At that point the teacher and students work together to develop a math goal for the next unit.

Peers

Students work together often in my class. I use a randomizer and group students so they tend to have different partners daily. After they complete a task I give the students a couple minutes to discuss with their partner the effort level and challenge of a particular assignment. I tend to use a timer and encourage students to be honest in the process. Hearing how other students feel about the effort and challenge level can help students be more aware of the struggle that is part of the process. Certainly not all, but I’ve seen some students thrive with this type of reflection.

Independent

Before students complete a project teachers give a sheet indicating the criteria for success. This looks like a checklist with statement indicating what’s needed to meet the expectation of a particular assignments. As students complete each component they reflect on whether they’ve met the criteria and place a check. Students will attach the criteria for success sheet to their assignment

Digital Platform

Along with the criteria for success, students may submit a project to a digital platform like SeeSaw or Canvas. Other students in the class are randomly selected to give feedback on other projects. Students follow a prompt that asks whether a student has met the criteria for success or not. They then re-check the work and ask a question or provide a positive comment about the work. After the comments are submitted, the original poster reviews the comment, reflects and responds to the question or comment.

Each one of these mediums has pros and cons. I’m finding that the classroom environment plays a major role in how comfortable students are in sharing their thoughts with the class. Some students are much more willing to independently reflect and speak with the teachers than others. I find that students take more of an ownership role when they analyze their own performance in context and make steps to improve. Bypassing the “I’m good at math” or “I’m bad at math” type of thinking can be a challenge, but providing ample opportunities to reflect can move students away from generalizing and be more specific about their analysis.

The next step in my process is to take these reflection opportunities and transition it to meaningful individual goal setting.

Math Responses and Discussions

Screen Shot 2019-10-07 at 7.37.13 PM

Last year I experimented with a couple different ways to encourage students to discuss mathematics. I used a form of a number talk last year and found some success. Students were engaged the conversations were more productive than in the past. I also noticed that not all students participated in the conversation. Even with manipulatives, some students participated minimally and shied away from being called on. I found that some students dominated the discussion more than others. This was taking place in most of my classes and I kept on reinforcing the importance of having a positive classroom climate where mistakes were honored. I thought emphasizing the climate and providing support would help encourage participation from everyone involved. For some that worked, others not so much.

This year is a bit different. I’m still using a form of number talks with success. I’m still looking for ways to help improve this process. I also introduced a more organized way to incorporate math discussion prompts with students. I first organized students into groups using a randomizing student spreadsheet.

Screen Shot 2019-10-07 at 7.20.21 PM.png

Students are put into groups and a destination in the classroom. I put a new slide on the whiteboard once everyone finds their assigned location.

Screen Shot 2019-10-07 at 7.23.01 PM.png

Students get into their groups and identify themselves as partner A or B. Usually I use the spreadsheet to indicate the partners. Partner A starts with the first prompt and I display it on the whiteboard.

Screen Shot 2019-10-07 at 7.28.31 PM

I click the timer and partner A has 40 seconds to respond to the prompt while partner B listens. After the 40 seconds I pick a few different people in class and ask them about their thoughts about the prompt and their answer. Partner B then gets a different prompt.

Screen Shot 2019-10-07 at 7.31.05 PM.png

Partner B gets to respond to the prompt while partner A listens. I’ve toyed around with 20 – 40 seconds and have landed on 40 because it gives students an ample amount of time, but also the limit encourages them to be concise. Students usually go through 2-3 questions each and then we have a whole class debrief session. So far students have been receptive to this medium and I’m hoping to expand it to other classes that I teach.

Files referenced in this post: