“I’m not sure this is working. Only five of my students are participating and commenting each day. The rest sit there and look at me.”
This was my conversation with our math coordinator after my first few days of teaching IM K–5 MathTM with my third graders. Those five students were having great conversations. However, my other students just sat there wide-eyed, silent, and staring blankly at their papers. I felt lost. Was this the best for my students? Could we survive a whole year of math like this? I wanted my students to love math and have a deeper understanding of mathematical concepts. How would this get them there?
The next week, while outside at recess, a handful of my students came up and asked what we were doing next in class. I told them we were working on Illustrative Math and they cheered. I stood there looking confused. We were eight lessons into the first unit, and it didn’t feel like a success worth cheering about. In my head I was thinking, “For real? You guys are enjoying this?” These were students who never said anything in math and rarely were able to explain how they got their answer. I walked away even more perplexed than I already was about my math instruction.
Heading into the following week I was beginning to see a difference in my kids. I started to get why they loved it so much: They all felt successful. There was an entry point for each student. They were all learning the same standard but it was designed in a way that allowed each student to contribute in math class each day. I had so many students wanting to show their work and defend their work that we couldn’t get through them all in a day. They were also giving each other constant feedback on their work.
During one lesson, multiple students gave feedback on a bar graph a student had presented. All of these students agreed with the way the student had created the bar graph from a set of data. Another student signaled with her thumb and said she disagreed. The whole class turned to this student and listened intently. This was one of the first times a student had disagreed. She went up to the front with the student who was presenting their work and explained how their scale on the left hand side was incorrect due to the placement of their zero. They placed the zero on the first section of the bar graph and it should have been down on the x-axis. The whole class goes “Oh ya!” and the student who had originally shared immediately started fixing her bar graph. I had noticed this mistake as I was walking around the room monitoring their work, but had refrained from saying anything. This paid off big time! My students were now learning from each other and teaching math to one another. It was a huge moment in our classroom.
There were still days that were difficult—with only a few students participating—but we pushed through and continued to build our mathematical community. I began to examine how my facilitation shaped the experience in the classroom. There were days when I didn’t ask my students the right questions or push them in their struggle. That is when I saw my students have less ownership in their learning. Whenever this happened, discourse flattened. When asked to give feedback to a peer, students would say “I agree with you because I did the same thing.” However, when I stepped back and let students construct meaning from the task and strategies of others, our conversations completely changed. Students were defending their thinking and questioning the thinking of others.
Now my students’ mathematical thinking blows my mind!
Each and every student in my classroom can explain their answer. Their strategies look different because they all approach and solve problems in different ways, but they can use words, diagrams, equations, skip counting, whatever it may be to explain how they got their answer. This started happening before we even completed Unit 1.
One more huge moment happened in our room when a student gave feedback to another student while presenting work to the class. The student had written 4 x 5 = 20 for the given array. A student popped her thumb to give feedback and she said she disagreed. Once again it was one of those problems where almost everyone had the exact same thing, so they were anxious to hear more. She said that the student had written an equation but the directions said to write an expression. She explained to the class that an equation has the whole number sentence with the equal sign and product but an expression doesn’t have those things so it should just be 4 x 5. I think my mouth fell open as I heard her use those mathematical vocabulary words that we had only recently discovered. I watched my students immediately go through and start correcting their work without a teacher standing up there saying they needed to correct it. In fact, I rarely tell students to correct their work. They listen to each other and do it by themselves. Which is so much more powerful! I was in. This was the best. Only 30 days into the school year,I was watching and listening to students deeply discuss math. There could be nothing better than that!
In my classroom, there are still days in which we struggle, but we have committed to struggling productively and learning from our mistakes. Our greatest success is that my students love math. They feel successful in math. They have a growth mindset everyday in math. I firmly believe that having a growth mindset and being able to think about and reason in math will start to show on assessments in a positive way. I can’t wait to continue this journey through IM with my students, and I truly cannot imagine the kind of math thinkers that I will have in my room after another 30 days.
If you are interested in piloting IM K–5 Math beta at your school or district for the 2020-21 school year, Illustrative Mathematics recently announced that they have opened the application process to interested districts. Participants of the pilot get early access to the highly anticipated K–5 math curriculum, professional learning, and the opportunity to provide regular feedback to influence future versions.