Author Archives: Beverly Ford
In my last blog I talked about tasks I chose for my students based off of their mathematical thinking. I was able to do that because the research on student adaptive pedagogy developed a progression that allowed me as a teacher to look for some classic behavior. Last time I wrote about students who use fixed finger patterns or reused fingers. There are so many ways students use their fingers, but they don’t all mean the same thing. In fact, how they use their fingers can allow me as the teacher to understand their thinking.
The next significant classic behavior I noticed in my students is when they only said the number words for the first addend. If they were solving 47 + 8, they would say typically under their breath, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11….47.” Lifting fingers sequentially, they would continue to count, “48, 49, 50, 51, 52, 53, 54, 55.” Now they did not need to reuse fingers for the first addend. They simply had to say the number words. This process may seem like a small thing for us as adults, but it is an exciting step towards the abstract for students. I remember when I was first teaching I would tell my students that mathematicians loved to look for efficiency. Students are on this journey of stripping away everything they don’t need in order to solve these addition tasks.
We usually call this type of method “counting on.” When a student can solve a problem like 47+8 in the manner described above, I know that this student is ready to work with more abstract material. Check out this video of Arya counting on.
At the point a student has begun to count on, they are ready for “change unknown” tasks. Too often we are presenting tasks for students that don’t make sense for them. Below is a video of a child solving for an unknown change. Look at how she is using her fingers.
It appears to be very similar to how a student might have used them in the “result unknown” addition task, but there is so much more going on. Knowing that it is not a good fit to present a “change unknown” task to my students who reuse fingers is so critical for both my students and me. I don’t want to give students the message that math doesn’t make sense, and they should only do what I do. That is what I think happens to students all the time because we don’t realize they aren’t ready for that type of problem. The progression allowed me to be in the “sweet spot” of all my students. This empowered us all to learn and grow.
In my last blog post, I talked about how Student Adaptive Pedagogy allowed me to meet the diverse needs in my classroom in a way that left my students and me feeling empowered. They were empowered as mathematicians, and I was empowered to use their math to support their academic growth. I mirrored teaching math… Continue Reading
I started teaching because I love to learn and I wanted to make a difference in my students’ lives. I quickly learned that what a child was learning could be academic, social, or simply personal growth. Learning is complex. Teaching is complex. As a teacher I was making so many decisions everyday. When I taught… Continue Reading
In my last blog post I talked about how reading the research on student adaptive pedagogy has given me a new lens in which to facilitate productive struggle with students. It has been so exciting to see the great effort that students will naturally put forth when a math task is in their zone of… Continue Reading
When I first heard the words “productive struggle,” I imagined the many times I have watched students struggle to learn a math concept. My heart has always been sensitive to the children that would have to work to learn an idea. Growing up, I had cousin to whom learning appeared to come very easily. I… Continue Reading
This week is my last in working in a first grade classroom every day. It is hard to say goodbye to the students. I have watched them grow so much in their math knowledge during our time together. I am more convinced than ever that the research we have read and come to know at… Continue Reading
Today I want to reflect a little about my struggles with grades, students’ conceptual understanding, and students’ disposition towards math. In my last post, I talked about how I used a bulletin board with an ocean scene and fish number stories to engage my students in meaningful experiences around addition. Students were connecting the addition… Continue Reading
Our learning begins as children when we start to make sense of our world. When we count objects in our world and identify how many of something there are we are actually working on understanding number. Learning about addition is no different. It needs to start in a child’s world. So, in my 1st grade… Continue Reading
My great adventure in the classroom has been going on a little over a week. I have absolutely loved doing math with 1st graders. In my last blog, I wrote about how important reflection is in learning, and how I would need to prioritize time for reflection. Teaching has reminded me of the amazing amount… Continue Reading
One of the best experiences as a teacher for me is when you see a child have an “ah-ha” moment. The look on their face, their body language, their emotion. These moments bring me so much joy. I have seen so many of these moments working with 1st graders over the last few years. I… Continue Reading