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 they were doing to the fish number stories in the real world of their class. One of the big ideas I have taken away from reading the research on radical constructivism and student adaptive pedagogy is that conceptual understanding begins from our experiences in the real world. Too often, I see kids trained to function in the abstract with number before they have had the time to construct the meaning behind the concepts. I think some of the reasons are because of the pressures teacher feel from pacing guides and benchmarks, and a lack of understanding of the difference between conceptual understanding and procedural understanding. I had hoped to write about the next phase of the fish number story bulletin board for this post; however, I haven’t had the chance to do it with my students yet due to necessary adjustments related to benchmarks and upcoming report cards.
Teachers are always being pulled in many directions. Teaching first grade every day has reminded me that I am constantly choosing what to work with a child on. A few of my students that are numeric (a good place to be conceptually in first grade) are struggling to demonstrate that understanding with paper and pencil. When I interviewed them one on one, they were able to communicate sophisticated thinking, but when I ask them to do the same math on a worksheet, they can’t seem to do it. If I had not interviewed them I would be much more concerned about their math, but I know the problem isn’t their math. It could be their lack of maturity, or lack of exposure to paper & pencil problems, fine motor skills, ability to follow directions, and/or self-disciple. So, then, how do I grade them? I have really been wrestling with what the purpose of a grade is and what it communicates to the child (and to the parent). I want to constantly be sharpening their mathematical understanding and their ability to accurately recognize their math progress, but a first grader may not understand the difference between feedback regarding their conceptual understanding and feedback regarding their maturity and effort. I wish I could explore this more, but I only have five weeks left with them for this study.
I have seen a similar example with my son. He is given a writing grade and a conceptual understanding grade for his science paper. This allows him to distinguish his progress in both things. I’m not sure what this might look like for first grade, but I think it is an important conversation to have. Student disposition and reflections on their mathematical thinking are essential for them to continue to construct their mathematical understanding. It saddens me to think students may get negative feedback about math when it is really their effort and maturity that needs improvement. How have you helped a student who struggles with maturity and effort have an accurate understanding of their mathematical development and their maturity?
Stef was born out of the desire to put Steffe in every classroom. After several conversations with Dr. Leslie Steffe (the originator of much of the research we study at AIMS and longtime researcher at the University of Georgia), the AIMS Research Associates brainstormed ways to encourage children to see the math in their world.… Continue Reading
It is time for a story about a pig. It’s a true story, and while I have laughed a lot about it since it happened, there are important lessons to learn from it. My purpose in sharing the story is to also share one of those lessons, and how it is important to us at… Continue Reading
I have been reading and thinking a lot about the power of imagination in learning — specifically, learning mathematics. In this and successive blog posts, I will discuss one role imagination plays in helping children form number sense. Merriam-Webster’s definition for imagine: “to form a mental image of (something not present),” is what I mean… Continue Reading
When I taught middle school, I always found it interesting that my students could do this task: Johnny rode 34 miles on Tuesday and on Wednesday he rode 27 miles. How far did he ride over the two days? Yet they often had no idea what to do when I gave them this task: Johnny… Continue Reading
My last blog post focused on the calendar that I have been using in kindergarten. This week, I want to focus on what students are doing during our math center time. I am running a two-center a-day rotation, making it possible for me to work with two groups of six students for 13 minutes each.… Continue Reading
I wrote a blog post at the beginning of the school year talking about our plans for research this semester. I’ve been reflecting on our project and the progress we have made so far, and I thought I would share a few of those reflections with you. As I mentioned previously, we have been working… Continue Reading
In the August and September installments of my blog, I’ve been telling the story of Christian and our mathematical interactions with him. Christian is a second grader who came to us with mathematical skills that had been taught through his first years of schooling. He was bright, eager to work with us, and considered, by… 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
I have heard the claim “calculus is easy, algebra is difficult, and arithmetic is impossible,” but if that is true, then what does that make counting? We often hear little ones proudly singing the alphabet song or reciting a string of numbers from 1 to 20. Have you ever asked one of those who now… Continue Reading