Author Archives: Beverly Ford

What Does a Math Grade Mean to a 1st Grader?

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?

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Learning and My New Role

Today I want to write about how the mathematics of students helps me to see my role as a teacher and learning a bit differently. In my last few posts, I have been telling you the story of Grace. Today, I wanted to share Grace’s story because it is an example of a time where… Continue Reading

Sparks in the Desert – A Beginning Conversation on Counting On – Part 2

Are there any dangers in training your students in the “strategy” of counting-on? After reading Dr. Les Steffe’s work, I would argue it is harmful. He calls counting-on a non-teachable scheme.  This means that if you want counting-on to be meaningful for students you can present situations that would promote their construction of counting-on, but… Continue Reading