Author Archives: Beverly Ford
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?
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
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
One of my favorite questions to ask a toddler is, “How old are you?” They will often proudly hold up two, three, or four fingers. Most of the time these fingers come up all at once. This is their first experience connecting a number word and their fingers and can be a foundation to building… Continue Reading
In my first blog about the Mathematics of Grace, I mentioned that by the end of our six week study she was able to answer 98 + 5. This was exciting for me because when we first interviewed her she wasn’t able to combine 19 + 3. She was limited to solving sums within 20.… Continue Reading
In my last blog I wrote about one of the first things I noticed about the mathematics of Grace. She used her fingers to solve addition situations like 7+4 by constructing more advanced finger patterns, where one finger could mean one or eleven and six fingers could mean six or sixteen. This allowed her to… Continue Reading
The mathematics of students is a powerful tool for a teacher. It allows a teacher to hypothesize what is happening in the mind of a child and plan a next step that will allow that child to construct more sophisticated understanding. Today I want to look at the mathematics of a student we call Grace… Continue Reading
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