As a teacher, I want to know what I can do to support my students’ mathematical development. One of the new “teacher moves” I have learned from our research into Student Adaptive Pedagogy is giving a child a “recent experience of counting.” Today I want you to watch a video of me interviewing Eden. She solves the following three problems: 6 + 3, 7 + 4, and 8 + 5. Let’s think about the same questions we did in my last blog (link previous blog) on a Counting All student:
- Did she solve each problem in the same way?
- Was one problem more challenging than another?
- If so, what did you notice that led you to that conclusion?
Eden needed to count an item for each of the addends before she could create material to use to solve the problem. Hiding the blocks after she counted them engaged her need to retrieve a mental image of the blocks and her counting experience. This teacher move supports her development in the abstraction of number. Allowing a child to count something and then hiding it before solving the problem is critical to their development. Before engaging in this area research, I hadn’t realized I should hide material for students. Now I know that hiding material and giving students a recent experience of counting can support their mathematical development.
You may be wondering why we should hide the blocks after a student counts them. The developmental progression we have studied found that as students develop their concepts of number, they move through levels of working with perceptual material (anything visible or tactile, including a drawing), figurative material (mental images of material), and abstract material. If I let her only count the visible blocks, I am not encouraging her growth toward the abstract. Although it is not explicitly stated in common core standards, developing an abstract concept of number is foundational for a student’s mathematical development. Try giving your students a recent experience of counting and let me know how it goes?
I remember getting a Rubik’s cube when I was younger. I sat down immediately scrambled it up, put in the Def Leppard cassette on my Walkman and set out to solve the puzzle. It soon became apparent to me that it was not going to easy or quick. I would play with it for a… Continue Reading
Tiger got to hunt, Bird got to fly; Man got to sit and wonder, ‘Why, why, why?’ Tiger got to sleep, Bird got to land, Man got to tell himself he understand. -Kurt Vonnegut This poem nicely sums up part of our human nature in that we are at rest when we understand our experiences.… Continue Reading
As educators, we have all heard of the benefits of wait time after you ask students a question. In this video, you will see proof of it. At the beginning of our pilot with K-2 teachers we shared many student videos and, although they noticed a lot of student’s math behavior, they also noticed how… Continue Reading
This blog is related to a multi-part series titled “Creating Centers in the Classroom.” If you have missed that series, you can read part 1 HERE, part 2 HERE, part 3 HERE, part 4 HERE, and part 5 HERE. You are ready!! You’ve planned your centers and are excited about differentiating them based on student… Continue Reading
Currently, I am in the midst of raising a 16-year-old who has been learning to drive. Recently, I was reminded of what it feels like to do something new while I was doing a math demo lesson in a classroom and how circumstances can bring us back to those early behaviors. Fog. Here in the… Continue Reading
Have you ever had one of those “aha!” moments when the light bulb goes off, and you come to understand something that makes your whole life easier? Or better yet as a teacher, you witness your students have one of those “aha!” moments. For us, at the AIMS Center for Math and Science, we have… Continue Reading
Which came first: the chicken or the egg? This is an age-old question based on the observation that all chickens hatch from eggs, and all chicken eggs are laid by chickens. The problem is it’s difficult to answer because it is not clear which of the two events is the cause and which is the… Continue Reading
meraki [may-rah-kee] (adjective) This is a word that modern Greeks often use to describe doing something with soul, creativity, or love — when you put “something of yourself” into what you’re doing, whatever it may be. Do you love your work? Is it more than just a job? The above word (as defined in Christopher J.… Continue Reading
This blog is the fifth part of a multi-part series titled “Creating Centers in the Classroom.” If you’ve missed the previous installments, you can read part 1 HERE, part 2 HERE, part 3 HERE, and part 4 HERE. Through our experiences with children here at the AIMS Center, based on the research of Dr. Les… Continue Reading