We recently attended the annual meeting of the National Council of Teachers of Mathematics, NCTM. This year’s conference was in San Antonio, Texas. We were mostly a group of research associates from the AIMS Center. The size of the conference (over 7000 attendees) and the wide range of presentation topics worked together to create a dynamic atmosphere.
One of the “big ideas” of the conference was how to elicit student thinking. One way is to ask for students’ responses in class. Young students are sometimes even eager to give responses, and tell you what they’re thinking. There is a problem, as I see it, not in getting student responses, but in interpreting student responses. When a teacher views responses only from their adult perspective, the children’s responses can sometimes seem to be illogical and even nonsensical.
Here’s an example of student thinking that a teacher might shut down without realizing what is going on. My team has been recently working with a student who did not know multiplication. She was beginning to skip count, and she was quite limited in that. To solve a particular problem we gave her, she needed to figure out the value of ten 3s. She said she couldn’t count that high by threes. Instead, she proceeded with 2,4,6,…, 20, 21,22,23,…,29,30. What she did was replace each 3 by and a 2 and a 1. Then she counted ten 2s followed by ten 1s. This was a brilliant scheme that a child came up with to accomplish her goal. In a normal classroom setting, the teacher may have stopped her quickly because she was not counting by 3s.
Six attendees from our group discussed our take-aways from the conference. We had collectively participated in at least five dozen of the various workshops and other sessions. We all agreed that the workshop presentations were mostly traditional, generally given from an adult perspective, and gave little if any credence to math from the child’s point of view. We also agreed that we had all been in that traditional education mold prior to our work in researching how children learn math.
A classroom lesson may seem to be very interesting, inspiring, and well designed to an adult, but at the same time it might be just the opposite to a child. How do we get teachers to consider the mathematics of children? That is one of our big challenges at AIMS. If you are a teacher, you will encounter situations where student thinking may be occurring, but you will have to be patient and aware to notice evidence of that thinking. Have you ever thought about the mathematics of children?
Mathematizing defined by Allen Rosales is “the process of understanding math within the context of children’s daily lives”. Last weekend, while cleaning my garage, I came across three lesson plan books from when I taught Kindergarten and First grade. Why I hadn’t gotten rid of them earlier, I don’t know. Rather than immediately tossing them… Continue Reading
The power of play is a foundational idea in education, especially in regards to young children. It is something I have been thinking about a lot lately within the context of spatial learning. Seymour Papert, who passed away in 2016, was a visionary in the field of education and was a huge proponent of the… Continue Reading
Today we have a brief podcast remembering a friend, colleague, and fellow mathematics educator. Diana Herrington demonstrated well how to passionately pursue helping others come to know and appreciate mathematics. She will be missed here in the Central Valley. Continue Reading
Students love to “do” science and be creative while engaged in the process. In order to be creative as they “do” it, they need know how scientists work. Students need to have an understanding of the practices that scientists use while working and be able to apply those practices in their classrooms. One way that… Continue Reading
You have probably all heard the statement, “If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck.” Generally this statement is used to convince ourselves that we can trust what we see, or that we can make sense of our world by gathering evidence… Continue Reading
The AIMS Center Research Associates who regularly post on this blog site are challenged to not only read, understand, and translate into practice research related to how children come to acquire knowledge of mathematics—specifically we are presently focused on how children acquire knowledge of number—but also to read and come to know the theoretical underpinnings… Continue Reading
The 2016-17 school year will be coming to an end in just a few weeks. This is a significant milestone for children completing preschool and beginning transitional kindergarten or kindergarten in the fall. In state and federally funded preschool programs, the DRDP (2015) will be given to each of the children and will allow parents… Continue Reading
I have facilitated many demonstration “number talks” this year throughout Fresno County. I even blogged about it earlier this school year. Talking mathematically in our classrooms is so important that I can’t stop sharing the idea of number talks, even if it is being repeated for some of the teachers that I work alongside. … Continue Reading
Eddie Campos Jr.(@edcamposjr), a staple on the Mathematics Twitter Blogospere (#MTBoS) joins us via Skype this week to discuss how he has transformed his classroom environment. Through the use of vertical and horizontal whiteboard surfaces, rich problems, and visual random grouping; Mr. Campos has completely changed his workplace. He talks with us about the effects… Continue Reading