In my last blog I talked about how the research I have been studying focuses on the “mathematics of children” and I claimed that research that articulates “mathematics of children” can provide powerful tools for a teacher.
Many of us experienced elementary school a long time ago and this creates a challenge for our teaching. We probably don’t remember how we came to know concepts like addition and subtraction. We may remember doing math, but we likely do not remember the task that allowed us to say, “Oh that is why you do this!”
Another potential challenge may be our limited procedural experience with mathematics. As a teacher, I worked diligently to proceed slowly and to show all steps as I taught procedures. I hoped that this would help my students understand new procedures and how they worked. I now recognize that I had a narrow view of math as procedures and I lacked tools to draw from, as I tried to provide students with experiences that would cause them to reflect and construct math concepts.
I have a deep respect for the amount of work it takes to construct meaning around math concepts. Our charge as teachers is to relate to what a child is going through and to know how to support them. I would like to attempt to draw an analogy to a construction I have recently experienced: cooking.
I love food and thoroughly enjoy tasting new combinations of flavors. My cooking experience began using a recipe, but I found myself (as a wife and working mother of 3 children) struggling to have all the ingredients on hand for a given recipe. I had to take risks and veer away from the recipe. It began with some substitution of ingredients… Rather than look at a recipe as locked rules, my recipe became a stepping off point. I began to look at ingredients such as chicken, onion, and garlic salt as fitting into categories. Did you know you can use butter, coconut oil, olive oil, and many other ingredients to saute onion and garlic for flavor? If you add meat and some sauce, presto!, you have something yummy to put over rice or pasta!
My friend and I often talk about healthy cooking for our families. Before she met me, she only cooked with a recipe. Now, with a little moral support, she has ventured into exploring adaptations and, like me, is creating meals without recipes.
I think that many of our students are only “recipe cooks”. They struggle to make sense of the mathematics and to understand math problems because the only tool in their tool belt is procedures. Understanding the “mathematics of students” has given me a tool to change that.
In following blogs I will tell some stories focused around the mathematics of students. I’ll discuss some of the following questions: How does the student see the problem? How does she solve it? What does the research tell me about her behavior? How can that inform a teacher move that I should make with the student?
This post continues my September 20, 2016 post, “Coordinating Units: A Brief Introduction”. Last time, I introduced a problem to illustrate the basic differences between additive reasoning and multiplicative reasoning used to solve a problem. I also defined levels of units and what it means to “coordinate units”. In addition, I said that “in activity”… Continue Reading
I use this quote from Steve Jobs as my title because this is how I feel about the place I work and the work that I do. Everyday I am tasked with learning more about how children acquire their mathematical knowledge; how do children come to know? Does this sound like a daunting task? Does… Continue Reading
As we have launched the Research Division of the AIMS Center for Math and Science Education we have found that there is extensive financial backing for educational research and there are increasing funds for the professional development of our teachers. Yet, there appears to be a gaping hole in this continuum – the funding for… Continue Reading
In the mid-1980’s after becoming a teacher with my own classroom, finding a learning community to think and reflect with was difficult. I wonder what I might have changed, given the chance to work with colleagues, and how I could have been an even better educator. My thoughts wandered to that place again last week… Continue Reading
As a classroom teacher I worked tirelessly to create tasks, problems and questions that I thought would be good for students. I thought that the tasks I was creating were equal to what the students would be thinking. I am constantly reminded that what I perceive to be the question is not always what the… Continue Reading
In previous blog posts we have, in various ways, talked about the commitment of the AIMS Center to a constructivist understanding of how children come to know. There are several reasons for this choice, but probably the most relevant is that the most significant and extensive research related to how children come to know whole… Continue Reading
Welcome (back) to the AIMS Center for Math and Science Education blog! The four early math research associates started the 2016-17 academic year by interviewing more than 70 children in ten Head Start programs to begin year 2 of our study. The number will be narrowed to 24 as we observe and document the children’s… Continue Reading
A Center for thinking about learning and thinking ought to do so within a public forum. Well at least that is how I see things. As I have mentioned in other blog posts, one of my tasks here at the Center is to spearhead the Colloquium Series. I will be visiting the topics from the… Continue Reading
The benefits of being an AIMS Facilitator are many, but when I started I did not know that I would get to know so many amazing educators from around the United States. Paul Agranoff is another one of our AIMS Professional Learning Facilitators and he hails from Minnesota. His teaching career has been spent in… Continue Reading