AIMS Center

Colloquium Series: Further Impressions

The Colloquium Series here at the AIMS Center has been chugging along nicely this year. We have an average attendance of a little over 39 people, including online and face to face attendees. Our topics have ranged from philosophical to pedagogical, with a healthy dose of content and technology thrown in for flavor. The overall impressions we are getting from these events have been positive and encouraging.

I’d like to talk about two very recent talks that have left an impression on me for the potential impact they have on classroom practice.

Dr. Steve Pauls (FPU/AIMS) stimulated conversation around what he called, “Discrepant Events.” These are phenomena that would tend to defy the expectation or preconceptions of what might happen (no I am not referring to political science, but rather physical science was the context this day). Since childhood I have learned that when I turn a cup full of water over the liquid pours out. So when Steve had us turn over cups of water with a thin sheet of paper over the lip of the cup, I was glad he had provided a basin at each table for us to do the experiment over. When the paper adhered to the cup, and held in the large mass of water I, and everyone in the room were immediately put into a state of perturbation (our conception was being challenged by our perception). We were primed to question, “why, how, what” types of questions regarding this new reality. The fun and somewhat wet talk can be viewed here.

Lori Hamada (Executive Director at AIMS) came along a few weeks later and in her discussion of “Productive Struggle” demonstrated for us how a different representation of a simple concept such as a prime number sieve, could elicit deep thoughts and conjectures, even among knowledgeable experts and teachers. (Imagine what it could do with highly flexible minds of children!!)  We were intrigued, impassioned, and incited to make sense of the situation. If you are wondering what simple ideas can do when people are set to struggle with them I encourage you to view the archive here.

While these two talks were separate, delivered by two different people, and with different sets of intentions, I would like to posit that they were in some important ways very much about the same idea.

Learning, active, passionate, even angst-filled, taking place within the mind of the learner is coupled with feelings. One of the researchers we have spent some time reading here at the Center is Mary Helen Immordino-Yang. In her 2007 article (1), “We Feel Therefore We Learn”, she provides this nugget: “neurobiological evidence suggests that the aspects of cognition that we recruit most heavily in schools…are profoundly affected and subsumed within the process of emotion…” Watch the archive, see the participants, and observe their emotions, then listen to how they are thinking and talking about what they think.  You will see the linkage Dr. Immordino-Yang describes in action.

  1. Immordino-Yang, M.H., Damasio, A. (2007). “We feel therefore we learn: The relevance of affective and social neuroscience to education.” International Mind, Brain, and Education Society and Blackwell Publishing; vol. 1 number 1 p.3

Mathematical Discourse Check-Up

When I was in school, I was never asked what I knew, what I thought about, or how I processed mathematical information. I’m happy that this is different today and that valuing mathematical communication in today’s classrooms is recognized as important. Better known as mathematical discourse, whole-class discussions where students talk about mathematics can reveal… 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

The Work of the AIMS Center

I am writing this post from the annual conference of Learning Forward, an organization whose mission it is to “build the capacity of leaders to establish and sustain highly effective professional learning.”   When I became the Mathematics Coordinator at the Fresno County Office of Education in 1998, I turned to this professional organization (then called… Continue Reading

The Gift of Mathematics

Earlier this month my colleagues and I had the privilege of attending the National Association for the Education of Young Children Conference in Los Angeles. Professional learning is a wonderful opportunity where one can validate ideas, gain new insights, and network with others in the field. This was my first attendance at a preschool level… Continue Reading

Attitudes Towards Play in the Classroom

There has been renewed interest among science educational researchers over the past decade in the power of “play” in the classroom. One of the researchers that I have been following is Dr. Kathy Hirsh-Pasek, a psychologist at Temple University. She is one of the founders of the Ultimate Block Party which brings together companies, makers,… Continue Reading

Carving Canyons

I hope that you have had the chance to personally experience an AIMS professional learning opportunity. We AIMS facilitators have multiple goals as we lead workshops. We provide classroom teachers an opportunity to increase and/or strengthen their own content knowledge, explore their teaching practices, and we strive to help teachers find ways to improve their… Continue Reading

Coordinating Units, Part 3: Fractions

When looking at coordinating units, it is important to consider concepts other than just multiplying. One of those is fractions. Fractions would be first among these encountered by a child in school. Mental operations that must develop for a child to understand fractional ideas include partitioning, iterating, and splitting. These developments are not taught, much… Continue Reading

Subitizing, Part 2

In my last blog I mentioned that there are two distinct types of subitizing – perceptual and conceptual. I am fascinated by the subtle differences that students show and what that means about their thinking. Perceptual subitizing is the ability to recognize a number without using other mathematical processes (Clements 1999) and there are four… Continue Reading