Author Archives: Chris Brownell
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.
- 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
In this episode recorded in September but released in December, Matthew and I discuss a few of his projects, music videos, TV shows, and books. His mission is to affect as many people as he can with the joy of doing mathematics in multiple ways. His focus has been upon student representations of concepts. We end up discussing how pop-culture can be leveraged to engage students. For him, knowledge is constructed by students in the doing of mathematics. Finally we look at a couple of organizations he supports “With Math I Can” on Amazon, and “The Global Math Project” sponsored originally by the Mathematical Association of America via James Tanton.
Lesley Gates joins us on the podcast this week. She briefly describes some of the goals, purposes, and benefits of the new science standards that are in the process of being incorporated in public schools across the US. With an emphasis on the “Doing” of science rather than reading about it from books; along with developing and fostering a sense of curiosity and wonder about the natural and human-made worlds, the NGSS hope to bring science back to a more prominent role in schooling than it has been over the last few decades. Lesley describes with great passion some of her hopes for these standards.
Lori Hamada, the Executive Director of the AIMS Center for Math & Science Education, joins me in the studio this week to flesh out her recent talk on Productive Struggle. We explore a little the four different perspectives of: Teacher, Student, Administrator, and Parent when it comes to this topic. We end with some descriptions of how teachers can access tasks that enhance or provide opportunity for students to productively struggle in their classroom.
So here we are, at the time I write this we have “dropped” (made public) 10 individual podcast sessions. These have come from a wide variety of perspectives and a span of preferences. Don’t be fooled though, while we have dropped these ten, we have almost ten more “in the can” (recorded and nearing their… Continue Reading
Dr. Les Steffe joins us in studio for our longest podcast yet. From his earliest days as a High School Mathematics teacher, Dr. Steffe has focused on what it means to know math. With a research career that spans six decades of consistent investigation into the mathematics of children, Dr. Steffe encourages us all to, “Listen to the student.” and through this join them in the learning process.
A man on a mission to reveal to the world that mathematics is a human endeavor, one filled with joy, discovery, and lots of passion. We explore a topic within the High School experience in algebra, quadratics, and ask, “Why do we want to teach this?” James sees this topic as a “story, a piece of poetry…” We then pursue a question of, “How does a mathematician stay interested in elementary mathematics?” A brief re-statement of Dr. Tanton’s “Fractions are a really deep and incredibly interesting.” “Do not run away from the feeling of ‘hazy thinking’.
After a description of a few demonstrations regarding the nature and behavior of water, each that have a “surprising” finish, we discuss how these sort of surprises constitute “discrepant” events. This then leads to a discussion of the “Why” do these events occur, what are the chemical and physical properties at work. We explore how discrepancies can constitute opportunities to cause “perturbation” or a space in the learner to come to a new understanding. We wander off on a minor tangent that generates, for us, a way to more fully investigate these properties. These perturbative events generate within the learner a state of “cognitive disequilibrium” which can then be capitalized upon by a guiding hand to create new knowledge within the learner. We include som […]
After stating a rather shocking statistic that indicates the overwhelming majority of five year olds enter Kindergarten “not ready” according to one assessment. Tim talks to us about how two varieties of early learning based on two professors theories on how children learn. After a failure in efforts, these professors stepped back from an effort to, “catch children up,” and began to focus on the idea that children are constantly learning. We discuss what comes out of this research, specifically two varieties of learning in children: Naming, and Observational.
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