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.
In today’s episode, we explore some of the genesis of Richard’s fascination with puzzle making and solving. Richard describes, in depth a puzzle similar to O’Beirne’s step-cut that he himself created. Then expands on O’Beirne’s puzzle itself. This link will take you to a page with three videos he references in http://goo.gl/Y3ta7C
Wilma Hashimoto is one of the AIMS Center’s Research Associates working on a project focused on the pre-school years and how children build their earliest understandings of mathematical thought. We focus on how early understandings of mathematics affect learning trajectories can influence success in later schooling. We also examine what sort of things can and should comprise early mathematics instruction. A point about creating “intentional” mathematical learning opportunities is also examined. We get to talk about Spew too!
In the studio with Mike Fenton, an Activity Constructor for the Desmos graphing calculator company. We talk about the Desmos Guidelines for Activity Development, and how they reflect a solid commitment to student centered learning, and developing lessons that require and encourage discussion in the classroom. A little discussion into what he refers to as… Continue Reading
Sunil Singh is mathematics educator in Canada talks to us about his book, the reasons for its inception, and his hopes for how math ought to be taught. Based upon the idea that mathematics, as a human adventure, Sunil describes how this subject can embody such beauty and passion. He has a hope that while… Continue Reading
In this podcast we explore what it means to do mathematical modeling and why it should be a part of the K-12 classroom. Dr. Steve Pauls, in a table-turning episode, interviews Dr. Chris Brownell about this somewhat murky topic. Within the talk we explore how modeling can and ought to be a way for teachers… Continue Reading
Joining us today via Skype is Dr. Andy Norton of Virginia Tech University. He will be discussing an area of research he is focused upon known as Units Coordination. This is an idea that has been shown to be critical to students’ abilities to understand the Part to Whole relationship in fractions, and more abstract… Continue Reading