ZPC - Zone of Potential Construction

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 way for teachers to understand students’ thinking. Modeling, with its focus on contextualized mathematics, develops students’ ability to consume information intelligently. We go on to explore the difference between modeling and traditional “story problems” within a school classroom. Finally we discuss where else modeling takes place.

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 ideas within algebra and analysis.

----more----Working from a philosophical question about how mathematical thinking is fundamentally different from other forms of thought, Dr. Norton talks to us about how “units-coordination” or “coordinating units” forms a basis of how the nature of mathematical knowledge in general. Finding connections to cognitive psychology, working memory, and how it is students strive to understand. Giving students items or devices to store levels of units allows them to go to one level higher in their coordinating schemes. Middles School curriculum is often where students are required to develop a flexibility within their number scheme or create their own compensatory actions. Dr. Norton closes his chat with a reference to a written assessment of students’ level of units-coordination. “A Written Instrument for Assessing Students’ Units Coordination Structures.”

Today we learn one of our researchers' conceptualization of what ZPC is,

and what its role is in learning. Dr. Tiffany Friesen joins us in the

studio to discuss this and drops a nugget or two of wisdom on us about

children's conceptualizations and their viability.

Today we are joined in the studio by Dr. Richard Thiessen, fresh off his colloquium talk yesterday.  This talk focused primarily on Piagetian Constructivism and how it views knowledge and understanding.  Today's podcast will dig deeper into these ideas.