ZPC - Zone of Potential Construction

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.

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 some talk on the reasons behind the structure Dr. Steve chose to get the learners to the place he was aiming.

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.

We go on to explore an event known as “Puzzle Party” which is a gathering of other puzzle makers. We pursue and explore what it means to be seriously, passionately involved in a playful act of puzzling. “If kids could just have that sense of joy of solving a problem…”

Since we mention it in the podcast, below you can find a link to an online version of the “Towers of Hanoi” puzzle. Enjoy!

https://www.mathsisfun.com/games/towerofhanoi.html

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 “Interference in the Feedback Loop,” takes place. This is a practice through which students are provided the opportunity to reflect before they are informed. We then wrap up with a brief discussion of the tools for development Desmos has chosen, and end talking about the use of “collective effervescence,” as a norm for these activities.

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 this is a general interest book, that teachers would use “Pi of Life” to disarm the subject. Connections are made between the writings of Paul Lockhart, Keith Devlin, Alfred North Whitehead and Bertrand Russell. This is a talk that heads into philosophy, and number ideas, a topic that resonates with the AIMS Center in ways that are foundational. We end up discussing inquiry and discovery in a classroom experience.