ZPC - Zone of Potential Construction

Today we look back at one of our first episodes in September 2016 where we chatted with Dr. Andy Norton. Original episode description follows.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.

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.”

Jon Dueck from the Fresno County Superintendent of Schools Office joins Chris in the studio this week. They discuss various ways in which Mathematics and Science teaching can be enhanced through the use of literature. This podcast accompanies the Colloquium Talk Jon gave on April 24, 2017. For more good resources watch that recording, after you listen to this episode.

 

Jon Dueck Colloquium Talk

AIMS Literature Links

Leslie Love Stone joins Chris to describe how art, and mathematics come together in her Geometric Abstract style of painting. With an incredible collection of processes, and metaphors Leslie typically collects and layers information sets upon layers. Chris and Leslie spend some time describing a series she recently painted, “California National Parks ∩ Last of the Mohicans ∩ Blue, Green, Brown” wherein she gives some information about the ideas she tries to communicate in her paintings. We also discuss her ideas on “Versatile Genius” which includes and emphasizes the linkage of many intelligences. She is an analytical person, and therefore her work is also quite analytical.

 

"Kings Canyon National Park" from Leslie Love Stone

 

Here are some links to Leslie’s art pages

Website

www.leslielovestone.com

Facebook Art Page for Process Pictures

www.facebook.com/leslielovestonestudio/

The Nine Unknown, The Steam Journal

scholarship.claremont.edu/steam/vol1/iss2/

Based on the vision of education contained with the writings of Paulo Freire and others; Dr. Joseph has studied within the field of Teaching With Social Justice. This is to say she has sought to create, within her classes, a socially just system for learning. This podcast, we discuss the three aspects of teaching with a mindset that says students should learn to “Read and Write Their World with Mathematics,” as Gutstein tells us. This is a lively discussion, filled with hope and commitment.

We at AIMS are focused upon helping teachers to understand and create useful models of their student’s thinking. This requires a shift in emphasis for some. This week Chris interviews Nicola Hodkowski, a doctoral student in Mathematics Education at the University of Colorado, Denver. She tells, first hand, how this shift can take place, and what it means for instruction.

Cathy Carroll is a Senior Researcher in Mathematics Education for WestEd, an educational research labratory and center. She joins Chris in the studio to talk about what it means to be mathematically fluent and how important this fluency is. Connecting fluency with flexibility rather than automaticity seems to be a core idea within her description and definition for this goal of mathematics education.

Joining Chris in the studio this week is Paul Reimer, a Sr. Researcher at the AIMS Center working with our Early Mathematics studies. Paul is also a student in the Michigan State University Doctoral Program, studying the effects of teacher beliefs on student learning. We discuss his studies and how they connect with our work here at the AIMS Center.

In the studio with David Pearce and Wilma Hashimoto two of the AIMS Center’s Research Associates, and we discuss the third aspect of Professional Noticing: Deciding. We discuss how this aspect takes place in the midst of classroom activity, and how it is dependent upon the two prior aspects of: Attend and Interpret. We end up discussing how this supports the goal of creating a student centered classroom, one in which the learner’s thinking and conceptualization is valued as the starting place for academic learning.

Dr. James Tanton returns to the ZPC to discuss the Global Mathematics Project and its goal of reaching 1 million students with some joyous, uplifting, and powerful mathematics. A few years ago, six colleagues at the Mathematical Association of America and a few other organizations came together with an idea…”What if the world could an “hour of code” like experience with mathematics?” We chat about the hopes, the goals, and the network that is building around this movement. During the week of October 10, 2017 the hope is to have these million students, their teachers, parents and friends working through some very fun, puzzling mathematics, centered on a place value representation Dr. Tanton has developed called “Exploding Dots.” For an audacious introduction to these both you can follow the links below.

For more information on the Global Mathematics Project, and how you can get involved, please visit:

https://www.theglobalmathproject.org/

For more information on Exploding Dots watch this video of Dr. Tanton giving a recent demonstration at a community college in Arizona:

https://vimeo.com/204368634

Carl Veater joins us in the studio this week. He has spent a large amount of time examining the “Progressions” documents that were the genesis of the standards that have become the California Core State Standards in Mathematics. These document outline how several content themes are coherently linked through the grade levels and were in fact constructed in this manner for the first time in the Standards era of education. Carl describes how teachers can make use of these threads to make curricular decisions, and most importantly how to decide which topics are not specifically warranted for their grade or course level. A very engaging topic for teachers concerned with how to decide what to keep and what to let go of in order to address at appropriate depth the core topics in their curriculum.