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This week we take a look back at our most popular episode we've ever produced. If you've heard it already, listen again...you may find something new. If you missed it the first time around, you're in for a treat!   Chris is joined via Google Hangout by Karen Wootton an author and director for CPM Education (formerly College Preparatory Mathematics). They discuss a project CPM has in the design phase right now. Students who have struggled with Algebra 1 or some of its precursor courses are often directed into a second course in mathematics typically called “Math Intervention.” Typically the structure of Intervention courses is that of a deficit model of student. “These students do not have enough mathematics, therefore we need to give them more of the same mathematics in the same way to support the ‘Real’ math they do in their core course.” What Karen, and the team at CPM are doing is turn this idea aside, based on the idea that mathematics is a human attribute and all the students they teach are human, mathematics is a part of who these students are. The trouble, as they see it, is the mathematics that the students are given to study  does not connect to them at all. Therefore the content of the CPM Intervention course is intended to be more fluid, flexible and open to adaptation.

We're reaching back into the archives this week to bring back a fun one. WHAT IS A FLEEGLE? Jason and Scott will try and tell you!Jason Chamberlain and Scott Nielsen are a pair of Research Associates at the AIMS Center, they work together in our K-1 team studying how children of this age form their understanding of number concepts.  These two gave a Colloquium talk  on Monday February 26, 2018 (if you go watch the archive please note that we had a power outage for several minutes mid talk, but these two men kept right on rolling) that focused upon the Von Glasersfeldian concept of re-presentation as a portion of the process of understanding.  They join Chris in the studio to discuss this critical ability that all learners need to possess for deep conceptual understanding.  In their talk they take the attendees through an experience where we all built a concept of an object they called a Fleegle.  The conversation in this podcast ranges across several topics but always returns to the main idea of learners needing to experience concepts so that they have a collection of those experiences to draw upon when they are asked to act upon that knowledge. The idea of collective understanding and the role of society in individual understandings is hinted at as well.

This week, Dr. Tiffany Friesen, one of our Senior Researchers, chats with Research Associates Jason Chamberlain and David Pearce about their recent presentation at the Early Math Symposium. They discuss the idea of subitizing and the important role it plays in students' construction of addition concepts.

Chris Brownell is still enjoying his Summer so Paul Reimer is guest hosting for us again this week. This week we wrap up a quick 3-part series with our Early Math Team as they reflect on an opportunity they had to take their learning about Mathematical Play into the classroom. Hear how the kids engaged and some of the takeaways from their time. Make sure to listen to Episodes 90 and 91 to get some context and understanding on the subject if you'd like to know more.

Chris Brownell is continuing to enjoy his well deserved vacation and stepping out from the shadows to host today is our producer, Chris Bennett.We continue our conversation about presentations that were given at the recent Early Math Symposium with Aileen and Liz. They gave teachers an opportunity to not only learn about the importance of play in their classrooms, but to experience examples of it for themselves. We discuss how teachers can incorporate play into their classrooms as well as how it might change the way they assess their students.

With Chris gone for the next few weeks at conferences, we're doing our best to fill his chair. This week, Paul Reimer, one of our Senior Researchers, sits down with Jaclyn Russell and Wilma Hashimoto to discuss their presentation at the recent Early Math Symposium. They take the time to talk about their experiences with spatial reasoning in preschool classes and what brought them to put together a presentation about the importance of spatial reasoning and awareness for teachers in their classrooms.

In May 2018 FPU will graduate the first group of Master’s degree students, who have been scholarshipped by AIMS in the present manner.  During the Summer of 2018 we will be hearing from some of them on ZPC. Chris is joined by Mr. Joseph Schuster who teaches mathematics in a small, rural, high school in Central California.  Joe completed his research this past academic year and graduated in May of 2018. He focused on the effects of first informing students of Georg Polya’s, Four Step Problem Solving Process, and then helping them to bring them to recollection while they are working though various problems in the curriculum. He conducted a quantitative study in which he assessed his students at the beginning and end of a period weeks of instruction. The assessment used was a validated and considered reliable Assessment of Student Attitudes Towards Mathematics battery. His results are reported here.

In May 2018 FPU will graduate the first group of Master’s degree students, who have been scholarshipped by AIMS in the present manner.  During the Summer of 2018 we will be hearing from some of them on ZPC. Cassie Siesemore joins Chris via Zoom this week, there are some audio difficulties because of internet connection problems for this we apologize. Cassie recently conducted an active study in a classroom in which she attempted a Controlled experiment in which she taught students in a mode she characterizes as “Constructivist,” while another teacher maintained a more “traditional” approach. Both teachers taught a unit in the same content and topics, pre & post assessments were conducted and compared.

In May 2018 FPU will graduate the first group of Master’s degree students, who have been scholarshipped by AIMS in the present manner.  During the Summer of 2018 we will be hearing from some of them on ZPC. Chris is joined by Laurie Duerksen via Zoom this week. Laurie recently graduated from FPU with her MA in Mathematics Education. Her thesis focused upon the impact of teacher “Mathematical Knowledge for Teaching,” a theory base championed by Dr. Debra Lowenburg Ball and Dr. Hyman Bass. It is specifically Dr. Ball who Laurie is referring to with the quote in the title. Laurie’s study focused upon conducting several Professional Development courses in which she narrowed her own focus to aspects of teacher content and pedagogical knowledge for teaching, and observed a noticeable improvement in teacher performance.

In May 2018 FPU will graduate the first group of Master’s degree students, who have been scholarshipped by AIMS in the present manner.  During the Summer of 2018 we will be hearing from some of them on ZPC. David Pearce joins Chris in the studio this week to discuss his thesis work. David is a Research Associate at the AIMS Center and has been working with Kindergarteners all year to develop their sense of number. His thesis focused specifically on how students’ concepts can be enhanced through encouraging the use of counting on objects like their fingers. His results are encouraging to hear, and he is clearly convinced that this method is useful for furthering learning.

In May 2018 FPU will graduate the first group of Master’s degree students, who have been scholarshipped by AIMS in the present manner.  During the Summer of 2018 we will be hearing from some of them on ZPC.   Chris interviews Sandra Young today. Sandra’s thesis topic was inquiring about the use of Exploding Dots (a technique made popular by Dr. James Tanton and the Global Math Project www.explodingdots.org) to teach or enhance student understanding of the concept of Place Value. She describes her methodology, some findings and her conclusions. Interestingly enough, on top of the concept enhancement she did also notice expressions of enjoyment and joy in doing mathematics in her students; which is the primary focus of the Global Math Project.

Chris is alone in the studio this week and provides an introduction to this summer’s series which we are calling “In Their Voice.”  This is a brief, impassioned, description of what and why this series will exist and what he hopes will be the outcomes of the series. This talk is short, so download some of the back catalog and have a listen if you just can’t get enough. ;)

In May 2018 FPU will graduate the first group of Master’s degree students, who have been scholarshipped by AIMS in the present manner.  During the Summer of 2018 we will be hearing from some of them on ZPC. Jaclyn Russell joins Chris in the studio to discuss her thesis topic in which she sought to understand the relationship between teachers experience with professional learning around the Next Generation Science Standards (NGSS) and how much time is spent in teaching scientific concepts to our earliest of learners, kindergarteners.  She also created a piece of professional learning for a group of teachers which included a simple daily format for teachers to provide lessons that incorporate science and scientific processes to these children.

Chris is joined in studio by AIMS Director of Professional Learning, Debbie Porcarelli.  They discuss the evolving culture surrounding teachers’ professional lives, she casts a vision for planning with districts and individual schools that are completed, this is in response to what she has observed where districts begin down a path of professional support only to be side-tracked by test scores.  Debbie makes a call for taking a long view for changing teaching practice which requires and provides the opportunities for teachers to cycle through a process of personal change. She discusses a project at AIMS with an organization known as “Learning Forward,” wherein the Center is addressing a problem of practice that we have identified

Bev Ford, a Research Associate here at AIMS, spent the Fall of 2017 as a classroom teacher again after spending several years in deep study of the research around how students form the concept of number.  She relates how her awareness of “the mathematics of students” that she does not recall possessing prior to the work she has undertaken in the past several years. She describes how was confronted with how she no longer recalled how she learned mathematics herself. She was also confronted by the sheer magnitude of working within a full classroom. She describes several observed behaviors in students and how she interpreted them as indicators of student understanding.

Grace Florez took the Fall of 2018 and taught in a Kindergarten classroom. She had spent the previous year and half focusing her mental efforts on learning the theoretical framework outlined by the researchers she and her fellow associates have been studying.  She tells us of some of her experiences as the mathematics instructor for her group of five-year olds. Our discussion focuses upon the expectation that children would come in to school as students who began as “perceptual” students (if a collection of objects were hidden from view they could not begin to count them in the abstract). She discusses what she saw change within those students between August and December. Her experiences both confirmed and challenged her expectations and affirmed her love for teaching, it is obvious in her own talk.

Chris is joined via Google Hangout by Karen Wootton an author and director for CPM Education (formerly College Preparatory Mathematics). They discuss a project CPM has in the design phase right now. Students who have struggled with Algebra 1 or some of its precursor courses are often directed into a second course in mathematics typically called “Math Intervention.” Typically the structure of Intervention courses is that of a deficit model of student. “These students do not have enough mathematics, therefore we need to give them more of the same mathematics in the same way to support the ‘Real’ math they do in their core course.” What Karen, and the team at CPM are doing is turn this idea aside, based on the idea that mathematics is a human attribute and all the students they teach are human, mathematics is a part of who these students are. The trouble, as they see it, is the mathematics that the students are given to study  does not connect to them at all. Therefore the content of the CPM Intervention course is intended to be more fluid, flexible and open to adaptation.

After providing the gathered AIMS Scholars with an opportunity to ponder their own thinking and use their spatial reasoning skills in a Colloquium Talk on Monday the 26th of March, 2018, Steve Pauls sits down with Chris to discuss some of the grand implications of his talk.  They talk through the sequencing he employed, and why, along with the implications of thinking and approaching teaching through a Constructivist lens. The core ideas are wrapped in an activity he guided the participants through. Consider a cube, made of cubes (27 in all)...paint the outside of the larger cube in one color...A simple mental puzzle to begin an wonderfilled discovery process.

This week Chris is joined in the studio with a former student Mario Ordaz. Mario is not shy about describing himself as, “The big, brown, scary-looking, bald man, you might be nervous to meet.”  Chris and Mario met originally when Mario started his undergraduate degree in mathematics at Fresno Pacific University, back around the turn of the century. Mario, a legitimate Division I football playing recruit had chosen to stay closer to home, study an academic subject he had excelled at in High School and go on and enter a stable and very productive career.  Today he teaches at a local Middle School, where his defensive front-lineman physique garners instant respect, but his love of learning, mathematics, and people wins the day.

In this second part of their conversation Matt and Chris talk about the implications of research in teaching, and dream a little together about what a mathematics curriculum could look like if they could reshape it from the ground up. They also wrap up their talk about how the NCTM must keep a nimble presence in the world as it continues to advocate for better mathematics instruction for all students into the future.