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.
Dr. Matthew Larson is the outgoing President of the National Council of Teachers of Mathematics joins Chris via Google Hangout to discuss a new book that the Council will be releasing in April at the National Exhibition. In this first part in a two part series we focus upon this book and how it can be viewed as a critical collection of recommendations to initiate conversations around what mathematics should be taught in high schools. What is the purpose of teaching mathematics in the 21st century? What essential concepts ought to be the goals of of a well structured curriculum for all students? We discuss other issues related to the council itself that are of importance to all interested in Mathematics education as well.
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 is the third and final segment with Dr. Scott Baldridge in which we closeout the discussion of the use of a narrative structure and how teachers who are aware of this can make use of it in their classroom.
This is a second episode of a three-part series where Chris interviews Dr. Scott Baldridge, primary author of the Eureka Math book series. They explore specific examples of narrative elements that were incorporated. Themes, Characters, and Plot devices are the subject this week. Who are the characters? What sort of Plot devices can be used? How does he include a plot, and why?
Employing Aristotle’s definition of Plot, Eureka Math brings about a series of increasingly serious problems that lead to a conclusion. Thinking about the joyful communication of mathematical ideas, Scott describes how the first textbook was built upon a narrative structure with a plot and final climactic conclusion.