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.
This is the first of a three part series with Dr. Scott Baldridge of the Louisiana State Univiersity. Scott is a mathematician whose work in Gauge Theory means his work is at the “Bleeding Edge” of human understanding of the universe and its physical structure. However, he also has a deep interest in the K-12 learning experience children have in mathematics; so much interest in fact that he has been the chief author of the Engage New York, now Eureka Math curriculum from its inception. Over the course of this series we develop that concept.
Part 1 of this series has Scott developing a contrast between present textbook writing structures and the structure he incorporated. He lays a foundation of “Encyclopedic” approaches and the “Narrative” approach he purposefully incorporated. In later episodes in this series more details are revealed.
The teaching of mathematics, like all teaching, is a cultural activity. There is no escaping this as mathematics is constructed by and for humans who live within cultures. Majority cultures have placed a stamp upon the teaching practice of mathematics and upon the content of this course. Dr. Laurie Rubel has applied an interesting and research based lens to these facts. Recently her research brought her to the forefront of controversy with elements and purveyors of radical politics in the USA. Her life was threatened, her work was attacked by those who had not read it nor sought out her clarifying comments.
Dr. Rubel joins Chris via Google Hangouts from abroad where she is studying similar situations in the country of Israel. They discuss the two axes of her framework, originally part of the work of Dr. Rochelle Gutierrez, and how she used these axes to analyze the teaching of several successful teachers who were working in “high needs” schools. Her work has important things to say to all teachers who care about their students.
Chris is joined in the studio by Dr. Steffe, one of the foundational researchers to describe the various stages in the human development and construction of the number concept. After speaking to the AIMS research teams and the gathered Scholars we discuss in further depth, how important it is to recognize that ALL mathematics is constructed by the person, the learning of mathematics is not reading, “the Book,” as some would describe it. Rather each concept, for each learner must be constructed by that learner. The implications of this fact for teaching are considered, described in some detail and suggestions are made. If mathematics education is undergoing a revolution as some say it needs, this may very well be the Siren call. Each child is an autonomous mathematizer of their sensory-motor experiences, it is the role of the teacher to infer what the child is constructing and assist in clarifying it.
This week’s episode provides us with an opportunity to hear from a teacher in Finland on what a strong emphasis in the whole child can accomplish in the classroom. Jukka Sinnemaki is a top 50 finalist in the Global Teacher Award for 2018, and he joins Chris this week to describe how the autonomy teachers in Finland has allowed him the freedom to continuously analyze, experiment with, and mold his pedagogical approach to increase the motivation and overall health of his students while he teaches mathematics and science. His holistic approach to learning, acknowledgement of the needs of the child to move and be active has helped him become a risk-taking innovative teacher whose students are showing dramatic results in both attitude and achievement. The coming revolution in education will be realized when all students can learn in environments that foster full inclusion of each person in the room, and Jukka’s classes are well on their way in this direction already.
Starting with an inquisitive mind regarding how children think about and develop their mathematical concepts; Rachael Risley has spent the last several years focused on how teachers can help students to migrate into multiplicative thinking. She is a student of Dr. Ron Tzur, another friend of the work we do here at the AIMS Center. She tells a portion of her story and persuades us of the importance of helping teachers as they seek to help children. Her work has been focused largely upon what effect of number choice when working with students as they cross back and forth between readiness for multiplicative reasoning.