Conference in Macau

Biyao and Rui attended the 3rd International Exchange Forum for Early to Mid-Career Mathematics Educators

Rui gave a presentation titled Backward Transfer in Function Learning: Research

Status and Instructional Implications. This work is in collaboration with Dr. Charles Hohensee from the University of Delaware.

Abstract: The majority of research on transfer of learning focuses on the phenomenon that people

apply past learning to new learning in different contexts, which is sometimes called

forward transfer. By contrast, a backward transfer from new learning to impact previous

learning outcomes is understudied, especially in the area of mathematics education.

Extant backward transfer studies in mathematics education have investigated the way

students change their mathematical reasoning on a prior concept, linear function, after

they learn the new concept, quadratic function. These studies provide instructional

suggestions on how to promote productive backward transfers and restrain unproductive

backward transfer in learning functions. The current article provides first-hand data from a

series of tests on the students from an algebra class in a US high school and secondary

evidence from the literature to illustrate both productive and unproductive types of

backward transfers in function learning and their generating mechanisms in terms of

teaching. Then, we present an analysis of China's textbooks for middle schools, focusing

on where functions are covered, to identify potential points in these curricular materials

where the production of backward transfer might be likely and how that backward transfer

might impact the teaching and learning of functions.

Biyao gave a presentation titled At the Intersection of Piaget, GenAI, and Mathematics

Teacher Education

Abstract: Piaget’s learning theory, speciffcally his view of learning as a result of

accommodation and reconciling perturbations, has been inffuential in research on

students’ mathematical learning. In this presentation, we discuss how the construct of

perturbation is used in mathematics education research. Illustrating with empirical

examples, we will discuss how the notion of perturbation informs teacher education to

promote teachers’ development in knowledge of students’ mathematical thinking. We will

focus on ffndings from prior studies involving teachers conducting task-based interviews

with students and an ongoing study involving teachers interacting with an AIbased

teachable agent to learn about student thinking.