2025年10月18日
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.
