Title:Translating Research Findings into Classroom Practices that Give Students Agency, Competency, Commitment, and Authority

Abstract: Many students in the United States lack opportunities to learn and understand quality mathematics. This presentation translates results of research on cognitive and social processes that underlie students’ growth in mathematics conceptual understanding in middle grades into instructional actions needed to improve student achievement. Particular attention will be given to the establishment of classroom instruction and climates that provide students with a sense of agency over their own learning, a sense of competency in and commitment to their mathematical thinking, and a sense of authority in the creation and verification of mathematical ideas.

Title: Learning of Fractions: How Could it be Built on the Learning of Whole Numbers?

Abstract: Recently, the importance of learning fractions has been emphasized in the field of math education.  There are two traditions of teaching fractions. One teaches fractions in an approach almost independent from students’ learning of whole numbers.  Another builds the learning of fractions on the foundation of the learning of whole numbers.  The latter is not known by most of today’s US elementary teachers. In the talk I will first inform my audience with the tradition of teaching fractions based on the learning of whole numbers.  Then I will discuss the inspirations we can get from it.

Title: Finding the Thread: Tracing a Mathematical Idea from Elementary to High School

Abstract: Mathematicians' view of their subject is strikingly different from the experience of students. The mathematician I.R. Shafarevich said that mathematics "resembles the work of a single intellect ... much as in an orchestra ... the theme moves from one instrument to another." In contrast, the student's experience is often, in the words of Morris Kline, "like pages torn from a hundred different books, no one of which conveys the life, meaning and spirit of mathematics." I will trace the development of a mathematical idea through several grade levels, illustrating both the underlying unity and surface cacophony of the curriculum.