Episode 11: Using Coordinated Measurement with Future Teachers to Connect Multiplication, Division, and Proportional Relationships
March 26th, 2020 | Season 3 | 29 mins 43 secs
We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and
division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as an equation, to support future teachers’ understanding of these topics. We also used 2 types of length- based math drawings—double number lines and strip diagrams—as media with which to represent relationships among quantities and solve problems. To illustrate the promise of this approach, we share data in which future secondary mathematics teachers generated and explained without direct instruction sound methods for dividing by fractions
and solving proportional relationships. The results are noteworthy, because these and other topics related to multiplication pose perennial challenges for many teachers.
Episode 10: Engaging Preservice Secondary Mathematics Teachers in Authentic Mathematical Modeling: Deriving Ampere’s Law
March 21st, 2020 | Season 3 | 19 mins 56 secs
Incorporating modeling activities into classroom instruction requires flexibility
with pedagogical content knowledge and
the ability to understand and interpret students’ thinking, skills that teachers often develop through experience. One way to support preservice mathematics teachers’ (PSMTs) proficiency with mathematical modeling is by incorporating modeling
tasks into mathematics pedagogy courses, allowing PSMTs to engage with mathematical modeling as students and as future teachers. Eight PSMTs participated in a model-eliciting activity (MEA) in which they were asked to develop a model that describes the strength of the magnetic field generated by a solenoid. By engaging in mathematical modeling as students, these PSMTs became aware of their own proficiency with and understanding
of mathematical modeling. By engaging in mathematical modeling as future teachers, these PSMTs were able to articulate the importance of incorporating MEAs into their own instruction.
February 26th, 2020 | Season 3 | 21 mins