Abstract: Equivalence - and the specific example of equality - are among the most foundational topics in all of mathematics. We note, however, that these core ideas have not been treated consistently in the educational literature. Characterizations of the relationship between equivalence and equality are either context-specific (and thus do not generalize across domains) or are contradictory. While an incoherent literature base is problematic in its own right, there are also implications for students’ learning. A prevailing explanation for some of the difficulties students experience with equivalence and equality is that they struggle to identify and characterize the various forms of equivalence at play in a given situation. Indeed, if we, as researchers and educators, are to support students in reasoning coherently about equivalence and equality, a key precursor to these efforts is to clearly characterize these key ideas in a way that is both coherent and generalizable. To this end, in this talk we report on a series of interviews we conducted with mathematicians to see how they characterize and differentiate between these terms. We report on themes that emerged across these interviews, which include (a) coherent and accessible characterizations of equivalence and equality at both a local (element-to-element) and a global (equivalence class-based) level, along with (b) a multitude of illustrations and examples from the K16 curriculum.
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: