A branch of mathematics—combinatorics—is explored through counting problems.
research matters for teachers
Using sets of outcomes to reconcile differing answers in counting problems.
Elise Lockwood and Eric Weber
The authors consider the Common Core State Standards for Mathematics (CCSSM) standards for content and practice through the lens of Harel's (2008a) Duality Principle to help empower teachers as they interpret and implement the CCSSM.
Elise Lockwood and Eric Knuth
In many STEM-related fields, graduating doctoral students are often expected to assume a postdoctoral position as a prerequisite to a faculty position, yet there is no such expectation in mathematics education. In this commentary, the authors call on the mathematics education research community to consider the importance of postdoctoral fellows and make the case that prioritizing postdoctoral positions could afford mutual benefits to the postdocs, to faculty mentors, and to the field at large.
Elise Lockwood and Branwen Purdy
The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration, serving as an effective tool for solving counting problems and underlying many key combinatorial formulas. In this study, the authors used guided reinvention to investigate 2 undergraduate students' reasoning about the MP, and they sought to answer the following research questions: How do students come to understand and make sense of the MP? Specifically, while a pair of students reinvented a statement of the MP, how did they attend to and reason about key mathematical features of the MP? The students participated in a paired 8-session teaching experiment during which they progressed from a nascent to a sophisticated statement of the MP. Two key mathematical features emerged for the students through this process, including independence and distinct composite outcomes, and we discuss ways in which these ideas informed the students' reinvention of the statement. In addition, we present potential implications and directions for future research.