Math Pathways & Pitfalls® provides practical professional development options that respond to different needs, budgetary constraints, and time allocations. Teachers can learn how to use Math Pathways & Pitfalls on their own or with colleagues by viewing our video for teachers while completing the professional development tasks also found in each book.
The Math Pathways & Pitfalls teaching guides have served as a resource for lesson study groups. Each teaching guide provides mathematical insights and teaching tips for every lesson. Even more, each lesson embeds structures and prompts that support the development of effective and equitable teaching habits. Additional professional development opportunities are available.
Findings From Studies
Examining Academic Language in Mathematics Test Items for English Language Learners
This qualitative, mixed-methods study was conducted by external researchers: Guillermo Solano-Flores and Rachel Prosser at the University of Colorado, Boulder; and Maxie Alexandra Gluckman at the University of California, Los Angeles. Carne Barnett-Clarke at WestEd also participated.
Abstract: This paper reports on an investigation which examined academic language in mathematics tests for English language learners (ELLs). The investigation is part of a broader project, Math Pathways & Pitfalls. Researchers investigated whether Math Pathways & Pitfalls tests intended to assess mathematical content knowledge and tests intended to assess mathematics academic language differ in their mathematical academic language load (ALL). To achieve this goal, we developed a conceptual framework on mathematical academic language and a rubric for coding academic language in mathematics test items. Our conceptual framework identifies five academic language dimensions: symbolic; lexical; analytical; visual; and register. Two independent coders coded the items according to a double-blind review procedure. These coders coded the items in sequences determined randomly with the intent to control for the effects of fatigue and practice. From this coding, we were able to determine whether the coding categories were understood consistently by independent coders and to identify any statistically significant differences in ALL between the items that assess mathematics content knowledge and those that assess mathematical academic language. We found that Math Pathways & Pitfalls effectively generated items that differed on their emphasis of academic language. Content knowledge (CK) items and mathematical language (ML) items were distinguishable by the frequency of types of their ALLs. The ALL of ML items was significantly greater than the ALL of CK items.