First-grade teacher Carolyn loves literature. She finds that reading stories to her students sparks their imaginations and motivates them to learn. Wanting to leverage their enthusiasm, Carolyn researched how to use literature in math class. She learned that stories establish familiar, interesting, realworld scenarios where students can explore mathematics within context and communicate their thinking in ways that makes sense to them (Moyer 2000). Storybooks present opportunities to examine mathematics in ways that reflect children's own experiences and interests and to talk about math in a “natural context” (Moyer 2000; McDuffie and Young 2003).
Teruni Lamberg and Carolyn Andrews
Teruni de Silva Lamberg
How do your students unitize when solving problems that involve fair sharing? Do they visualize the unit, partition it when needed, and distribute the pieces equally? Can your students explain their thinking and keep track of what they are doing? Unitizing involves identifying a reference unit, such as a box of crayons or a candy bar, based on the problem context; breaking the unit into smaller chunks; and regrouping pieces to make the problem easier to solve (Lamon 1996). It is a way of conceptualizing an amount before, during, and after the sharing process (Lamon 1996).
Teruni Lamberg and Lynda R. Wiest
Third graders' struggles to solve contextualized, student-generated division problems with remainders offer insights to guide instruction.
Teruni Lamberg, Linda Gillette-Koyen and Diana Moss
Formative assessment helps teachers make effective instructional decisions to support students to learn mathematics. Yet, many teachers struggle to effectively use formative assessment to support student learning. Therefore, teacher educators must find ways to support teachers to use formative assessment to inform instruction. This case study documents shifts in teachers’ views and reported use of formative assessment that took place as they engaged in professional development (PD). The PD design considered the formative assessment cycle (Otero, 2006; Popham, 2008) and embedded it within a pedagogical framework (Lamberg, 2013, in press) that took into account the process of mathematics planning and teaching while supporting teachers to learn math content. Teachers restructured their definition of student understanding, which influenced how they interpreted student work and made instructional decisions. Teachers’ pre-PD instructional decisions focused on looking for right and wrong answers to determine mastery and focused on pacing decisions. Their post-PD decisions focused on student thinking and adapting teaching to support student thinking and learning. Implications for PD to support teachers to use formative assessment and research are discussed.
Diana L. Moss, Jennifer A. Czocher and Teruni Lamberg
For these sixth graders, transitioning from arithmetic to algebraic thinking involved developing new meanings for symbols in expressions and equations.