In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessons in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

Many children are in dire need of differentiated instruction to support their unique learning needs. Differentiated instruction seeks to maximize each student's growth by recognizing that students have different ways of learning, different interests, different ways of responding to instruction, and preferred ways of learning or expressing…

The National Science Education Standards are designed to provide a vision of scientific literacy for "all" students--regardless of age, race, ethnic background, English-language proficiency, socioeconomic status, disability, or giftedness. One of the most powerful strategies in science instruction--which aligns with the Standards--is the use of…