Via vignettes, look inside first- and fourth-grade classrooms where teachers demonstrate how to use a research-based structure during instruction to choose tasks that elicit different levels of comprehension.

It is important to recognize the critical role spatial reasoning, relational thinking, and mathematical modeling play in the overall development of students' central understanding of mathematics. Spatial reasoning predicts students' later success in higher levels of mathematics, such as proportional thinking and algebraic reasoning. The National Research Council report implores educators to recognize the importance of developing spatial reasoning skills with students across all areas of mathematics. This chapter describes a study that used the Primary Math Assessment-Screener and Diagnostic to assess students' spatial reasoning and relational thinking. The results highlighted curricular resources to improve students' understanding of mathematics. Students' mathematical spatial reasoning improved significantly.

The equal sign is prevalent at all levels of mathematics however many students misunderstand the meaning of the equal sign and consider it an operational symbol for the completion of an algorithm (Baroody & Ginsburg, 1983; Rittle-Johnson & Alibali, 1999). Three constructs were studied through the lens of the Developing Mathematical Thinking (Brendefur, 2008), Relational Thinking, Spatial Reasoning and Modes of Representation. A review of literature was conducted to examine the effects of mathematics instruction on the development of students' conceptual understanding of equivalence through the integration of spatial reasoning and relational thinking. The Developing Mathematical Thinking (DMT) curricular resources integrate Bruner's enactive, iconic, and symbolic modes of representations (1966), using tasks designed to strengthen students' spatial reasoning and relational thinking to develop mathematical equivalence. The research question "What is the effect of integrating iconic teaching methodology into mathematics instruction on first grade students' relational thinking and spatial reasoning performance?" was analyzed to determine whether there was a significant difference in pre-and posttest scores for the two groups. Students were found to have a better opportunity to develop conceptual understanding of mathematics in their early years of school when taught with the progression of EIS, relational thinking and spatial reasoning.