Embrace Cultural Relevance with Mathematical Decision-Making

We share and implement a multi-step strategy for adapting tasks by opening contexts to student decisionmaking and exploratio

Supporting Spatial Reasoning: Identifying Aspects of Length, Area, and Volume in Textbook Definitions

Length, area, and volume share structural similarities enabling flexibility in reasoning for real-world applications. Deep understanding of structures can help teachers connect these concepts to support their students’ mathematical reasoning and practices involving real-world situations. In mathematics textbooks designed for future teachers, definitions of length, area, and volume vary from procedural (e.g., use a ruler to measure side lengths, use formulas to calculate measures) to conceptual (e.g., construct appropriate n-dimensional units that tessellate the n-dimensional space) to formal (e.g., construct a function mapping qualitative size to a quantity of appropriate units). Most textbooks describe length, area, and volume as quantitative measurements and provide examples of standard units. Definitional aspects such as describing size as an attribute or measurement, identifying dimensionality of a space, or constructing appropriate nonstandard units are inconsistently acknowledged across textbooks. Attending to definitional aspects of spatial attributes and their quantification can open conversations about the structure and essential meanings of length, area, and volume

Mathematics Learning, Teaching, and Equity in Policy and Programs: The Case of Secondary Mathematics Teacher Education in the United States

Professional organizations have provided recommendations for mathematics teaching and learning; however, few studies have investigated the practical integration of those recommendations into mathematics teacher education programs. In this study, we examine how the reported “big ideas” of courses in secondary mathematics teacher education programs emphasized the content and teaching practices necessary for future mathematics teachers, as recommended by policy documents. As part of a larger study, we conducted a series of interviews in secondary mathematics teacher education programs at four universities (names are descriptive pseudonyms): Great Lakes University (GLU), Midwestern Research University (MRU), Midwestern Urban University (MUU), and Southeastern Research University (SRU). We selected the institutions and programs based on their Carnegie Classification, the types of communities in which they were situated, the average number of graduates from a program, the departmental homes of their secondary mathematics education programs, and the demographics of their student populations. The analysis of data collected from 12 courses across four universities revealed specific ways in which big ideas in secondary mathematics teacher education programs emphasized areas related to mathematics learning, teaching, and issues of equity and access

K-8 Preservice Teachers’ Statistical Thinking When Determining Best Measure of Center

The purpose of this study was to determine K-8 preservice teacher (PST) candidates’ statistical thinking when selecting the best center representation for the given data. Forty-four PSTs enrolled in a Statistics and Probability for K-8 Teachers course in a university located in the southeastern region of the United States were asked to complete a 2007 National Assessment of Educational Progress test item. All 44 PSTs’ data were qualitatively analyzed for correctness and statistical thinking strategies used. Findings were that most PSTs either incorrectly selected the mean, rather than median, as the best measure of center for the given data or did not use appropriate statistical reasoning when explaining their answers. Future research includes modifying the explanation component so PSTs must better explain their statistical thinking for their choice of best measure of center using the context of the problem. Future research could also include implementing a pre- and post-test design with the post-test item embedded in the final exam. This design will provide additional understanding of how much knowledge PSTs bring to the course versus how much they learn in the course and provide incentive for giving thoughtful consideration for their answers

Addressing Neurodiversity by Adapting Math Tasks

Addresses how teaching neurodiverse students to use one procedure forces some to work harder, and how to open tasks to correct this issue