Leslie Dietiker

Curricular Treatments of Length Measurement in the United States: Do They Address Known Learning Challenges?

Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students’ difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K–3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3.

What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education.

Eisner (2002) proposes that educational challenges can be met by applying an artful lens. In this article, I draw from Eisners proposal to consider the assumptions, values, and vision of mathematics education by theorizing mathematics curriculum as an art form specifically, I argue that by conceptualizing mathematics curriculum (both in written and enacted forms) as stories, the mathematical lessons experienced by students can be artfully crafted to inspire wonder or grab attention through surprise. An example of a mathematical story from a Grade 7 mathematics textbook is presented and discussed. By framing mathematical content in narrative terms, I seek to enable a rewriting of mathematical expeneces for learners.

Statistics Education in the United States: Statistical Reasoning and the Statistical Process

Two important components of statistical literacy are statistical reasoning and the statistical process. This chapter summarises a study that analysed 41 mathematics state standards documents as they existed in 2006 to surmise the extent to which learning these components is expected of students in the United States. Most prominent among the findings were the overrepresentation of isolated statistical procedures and the corresponding scarcity of expectations addressing statistical reasoning and the statistical process.

Curricular Noticing: Theory on and Practice of Teachers’ Curricular Use

This chapter presents a new theoretical construct, curricular noticing, used to understand how teachers interact with curriculum materials, and shares findings from four coordinated research studies. Curricular noticing draws from work on professional noticing of children’s mathematical thinking and is defined as how teachers make sense of the complexity of content and pedagogical opportunities in written or digital curricular materials. This construct is situated within existing literature on curriculum use, documenting growing concerns about teachers’ curricular reasoning and decision-making. Taken together, these studies explore the curricular noticing of 62 preservice teachers (PSTs) in elementary and secondary mathematics methods courses at four institutions. Participants engaged in one of two aspects of noticing: (a) attending and interpreting in the context of particular tasks; or (b) noticing (attend, interpret and respond) in the context of multiple published curricula. Data include pre/post measures, video of interventions, and written assignments that were collected and qualitatively analyzed. Dimensions of curricular noticing highlight the importance of noticing at the task level and raise questions around curricular sequencing and comparisons of curricula. Findings imply that PSTs would benefit from evaluating curriculum materials using specifically designed analysis tools, and highlight the importance of curricular noticing as a framing for understanding PSTs practices with curricula.

Using plot twists to engage learners

To deepen students’ mathematical interest and knowledge, the authors use a mathematical story-planning framework to design and enact a fifth-grade measurement lesson