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Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks

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Abstract

While recent national and international assessments have shown mathematical progress being made by US students, little to no gains are evident in the areas of geometry and measurement. These reports also suggest that practicing teachers have traditionally had few opportunities to engage in content learning around topics in geometry and measurement. This article describes a set of assessment tasks designed to measure teachers’ mathematical knowledge for teaching geometry and measurement in a nuanced way. The tasks, focused on relationships between measurable quantities of figures, adhere to three key design principles: Tasks are grounded in the context of teaching, measure common and specialized content knowledge, and capture nuanced performance beyond correct and incorrect answers. Six tasks are presented that reflect these design principles, with teacher data illustrating the ways in which the tasks differentiate performance and reveal important aspects of teacher knowledge.

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Notes

  1. In this work, I use the term ‘length’ to denote one-dimensional measurable attributes of two- and three-dimensional figures. This might include the sides or edges of polygons or polyhedra or non-side distances such as the height of a non-rectangular parallelogram or an oblique prism.

  2. While the tasks were designed in part to measure teacher learning, a detailed reporting of what teachers learned is beyond the scope of this article (see Steele 2006 for more detail).

  3. In addition to the secondary-certified teachers, two additional populations are included: elementary-certified teachers and teacher leaders. At the time of the study, elementary-certified teachers were able to teach middle grades mathematics, and the elementary teachers in the course either were or had an interest in teaching middle school. Similarly, the teacher leaders in the course were all secondary-certified teachers who had recently left the classroom, tasked with supporting secondary teachers throughout the region. As such, including these teachers in the population is representative of the range of teachers likely to be teaching middle grades mathematics.

  4. Tangram tiles, rulers, and grid paper were available to teachers during the assessment.

  5. While this task does ask teachers to think about classroom practice, the fact that they are considering in general how this task might be implemented, and not with respect to a specific group of students or in the context of a class, distinguishes the measurement of SCK from knowledge of content and students or knowledge of content and teaching.

  6. The nature of these formulas and their typical use in schools can obscure the distinctions between geometric and measurement quantities. However, the formulas are ubiquitous in their use and a discussion of these geometry and measurement distinctions was beyond the scope of both the task and this article.

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  1. Michigan State University, East Lansing, MI, USA

    Michael D. Steele

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Steele, M.D. Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. J Math Teacher Educ 16, 245–268 (2013). https://doi.org/10.1007/s10857-012-9230-3

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