Mathematics Teachers' Perspectives on Professional Development Around Implementing High Cognitive Demand Tasks

Mathematics Teachers' Perspectives on Professional Development Around Implementing High Cognitive Demand Tasks

Amber G. Candela (University of Missouri - St. Louis, USA)
DOI: 10.4018/978-1-5225-1067-3.ch030


This chapter will provide readers with an overview of a professional development created and enacted to support teachers' implementation of high cognitive demand tasks (Smith & Stein, 2011). This multiple case study seeks to give voice to the three seventh grade mathematics teachers who participated in the professional development as they share their perspectives on what factors affected their implementation of high cognitive demand tasks. The goal of this chapter is to provide an overview of the structure of the professional development, share the aspects of the professional development the teachers identified as supportive when planning and implementing high cognitive demand tasks in their mathematics classrooms, and discuss ideas for future professional development aimed at providing teachers with instructional practices to incorporate into classrooms.
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There is “no decision teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of tasks with which the teacher engages students in studying mathematics” (Lappan & Briars, 1995, p. 139). With this is mind, it is crucial that teachers not only realize the importance of choosing tasks, but also have the knowledge of what tasks can engage students.

Martin (2007) outlined seven standards that represent the core dimensions of teaching and learning mathematics with one being the selection of worthwhile mathematical tasks and explained that teachers should pose tasks that help students develop mathematical understanding, help students make mathematical connections, require problem formulation and problem solving, and help students communicate about mathematics. Research shows that successful mathematics teachers give students mathematical tasks like the ones described by Martin. Teachers in high achieving schools engaged their students in conversations about mathematics and did not focus solely on basic facts and processes (Edmonds, 1979; Kitchen, Row, Lee, & Secada, 2009). Those teachers who focused on higher order thinking and less on routine skills allowed students to think critically about mathematics, develop better mathematical vocabulary, provide justification for their answers and learn how to collaboratively work with other students (Gutierrez, 2000; Staples & Truxaw, 2010).

One way teachers can impact students’ opportunities to learn is by engaging students in high cognitive demand tasks (Smith & Stein, 2011). Cognitive demand refers to the amount of effort a student needs to expend to think about a problem. Smith and Stein outlined and characterized four different demands of tasks: memorization tasks, procedures without connections tasks, procedures with connections tasks, and doing mathematics. Memorization and procedures without connections are low cognitive demand tasks while procedures with connections and doing mathematics are high cognitive. Memorization tasks involve recalling facts or definitions and do not require computation. An example of a memorization task is stating the Pythagorean Theorem. Tasks labeled as procedures without connections involve using a procedure to solve a problem but do not connect it to any other mathematical ideas, such as solving equations for missing variables. Procedures with connections tasks involve using a procedure but connecting it to other mathematical ideas. One such problem is solving a quadratic function, interpreting what the solution means, and relating these values to the graph of the function and the overall given situation. A task labeled doing mathematics does not give an explicit way to solve the problem and may include multiple solution methods, such as figuring out a pattern and coming up with generalized formula. (See Figure 1 for descriptions of the four levels of demand). Many of the descriptors of tasks with a high level of demand align with characteristics of tasks that promote conceptual understanding of mathematics (Doyle, 1983).

Figure 1.

The task analysis guide

(Boston & Smith, 2009, p. 122)

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