The document discusses the relationship between the cognitive demand of math tasks and student achievement. It finds that maintaining high cognitive demand throughout the setup and implementation of math tasks is linked to higher achievement. When tasks involve memorization or procedures without meaning, learning gains are lower. However, tasks requiring procedures with understanding or doing mathematics fully lead to greater gains. The document recommends further research on how the cognitive demand of math instruction changes from K-12 and how teachers' perceptions of task demands may also change.

1. The effect of the cognitive demand of math task on achievement. Jozsef Horvath SOE Learning and Instruction University of San Francisco December 4, 2010

2. Linking to Research: The QUASAR Project Low-Level Tasks memorization procedures without connections to meaning (e.g., Martha’s Carpeting Task) High-Level Tasks procedures with connections to meaning doing mathematics (e.g., The Fencing Task)

3. Abstract The purpose of this paper is twofold: to review the relevant literature on cognitive load theory (CLT), mathematics tasks and achievement and, to present a solid rationale for hypothesis that “The cognitive demand level of math task and math achievement are interdependent.” Definitions for operational terms such as CLT, cognitive demand/load, math task and math achievement are provided and evidence will be presented to show how CLT has influenced both math education and math achievement. Contact info: jhorvath@dons.usfca.edu

4. Introduction Student’s math fluency is considered both as a national interest and a moral imperative by highly industrialized nations. U.S. students repeatedly score well below their comparable counterparts in international math and science tests (PISA, TIMMS). Scores on math tests are linked to the cognitive demand of the math tasks.

5. Research Objective This paper aims to describe how the cognitive demands of math tasks influence achievement. Math achievement will be operationalized as a proxy for learning.

6. Student Learning TASKS As implemented by students TASKS As they appear in curricular/ instructional materials TASKS As set up by teachers Mathematical task framework, (Stein & Smith, 1998).

7. Mathematical task and framework Mathematical task is defined as a classroom activity, the purpose of which is to focus students attention on a particular mathematical idea (Stein et al., 1996).

8. Cognitive demand Cognitive demand refers to the kind of thinking processes entailed in solving the task as announced by the teacher (during the setup phase) and the thinking processes in which students engage (during the implementation phase). These thinking processes can range from memorization to the use of procedures and algorithms (with or without attention to concepts, understanding, or meaning) to complex thinking and reasoning strategies that would be typical of “doing mathematics” (e.g., conjecturing, justifying, or interpreting). (Henningsen & Stein, 1997)

9. Comparing cognitive demand of math tasks around the world U.S. Math task cognitive demand Low Memorization Tasks Procedures Without Connections to understanding, meaning or concepts Tasks Top 10 performer’s Math task cognitive demand High Procedures With Connections to understanding, meaning or concepts Tasks Doing Mathematics Tasks (Klieme & Baumert, 2001)

10. Cognitive demand and achievment Greatest student learning gains occur in classrooms with high cognitive demand instruction ( Boaler & Staples, 2008). U.S. teacher’s do not maintain a high demand instruction during class (Stigler et al., 2004). TIMSS 1999 video (n=18) study found that sustained high cognitive demand instruction resulted in high-level student engagement and achievement on TIMSS.

11. Cognitive load theory (CLT) CLT is an instructional theory based on our knowledge of human cognitive architecture. CLT employs aspects of information processing theory to emphasize the inherent limitations of concurrent working memory load on learning during instruction (Sweller et al., 1998) Cognitive load measurement is based on a construct known as relative condition efficiency which measure perceived mental effort, an index of cognitive load during various instructional conditions (Paas et al., 2003)

12. Math Achievement In general math achievement is defined as a level of attainment in any or all mathematics skills, usually estimated by performance on a test (Webster 2003). Researchers operationalized the term, as “a composite of scores made up of grade point average, persistence/retention as measured by some kind of a standardized test” (Brown et. al., 1989).

13. Cognitive demand of tasks: Patterns of Set up, Implementation, andLearning Task Set Up Task Implementation Student Learning A. High High High B. Low Low Low C. High Low Moderate Stein & Lane, 1996

14. Research found… That maintaining the cognitive complexity of instructional tasks through the task enactment phase is associated with higher student achievement. The QUASAR Project. Students who performed the best on project-based measures of reasoning and problem solving were in classrooms in which tasks were more likely to be set up and enacted at high levels of cognitive demand (Stein & Lane, 1996).

15. Research found … cont. The QUASAR Project TIMSS Video Study Students who performed the best on project-based measures of reasoning and problem solving were in classrooms in which tasks were more likely to be set up and enacted at high levels of cognitive demand (Stein & Lane, 1996). Virtually noneof the making-connections problems in the U.S. were discussed in a way that made the mathematical connections or relationships visible for students. Mostly, they turned into opportunities to apply procedures (TIMSS Video Mathematics Research Group, 2003).

16. Conclusion Not all tasks are created equal -- they provided different opportunities for students to learn mathematics. Engagement in a sustained cognitively demanding mathematical tasks leads to the greatest learning gains for students. Cognitive load as a valid predictor value or independent variable when measuring or predicting future math academic achievement is overwhelmingly supported by the research literature.

17. Recommendations for future research Investigate whether cognitive demand of instruction changes in K-12. Investigate whether teachers perception of the cognitive demand level of task changes in K-12. Conduct a hypothesis testing whether there is a significant change in the levels of cognitive demand of math instruction and the teacher’s perception of cognitive demand levels of the math instruction in fifth grade.