The effect of the cognitive demand of math task on achievement.

Jozsef HorvathSOE Learning and Instruction University of San FranciscoDecember 4, 2010

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)

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

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.

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.

TASKSAs they appear in curricular/ instructional materials

TASKSAs implemented by students Student

Learning

Mathematical task framework, (Stein & Smith, 1998).

TASKS

As set up by teachers

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).

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)

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 DEMANDHigh Procedures With

Connections to understanding, meaning or concepts Tasks

Doing Mathematics Tasks

(Klieme & Baumert, 2001)

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.

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)

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).

Stein & Lane, 1996

A.

B.

C.

High High

Low Low

High LowModerate

High

Low

Task Set Up Task Implementation Student Learning

Cognitive demand of tasks: Patterns of Set up, Implementation, and Learning

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).

Research found … cont.

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).

TIMSS VIDEO STUDY

Virtually none of 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).

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.

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.