MAINTAINING THE
COGNITIVE DEMANDS
OF A TASK USING
DISCOURSE-BASED
INSTRUCTION
CoMERG St. Joseph’s University
September 14, 2011
Diana Cheng (Towson University, MD)
Ziv Feldman (Boston University, MA)
Suzanne Chapin (Boston University, MA)
THE ELEMENTARY PRESERVICE TEACHERS
MATHEMATICS PROJECT
Funded by National Science Foundation
(Suzanne Chapin, PI) – Division of
Undergraduate Education
 Goal: Development & evaluation of instructional
materials

MKT

Positively associated with
Increased student achievement
 Increased instructional quality
(Hill, Rowan, & Ball, 2005; Hill, Blunk,
Charalambous, Lewis, Phelps, Sleep, & Ball, 2008 )

COGNITIVE DEMANDING TASKS
 “Doing
mathematics” tasks prompt
students to:
make mathematical generalizations
 explain their reasoning
 focus on making sense of important
mathematical ideas
(Stein, Smith, Henningsen, & Silver, 2000)

 Those
who experience learning from
highly cognitively demanding tasks are
more
likely to use such tasks in
their classes
(Loucks-Horsley, 2003)
IMPLEMENTING CHALLENGING
TASKS
Task-as-written
 Task set-up
 Implementation

(Stein et al, 2010; Suzuka et al, 2009)
DISCOURSE-BASED INSTRUCTION

Includes:
Explaining, justifying, generalizing
 Creating convincing arguments

(Carpenter & Lehrer 1999)

Should be used regularly in mathematics classes for
future elementary teachers (Simon, 1994).
SMALL GROUP DISCUSSIONS

Small group interactions provide additional
opportunities for learning
Preservice teachers may feel more comfortable
sharing their ideas in a small group setting
(Yackel et al, 1991)
 Preservice teachers have an opportunity to examine
and respond to each others’ misconceptions

(Van Zoest et al, 2010)
GOAL OF THIS STUDY

To illustrate characteristics of productive small
group discussions while solving a mathematical
task
METHODS
Participants: 2 classes of preservice teachers
enrolled in a mathematics content course
 Videotapes and transcripts were analyzed using
the Levels of Math Talk rubrics (Hufferd-Ackles
et al, 2004) and the Instructional Quality
Assessment rubrics (Boston & Smith, 2009)

TASK USED IN THE STUDY
 Participants
learned the lateral
surface area method of computing
the surface area of a rectangular
prism:
SA= (Perimeter of base × Height) + 2 ×
(Area of a base)
 Another
formula for the surface area
of a rectangular prism is given below:
SA=2lw+2wh+2lh. Explain how this
formula determines the surface area
of a rectangular prism. Compare and
contrast this formula to the lateral
surface area method for surface area.
TRANSCRIPT ANALYSIS
Participant-questioner, participant-explainer,
non-participant
 Interchanging roles during discussion
 Cognitive demand analysis
 Levels of math-talk analysis

questioning
 explaining mathematical thinking
 source of mathematical ideas
 responsibility for learning

TRANSCRIPT #1
Two questioners become explainers
 Roles during conversation shift
 Levels of Math Talk high
 Cognitive Demands high

TRANSCRIPT #2
Roles stay the same during discussion
 Levels of Math talk low (especially responsibility
for learning)
 Cognitive demands low (only responded to first
part of question)

CREATING PRODUCTIVE
DISCUSSIONS
Pushing for understanding vs. Getting the
answers
 Creating a norm

Providing support
 Providing examples

IMPLICATIONS
It is possible to have productive discussions!
 Participants should be comfortable with a variety
of roles during discussion
 Cognitive demands of task as written can be
maintained when task is implemented

ADDITIONAL RESEARCH
FROM THIS PROJECT:
Statistical data gains in MKT when using EMP
curricular materials
 Instructors’ questioning strategies used to help
develop preservice teachers’ explanation and
justification abilities
 Support for learning by argumentation in the
preservice elementary teacher classroom

REFERENCES
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Boston, M.D., & Smith, M.S. (2009). Transforming secondary mathematics teaching: Increasing
the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research
in Mathematics Education, 40(2), 119-156.
Hill, H.C., Rowan, B., & Ball, D. (2005). Effects of teachers' mathematical knowledge
for teaching on student achievement. American Educational Research Journal, 42(2),
371- 406.
Hill, H. C., Blunk, M., Charalambous, C., Lewis, J., Phelps, G., Sleep, L., & Ball, D. L. (2008).
Mathematical knowledge for teaching and the mathematical quality of instruction: An
exploratory study. Cognition and Instruction, 26(4), 430-511.
Hufferd-Ackles, K., Fuson, K.C., & Sherin, M.G. (2004). Describing Levels and Components of a
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