Describing Teaching from a Describing Teaching from a Constructivist PerspectiveConstructivist Perspective

Duane GraysayKim Johnson

Shiv Karunakaran

The Pennsylvania State University

Theoretical FrameworkTheoretical Framework

The ContextThe lesson chosen for the study involved statistical concepts taught as part of a course in teaching with technology for pre-service secondary math educators.

Learning goals outlined in the plan involved concepts related to statistical regression.

What is mathematics teaching?

A system of actions through which a teacher attempts to

create opportunities for change in the mathematical knowledge, skills, or

understanding of an individual.

Theoretical FrameworkAttempts to describe teaching

actions in a way that reflects our constructivist paradigm.

Models mathematics learning as the outcome of two processes: mathematical activity and reflection on one’s mathematical activity.Influenced by Piaget (1977).

Theoretical Model of TeachingCharacterizes teaching actions as

including, but not limited to:Activity supporting actionsReflection supporting actionsModel-constructing actions

Influenced by Cobb and Steffe (1983), Confrey (1990), Simon (1995)

The questions:To what extent can teaching actions

within a statistics lesson be characterized using this model?

How do teacher and learner actions link to form chains of activity within the statistics lesson?

How do these teaching actions appear to relate to changes in students’ learning relative to coefficient of determination and residuals?

Data CollectionData Collection

Instructional SettingA methods course for pre-service mathematics

teachers geared towards teaching mathematics using technology

Classes were taught by a guest instructor over two class sessions

Students were given preliminary instruction by their teacher of record prior to the implementation of the lesson on how to use FATHOM and basic regression calculation on a graphing calculator

The sessions were videotaped and select small group interactions were audio-taped

Preliminary Data SourcesStudents were asked to complete a pre-

assessment to gauge their understanding of basic regression conceptsWhat does the correlation coefficient tell us? What is a residual? Why do we need least squares regression?

Reviewed and coded the potential teacher actions within the lesson plansVideotaped both class sessionsAudio taped small group activities

The first question asks, “To what extent can teaching actions within a statistics lesson be characterized using this model?” In order to address this question we:

• Transcribed and annotated both class sessions and small group activities

• Coded the teacher actions from the transcriptions

• Analyze transcripts to see if patterns emerge within the coded actions in the transcriptions

The second question is, “How do teacher and learner actions link to form chains of activity within the statistics lesson?” In order to address this question we:

• Coded teacher actions and student actions from transcripts and lesson plans

• Analyze transcripts to look for patterns of interaction within these actions to find chains of activities• Student actions in response to teacher actions and vice-versa

The third question that our study investigates is, “How do the teaching actions appear to relate to changes in students' understandings relative to coefficient of determination and residuals?” In order to address this question we:

Decided to chose two students from the class to interview Insufficient resources to interview all the studentsIdentified ten students based on their answers to the

teacher’s pre-assessment and potential for change in understanding

Contacted all ten, and randomly selected from those that responded that they would be willing to be interviewed

Recorded the group interactions of the two students selected to be interviewed

Collected handouts completed by students in the groupInterviewed two students to find out their understanding of

the learning objectives

Analysis of the DataAnalysis of the Data

Two large class

interactions

Small group

interactions w/

documents

Interviews with two students, along with

pre-assessment

Video and audio data was transcribed, annotated using fieldnotes, and then coded

using three codes for teacher actions & two codes for student

actions

Evidence of student

understanding

1. Effectivenes

s of theoretical

model

2. Interplay between

student and teacher actions

3. Connections of interplay to learning

Coding DetailsThree codes for Teacher Actions

AS: Activity Supporting ActionsRS: Reflection Supporting ActionsMC: Model-Constructing Actions

Two codes for Student ActionsA: Actions involving Mathematical ActivityR: Actions involving Reflections on Mathematical Activity

Examples of Coding: Teacher Actions: MC

Examples of Coding: Teacher Actions: RS

Examples of Coding: Teacher Actions: AS

Examples of Coding: Student Actions: A & R

Preliminary ResultsDirections on handout from teacher acts as proxy for

teacher’s actionsAS and RS are communicated through the

documentCollection of responses may represent MC

Model-supporting instead of Model-constructingChains of teacher and student actions exist

Usually begins with MCMC seems to give teacher access to information

enabling decisions on further actionsEmergence of other types of teacher/student actions

via analysisRelation between actions and student understanding

To be continued…

ReferencesCobb, P. and Steffe, L. (1983). The constructivist researcher

as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83-94.

Confrey, J. (1990). What constructivism implies for teaching. In R. B. Davis, C. A. Maher, and N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 107-122). Reston, VA: National Council of Teachers of Mathematics.

Piaget, J. (1977). The development of thought: Equilibration of cognitive structures. (A. Rosen, Tr.) New York: Viking Press.

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145.