1. Bal Chandra Luitel Binod Prasad Pant
The Constructivist Researcher as Teacher and Model Builder Paul Cobb and Leslie P. Steffe
Bal Chandra Luitel
Binod Prasad Pant

2. Why We, as Researchers, Act as Teachers
Assumption: The activity of exploring children’s construction of mathematical knowledge must involve teaching.
First Reason: When knowledge gained through theoretical analysis has failed to be of value in understanding children’s mathematical realities.
Second reason: The experiences children gain through interactions with adults greatly influence their construction of mathematical knowledge.

3. Why We, as Researchers, Act as Teachers
Third reason: Teacher stems from the importance we attribute to the context within which the child constructs mathematical knowledge.
It is meta-learning (Awareness and understanding of Phenomenon rather than subject knowledge)
Teachers need to differentiate between the contexts of doing mathematics in class and doing mathematics with teachers.

4. The Constructivist View of Teaching
Teachers should continually make a conscious attempt to “see” both their own and the children’s actions from the children’s points of view.
make sense of each others’ verbal and nonverbal activity.
The teacher acts with an intended meaning, and the children interpret the actions within their mathematical realities, creating actual meanings (MacKay, 1969; von Glasersfeld, 1978).
dialectic between modeling and practice

5. Teaching Episodes and Clinical Interviews
Emphasis is on the teaching episodes, as these give us a better opportunity to investigate children’s mathematical constructions.
Using sensory-motor and conceptual activities
Longitudinal analysis of a child’s mathematical development and recording the events

6. Teaching Episodes and Clinical Interviews
Help from Research Team:
First, they help the teacher clarify his or her intentions and interpretations by asking appropriate questions.
Second, they suggest alternative interpretations and propose activities that the teacher might wish to initiate.
Focus on: Vygotsky’s research as modeling rather than empirically studying mathematical processes

7. Teaching Experiments
A teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time—anywhere from 6 weeks to 2 years.
“long-term” interaction between the experimenters and a group of children
The processes of a dynamic passage from one state of knowledge to another are studied.
What students do is of concern, but of greater concern is how they do it.
The data are generally qualitative rather than quantitative.

8. Two types of Teaching Experiments: Macroschemes and Microschemes
Macroschemes: “Changes are studied in a pupil’s school activity and development as s/he makes the transition from one age level to another, from one level of instruction to another” (Curriculum Orientation)
Microschemes: “In a single pupil the transition is observed from ignorance to knowledge, from a less perfect mode of school work to a more perfect one” (Psychological Orientation)

9. Model Building in a Teaching Experiment
The goal is to specify the schemes and to intervene in an attempt to help the children as they build more sophisticated and powerful schemes.
Experiential Analysis

10. Development of Jason’s Counting Schemes
Reciting and counting
How Jason’s develop counting strategies?
Counting 3 and 4 separately and adding them
Counting 3, and adding 4 to 3
Counting backwards
Counting differently: 5 + ____ = 12

11. Model Building—The Quest for Generality and Specificity
Dialectical Relation:
The model should be general enough to account for other children’s mathematical progress.
It should be specific enough to account for a particular child’s progress in a particular instructional setting.

12. Model Building—The Quest for Generality and Specificity
The emphasis in the initial phase was empirical.
The next phase of the modeling process involved reformulating the initial model, aided by a theoretical model of the construction of units and number (von Glasersfeld, 1981).
We firmly believe that this method is essential and contributes extremely to the understanding of how children might construct their mathematical realities.

13. The Educational Significance of Models
There is a trial-and-error of communication, further observation, a gradual and still tentative sort involving the child’s style, strengths, weakness, skills, fears,…
The really interesting problems of education are hard to study. They are long-term and too complex for the laboratory, and too diverse and nonlinear for the comparative method.

14. The Educational Significance of Models
The difference between the researcher and the teacher is that the researcher interacts with fewer children and has greater opportunity and more time to make sense of their behavior.
Children construct mathematical knowledge, so teachers construct their own understanding of children’s mathematical realities.
Although a model can be viable, it can never be verified.