Circulation of knowledge : from research to teacher training

Conference Presentation

Reference

Circulation of knowledge : from research to teacher training

DEL NOTARO, Christine

Abstract

In a situation of observation of a trainee giving a mathematics lesson, we noticed that knowledge resulting from a task developed by researchers for teaching purposes was not circulating as smoothly as expected between the two institutions, research and teaching. This is due to the emergence of certain phenomena produced by the application of this task in the class contingency. Our presentation will show the effects of the didactical transposition, trying to interpret this fact. We will show that it is due to the fact that the pupils' knowledge, in this particular case, is rapidly manifesting from all sides, creating a kind of overflow effect among the trainees, that we have called saturation of the milieu. That means too much knowledge in the milieu at the same time. We observed then, that the trainees stop the pupils' exploration to lead them to the calculation. What appears as a transparent task at the outset is, in fact, highly complex in terms of the knowledge it generates for pupils and interactions with trainees it creates. The underlying theoretical-didactical background is so opaque that it obscures both the [...]

DEL NOTARO, Christine. Circulation of knowledge : from research to teacher training. In:

Winter GETL (Global Education Teaching & Learning) , Tignes (France), 27th-31st January, 2020

Available at:

http://archive-ouverte.unige.ch/unige:134612

Disclaimer: layout of this document may differ from the published version.

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Winter Global Education, Teaching & Learning Conference 2020 January 27 ^th – 31 ^st

Tignes

Winter Global Education, Teaching & Learning Conference

January 27 ^th - 31 ^st Tignes

Circulation of Knowledge : From Research to Teacher Training

Didactics of mathematics

Question

What are the effects of introducing research into teacher training and what is the change in the students and trainers posture ?

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This exercise about divisibility criteria is very tempting for a teacher who wants to combine some research and learning for his students.

An example…

“Find and write down all the ways to complete this number so that the division

But what happened?

 The task was a complete

failure…

There's no time to experiment

I observed that

• Trainees were completely overwhelmed

• Pupils’ knowledge rapidly manifesting from all sides

 overflow effect among the trainees, that we have called saturation of the milieu

 Too much knowledge in the milieu at the same time

• Trainee stopped the pupils’ exploration to lead them to the calculation

• Trainees in general respond to this overflow by cutting short these interactions that surpass them…

• … and validate in the place of the pupils

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Pupils need to experiment a lot, not only do calculations to build up their own

knowledge

The task has been in turn:

• designed by researchers to introduce pupils to mathematical research

• taken up again in initial training to introduce students to prior analysis

• used by trainees to teach divisibility criteria.

Who is supposed to pass on the knowledge?

Formation Noosphère

Ecole Ecole Ecole Ecole Ecole

Recherche

Initier les étudiants à l’analyse a priori

Initier les élèves à la recherche

From the point of view of the didactical transposition…

Knowledge is supposed to be passed on between school and initial training

Introduce pupils to research Introduce students to prior analysis

École Formation Recherche

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Trainees (and teachers) use the situation for teaching purposes of the divisibility criteria and not as a research situation

At that point, the system is completely blocked

→ Does not circulate as planned

→ Not taken up by teachers

→ Remains a training task

From the point of view of the didactical

transposition…

Hypothesis

1. The underlying theoretical-didactical background is not transparent

→It obscures both the mathematical content and the knowledge manifested by the students

EFFECTS

Trainees I observed

→ cut short these interactions

→ validate in the place of students

→ institutionalize knowledge

• The theoretical-epistemological milieu refers to the study of the ring of relative integers

• The meaning of divisibility criteria is generally related to their usefulness

• verification tool linked to the structure of numbers, must be more economical and simple to memorize

• Divisibility is a property, the criterion is an index of this property

Function: convert division into divisibility

Effects

• Production of phenomena such as saturation of the milieu if

experimentation is not allowed

Changes

• Epistemological posture: how do we think about relationships between experience ↔ experimentation

• Exploring feeds the experiment (ease in making hypotheses, developing rules, expressing suppositions, findings, …)

• Experiment… to adapt one's knowledge

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Conclusion

What are the effects of introducing research into teacher training and

what is the change in the students and trainers posture ?

Experimenting to adapt one's knowledge…?

 To adapt his knowledge, the pupil must have a pool of experience on which to draw.

 These experiences take place into the exploration of mathematical content.

 The exploration can only take place if the pupils can experiment

with a task