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TSG TSG 5.10: Methods and methodologies in mathematics education research

EXAMINATION OF THE FORMATION PROCESS OFLEARNERS' DEVELOPING WAY IN MATHEMATICS
Manabu SATO
Akita University

310417@math.akita-u.ac.jp

The purpose of this study was to obtain suggestions for a framework to capture the formation Process of Learners‘
Developing Way．
Developmental knowledge (hereafter DK) is “Three situations for the Developmental approach (hereafter 3DA)” and“Knowledge based on Developing way (hereafter KD)”) and constructed four stages: “Experience,” “Understanding,”“Trial,” and “Independence” (slide 2).

A framework to capture the formation PLD

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Developmental knowledge(DK)StagesStages：The four levels ofinquiry (Banchi & Bell, 2008)

Three Situations for the Developmental
approach (3SD)
Discovery
Developmenta*b*

Independence

Trial

StructuralNew
Development Developmentc*d*Intrinsic，ConceptualExperience

Aspects of the learner

Unconscious

Continue 3SD autonomously andcreatively by making full use of DK onself．

Ⅱ*slide 4

Understanding

Noticinge*Ⅳ. Integration

Ⅲ. Identification

FeaturesTake note ofthe Usefulness
Ⅱ. Introjection

Ⅰ*Ⅰ. External regulation

slide 3
TSG TSG 5.10: Methods andmethodologies in mathematics
education research

Extrinsic，Procedural

Ⅰ～Ⅳ：The Regulatory styles (Ryan & Deci, 2000)

Unaware，
Don't accept

Based on the utility of DK obtained
from the past efforts, we will continue
3SD using DK．
They start to take note of theUsefulness of DK through theiractivities．
Experienced 3SD and accept DK"Piecemeal" and "Procedurally"．

*Knowledge based on Developing way：a. Focus on numbers, quantity, and shapes, b. Analysis of numbers, quantity, and shapes, c. Problem-solving and ensuring clarity, conciseness, and precision, d.
Generalizing, e. Engaging with New Development, valuing* Regulatory styles：Ⅰ.External regulation, Ⅱ.Introjection, Ⅲ.Identification, Ⅳ.Integration

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Characteristics of the Experience Stage
Three Situations for the Developmental approach (3SD) by a university student
Introduction

Q．Create two twodigit integers using
two numbers from 1
to 9 and subtract
the smaller number
from the larger
number.

Discovery Development

Structural Development

New Development

S：I want to calculate S：I have nothing more to think about! S：I have nothing morewith other numbers. T：What did you do when you foundto think about!
regularity?
T：How about changing
the number of digits?

ex.1and 9
9 1 − 1 9 = 72〇

Try various things
to find regularity.
TSG TSG 5.10: Methods and methodologies inmathematics education researchPresenting a way to elucidate theStructure and Express it inrelational formulas.

×

External regulatory status×

Calculate diversely, but
do not express inrelational formulas.

4/4Characteristics of the Trial Stage
Three Situations for the Developmental approach (3SD) by a university student
Introduction

Q．Add the adjacent
numbers and fill inthe box above.

Discovery Development

Structural Development

New Development

S：What should I
S：It seems to be a regularity.
S：Isn’t there a similar
focus on to solve it? S:：I have not been able toplace?
generalize well, so let's do that first.

〇

Examine in order.

Clarification of structure,awareness of expression throughrelationships〇

S：If I had worked alone, I
might not have gotten
this far.
3SD unfolds smoothly.
Teachers affect ?

From Introductory Status to External Regulatory Status
TSG TSG 5.10: Methods and methodologies inmathematics education research

References
Banchi, H. & Bell, R. (2008). The many levels of inquiry. Science and Children, 46(2), pp.26-29．
Ryan, R. M. & Deci, E. L. (2000). Intrinsic and extrinsic motivations: Classic definitions and new directions. Contemporary Educational Psychology, 25(1), pp.54-67．