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Mathematics Education to Develop Students Agency
Part III: Measurement
How to introduce the unit for measuremt

How can you compare?
• Let’s critique the ways to compare!
• To compare we should set thesame conditions such as thestarting points and the directions.

ISODA Masami, Prof/PhD
Director of CRICED
University of Tsukuba, Japan

What activity theyare engaging in.

Direct Comparison

1Isoda & Murata (2011). Study withYour Friends Mathematics for
Elementary School 1st Grade。
Gakko Tosho.

What activity they are engaging in.

IndirectComparison 2

Isoda & Murata (2011). Study withYour Friends Mathematics for
Elementary School 1st Grade。
Gakko Tosho.

Arbitrary Unit

Indirect Comparison

Direct Comparison

Indirect Comparison

3

Direct Comparison

4

Arbitrary Unit1

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PhasesActivity

P1

Direct Comparison

P2

Indirect Comparison

P3

Arbitrary Unit

P4

Standard Unit

The manner tointroduce themeasurement unit.

Why we need this manner?
 Provide the necessity for themeasurement unit Experience the activity tocreate necessary measurementunit.
 Task sequence to provide thepre-concept before
mathematical definition

Student Agency:
Learned how to learn Globalization is going throughstandardization:
 Technological Innovation
 Politics for standardization
 Business innovation

 It is a story of business control
with politicians: small traditional
shops/companies are gone forinnovative convenience of mass.
 How to create the measurement
unit beyond/before how tomeasure. It means to produce
new standard for new welfare
depending on what people wantto be.

5 If measurement strand onlymeans how to measure, yourstudents can use existed
technology and follows others’
business. It is necessary
however they could not lead
6
innovation itself.

PhasesActivity

Mathematical Nature of each phase

Compare two objects on the same conditions
P1 DirectComparison  Can compare more objects when we can apply thetransitive low: If a>b, b>c, then a>c.
If a>b, a>c, then we have to compare a and b: wehave to set the algorithm to make an order ofcomparisons.

Behind mathematics

Euclidean Algorithm:Review of Part II-Lesson 2, Fraction for Teachers (Isoda, 2012)

Axioms for comparison:
Mathematical relationships
for grater than, less thanand equal.

Compare any objects on the same conditions +The line/ray only havethe origin point andComparison by using the alternative material such as adirection.
tape.
+The number line set

P2 Indirect

P3 Arbitrary
Unit

We can specify the difference as long as wecan measure by using the arbitrary unit on
the alternative material.
P4 StandardUnit

We can make an order but not sure the difference,
how much more.

It works only locally as long as we use the same unit.
If not, we have to seqe the new scale for measurement.

Standard unit is universal and can use onlyat the politically accepted countries.

by the origin. the unitand direction.
.
As long as we can findgreatest common divisor,
we can measure withsupport of Euclidian
Algorithm.
 Mathematically,irrational number isproblem however it does
not appear practically.

Producethe unit
by using
remaining part82

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All these are
the contentof learning!!

This lecture use SEA-BES: CCRLS to explain objectives

Appreciation(6)

Why we need it?

These terminology explain the process. Thus, if you can imagine
concrete materials for each class, you are able to develop it inyour classroom. That’s why we have been discussing materials.

Reflection(5)

Acquisition

10(4)93