Unplugged Computational Thinking
on the Mathematical Thinking
Masami Isoda

Professor of the Faculty of Human Sciences
Director of CRICED, University of Tsukuba, Japan

PhD in Education (Waseda University, Japan)
Honorary PhD in Mathematics Education (Khon Kaen University, Thailand)
Honorary Professor, Pontificia Universidad Católica de Valparaíso (Faculty of Science), Chile
Honorary Professor, Universidad San Ignacio de Loyola (Faculty of Education), Peru

What is Mathematics for you?
On the Era of Generative AI, Mathematics is the reasoning!

Inprasitha, Isoda & Araya(2023)

Primary School Mathematics

Mathema: Any subject of Learning= All Basic Literacy for Greek Reasoning

Mathematics used to be any subject to develop Logical Thinking to grown up
Philosopher on their languages.
• In Ancient Greece, μάθημα (máthēma) means the “the subjects of instruction
and learning” in Ancitent Greek.
• At Roman Empire, its focused-on Geometry, Arithmetic, Astronomy and Music
Mathema: Music, Astronomy,(mathematical science with figural representations).
Arithmetic & Geometry• In the Middle Age, it become the four subjects of seven= Latin-Reasoning withliberal arts in Latin.
Figural Representation↓Arabic Numeral and Algebra

After Renaissance, Universal Mathematics was proposed
by Descartes to reintegrate mathematical sciences
into one with Algebraic language.

↓ Algebra become the bases for mathematical sciences.
Primary School Mathematics is under local language!

Universal Mathematics:= Algebraic Representation
Mathematical Science on Digital Era= Computational & Visual

Representation

GenerativeAI runs
throughNaturalLanguage!!

• Difficulty: Inconsistency in school mathematics curriculum. Mathematics has been the ways of reasoning which have• Through the overcoming, we develop human character! changed depending on the representations and Language.

can be developed throughthe task sequence.

Acquisition

Reflection

Appreciation

Mathematical Thinking

How to add Rung. TochangetheRuteChapter 2. Example 2.10
Connections: A Case of Ladder Lottery
Let’s think inductively to find the algorism!
By Takao Seiyama

Task 1. Let’s change the root!
What will
happen？

If I addone morethen headd onemore.
It doesnotchange!

Q1. How about three ladder?
Pigeondog

catNO!!

Task 2. Let’s develop further ladder lottery
and pose questions to your friends!
PigeoncatdogbicycleNO!!!
HOW?
HOW??

YES!!!
YES!!!!

Connections: A Case of Ladder Lottery
Let’s think inductively to find the algorism!
Wow, to many ladders!

Let’s reflect on what we learned!

Through Challenges of Problematic, andReflection & Appreciation of their learned waysof thinking and values in the previous tasks,
students are able to think by and for themselves.

Mathematical Thinking

Acquisition

Reflection

Appreciation

can be developed throughthe task sequence.

What is Mathematics for you?
On the Era of Generative AI, Mathematics is the reasoning!

Inprasitha, Isoda & Araya(2023)

Primary School Mathematics

Mathema: Any subject of Learning= All Basic Literacy for Greek Reasoning

Mathematics used to be any subject to develop Logical Thinking to grown up
Philosopher on their languages.
• In Ancient Greece, μάθημα (máthēma) means the “the subjects of instruction
and learning” in Ancitent Greek.
• At Roman Empire, its focused-on Geometry, Arithmetic, Astronomy and Music
Mathema: Music, Astronomy,(mathematical science with figural representations).
Arithmetic & Geometry• In the Middle Age, it become the four subjects of seven= Latin-Reasoning withliberal arts in Latin.
Figural Representation↓Arabic Numeral and Algebra

After Renaissance, Universal Mathematics was proposed
by Descartes to reintegrate mathematical sciences
into one with Algebraic language.

↓ Algebra become the bases for mathematical sciences.
Primary School Mathematics is under local language!
• Difficulty: Inconsistency in school mathematics curriculum.

 Through the overcoming, we develop human character!

Universal Mathematics:= Algebraic Representation
Mathematical Science on Digital Era= Computational and Visual
Representation

Mathematics has been the ways of reasoning which havechanged depending on the representations and Language.