Tokapu and Yupana

Project

Tokapu Workshop

Mathematical Design Puzzles

Teachers:

Aguilar Alcedo, César

Valderrama Solé, Carlos Jordy

1.-IDENTIFICATION

NAME OF THE PROJECT: TOKAPU WORKSHOP-MATHEMATICAL DESIGN PUZZLES

1.1 WORKSHOPS: 90 Minutes/ 5 Sessions

1.2 RESPONSIBLE INSTITUTIONS: KULKIJAT, CAISA, SCHOOLS INVOLVED

1.3 SPONSORS: CAISA AND SCHOOLS ATTENDINING THE WORKSHOPS

1.4 ACADEMIC TRAINNERS:

CÉSAR AGUILAR ALCEDO:

CARLOS JORDY VALDERRAMA SOLÉ

1.5 VENUES: PHYSICAL NEEDS, TABLES, MANUALS AND PUZZLES

1.6 PARTICIPANTS: 20 to 30 PEOPLE: CHILDREN, ADOLESCENTS, TEACHERS, VOCATIONAL

EDUCATION STUDENTS, PARENTS

2. DESCRIPTION OF THE WORKSHOP

The Tokapu workshop uses mathematical Andean design as a way to introduce children into simple calculation and mathematical thinking.

With the use of the puzzles the participants find their way into designing since the puzzles have not one, but many possible answers. This educational and playful project has been developed since 2010 by Cesar Aguilar, a Peruvian multidisciplinary artist based in Finland.

The puzzle games are simple and easy to play. They are based and inspired by an interactive implementation of a series of logical, spatial and creative puzzles which take the Andean Cosmo vision.

The calculations will be made using a YUPANA, mathematical calculating device, created by ancient Andean cultures, included in the User’s Manual.

The word “Tokapu” is referred to the Andean system of ordering the space and is related to the Golden Ratio in Fibonacci progression.

These puzzles promote learning of mathematical skills and concepts, exercising logical reasoning plus chromatic and spatial relationships.

The puzzles include one specially designed for the visually impaired.

Because of its dimensions and nature of the “Tokapu” puzzles they do not require more logistic than other boards games.

The puzzle games are very appealing to the public and can be practiced individually, in couples or in teams. They are not competitive but rather complementary.

Finally it is possible that the workshop could end up with an exposition of the designs made by the participants, since they will find their own creations and answers in design and Maths.

3. GENERAL OBJECTIVES

· ARTISTIC DESIGN

· AQUISITION OF MATHEMATICAL SKILLS AND CONCEPTS

· SHARING OF ANSWERS AND CREATING PROBLEMS

· TO RELATE NATURALLY TO MATHS

· TO DISCOVER A NEW WAY OF DESIGNING

· TO EXPERIMENT WITH A MATHEMATICAL ANCIENT DEVICE

4. SPECIFIC OBJECTIVES

4.1 Of the workshops

· Facilitate a tool for teachers and students to see mathematics from a different point of view.

· Create a new approach towards art and math

· Preserve the use of the ancient Yupana as a mathematical device.

· Enjoy solving problems since this puzzle games encourage and a creative mathematical thinking and the

creation of new problems.

7. BENEFICIARIES

Children, teachers, students, parents, elder people, and the whole society.

8. GOALS

To encourage the use of Tokapu puzzles and Yupana to approach math and design.

To rescue ancient knowledge and make it popular again integrating the arts with the sciences.

9 NEEDS:

9.1.1 PHISYCAL:

Workshop space could be an Auditorium, a large class or a patio.

Materials: Puzzles, tables and chairs. Pencils and notebooks.

Photographic Camera

9.1.2 Human:

· Teachers

· Participants (30 maximum)

· Organizers

9.1.3 Technological

- Puzzles

- Yupanas

- Paper and Colors

9.1.4 Economic

- Teachers salaries

10. ADMINISTRATION

· Kulkijat ry Cultural Association

11. CRONOGRAMME OF ACTIVITIES

11.1 ACTIVITIES

a) Elaboration and approval of the project.

b) Design of the chronogram of spaces to take the workshop

c) Calendar

d) Project experimentation

e) Assessment

f) Final Report and Memoirs of the experience

12.- Feedback and evaluation.

Helsinki, January 2017

Tokapu and Yupana

Design Puzzles for mathematical comprehension

To name our games has resulted a very interesting task, because from the very beginning we do not want our students to believe this will be a practice could be tiresome or too difficult. We know from teaching experience that if you approach an audience with the words “work”, “mathematic” or even “practice” or “repeating” students will put some preconception to work in mind. On the other hand if you, as a teacher use the word: “game”, “create” or “research” they will be eager to know what is coming next.

Tokapu and Yupana Mathematical design puzzle and Inca Calculating device has all these facts in their advantage.

Tokapus are puzzle games with many design possible answers and the Yupana is a device that encourages students from all ages to calculate through playful routines.

Creating problems, unknowingly at the beginning, instead of solving them is one of the wonders of these games. Encouraging the students to design harmonic symmetries is something that everybody enjoys, especially when your design can be unique.

Based in ancient dualistic and complementary cosmovision of ancient Andean cultures Tokapu Kelka design and Yupana mathematical device arise to show us how they relate and thought of nature through harmony and complementarity.

Some inspirational videos:

Topaku Programming Workshop

Five sessions

UNIT OF LEARNING # 1

1. General Data

Institution Centre: OOO

Grade: OOO

Level: Primary

Nº of Students: OOO

Name of the Unit: Tokapu Kelka, Mathematical puzzle and

Yupana, Inka calculating device

Lenght: 10 academicals hours.

Teachers: César Arturo Aguilar Alcedo

Carlos Jordy Valderrama Solé

2. JUSTIFICATION

Mathematics is seen nowadays as a problematic matter instead as a tool of amusement.

Through our workshop we encourage children to design, play and create problems that they will love to solve

and share with their pairs.

3. TRANSVERSAL CONTENT

CHART OF CAPACITIES BY AREAS

AREA: Math and Design
CAPACITY: Creativity, calculation, prediction, analysis
ASSESSMENT ; Self and co-Assessment
ART: Design and recycling

- Develops interest in creating new designs following patterns and sharing them.

- Experiments calculating from his own creations.

- Registers their designs through photography, keeping a file of them.

- Recognizes the mechanisms of the Tokapu Kelka puzzle.

- Creates his own designs

- Discovers the use of the Yupana to make calculations.

- Relates to the puzzle and the calculating device accordingly and freely with interest.

-PERSONAL SOCIAL

- Encourages his pairs to solve the problems that creates.

- Understands and shares his achievements with others.

1. PROGRAMATION OF ACTIVITIES FOR SIGNIFICATIVE LEARNING

Learning Activities
Date
Strategies
Means and materials
Activity 1
Tokapu Kelka & Yupana

1st session

How the puzzle works?

Children will work in pairs, to have someone to help and get advice from. They may also produce a shared design.

How to use the Yupana calculating device?

The children will learn how the yupana works and how they can design one using simple materials they can find

at any home.

Tokapu Kelka Puzzles, one for each couple of students.

Board, paper, pencils, colours and beans.

Activity 2

Giving values to colours

2nd session

The children, in pairs create their new designs.
The teacher gives values to each colour and shape.
They calculate the different values of the designs they created using the Yupana calculating device.
The children share their findings.

Tokapu Kelka puzzles Two for each couple .

Yupanas and beans.

Paper and pencil for each student.

Activity 3

Creating fun problems

3rd session

The teacher will propose different ways of looking at the Tokapu puzzles.

The children create their new designs.

The children share their findings using the Yupana to do so.

Tokapu Kelka Puzzles

One for each student.

Yupanas and beans