Learning Mathematics with a Strategy Games Environment.

Asher

Bishop

Corbalan

Polya

Etnomathematics (1991)

Mathematical Enculturation: A Cultural Perspective On Mathematics Education

(1991)

Los juegos, las matematicas

y su enseñanza (1998)

What is a game?

The games are situations that point out an objective and we must reach it following certain rules.

(Asher 1991)

A game could be considered

as a particular class of problem

Corbalan (1998)

Problem

1.- Understand the problem

2.- Make a plan

3.- Carry out the plan

4.- Look back on your work

1.- Understand the game rules

2.- Elaborate a game strategy

3.- Apply the strategy while playing

4.- Review the results of the game

How to solve it

Niss

Mathematical competences (1999)

DESECO

PISA Study

1.- Ask and answer questions about, within, and by means of mathematics (4)

2.- Understanding and using mathematical language and tools(4)

Thinking mathematically

Posing and solving mathematical problems

Modelling mathematically

Reasoning mathematically

Representing mathematical entities

Handling mathematical symbols and formalisms

Communicating in, with, and about mathematics

Making use of aids and tools

Gifted students, usually boys, failed in his compulsory

secondary school studies.

Problem solving is a very important way to learn mathematics

Curriculum, in Catalonia, introduce the mathematical competence or mathematical literacy

A big number of immigrants have been incorporated into our classrooms

Culture and games

Problem solving

Mathematical

competences

Dean Taplin

Ulrich Munstermann

There are up to six important mathematical activities that all cultures practice:

count, locate, measure, draw, play and explain

(Bishop 1991)

Games is a universal activity and Mathematics is a universal area of knowledge

Typology of the research

Qualitative: Case study by following two students

Group C is made out, also, by two repeaters, one student that has needed special attention during the two previous years, and 4 students that have passed with 2nd. Grade mathematics not passed. By the end of our study, the group had been reduced to 13 students.

Research tools

A summary of the works done by the students along the five experiment sessions.

A video recording of the sessions where both groups participated.

Dra. Núria Rosich Sala

nuriarosich@ub.edu

Lluís Mora Cañellas

lluismora.walipi@gmail.com

**1.- Previous ideas and, what**

will be our question research?

will be our question research?

**2.- Theoretical background**

**4.- Experience design**

Four aspects

**and**

one question

Gifted and de-motivated students could

achieve some mathematical

competences with the strategic games?

Game

3r ESO Sant Andreu de Llavaneres

14, 15 and 16 year-old

2 groups

Group A

Group B

There are 16 students in this group and:

one of them had special needs

one of them failed all the subjects the year before

one of them with a disorder of the feeding

the experience finalized with 11 students in the classroom

There are 16 students in this group and:

two students were repeating the course

one of them had a special curriculum since two years ago

4 students failed maths in 2n ESO (the year before)

the experience finalized with 13 students in the classroom

Gifted and de-motivated students of whom we showed its results (teacher opinion)

LAURA

Small daughter of a family with own business

Scholastic absenteeism favored by the family

Little implication in the scholastic education

FRAN

Small son of a well-being family.

Scholastic absenteeism favored by the family

Inconstant character. It always wants to be the centre of attention in any activity.

**3.- Description of the game**

Sprouds is a strategy game created by John N. Conway in 1966

Materials: pencil and paper

Game rules

The players must decide the points

with which the game will begin

The player that starts has, to link two points with a continuous line, or one point with itself. Once done this, the player has to draw

a new point in the arc just drawn.

From one point, no more than three

lines can be drawn

The lines never can be crossed.

The winner is the last player to do a valid movement.

Mathematical interest of the game

The relationship between the initial number of points and the maximum or minimum number of movements that can be done

To find, and be able to explain, which is the best strategy to win

According to Gómez-Chacón (1991)

It must be able to play one or more players

It must have a set of fixed rules

The rules establish the goals that the players must reach

The players must be able to follow their individual ways

The rules must establish clearly when a player has won

Why SPROUDS?

**5.- Results and strategies followed by the students during the sessions**

Understanding the game

Work presentation

Algebraic expression

To find and communicate the best strategy to play

Interest by the work

Teacher interventions

Laura is the first in seeing the importance on non-blocked points to understand the game running. Fran is also able to visualize that importance, but it is not able to write it. Work presentation in a whole group is important in order to achieve this goal for all the students.

If we want that all students fully understand the game, we need the teacher

intervention.

With the data displayed in a table, they are able to deduce the final number of points without playing.

In spite of the students know the best strategy to win, they have a big dificulty to explain it. Fran and Laura give partial explanations like others mates.

Troughout all the sessions, the work's level of ALL students has been excellent.

Teacher take part at two moments 1) in the initial moment of the experience and, 2) driving the work group in each session.

**6.- Conclusions**

1.- Strategy games are a very important motivating element

2.- Strategy games help to develop the mathematical literacy in a very useful way.

3.- Strategy games can be used in any social context

4.- The teacher work is very important to help students to achieve the mathematical competence

5.- Strategy games favours the work of de-motivated students, and help them to imply itself into problem solving.

final suggestions

1.- There're a lot of games for all subjects in the maths curriculum

2.- All the teachers should work together to get that gifted students do not fail in his studies.

**THANK YOU FOR YOUR ATTENTION!**

Mathematical

competences

As we have seen before, there are involved several mathematic competences in this kind of work.

We suggest that