Friday, October 1, 2010

Math and Mathematical Games

Mathematical games develop mathematical communication as children explain and justify their moves to one another. Communication is an essential part of mathematics and mathematics education because it is a “way of sharing ideas and clarifying understanding".

In addition, games can motivate students and engage them in thinking about, and applying, concepts and skills. Games give pupils an opportunity to communicate their ideas and justify their thinking.



In using games, the teacher plays an important role in encouraging pupils to explain their thinking and in keeping them focused on mathematical ideas. Asking them to explain and justify their moves during a trial round of the game played as a whole class demonstrates the type of thinking and communicating. That is important for students to use later when they play the game in pairs.

Games contribute to the development of knowledge by having a positive affect on the atmosphere in the class which in turn produces a better mental attitude towards math in the children. Educational games provide a unique opportunity for integrating the cognitive, affective and social aspects of learning.

Using Games Successfully

The success of the mathematical games as learning tools depends on the teacher's talent in asking probing, open questions and ultimately how well the teacher establishes a classroom climate that encourages experimentation. Ultimately the focus must be on cognitive processes rather than on the correctness of final outcomes. The process by which 'wrong' answers are reached should be valued as much as processes producing 'right' answers.

Ernest (1986) claims that the success of mathematics teaching depends to a large extent on the active involvement of the learner and playing games demands involvement. Games cannot be played passively: players have to be actively involved. For this reason psychologists including Piaget, Bruner and Dienes suggest games have a very important part to play in learning, particularly in the learning of mathematics.

Selecting a Game to Use

When considering what games to use it is vital that the context which they are to be used is considered. The thinking behind each game should be analyzed and matched to the learning objectives that are to be met.

Looking at some of the questions which children should ask themselves when starting to play a game, and putting them under a mathematical heading gives a good idea to the higher order skills involved.

Form of question                                  Mathematical heading
How do I play this?                                       Interpretation
What is the best way of playing?                    Optimisation
How can I make sure of winning?                    Analysis
What happens if...?                                        Variation
What are the chances of...?                           Probability

Form of statement                                Mathematical idea
This game is the same as...                           Isomorphism
You can win by...                                    A particular case
This works with all these games.                Generalisation
Look, I can show you it does...                      Proving
I record the game like this...                Symbolisation and Notation

Clearly the strategy to be used is the decision of the teacher, and is dependent upon various factors like the ability of the children, their motivation and sociability, the ethos of the school, and the degree of control that the teacher has.

Methods of Playing Games

When mathematical games are used, it is important that they are played properly for three reasons:
• #1: First of all there is the intrinsic mathematics which is always present.
• #2: Second, there is the high level of interest and motivation which playing games generates.
• #3: Third, and perhaps most important, is the higher order understanding of the problem to be solved, which can only be gained by playing through different games.

From this there are lines of attack which can be used when analyzing games and trying to find a winning strategy. The teacher should demonstrate these and develop the skill in the pupils.

For instance try making it simpler in some way, usually by making it smaller. If the full game is played on a grid of five by five cells, start the pupils playing and finding solutions on a three by three grid. If a solution cannot be found for the simpler version, it is very unlikely they will for the more complex case.

Different Types of Games

It is important to remember that not all children like playing games, especially if they have weaker social skills.

Others may not like playing games of any type because they do not like the competition. However, these pupils seem to be a minority.

Children with weak number skills will not enjoy activities where this puts them at a disadvantage so using mathematical games which are non-competitive or involve an element of chance are best.

Games in which chance plays a part can be helpful by giving weaker players a more level playing field. Such games are also a good introduction to the topic of probability.

Example of different types of games.

#1 Pontoon
Pontoon is an excellent game for practicing addition and subtraction of numbers up to 21. Because it contains an element of chance, pupils can play happily with the rest of the class without being at a disadvantage because they are weaker at maths. The gambling aspect can be left out of the game, but playing with matchsticks or other small objects adds more fun and extra counting practice.

#2 Dice and Counters
Any game which involves throwing dice and moving counters helps build confidence with numbers. These games can be made more difficult by using two dice and working out the move by adding the two numbers or finding the difference between them. The numbers can also be multiplied together but this often means that the games are completed too quickly unless, like Monopoly, it involves travelling around a board many times.

#3 Score-Keeping
Score keeping comes into many games. Mostly this just means adding numbers together but some games are more complicated. Scrabble and darts both involve multiplying by 2 and 3. The darts game 301 provides excellent practice at subtraction and this can be developed to work with negative numbers.

#4 Pairs
Games involving pairing cards can be very flexible. For instance the pairs of cards can form the two halves of an equation, marked with two equivalent fractions or a percentage and its decimal equivalent.

#5 Computer Games
When choosing computers and electronic games, they should contain the following features:

• Several levels of difficulty so that differentiation is allowed.

• The ability to practice one skill at a time.

• More than one attempt allowed before the correct answer is given. This allows time for rethinking and means that accidentally pressing the wrong key isn't a disaster.

• A response to a wrong answer which is less interesting than the response to a correct one. Many games fail on this point.

No comments:

Post a Comment