Recent research (Bragg, 2006), has questioned the way games are used in the teaching of mathematics. Given the large uptake of Interactive Whiteboards, computer and electronic games, it is timely that research on the use of games in the teaching of mathematics be re-examined. There appears to be little clear research evidence about how to derive effective mathematics learning from a game.
In this study teachers reported games being used as:
Time fillers
Something to be used as an incentive or reward for finishing work or producing work of a high standard or
To introduce a lesson
Anecdotal evidence suggests that similar sentiments would be made by many primary teachers. Rarely are games reported as being used as the basis of a lesson or to encourage discussion of a concept. More rarely, it seemed, was a game taught systematically so that effective mathematical learning and subsequent experiences could take place. The researchers were interested in how games were being used in the teaching of mathematics and whether they were viewed as a legitimate pedagogical tool or were viewed with some skepticism.
Games have been presented by many authors as a beneficial tool in the mathematics classroom (Ernest, 1986, Gough, 1999; Ainly, 1990,). Also numerous authors assert that games should not be restricted just to practice and that they can be an effective vehicle for teaching new concepts to children (Bright, Harvey & Wheeler, 1985, Kamii & De Clark, 1985; Krulik & Rudnick, 1983; Oldfield, 1991b; Booker, 2000).
What is clearly important is the structure of the games used (Ainley, 1990; Booker, 2000) and the literature does highlight that if this structure is not provided, learning does not always take place (Onslow, 1990; Burnett, 1992).
The first issue the researchers encountered when examining the literature was the variation in definitions of what constitutes a game. Harvey and Bright (1985) listed a set of criteria by which a task or activity could be defined as a game:
A game involves a challenge against either a task or an opponent
A game is governed by a definite set of rules
A game is freely engaged in
Psychologically, a game is an arbitrary situation clearly separate from real-life activity
Socially, the events of a game situation are considered, in and of themselves, to be of minimal importance
A game has a definite number of possible solutions; that is, only a finite number of things can happen during play
A game must always end, although the end may come simply because time has run out.
This set of criteria is general in nature so a definition that focussed more on mathematics games was sought. Oldfield (1991a) produced a general definition with one addition – the need for specific mathematical objectives.
It is an activity involving:
EITHER a challenge against a task or one or more opponents
OR a common task to be tackled either alone or in conjunction with others.
The activity is governed by a set of rules, and has a clear underlying structure to it.
The activity normally has a distinct finishing point
The activity has specific mathematical cognitive objectives.
Oldfield‟s definition hints at the social constructivist nature of game playing when it refers to a common task to be tackled either alone or in conjunction with others. Gough (1999) added the notion of choice and interaction when developing his definition of games.
A game needs to have two or more players, who take turns competing to achieve a „winning‟ situation of some kind, each able to exercise some choice about how to move at any time through the playing. (p. 12)
While the interaction might be deemed as the point at which mathematical thinking and problem solving occurs, this definition rules out „solitaire‟ games and possibly those played against a computer or an unseen player over the internet. Likewise, any track game where there is no choice of which path to take would not qualify as a game. Defining the nature of a mathematical game is somewhat problematic and may be a factor that contributes to games being relegated to Friday afternoon when all the real work is finished, or as a filler rather than as a genuine pedagogical choice.
Within the game genre lie various game types. Initially, the researchers had hoped to develop a taxonomy of games so they could be better described and hopefully matched to the needs of the learner. This proved problematic also. Several authors (Oldfield, 1991a; Tapson, 1997) have listed game types but some games fit into several categories. For example, a game such as Mastermind may be described as a strategy game, whereas Battleships may be described as both a strategy games and a content game designed to practise the reading of co-ordinates. To further muddy the water both games are offered on computer and in an online environment and therefore are sometimes classified as computer games. Other categories could be commercial, non-commercial game teacher made games; practice games, concept games, games used to diagnose specific misconceptions, etc.
The purpose of this study was exploratory in nature so the researchers decided there was no need to be overly pedantic about definitions or classifying games. The aim was to determine how the teachers defined a game and classified them. What became apparent early on in the research was that the teachers‟ use of games was limited. When games were used, they were typically to practise a skill or as disguised worksheets.
There is some suggestion that while games are used in the teaching of mathematics, they are not viewed as a legitimate or pedagogically sound approach to the teaching of mathematics. Anecdotal evidence and classroom observation would suggest games are often relegated as:
Palatable practice
A break from the normal routine
As a reward for finishing early – or simply to occupy some children while the rest of the class finish the real work.
Motivation (Burnett, 1992; Bright, Harvey, & Wheeler, 1985; Ernest, 1986)
Less common uses include as:
A form of enrichment, to develop thinking or problem-solving skills (Krulik & Rudnick, 1983).
A diagnostic tool (Booker, 2000). When observing children play and noting their interactions, teachers may learn a great deal about a student. Concept development games, rather than practice games tend to provide better opportunity for making such observations.
In this study teachers reported games being used as:
Time fillers
Something to be used as an incentive or reward for finishing work or producing work of a high standard or
To introduce a lesson
Anecdotal evidence suggests that similar sentiments would be made by many primary teachers. Rarely are games reported as being used as the basis of a lesson or to encourage discussion of a concept. More rarely, it seemed, was a game taught systematically so that effective mathematical learning and subsequent experiences could take place. The researchers were interested in how games were being used in the teaching of mathematics and whether they were viewed as a legitimate pedagogical tool or were viewed with some skepticism.
Games have been presented by many authors as a beneficial tool in the mathematics classroom (Ernest, 1986, Gough, 1999; Ainly, 1990,). Also numerous authors assert that games should not be restricted just to practice and that they can be an effective vehicle for teaching new concepts to children (Bright, Harvey & Wheeler, 1985, Kamii & De Clark, 1985; Krulik & Rudnick, 1983; Oldfield, 1991b; Booker, 2000).
What is clearly important is the structure of the games used (Ainley, 1990; Booker, 2000) and the literature does highlight that if this structure is not provided, learning does not always take place (Onslow, 1990; Burnett, 1992).
The first issue the researchers encountered when examining the literature was the variation in definitions of what constitutes a game. Harvey and Bright (1985) listed a set of criteria by which a task or activity could be defined as a game:
A game involves a challenge against either a task or an opponent
A game is governed by a definite set of rules
A game is freely engaged in
Psychologically, a game is an arbitrary situation clearly separate from real-life activity
Socially, the events of a game situation are considered, in and of themselves, to be of minimal importance
A game has a definite number of possible solutions; that is, only a finite number of things can happen during play
A game must always end, although the end may come simply because time has run out.
This set of criteria is general in nature so a definition that focussed more on mathematics games was sought. Oldfield (1991a) produced a general definition with one addition – the need for specific mathematical objectives.
It is an activity involving:
EITHER a challenge against a task or one or more opponents
OR a common task to be tackled either alone or in conjunction with others.
The activity is governed by a set of rules, and has a clear underlying structure to it.
The activity normally has a distinct finishing point
The activity has specific mathematical cognitive objectives.
Oldfield‟s definition hints at the social constructivist nature of game playing when it refers to a common task to be tackled either alone or in conjunction with others. Gough (1999) added the notion of choice and interaction when developing his definition of games.
A game needs to have two or more players, who take turns competing to achieve a „winning‟ situation of some kind, each able to exercise some choice about how to move at any time through the playing. (p. 12)
While the interaction might be deemed as the point at which mathematical thinking and problem solving occurs, this definition rules out „solitaire‟ games and possibly those played against a computer or an unseen player over the internet. Likewise, any track game where there is no choice of which path to take would not qualify as a game. Defining the nature of a mathematical game is somewhat problematic and may be a factor that contributes to games being relegated to Friday afternoon when all the real work is finished, or as a filler rather than as a genuine pedagogical choice.
Within the game genre lie various game types. Initially, the researchers had hoped to develop a taxonomy of games so they could be better described and hopefully matched to the needs of the learner. This proved problematic also. Several authors (Oldfield, 1991a; Tapson, 1997) have listed game types but some games fit into several categories. For example, a game such as Mastermind may be described as a strategy game, whereas Battleships may be described as both a strategy games and a content game designed to practise the reading of co-ordinates. To further muddy the water both games are offered on computer and in an online environment and therefore are sometimes classified as computer games. Other categories could be commercial, non-commercial game teacher made games; practice games, concept games, games used to diagnose specific misconceptions, etc.
The purpose of this study was exploratory in nature so the researchers decided there was no need to be overly pedantic about definitions or classifying games. The aim was to determine how the teachers defined a game and classified them. What became apparent early on in the research was that the teachers‟ use of games was limited. When games were used, they were typically to practise a skill or as disguised worksheets.
There is some suggestion that while games are used in the teaching of mathematics, they are not viewed as a legitimate or pedagogically sound approach to the teaching of mathematics. Anecdotal evidence and classroom observation would suggest games are often relegated as:
Palatable practice
A break from the normal routine
As a reward for finishing early – or simply to occupy some children while the rest of the class finish the real work.
Motivation (Burnett, 1992; Bright, Harvey, & Wheeler, 1985; Ernest, 1986)
Less common uses include as:
A form of enrichment, to develop thinking or problem-solving skills (Krulik & Rudnick, 1983).
A diagnostic tool (Booker, 2000). When observing children play and noting their interactions, teachers may learn a great deal about a student. Concept development games, rather than practice games tend to provide better opportunity for making such observations.
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