Evaluating mathematical games

It is the start of the school year in the northern hemisphere and the mathtwitterblogosphere (#mtbos) is full of ideas, and requests for ideas, for games that will help make learning in mathematics more fun.

At StatsLC we are releasing The Dragon Games, which is a collection of four different games, and a set of cards and accessories that can be used for an almost infinite number of games. We are also gearing up for a Kickstarter campaign for The Cat Herder Games for younger children.

My thoughts have turned to what makes a good mathematics game.

Candy cereal and pseudo-educational games

Educational games are a mixed bag. Some pseudo-educational games are like sugar-filled cereal. They pretend to be educational, just as the cereals pretend to be healthy. And just as candy cereals propose to be part of a healthy breakfast, the pseudo-educational games can offer to be part of a worthwhile educational programme. However, these games may have little benefit in terms of learning, and take up valuable learning time. There are many pseudo-educational games, particularly related to mathematics, and though most of them are not actually harmful, many are a waste of time. How much better to use games that are like a nutritious and tasty breakfast, being both educational and fun!

Why use games

People want to spend more time doing something if it is fun and rewarding and they feel as if they are making progress. Some games make practice or drill more palatable, some teach through the game mechanics, and some games can simulate real-life processes and decision-making

Considerations

  1. Games need to be fun.

It seems obvious that games should be fun, but sometimes that part gets missed out. The fun aspect should form part of a game evaluation. Of course fun, like beauty, can be in the eye of the beholder. Many children do like simple roll-and-move games like snakes and ladders, which adults might find boring. Snap and memory are very simple games, that can be played with any kinds of cards that pair, and these are fun for a certain age-group. Conversely, fun does not have to be easy. Struggle is good for learning and for satisfaction. It helps for a game to be easy to learn, especially in a classroom.

  1. Basic educational games can provide practice opportunities that lead to fluency.

There are things in mathematics that require practice. It is vital for children to have their number facts at their fingertips, and have confidence in their recall. Just as a good grasp of vocabulary helps in acquiring a new language, having automaticity in recalling the basic addition, subtraction, multiplication and division facts helps enormously in later mathematics learning. When I talk with Secondary school teachers, one of the main things they would love their students to have on arrival is knowledge of the basic facts.

In earlier times, these facts were drummed into pupils with drill and stick. This almost certainly contributed to undesirable outcomes such as antipathy towards mathematics and believing that being a mathematician is about speed of recall. But my mother’s generation sure could add, subtract, multiply and divide!

Games that require matching, such as memory, snap and happy families (Go fish) are useful mechanisms for reinforcing basic facts. However these are low-level games, as the mechanism is independent of the concepts being taught. A disadvantage of this kind of game is that the mechanism rewards speed or location memory. It does not develop understanding, though in my experience fluency can help understanding. We need to be careful about the use of speed in games. This works for some children, but not for others. In mathematics there is a place for automaticity, but there needs to be understanding as well.

  1. Games that involve mathematical thinking are a higher level of game.

Say, for example, we are trying to reinforce the names and properties of different geometric shapes. One way to do this is to have sets of cards with information about each shape, and use them in a game that references this information. This helps to teach properties and terminology in an abstract way. A higher level approach is to have a game that applies the properties of the shape in a meaningful way, perhaps filling a space or completing 360 degrees.

Another example is the game “How Close to 100” proposed by Jo Boaler in “Mathematical mindsets” that actively uses multiplication to draw arrays and label the number of squares occupied. This requires active application of multiplication in a way that a game of snap with question and answer cards does not.

We are developing Cat cards as a younger version of the Dragonistics Data cards. One class activity or game is called Cat Adoption. Pairs of children sit in a large circle on the mat, each pair with a whiteboard or paper and pen. Each pair of children is given a number of cat cards – say 10. The teacher turns over a criterion card, which might say “Playful”. This means that all the cats that are playful can be placed for adoption, by putting them in a separate adoption pile. Each pair of children then performs the subtraction on their whiteboard or paper and holds it up for the teacher to see. This is repeated until one pair of children has placed all their cats for adoption. This game gives practice at subtraction, at the same time as reinforcing the mechanism of subtraction. It also gives practice at representing an operation in two ways – with the cards and using mathematical notation.

Some of the cards from The Cat Herder Games

Some of the cards from The Cat Herder Games

  1. It is preferable to have control of error.

Self-correcting games reduce the likelihood that players will reinforce wrong facts. Having visuals that allow for self-correction make it easier for children to play without adult intervention. This is also where computer games have an advantage as they can provide instant feedback about incorrect responses.

  1. The extraneous activities must not be a distraction.

In some on-line games, students are rewarded for progress by improving their avatar or similar. This seemingly harmless reward can provide a distraction from the task at hand. I recently saw a game on a hand-held device that required the student to tip the device as well as recall numerical facts. The operation of the device provided a barrier and distraction.

  1. Games teach other skills

Games can teach how to win and lose graciously, play fair, and let others take turns. These are important life skills, that are included in the Key Competencies of the NZ curriculum. Some children do not have opportunities to play games and learn these skills at home, so it is important to provide these opportunities at school.

Games are great

It is a natural thing for children and adults to want to play. If we are going to help children learn through play, we need to make sure the games we provide are fun and teach the desired lessons.

The Dragon Games and The Cat Herder Games

At Statistics Learning Centre we are committed to helping all teachers to teach statistics, and all learners to understand statistics. In addition we aim to help families and children to have fun together in learning mathematics and statistics. Our game The Dragon Games has already proved popular. In October 2016 we are running a Kickstarter campaign for our new resource, The Cat Herder Games. We hope you can be part of developing this versatile resource and game combined.

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About Dr Nic

I love to teach just about anything. My specialties are statistics and operations research. I have insider knowledge on Autism through my family. I have a lovely husband, two grown-up sons, a fabulous daughter-in-law and an adorable grandson. I have several blogs - Learn and Teach Statistics, and Building a Statistics Learning Community, are the main ones.
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