Math games as instructional strategies
Math games as an instructional strategy or model in a classroom can have mixed results. Depending on if they are presented as competitive or cooperative; and if they provide a review of information or explore new information or develop concepts.
Mathematical games can have several formats.
The traditional math game is recognized as a competition that presents math fact or an operation where the student responds with a fact or performs a calculation. Earning points or moving on, if the answer is correct or given, or before others competing in the game. In these examples the student competes against other students in the class to be the first to give a correct answer or to be among those who give the correct answer. The procedure is:
 A problem is given. Usually in a computational format: 3+2=5, 6+8=14, 2* 5 =10, or 2614=12 ...
 Answers are given
 Answers are checked
 Solutions are reviewed for their accuracy and inaccuracy
 Points are awarded
 The procedure is repeated until a winning score is reached or time expires.
Other math game formats are simulations, and competitions.
Math competitions where paper and pencil math tests are usually given. In some competitions there are team and individual competition where contestants take an individual test during part of the competition and perform as teams in another part of the competition. A sample schedule:
 Arrive at the competition and complete registration
 Presentation of mathematician in the work force demonstrates and talks about math in their profession.
 Warmup activities.
 Individual paper & pencil math test is given
 Social time as students finish test and prepare for lunch
 Group competition
 Awards ceremony
Mathematics embedded in a competition. An example is cartography . In this activity students would have explored and practiced how to read and use maps. When they were skilled in doing so, they would gather in groups in a large park, provided with a map that has locations of places in an order in which they are to walk to, collect information at the location, and continue until they complete the course. Competition can be successful location of each point, collection of information, and time to complete the entire course. Kind of like the Amazing Race, only all the locations are given at the beginning of the competition.
Each of the examples require mathematical knowledge to be able to compete successfully.
Let me examine the range of strengths and weaknesses of different games and strategies for learning and reviewing the different dimensions of mathematical literacy.
Strategy 

Traditional paper & pencil, drill games, are heavy on memory recall of facts and often includes a limited time element that often creates a negative climate for some students. Team competition can be similar to traditional drill games or can be less competitive if all teams are simultaneously awarded points, if they are successful, and an is emphasis on learning by playing the game as a practice session and not a high pressure contest. 
Process 

Content 
The mathematical content will vary by the type of problems presented in the game or contest. However, games that provide complex problems and detailed requirements for solutions, and simulations can include the multiple dimensions of the following content in a problem or activity.

Disposition / Attitude 
Games, contests, and simulations can motivate students through success: being the first done, having the correct answer, finding information that others are not aware, sharing information with others, completing an activity. Negative dispositions and attitudes can be learned from the anxiety and pressure created by not having enough information or background experience to solve problems or complete activities successfully in the time provided. If students experiences are not enjoyable and they are not sufficiently successful, they will desire to avoid math and the discomfort they feel trying to solve problems or participate in math activities. 
Mathematical Perspective 
Promotes that accuracy and speed is essential in mathematics. Promotes mathematics as composed of one algorithm for each basic operation. Promotes that verification for accuracy comes from a knowledgeable source (teacher or mathematician). Promotes math a tool that can be used to understand and explain the world. 
I am not condemning math games and competitions. I am suggesting there are time when students are asked to participate in math games for which they are not prepared and teachers limit their participation to providing a solution.
Professional educators need to be careful students understand the information they need play a game successfully. If memory is required for success in a game, then students need to have been introduced to ways for them to remember and practice those memory retrieval strategies, before they play a game. Additionally that practice needs to be similar to how they will have to access it in the game. Practice with teacher selftalk can be an effective strategy to model for students and practice before game time.
Additionally, educators who think of creative ways to extend students experiences beyond a simple telling of an answer can achieve great gains with simple additions. Explanations, diagrams, multiple solutions, repeating similar problems in a 1, 3, 5, then random mix of problems.
Game anyone? (pun intended)...