Math Games Can Target Key Instruction Areas

Classroom games these days may seem like an indulgence, but math consultant Dr. Nanci Smith shows teachers how to use games to differentiate instruction and reinforce skills that students need to tackle higher math. Included: Examples of math games that can be used to differentiate instruction.

Many teachers today feel like they have no time for classroom games, particularly when it comes to heavily-assessed math skills, but Dr. Nanci Smith maintains that is precisely where games can make teachers jobs easier. Properly designed games are a simple way for teachers to differentiate math instruction and help students learn to solve problems rather than just memorize patterns or steps to do math, according to Smith.

Smith is a former college and high-school math teacher who now is a consultant in the areas of differentiated instruction and mathematics. She has been a national and international consultant in differentiated instruction for the Association for Supervision and Curriculum Development (ASCD) for seven years. Smith was the math consultant and author of the users guide for ASCDs Meaningful Math DVD series, and has developed a CD/DVD-based professional development series for middle-school math teachers.

Smith talked with Education World about the types of games she has used to differentiate math instruction and suggestions and guidelines for using math games.

Dr. Nanci Smith

Education World: How can teachers use games to differentiate instruction?

Dr. Nanci Smith: The easiest way to use games to differentiate math instruction is by offering a variety of choices within the games. For example, if you are practicing a specific skill, there are usually several different games that can practice that skill. Offering students choices as to how they want to practice can add to their motivation, and usually results in higher quality effort.

Another way to use games as a vehicle to differentiating instruction is to address different students readiness levels through the games. For example, if multiplication is being practiced, the same game can be used with single-digit practice for students who need to reinforce the basic facts, two-digit multiplied by one-digit for students ready to practice that skill, and two-digit by two-digit for students for whom that is appropriate. This is a simple example, but the premise of using the same game with multiple levels of challenge problems is usually not too difficult an adjustment on the teachers part. A note to consider whenever differentiating by readiness is to be sure to assess your students regularly -- informally or formally -- to be sure that you are appropriately challenging them. Students who are at the same approximate readiness level should be grouped together to work together and challenge each other.

Games can also be effectively used as anchor activities or learning stations. Once students have learned how to play a game, the game can become an option when students finish early or have other ragged time. Additionally, they can be an independent station or learning center during math.

Teachers should be aware that not all students enjoy playing games to learn math. Another aspect of differentiation might be to provide students who do not like to play the games a different vehicle by which to learn and practice the skills. It might be as simple as making a partner or group game into a solitaire game, or providing a worksheet or other activity in lieu of the game.

EW: What kind of impact have you seen games have on student learning?

Smith: The biggest impact I have seen from using games in math might be in the area of affect. Suddenly students are engaged in mathematics and do not see math as the class they hate or cant do. Math becomes more fun, energetic, and cooperative. Students attitudes are one of the greatest benefits or obstacles, depending on whether the attitude is positive or negative, in learning math.

When students use games to reinforce skills or memorize facts, they do more problems than can be worked through direct instruction with a sense of fun attached. This repetitive practice can reinforce facts and skills that usually are reinforced through rote repetition only. The automaticity of basic facts and operations are directly related to success in mathematics, especially as the content progresses and becomes more abstract through the years. Anything that can help students master this content is very important, and games seem to be an active and engaging way for students to get the repetitive practice they need.

EW: What are some of the skills that games can reinforce?

Smith: Games can be used to reinforce any skill, actually. It really only takes a little creativity.

A very simple way to practice any skill is to make a matching game with problems on half the cards and the corresponding answers on the other half of the cards. Making a very simple matching game like this can turn any type of skill or math problem into a game.

More complicated skills and procedures can also be reinforced through a game, such as building geometry proofs in high school or generating random word problems by creating stacks of cards with phrases, variables, and values and having students pick one card from each pile make a word problem.

EW: Can you describe some of your favorite games?

Smith: I really enjoy any type of card game. I tend to make up my own games based on my favorite games from childhood. For example, I have made a game for solving rational equations in algebra that is based on the card game Uno. Go Fish is an easy game to use as a model. I have also made many board games. One type of board game that can be very flexible is based loosely on the Candyland board. Create a winding path over an open file folder, or a design on two sheets of paper that could be run off on card stock and then taped together, with letters or symbols on each square of the path. Then, create a stack of cards with multiple choice answers on them. The players move their pieces on their turn by correctly answering the problem on the card, then moving to the next space with the same letter or symbol to match the answer.

Finally, dont forget about end-of-unit projects that would have students designing the games for you!

EW: With all the emphasis on testing and AYP, do you have a difficult time convincing administrators that games have a place in the classroom curriculum? What information do you use to sway them?

Smith: One of the misconceptions that I see related to AYP and standardized testing is [the idea that] if the teacher covers all the information students will do better. This simply is not the case. A hurried coverage of curriculum just does not increase test scores. What will increase test scores is developing mathematical concepts and understandings to make sense of the procedures and steps in solving problem types. Instead, math teachers tend to show steps to a type of problem, and students then try to memorize these steps or recognize the types of problems that would need a certain sequence of steps to solve. Instead of rote memorization, we need to engage students in learning and practicing math. Games are a natural way to do that.

A related concern is that there is not enough time to play games in an overcrowded curriculum. This is true. Games should not be and this too, but rather instead of. Instead of direct instruction with multiple problems as a whole class, games should be used for individual and paired practice.

EW: What are some things to be aware of when using games in math class?

Smith: One problem I have seen repeatedly with teachers who try to use games in math is that students dont do the math correctly, but often do not know they are not. Because of this they reinforce errors and misconceptions. It is important that there is some way for students to be accountable for the way they are doing the math when playing the game. I often have ways for them to check their work -- such as numbered cards and a corresponding answer key in case of debate -- and always have some form of an accountability sheet where they record their work and answers. This becomes an easy method for me to monitor students play.

Another pitfall of which to beware is that often students do not make the connections from a given game to symbolic writing of math. Transitions need to be made explicitly from the concrete manipulatives used or the process of playing a game to the symbolic process of mathematics. Often we assume our students understand how the game relates to the problems on the page, but this is often not the case.

EW: What are some other simple strategies teachers can use to differentiate math instruction?

Smith: This is not a simple question to answer. There are almost as many ways to differentiate as there are teachers and students. If teachers are familiar with strategies for differentiation, they can all be used in mathematics. Differentiation is really about allowing all students access to the content in ways that engage and intrigue.

Some of my favorite strategies include designing tasks according to students learning profiles, especially Dr. Robert Sternbergs Triarchic Theory of Intelligence, to have students reflect on the understanding and process involved in the specific content rather than working many of the same types of problems. Ive found that by having students reflect on the process involved in solving problems that they are more able to do the problems than when I tried to have students do more number crunching in class. I have found differentiating by learning profile to be highly effective for this.

Some basic strategies such as Role/Audience/Format/Topic (RAFT) or cubing are also very useful tools for differentiating by readiness or interest.

This e-interview with Dr. Nanci Smith is part of the Education World Wire Side Chat series.

Article by Ellen R. Delisio
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