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Market research reports that families are spending an increasing amount of money on computer games that are intended to educate as well as entertain their children. "Edutainment" products that promise to beef up children's mathematics skills are proliferating. Software packages entice parents with claims such as "Makes math skills a no-brainer" and "Learn the math you need to know for real life." Bombarded by this type of marketing, many parents find it difficult to choose software that can help their children with math. So what should parents look for and expect from good math-based computer games?

The critical question, one that needs more attention by software designers and educators alike, is "Where is the significant mathematics in math-based computer games?" Many games are entertaining and claim to be mathematical, but their math content is limited. They emphasize arithmetic, speed, and instant recall of facts, giving parents and children the message that computation is all there is to mathematics. Because the focus of many of these games is narrow and the presentation repetitive, many developers resort to using elaborate "bells and whistles" to keep children interested.

We believe that games can be both intellectually demanding and entertaining. They have the potential to engage children in a much broader range of mathematical content, including data analysis, logic, programming, 2- and 3-D geometry, and pattern finding. Games that make playing with mathematical ideas integral to the real play of the game can provide an arena for rich mathematical problem solving, and at the same time, be fun for children. Finding such games, however, is not easy.

As part of a project funded by the National Science Foundation, TERC researchers have reviewed a large set of mathematical computer games. We are studying how children interact with these games and what mathematics they learn as they play in an effort to develop some criteria for evaluating the software.

To examine the games in action, we observed middle school children working with the software in informal after-school settings, where playing the games was a voluntary activity. Two of the games we observed children playing are *Math Blaster: In Search of Spot*, published by Davidson & Associates, and *Logical Journey of the Zoombinis*, developed by TERC and published by Brøderbund Software. The games have many similarities. They begin with stories that put the player in the role of savior or protector of characters introduced in the story. They involve slapstick violence, and in both games the players spend the majority of their game play on mathematics. But looking at the dialogue of a pair of children playing each game reveals differences in the type and quality of the mathematics the children are engaged with.

The transcripts that follow are examples of what we consider typical play sessions of these two games. As we examine the dialogue, our focus is on mathematical content and the ways in which students express their ideas and learn from one another. What math are the players working on? Do we see evidence of students' mathematical thinking? How are the players interacting with each other? What is their discussion focused on (e.g., strategy, speed, reasoning, getting the right answer, the story line of the game)?

In *Math Blaster*, the player must save Spot and the environment from the Trash Alien by guiding the protagonist through four math activities. Players choose the mathematical content (addition, subtraction, multiplication, fractions, decimals, percents, estimation, or number patterns) and the level of difficulty.

In the following dialogue the players, G. and P., are entering the "Trash Zapper," the first activity encountered in *Math Blaster*. It is like a traditional math worksheet of multiple similar-type problems. Players type in answers to number problems that appear on the windshield of the spacecraft and then zap the trash floating outside the spacecraft. G. and P. chose to play "Addition at Level 4," which means they are answering problems such as 50 +30 =__.

(* = a computer noise signifying the correct answer)

P: I know this one. I know this one. [There's a pause while the game loads.]

G: 50 times... 5, 6, 7, 8.

P: 80. You have to write it fast because, (*).

P: Fast, fast! 90.

G: 90 (*).

G: 60 (*).

G: 40 (*).

P: 80 (*). [P. leans back.]

G: Take! Just press the button.

[P. shoots the trash. P. leans in again to type and gives an inaudible answer.]

G. and P.: 60 (*).

G: 100 (*).

G: 40 (*).

G: 30 (*).

G: Gotta get them all.

[P. shoots the trash.]

G: Yes! [P. shot all 5 pieces of trash.]

G. and P.: 70 (*).

G. and P.: 20 (*).

P: 50 (*).

(*) (*)

G: Get the fish [a piece of trash]!

[P. shoots the trash.]

Although the game does not reward quicker answers (or trash shooting), G. and P. are worried about the speed at which they are working. The video game feel of this section (and possibly the similarity of the screen to a flash-card-like activity) tends to inspire a focus on speed in the children we have observed playing the game.

The children's emphasis on speed leaves little time or inclination to talk or reason about the math. Except in the first section of dialogue, where G. seems to count up to solve the problem, there is no math talk other than the calling out of answers. We never even hear G. and P. repeat the questions they are answering.

The highest levels of engagement seem to be with shooting the trash at the end of the round. A common goal players set for themselves is getting every single piece.

In *Zoombinis*, the player must design and save small blue creatures with different kinds of hair, eyes, nose colors, and modes of transportation (see Figure 1) by guiding them through a variety of mathematical obstacles to a new homeland. In the following dialogue, R. and C. are taking eight pairs of "twin" Zoombinis through "Level 1" of "Allergic Cliffs," the first puzzle in the game. This puzzle emphasizes sets and attributes and using evidence to form and test hypotheses. To get as many Zoombinis across a chasm as possible, players must notice that each of two bridges accepts (or doesn't accept) Zoombinis based on some rule. For example, Zoombinis with sunglasses go over the bottom bridge, all others over the top bridge. Zoombinis that don't fit the rule are sneezed away by the cliff.

Figure 1

As R. explains the game to C., he articulates the goal of the puzzle (to get the Zoombinis across the bridge by seeing which Zoombini the bridges will take) as well as a strategy for doing so: once you get a Zoombini across, its twin will follow over the same bridge.

R: This is a hard one. You have to see which one they'll take. And if they take this, then put the other twin... right here. Think that's where, cause they sneeze [pointing to the cliffs beneath the bridges].

R: You think she should go there? You think... [R. sees and hears the cliff beginning to sneeze.] Oh man!

Game: Ahhh choo!

R: Just put her over here and put the same twin right there over there. No, right up, right thereŠ. Now put her there. We shoulda made all of them twins. That way all of them could go up here and all the girls, look just like that.

R. continues to develop his theories on using "twins." R. also develops categories of Zoombinis unrecognized by the game, such as girls and geeks. However, even when developing categories that are not recognized by the game, R. is thinking about categories, attributes, and strategies for sorting‹the mathematical emphases of this puzzle.

[Later in the same puzzle]

R: Put that geek up there. Put the... Even though he's not a geek but at least he's still the same kind. [The cliff begins to sneeze.] What?!

Game: Ahhh choo!

[C. looks to R. and laughs at the rejection.]

R: I just wish they could make it! OK we have 1, 2, 3, 4, 5, 6, 7....

C: They look alike.

R: [Points] Please please please... Do they have the same color nose? Put him over here [pointing].

C: Yes.

R: Just have a little [Zoombinis] left [to get across]... Now I hope they go in the right places.

C: Oh she did it too!

Here we see evidence of further strategy, as R. puts Zoombinis of "the same kind" on one bridge. He is surprised when that Zoombini is rejected. C. is amused by the narrative aspects of this puzzle, as is R., who is also worried about getting all the Zoombinis across safely. He counts how many are across and pleads with the prone-to-sneezing cliffs to let more by. He also introduces a new idea in terms of strategy, focusing on one particular trait-- nose color.

**The Mathematics**

In *Math Blaster*, the type of math (drill and practice of math facts) and the way math is presented in this activity (number problems resembling flashcards) do not seem to encourage mathematical or strategic talk. Because children attribute time pressure to this game, there is not much to talk about other than to call out answers in efforts to speedily get the right one. With the addition of the non-mathematical actions such as trash shooting, one gets the sense that kids are being fooled into having fun doing what they would prefer not to do if it were a paper and pencil task. In this sense, *Math Blaster* offers what we consider "sugar-coated math." This sugarcoating seems to reinforce the idea that mathematics, on its own, is boring.

*Zoombinis*, on the other hand, is built around a varied set of puzzles that draw from the mathematics of attributes, set theory, and logic. Because playing these puzzles requires developing and testing hypotheses, acquiring and using evidence, and refining and adapting those hypotheses, there is reason to talk while playing the game. Players discuss choosing a next move, predicting what will happen, reporting the results, and testing new theory.

**Integration of the Mathematics**

A related difference between *Math Blaster* and *Zoombinis* is the way story, characters, and mathematics are integrated. Although *Math Blaster* does indeed have a story, it does not mesh well with the mathematics in which players are engaged. Answering math problems that appear on the windshield of your spaceship is not what you would expect as you search the galaxy to save Spot. The math activities are not a part of the story, other than that they occur in the context (space) in which the story takes place. In *Zoombinis*, the mathematics is inextricably linked to the narrative of the game. There would be no game without the attribute structure of the Zoombinis. In a real sense, the Zoombinis are the math. This means that engagement with the story naturally leads to engagement with the mathematics.

**Mathematical Talk**

At first glance, the talk in the *Math Blaster* transcript seems to be mathematical. G. and P. spend much of their time calling out numbers, "90," "60," and directions, "Fast, fast!" "Gotta get them all." This shows their concern with answers and speed, but very little about any mathematical thinking they may be doing. By contrast, there is a great deal of mathematical talk about sorting, classifying, attributes, logic, and solution strategies in the Zoombinis transcript. R. explains the global idea of the puzzle when he says, "You have to see which one they'll take." They offer problem-solving strategies for this kind of puzzle, both more generally, "If they take this, then put the other twin," and more specifically, "Put that geek up there...even though he's not a geek but at least he's still the same kind," or "Do they have the same color nose?"

**Player and Game Interaction**

In the *Math Blaster* transcript, there is very little talk of any kind. There is no evidence of any connection to the characters or narrative of the game, other than a desire to zap all the trash. In addition to the mathematical talk in the *Zoombinis* dialogue, R. and C. discuss characters (twins, girls, geeks, the sneezing cliffs), show amusement and chagrin with them ("Oh man!" and laughter at the comical rejection of Zoombinis), and demonstrate their investment in them ("I just wish they could make it!"). In our observations, this kind of investment in characters and story extended both the amount of time and the focus of players' involvement with the games.

**Conclusion**

One of our purposes in conducting this research has been to help teachers and parents make more informed decisions about buying mathematical computer software. To this end we have developed a set of criteria for evaluating mathematical computer games. (See Figure 2.) We have also created a web site with a growing set of reviews of computer games that involve some mathematics. Many reviews have examples of dialogue that occurred with the game. Our hope is that this article and the web site will provide a guide for analyzing games as well as children's interactions with them.

## Criteria For Identifying Good Math Software |
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• Is the game based on mathematical problem solving rather than drill?
• Does mathematics take center stage in the software, or is mathematics treated as an obstacle to be overcome in order to win the game or get back to the real (non-mathematical) action of the game? • Are activities in the software built around a coherent and focused set of mathematical ideas, leading to progressively deeper mathematical thinking? Does the software encourage thoughtful discussion about the mathematical content of the game? • Can a range of children see their interests reflected in the game's activities? • Can children with different learning styles enter into the game's activities, or does the game encourage certain styles to the exclusion of others? • Do the software activities engage students deeply and over time, encouraging them to come back and play again? • What do you need to know in order to play the game? Can you enter the game if you are not already familiar with the mathematics involved? Can you learn or explore new mathematics? |

Figure 2

*Megan Murray, Jan Mokros, and Andee Rubin are researchers for the Through the Glass Wall project at TERC.
Through the Glass Wall is funded by the National Science Foundation, #REC-9555641.
Image from Logical Journey of the Zoombinis is used with permission of Brøderbund Software.*

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