## Mathematic Proficiency: A New Focus in Mathematics Education

By now, I hope I have managed to convince you that video games provide an excellent-I believe ideal-technology environment for learning everyday mathematics. What features should a video game have in order to provide an ef-fective mathematics learning experience? What kinds of game develop mathemat-ical thinking? In this chapter, I outline the basic pedagogic principles on which I think the design should be based. Those principles come with impressive cre-dentials-the National Research Council (NRC)—and are widely accepted in the United States mathematics education community. Some of the principles-there are five of them-may seem to bear little or no relation to the mathematics classes you had in school. The blue-ribbon committee that the NRC engaged to develop the principles did its work around the turn of the new millennium, and their mis-sion was to develop an educational framework that would prepare students for life in the twenty-first century. Much of what they recommended has yet to find its way into mainstream American mathematics education. The Five Strands Until the first half of the twentieth century, learning school mathematics usually meant becoming proficient in performing the procedures of arithmetic, with rela-tively little attention paid to students’ understanding. In the 1950s and 1960s, the “New Math” movement called for the focus to be shifted to understanding the concepts of mathematics (e.g., number concept, number bases, laws of arithme-tic). Although the concept was sound-focusing on conceptual understanding and computational skill-in transferring New Math from the universities, where the idea originated, to the nation’s classrooms, where many teachers were ill equipped

to handle the new material properly, the New Math idea was transformed in the minds of many to conceptual understanding alone. A popular joke at the time was “I don’t care if you get the wrong answer, as long as you understand the method.”The backlash created by New Math, or rather a result of the popular conception of New Math, was the rapid emergence of what was called by its proponents the “Back to Basics” movement, where the focus was once again on developing the ability to compute rapidly and accurately. The 1980s and 1990s saw the emphasis shift yet again, this time toward what was called “mathematical power”, which involved-in addition to arithmetical skill-logical reasoning, problem solving, connecting mathematical ideas, and communicating mathematical ideas to others. The mathematical power initiative led to two schools of thought, with one group once again promoting the primacy of memorization and the acquisition of rote-learned skills, and another arguing that, in addition to problem solving skills, students needed to be able to prove mathematical assertions.Meanwhile, as the educational sands kept shifting and researchers and educators argued the different viewpoints, many parents maintained a fairly constant viewpoint. Middle-class parents with sufficient means employed private tutors or enrolled their children in commercial Saturday morning academies where the emphasis was predominantly on the development of arithmetical skills through repeated practice-much like the kind of mathematical education you would have found in the church schools of medieval Europe.Today, there is a substantial consensus within the mathematical community centered on what has come to be called mathematical proficiency. This concept attempts to codify the mathematical knowledge and skills that are thought to be important in today’s society. The elements of mathematical proficiency were spelled out in a report from the National Research Council’s 1999-2000 Mathematics Learning Study Committee, titled Adding it Up: Helping Children Learn Mathematics, published by the National Academies Press in 2001. In my view, that volume provides the best single source for guidelines toward good mathematical instruction to date. I would strongly recommend that any designer of a math ed video game takes this as an initial guide. From the outset, however, you should recognize that the NRC report, together with practically everything that has been studied and written regarding mathematics education, is based on a classroom model involving the three-way interactive triumvirate:

For successful education in this environment, the teacher has to understand both what is being taught (the mathematics) and what is involved in learning mathematics (the student’s part), and the student has to interact with both the mathematics and the person teaching it. Almost all current pedagogic theory and practice is based on this model. But this is very different from the learning framework you will be working with when you select-or build-a math ed game. No student has yet experienced mathematics learning with a video game, where the framework looks like this:

There are no experts in the use of this kind of educational framework. There is no body of accumulated knowledge that you can draw upon. While you can and should take Adding It Up as a starting point and use it and the existing mathematics education research literature as a constant reference source, once you start you will be largely out on your own. The best you can do is keep one primary goal uppermost in your mind. The game should help students achieve mathematical proficiency, as articulated in Adding It Up, and it should do so using activities that arise naturally in the game.