Abstract:

This paper illustrates how algebra can be learned playfully and rigorously, with the aim of building a solid foundation and a positive attitude towards mathematics. In particular, we illustrate some of the many computer games that we've developed to empower the teaching and learning of elementary school mathematics, from preschool to grade 6. Our games are used by numerous teachers in more than 40 countries, and by now we've developed a great deal of field-tested insight about their educational value.

We start the paper with the following question: "What is the value of 26 - 17?" We argue that in order to understand this question deeply, children must be trained to implicitly understand many concepts: the meaning of numerals, the decimal system, the place value representation of numbers, grouping and regrouping operations, addition, and subtraction. Of course, children can be taught to calculate the value of 26 - 17 swiftly, without any thinking. All they have to do is follow the standard subtraction algorithm taught at elementary school, and come up with the right answer. However, since computers can subtract numbers far better than humans, teaching children to understand algebraic algorithms is far more important that training them to follow the algorithms.

Teaching children to follow algebraic algorithms is a solved issue: worksheets and problem sets carry the day. Teaching children to understand algebra is far more challenging, since it requires building motivation, interest, and curiosity. With that in mind, this paper is about understanding through engagement. We describe how we use computer games to teach mathematics in a deep, hands-on, and playful fashion that encourages trial-and-error and exploratory learning.

The paper is organised in six sections, each covering one of the following early age algebraic skills: comparing, ordering, counting, adding and subtracting 1-digit and 2-digit numbers (this corpus represents most of the algebraic component of the first-grade mathematics curriculum). In each section, we present one or more of the computer games that we designed to learn the subject matter, and explain the pedagogical virtue of the approach. We provide links that allow readers to try all the games themselves, and gain a first-hand appreciation of their educational value.

Keywords:

Game Based Learning, Mobile and Tablet Technologies, Educational/Serious Games, Gamification.