# Adaptive Instructional Systems and Recreational Mathematics

## Introduction

Mathematics is the queen of the sciences and vital to nations’ education objectives. How can it be made more enjoyable and fun for learners of all ages?

## Comparative Mathematics Curriculum

In the United States, while mathematics curriculum varies across schools and districts, traditionally, high-school mathematics has been separated by topics, each topic typically lasting for an entire school year. Students might study algebra, geometry, trigonometry, and calculus as separate courses.

In nearly all other countries throughout the world, a more integrated approach is followed. In integrated approaches, high-school students take mathematics courses which cover a variety of mathematical topics.

In integrated and holistic curricular approaches, adaptive instructional systems for scheduling educational exercises and activities would seemingly have greater opportunities for making use of variety to alleviate the tedium of rote exercise.

## Recreational Mathematics

Singmaster (1992) described recreational mathematics as being a treasury of problems which make mathematics more fun and he noted that, in medieval arithmetic texts, recreational questions were interspersed with more straightforward problems to provide breaks in the hard slog of learning.

How can the ancient art of interspersing fun and enjoyable items be analyzed and understood in a modern scientific manner?

## Mathematics Education

Rowlett, Smith, Corner, O'Sullivan, and Woldock (2019) indicated that teaching using games has been shown to improve engagement and attitudes and that recreational mathematics has the potential to develop and expand mathematical skills, including problem-solving, and to deepen understanding.

## Artificial Intelligence

Lopez-Morteo and Lopez (2007) indicated that uses of electronic learning environments for recreational mathematics learning objects positively affect student attitudes towards mathematics. They believed that such approaches have “the potential to promote the mathematics learning process, basically on its motivational aspects.”

McNamara, Jackson, and Graesser (2010) hypothesized that intelligent tutoring systems could be rendered more engaging to learners, and thus more effective in promoting learning by incorporating motivational components. They examined “benefits of incorporating game-based components within established tutoring systems to improve motivational aspects.”

They indicated several constructs related to and intertwined with motivation including self-regulation, self-efficacy, interest, and engagement. In addition to modeling learners’ mathematical proficiencies, learners could be modeled with respect to their affect, mood, self-efficacy, interest, engagement, flow (Csikszentmihalyi, 1988), and motivation.

## Conclusion

Recreational mathematics puzzles and games, making mathematics more fun, can be scheduled and interspersed by adaptive instructional systems, e.g., educational recommender systems and intelligent tutoring systems, to alleviate the tedium of rote exercise, the slog of learning, and to enhance affect, mood, self-efficacy, interest, engagement, flow, and motivation.

## Bibliography

Csikszentmihalyi, Mihaly. "The flow experience and its significance for human psychology." *Optimal Experience: Psychological Studies of Flow in Consciousness* 2 (1988): 15-35.

Lopez-Morteo, Gabriel, and Gilberto Lopez. "Computer support for learning mathematics: A learning environment based on recreational learning objects." *Computers & Education* 48, no. 4 (2007): 618-641.

McNamara, Danielle S., G. Tanner Jackson, and Art Graesser. "Intelligent tutoring and games (ITaG)." In *Gaming for Classroom-based learning: Digital Role Playing as a Motivator of Study*, pp. 44-65. IGI Global, 2010.

Rowlett, Peter, Edward Smith, Alexander S. Corner, David O'Sullivan, and Jeff Waldock. "The potential of recreational mathematics to support the development of mathematical learning." *International Journal of Mathematical Education in Science and Technology* 50, no. 7 (2019): 972-986.

Singmaster, David. "The unreasonable utility of recreational mathematics." In *Lecture for the First European Congress of Mathematics*, Paris. 1992.