A PROBLEM GENERATOR SYSTEM TO LEARN FIRST-DEGREE EQUATIONS

Year 2014, Volume: 1 , 361 - 366, 01.09.2014

Mir Mohammad Reza Alavi Milani Hüseyin Pehlivan Sahereh Hosseinpour

Abstract

Problem-based learning
enhances academic productivity, and improves long-term memory. Thus it is
better than traditional instruction. Meanwhile, the teaching of mathematics
education is more important than others. Much software is developed for visual
learning mathematics, but there is a great need for problem-based systems. This
is more visible, due to the increasing proliferation of e-learning education.
On the other hand, first degree equations are a uniquely important topic in
high school and collage algebra classes, for the simple reason that mastery of
a preponderance of later topics requires a student’s ability to solve these
equations. Such topics include absolute value equation, equation containing
fractions, radicals, and an abundance of applications. Proficiency at solving
first degree equations in one variable is literally essential to success in an
algebra class. Students often do not clearly understand the concepts of these
topics and make mistakes when they write homework’s or use these concepts in
the other topics. In order to help the students to learn these concepts by
solving problems, we have proposed a system that generate problems and evaluate
learner’s answers.  In this paper we
propose a methodological approach for automatic solving of mathematical equations,
especially in terms of the first degree equations in one variable, with the aim
of the practicing of mathematics subjects, by using of Computer Algebra System
(CAS) tools. The paper also addresses some specific fields such as the
simplification and automatic production of mathematical equations.

Keywords

First-degree equation, problem-based learning, computer algebra system, problem generator, problem solver

References

• Baldwin, D. (1996). Three years' experience with gateway labs. ACM SIGCSE Bulletin, 28(SI), 6-7. Barker, D. S. (1997, November). CHARLIE: A computer-managed homework, assignment and response, learning and instruction environment. In Frontiers in Education Conference, 1997. 27th Annual Conference. Teaching and Learning in an Era of Change. Proceedings. (Vol. 3, pp. 1503-1509). IEEE. Bridgeman, S., Goodrich, M. T., Kobourov, S. G., & Tamassia, R. (2000, May). PILOT: An interactive tool for learning and grading. In ACM SIGCSE Bulletin(Vol. 32, No. 1, pp. 139-143). ACM. Bridgeman, S., Goodrich, M. T., Kobourov, S. G., & Tamassia, R. (2000). SAIL: a system for generating, archiving, and retrieving specialized assignments using LATEX. ACM SIGCSE Bulletin, 32(1), 300-304. Dragon, T., Mavrikis, M., McLaren, B. M., Harrer, A., Kynigos, C., Wegerif, R., & Yang, Y. (2013). Metafora: A web-based platform for learning to learn together in science and mathematics. Learning Technologies, IEEE Transactions on,6(3), 197-207. Farnsworth, C. C. (1994) Using computer simulations in problem-based learning. In proceedings of Thirty Fifth ADCIS conference, Omni Press, Nashville, TN, 137-140 Gutierrez-Santos, S., Geraniou, E., Pearce-Lazard, D., & Poulovassilis, A. (2012). Design of Teacher Assistance Tools in an Exploratory Learning Environment for Algebraic Generalization. Learning Technologies, IEEE Transactions on, 5(4), 366-376. Kashy, E., Sherrill, B. M., Tsai, Y., Thaler, D., Weinshank, D., Engelmann, M., & Morrissey, D. J. (1993). CAPA-An integrated computer-assisted personalized assignment system. American Journal of Physics, 61(12), 1124-1130. Wolfram, S. (2011). Wolfram Alpha. 2011. URL: http://www. wolframalpha. com. Stand, 25