Wolfram alpha and maple as educational technology for future teachers of mathematics

The paper’s purpose is to present technology-enhanced activities with triangular, square, and other polygonal numbers arranged in basic geometric shapes – equilateral and isosceles triangles and squares. The author’s review of recently published mathematics education papers found no use of computing technology in teaching polygonal numbers either at the college or the pre-college levels worldwide. This omission served as a motivation to share and discuss computational algorithms designed by the author for the summation of such numbers within each geometric structure. A method through which those algorithms were used with teacher candidates is based on the technology-immune/technology-enabled problem-solving pedagogy. This method can be recommended for the modern-day teaching of elementary number theory and other mathematical topics across multiple grade levels and educational programs. The activities, supported by Wolfram Alpha and Maple, can be used by instructors of technology-motivated mathematics teacher education courses. The paper argues that the power of digital tools allows future teachers of mathematics, in the context of elementary number theory, to appreciate the use of simple algorithms in achieving sophisticated computational outcomes. Reflective comments of teacher candidates (the author’s students) are shared to indicate the importance of the history of mathematics and the focus on mathematical visualization as a pedagogical approach aimed at conceptual understanding of the subject matter.