The Mathematician Educator: Volume 5 (2024), Number 2
Contents
7. Flips With Bases Other Than 10 by Derek HOLTON, Paul ULRICK and Alex HOLTON (pp. 63-90)
Derek Holton^*, Paul Ulrick# and Alex Holton#
^ University of Otago, New Zealand
* University of Melbourne, Australia
# Indepent Researcher
Published in The Mathematician Educator, 2024, Vol 5, No. 2, pp 63-90.
Abstract
In 1987 Gardiner wrote a book that contains work on what he called ‘flips’. He considered all flips in base 10. In addition, he made a few considerations to other basses. As far as we know, this has been the only time flips in bases other than base 10 have been discussed. In this paper, we take Gardiner’s work further, considerably aided by the digital production of large numbers of flips. But the result is a little about a lot and the lot covers four areas: the structure of flips, extension of flips, enumeration of flips of a certain kind, and the relation between the numbers of the base, the number of digits and the multiplier of the flip. Because we have considered such a wide range of flips, there are many unresolved questions. We note that this paper, and Gardiner’s work, can be considered to be mathematical research as they both aim to produce new results. Because of this we have added some consideration of the motivation of the different sections of the work and their relation to Gardiner’s work. So, we have tried to give an impression of what aims mathematicians have when doing research and what questions they ask themselves in the process.
8. Two-sidedness of Matrix Inverse: A Proof from Scratch by YAP Von Bing (pp. 91-95)
YAP Von Bing
National University of Singapore, Singapore
Published in The Mathematician Educator, 2024, Vol 5, No. 2, pp 91-95.
Abstract
If n x n matrices A and V satisfy AV=I, then VA=I. This fact is proved using the concepts of linear independence and spanning defined only for n vectors in Rn . The concepts and associated facts then generalise smoothly to any number of vectors, affording a scaffolded approach for learning linear algebra.
9. The Impact of Interactive E-textbook-based Instruction on Higher-order Thinking in Mathematics by Xiaohui LI, Sihang ZHANG and Jijian LU (pp. 96-111)
Xiaohui Li^, Sihang Zhang^ and Jijian Lu^*
^ Jing Hengyi School of Education, Hangzhou Normal University, China
* Institute of China Innovation and Entrepreneurship Education, Hangzhou Normal University, China
Published in The Mathematician Educator, 2024, Vol 5, No. 2, pp 96-111.
Abstract
The use of digital textbooks is an inevitable trend in the future development of mathematics education. The purpose of this study was to explore the effects of interactive electronic textbooks on students’ higher-order thinking skills in mathematics. A quasi-experimental design was employed, wherein two groups comprising a total of 85 students were randomly selected to serve as the experimental group and the control group. The control group was taught using paper textbook, whereas the experimental group underwent teaching grounded in interactive E-textbook. The results of the study showed that the use of interactive E-textbook can effectively promote the development of higher-order thinking in mathematics among secondary school students, and both students and teachers had positive attitude toward interactive E-textbooks, which suggests that educators can experiment with interactive E-textbook as a teaching tool.