Provocations in Mathematics: Teachers’ Attitudes

This study analyses school mathematics teachers’ attitudes towards using provocative mathematics questions in teaching and assessment as a potential pedagogic innovation. By a provocative mathematics question, we mean here a question designed to deliberately mislead the solver. It normally calls for an impossible task. For example, the question might ask for a proof of something that is not provable or show the existence of a solution of an equation that does not have a solution. Often a catch is based on a restricted domain or indirectly prompts the use of a rule, formula, or theorem that is inapplicable due to their conditions/constraints. Five groups of school mathematics teachers did a mini-test consisting of provocative questions. A post-test questionnaire was given to the teachers to obtain their feedback on the possible use of provocative questions in their teaching practice to enhance students’ critical thinking skills. Teachers’ responses are discussed and analysed in the paper

Modelling the Transition from Secondary to Tertiary Mathematics Education: Teacher and Lecturer Perspectives

The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great need for improved communication between the two sectors

The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ

Counter Examples in Calculus

This book makes accessible to calculus students in high school, college and university a range of counter-examples to “conjectures” that many students erroneously make. In addition, it urges readers to construct their own examples by tinkering with the ones shown here in order to enrich the example spaces to which they have access, and to deepen their appreciation of conspectus and conditions applying to theorems

University STEM students' perceptions of creativity in non-routine problem-solving

The primary purpose of this study is to investigate students' perceptions about the characteristics of creativity and engagement in solving non-routine problems. It involved 64 science, technology, engineering, and mathematics (STEM) university students, who participated in a two-year research project in New Zealand during which participants were given opportunities to utilise puzzle-based learning in their courses. Comparing open-ended responses of two surveys, this article focuses on student perceptions about attributes of creativity in non-routine problem-solving. These results have pedagogical implications for tertiary stem education. References A. J. Baroody and A. Dowker. The development of arithmetic concepts and skills: Constructive adaptive expertise. Routledge, 2013. URL https://www.routledge.com/The-Development-of-Arithmetic-Concepts-and-Skills-Constructive-Adaptive/Baroody-Dowker/p/book/9780805831566. S. A. Costa. Puzzle-based learning: An approach to creativity, design thinking and problem solving. implications for engineering education. Proceedings of the Canadian Engineering Education Association (CEEA), 2017. doi:10.24908/pceea.v0i0.7365. N. Falkner, R. Sooriamurthi, and Z. Michalewicz. Teaching puzzle-based learning: Development of transferable skills. Teach. Math. Comput. Sci., 10(2):245–268, 2012. doi:10.5485/TMCS.2012.0304. A. Fisher. Critical thinking: An introduction. Cambridge University Press, 2011. URL https://www.cambridge.org/us/education/subject/humanities/critical-thinking/critical-thinking-2nd-edition/critical-thinking-introduction-2nd-edition-paperback?isbn=9781107401983. E. C. Fortes and R. R. Andrade. Mathematical creativity in solving non-routine problems. The Normal Lights, 13(1), 2019. URL http://po.pnuresearchportal.org/ejournal/index.php/normallights/article/view/1237. P. Gnadig, G. Honyek, and K. F. Riley. 200 puzzling physics problems: With hints and solutions. Cambridge University Press, 2001. URL https://www.cambridge.org/us/academic/subjects/physics/general-and-classical-physics/200-puzzling-physics-problems-hints-and-solutions?format=AR&isbn=9780521774802. J. P. Guilford. Creativity: Yesterday, today and tomorrow. J. Creative Behav., 1(1):3–14, 1967. doi:10.1002/j.2162-6057.1967.tb00002.x. J. P. Guilford. Characteristics of Creativity. Illinois State Office of the Superintendent of Public Instruction, Springfield. Gifted Children Section, 1973. URL https://eric.ed.gov/?id=ED080171. G. Hatano and Y. Oura. Commentary: Reconceptualizing school learning using insight from expertise research. Ed. Res., 32(8):26–29, 2003. doi:10.3102/0013189X032008026. S. Klymchuk. Puzzle-based learning in engineering mathematics: Students\T1\textquoteright attitudes. Int. J.Math. Ed. Sci. Tech., 48(7): 1106–1119, 2017. doi:10.1080/0020739X.2017.1327088. B. Martz, J. Hughes, and F. Braun. Developing a creativity and problem solving course in support of the information systems curriculum. J. Learn. High. Ed., 12(1):27–36, 2016. URL https://files.eric.ed.gov/fulltext/EJ1139749.pdf. Z. Michalewicz, N. Falkner, and R. Sooriamurthi. Puzzle-based learning: An introduction to critical thinking and problem solving. Hybrid Publishers, 2011. B. Parhami. A puzzle-based seminar for computer engineering freshmen. Comp. Sci. Ed., 18(4):261–277, 2008. doi:10.1080/08993400802594089. URL http://www.informaworld.com/openurl?genre=article&id. G. Polya. How to solve it: A new aspect of mathematical method. Princeton University Press, 2004. URL https://press.princeton.edu/books/paperback/9780691164076/how-to-solve-it. M. A. Runco. Creativity: Theories and themes: Research, development, and practice. Elsevier, 2014. URL https://www.elsevier.com/books/creativity/runco/978-0-12-410512-6. A. H. Schoenfeld. Mathematical problem solving. Elsevier, 2014. URL https://www.elsevier.com/books/mathematical-problem-solving/schoenfeld/978-0-12-628870-4. C. Thomas, M. Badger, E. Ventura-Medina, and C. Sangwin. Puzzle-based learning of mathematics in engineering. Eng. Ed., 8(1):122–134, 2013. doi:10.11120/ened.2013.00005. M. O. J. Thomas. Developing versatility in mathematical thinking. Med. J. Res. Math. Ed., 7(2):67–87, 2008. A. Valentine, I. Belski, and M. Hamilton. Developing creativity and problem-solving skills of engineering students: A comparison of web and pen-and-paper-based approaches. Eur. J. Eng. Ed., 42(6):1309–1329, 2017. doi:10.1080/03043797.2017.1291584. G. Wallas. The art of thought. Solis Press, 1926

Modelling the Transition from Secondary to Tertiary Mathematics Education: Teacher and Lecturer Perspectives

The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great need for improved communication between the two sectors

Modelling the Transition from Secondary to Tertiary Mathematics Education: Teacher and Lecturer Perspectives

The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great need for improved communication between the two sectors