# Student-Generated Examples and Group Work in Mathematics

## DOI:

https://doi.org/10.21100/msor.v19i1.1117## Keywords:

Student-generated examples, problem posing, collaborative learning, student perspective, assessment for learning.## Abstract

An assignment from Higher Education is presented within this paper as a case study of students generating their own examples whilst working in groups. The student perspective was gained through a questionnaire at the end of the assignment with each cohort over a three year period, which was completed by 123 students in total. The students provided insight on creating their own examples, as well as the group work aspect of the assignment. In particular, students indicated what they believe to be the most beneficial assessment approaches. Elements of learning, understanding and motivation are explored, and the student perspective is compared with the literature.Â## References

Ahn, R. and Class, M., 2011. Student-centred pedagogy: co-construction of knowledge through student-generated midterm exams. International Journal of Teaching and Learning in Higher Education, 23(2), pp. 269-281. Available via https://files.eric.ed.gov/fulltext/EJ946152.pdf (last accessed 10 June 2020)

Anderson, J. R., Reder, L. R. and Simon, H. A., 1996. Situation learning and education. Educational Researcher, 25(4), pp. 5-11 DOI: 10.3102/0013189X025004005

Anthony, G. and Walshaw, M., 2007. Effective pedagogy in mathematics. Educational Practices Series-19. International Academy of Education & International Bureau of Education. Available via http://www.ibe.unesco.org/fileadmin/user_upload/Publications/Educational_Practices/EdPractices_19.pdf (last accessed 10 June 2020)

Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A. and Zaslavsky, O., 2006. Exemplification in Mathematics Education. In J. NovotnÃ¡, H MoraovÃ¡, M KrÃ¡tkÃ¡ & N StehlÃkovÃ¡, eds. Proceedings of the 30th International Group of the Psychology of Mathematics Education (Vol. 1, pp. 1-125). Prague, Czech Republic: Charles University in Prague, Vol 1, pp. 1-125 Available via: http://mcs.open.ac.uk/jhm3/PME30RF/PME30RFPaper.pdf (last accessed 10 June 2020)

Chang, K.-E, Wu., L.-J., Weng, S.-E. and Sung, Y.-T., 2012. Embedding game-based problem-solving phase into problem-posing system for mathematics learning. Computers and Education, 58(2), pp.775-786 DOI: 10.1016/j.compedu.2011.10.002

Cornock, C., 2015. Teaching group theory using Rubik's cubes. International Journal of Mathematical Education in Science and Technology, 46(7), 957-967 DOI: 10.1080/0020739X.2015.1070442

Deslauriers, L., McCarty, L.S., Miller, K., Callaghan, K. and Kestin, G., 2019. Measuring actual learning versus feeling of learning in response to being actively engaged in the classroom, PNAS 116(39) pp. 19251-19257 DOI: 10.1073/pnas.1821936116

Dahlberg, R.P. and Housman, D.L., 1997. Facilitating learning

events through example generation. Educational Studies in Mathematics,33(3), pp. 283-299 DOI: 10.1023/A:1002999415887

Fried, M. N., 2006. Mathematics as a constructive activity: learners generating examples. ZDM, 38(2), pp. 209-211 DOI: 10.1007/BF02655890

Hargreaves, E., 2007. The validity of collaborative assessment for learning. Assessment in Education: Principles, Policy and Practice, 14(2), pp. 185-199 DOI: 10.1080/09695940701478594

Laal, M. and Ghodsi, S.M., 2012. Benefits of collaborative learning. Procedia - Social and Behavioral Sciences 31, pp. 486-490 DOI:10.1016/j.sbspro.2011.12.091

Lawson, M.V., 2004. Finite Automata. Chapman & Hall / CRC

Lithner, J., 2012. Learning Mathematics by Creative or Imitative Reasoning. In S. Cho, eds. Selected Regular Lectures from the 12th International Congress on Mathematical Education. Springer, Cham pp. 487-506 DOI: 10.1007/978-3-319-17187-6_28

Marton, F. and SÃ¤ljÃ¶, R., 2005. 'Approaches to Learning'. In: Marton, F., Hounsell, D. and Entwistle, N., eds. The Experience of Learning: Implications for teaching and studying in higher education. 3rd (Internet) edition. Edinburgh: University of Edinburgh, Centre for Teaching, Learning and Assessment. pp. 106-125. Available via: http://www.docs.hss.ed.ac.uk/iad/Learning_teaching/Academic_teaching/Resources/Experience_of_learning/EoLChapter3.pdf (last accessed 10 June 2020)

Smith, G. and Wood, L., 2000. Assessment of learning in university mathematics. International Journal of Mathematical Education in Science and Technology, 31(1), pp. 125-132 DOI: 10.1080/002073900287444

Silver, E.A., 1994. On mathematical problem posing. For the Learning of Mathematics, 14(1), pp. 19-28 Available via: https://www.researchgate.net/profile/Edward_Silver2/publication/284047623_On_mathematical_problem_posing/links/575988b308ae9a9c954f06f1/On-mathematical-problem-posing.pdf (last accessed 10 June 2020)

Smith, G., Wood, L., Coupland, M., Stephenson, B., Crawford, K. and Ball, G., 1996. Constructing mathematical examinations to assess a range of knowledge and skills. International Journal of Mathematical Education in Science and Technology, 27(1), pp. 65-77 DOI: 10.1080/0020739960270109

Stefanou, C.R., Perencevich, K.C., DiCintio, M. and Turner, J.C., 2004. Supporting Autonomy in the Classroom: Ways Teachers Encourage Student Decision Making and Ownership. Educational Psychologist, 39(2), pp. 97-110 DOI: 10.1207/s15326985ep3902_2

Stiggins, R., 2007. Assessment for learning: an essential foundation of productive instruction. In D.B. Reeves, eds. Ahead of the Curve: The Power of Assessment to Transform Teaching and Learning. Bloomington IN: Solution Tree Press, pp.59-76.

TichÃ¡, M and HoÅ¡pesovÃ¡, A., 2009. Problem posing and development of pedagogical content knowledge in pre-service teacher training. Proceedings of CERME (Vol. 6, pp. 1941-1950). Lyon, France. Available via: https://pdfs.semanticscholar.org/3320/5b6705c524c17c18ef505d28457c6d735568.pdf?_ga=2.224026259.923145160.1591807633-498329837.1591807633 (last accessed 10 June 2020)

Watson, A. and Mason, J., 2002a. Extending example spaces as a learning/teaching strategy in mathematics. In A. Cockburn and E. Nardi, eds. Proceedings of the 26th Conference of the International Group of the Psychology of Mathematics Education. Norwich, UK: University of East Anglia, Vol 4, pp. 377-385 Available via: http://mrbartonmaths.com/resourcesnew/8.%20Research/Inquries/Extending%20Example%20Spaces%20-%20Watson%20and%20Mason.pdf (last accessed 10 June 2020)

Watson, A. and Mason, J., 2002b. Student-generated examples in the learning of mathematics. Canadian Journal of Math, Science and Technology Education, 2(2), pp. 237-249 DOI: 10.1080/14926150209556516

Wiliam, D., 2011. What is assessment for learning? Studies in Educational Evaluation, 37(1), pp. 3-14 DOI: 10.1016/j.stueduc.2011.03.001