logo logo European Journal of Mathematics and Science Education

EJMSE is is a, peer reviewed, online academic research journal.

Subscribe to

Receive Email Alerts

for special events, calls for papers, and professional development opportunities.


Publisher (HQ)

Eurasian Society of Educational Research
7321 Parkway Drive South, Hanover, MD 21076, USA
7321 Parkway Drive South, Hanover, MD 21076, USA
points mathematics social mathematics realistic mathematics education adults learning mathematics context

Phenomenology of Points Mathematics

Eric Fredua-Kwarteng , Francis Ahia

This is a preliminary paper about a large research project on social mathematics. It proposes points mathematics, a variant of social mathematics, as .


This is a preliminary paper about a large research project on social mathematics. It proposes points mathematics, a variant of social mathematics, as a viable context for teaching mathematics to adults. Points mathematics, focuses on observing, representing and investigating patterns, regularities and quantitative relationships stemming from convertible points, that businesses offer to their customers/clients for the purpose of encouraging loyalty and for boosting up sales in competitive markets. Using ten illustrative examples, the paper asserts that points mathematics provides practical, realistic context for teaching fundamental mathematics concepts and skills to adult students. These include, but not limited to, the four operations of mathematics (addition, division, subtraction and multiplication), variable, linear equation, graph, rates, percent, ratio, patterns and proportion. The paper is grounded in the theory of realistic mathematics education (RME), that posits that the teaching and learning of mathematics should be contextually-based; entails explaining and solving contextual problems; and establishing high-level interactive relationship between learning and teaching. The paper concludes with three recommendations to guide mathematics teachers of adults who want to implement points mathematics as part of their mathematics curriculum. However, the paper is the first phase of a large research project that explores social mathematics and how it could be integrated in mathematics curricular contents for adult students.

Keywords: Points mathematics, social mathematics, realistic mathematics education, adults learning mathematics, context.

cloud_download PDF
Article Metrics


Baker, D. (2009). Using sand to count their number: Developing teachers' cultural and social sensitivities. WAALC. http://www.waalc.org.au/09Conf/docs/

Baker, D., Street, B., & Tomlin, A. (2008). Navigating numeracies: Home-School numeracy practices. Springer.

Balomenou, L., & Totsis, K. (2017, July 2-5). Adults solving realistic problems [Paper presentation].  ALM International Conference, Rotterdam, The Netherlands.

Barnes, H. (2004) Realistic mathematics education: Eliciting alternative mathematical conceptions of learners. African Journal of Research in Mathematics, Science and Technology Education, 8(1), 53-64. https://doi.org/10.1080/10288457.2004.10740560

Barnes, H. (2005). The theory of Realistic Mathematics Education as a theoretical framework for teaching low attainers in mathematics. Pythagoras, (61), 42-57. https://doi.org/10.4102/pythagoras.v0i61.120

Brooks, C. (2015). Making maths useful: How two teachers prepare adult learners to apply their numeracy skills in their lives outside the classroom. Adults Learning Mathematics: An International Journal, 10(1), 24-39.

Budd, C. (2018, July 1-3). Inspiring mathematics [Paper presentation]. ALM International Conference, London, UK.

Colwell, D., Duffin, J., & Elliott, S. (1998, July1-3). Whose numeracy? [Paper presentation]. ALM Utrecht, The Netherlands.

Dickinson, P., & Hough, S. (2012). Using realistic mathematics education in UK classrooms. Realistic Mathematics Education. 

Denvir, B., Stolz, C., & Brown, M. (1982). Low attainers in mathematics, 5-16: Policies and practices. Methuen Educational.

Ernest, P. (2002). Empowerment in mathematics education. Philosophy of Mathematics Education Journal, (15), 1-16.

Evans, J., Wedege, T., & Yasukawa, K. (2013). Critical perspectives on adult mathematics education. In M. A. Clements, A. Bishop, C. Keitel & J. Kilpatrick (Eds), Third International Handbook of Mathematics Education (pp.203-242). Springer.

Evans, J., Yasukawa, K., Mallows, D., & Creese, B. (2017). Numeracy skills and the numerate environment: Affordances and demands. Adults Learning Mathematics: An International Journal, 12(1), 17-26.

Fauzan, A., Slettenhaar, D., & Plomp, T. (2002). Traditional mathematics vs. realistic mathematics education: Hoping for changes? In P. Valero & O. Skovsmos (Eds), Proceedings of the 3rd international mathematics educational society conference (pp.1-4). Centre for Research in Learning Mathematics.

FitzSimons, G., & Godden, G. L. (2000). Review of research on adults learning mathematics.In D. Coben, J. O'Donoghue & G. FitzSimons (Eds), Perspectives on Adults Learning Mathematics (pp.13-46). Kluwer Academic Publishers.

Freudenthal, H. (1971). Geometry between the devil and the deep sea. Educational Studies in Mathematics, 3, 413-435.

Freudenthal, H. (1973). Mathematics as an educational task. Reidel Publishing Company.

Fredenthal, H. (1991). Revisiting Mathematics Education: China Lectures. Kluwer.

Gerger, E. (2014). Implications of social practice theory for the development of a numeracy programme. ALM International Journal, 9(2), 85-96.

Glasser, T. (2011). Investigating meaning in learning: A case study of adult developmental mathematics. Adults Learning Mathematics: An International Journal, 6(2), 42-77.

Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39,111-129.

Gravemeijer, K., & Terwel, J. (2000). Han Freudenthal: A mathematician didactic and curriculum theory. Journal of Curriculum Studies, 32(6), 777-796.

Gustafsson, L and Mouwitz, L. (2003).Adults and Mathematics-A Vital Subject. National Center for Mathematics Education (NCM).

Herges, R. M., Duffield, S., Martin, W., & Wageman, J. (2017). Motivation and achievement of middle school mathematics students. The Mathematics Educator, 26(1), 83-106.

Hoyles, C.,Noss, R., & Pozzi, S. (2001). Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32, 4-27.

Kelly, B. (2019). Motivating adults to learn mathematics in the workplace:A trade union approach. International Journal of Lifelong Education, 38(2), 132-147.

Leonelli, D. E. (1999). Teaching to the math standards with adult learners. Focus on Basics Connecting Research & Practice, 3(C).

Maloney, J. R. (2014). Teaching functions using a realistic mathematics education approach: A theoretical perspective. International Journal of Educational Sciences, 7(3), 653-663.

Mendick, H. (2015). Using popular culture to teach maths. Philosophy of Mathematics Education Journal, (29).

Morgan, D. (2017). Using culturally relevant teaching in a co-educational mathematics class of a patriarchal community. Educational Studies in Mathematics, 94, 293-307

Nonesuch, K.(2006). Changing the way we teach math: A manual for teaching basic math to adults. Malaspina University-College.

Ngu, B. H., & Phan, H. P. (2016). Comparing balance and inverse methods on learning conceptual and procedural knowledge in equation solving: A cognitive load perspective. Pedagogies: An International Journal, 11(1), 63-85.

Povey, H. (2010). Teaching for equity, teaching for mathematical engagement. Philosophy of Mathematics Education Journal, (25).

Swanson, D., & Williams, J. (2014). Making abstract mathematics concrete in and out of school. Educational Studies in Mathematics, 86, 193-209.

Theodora, N. R. F., & Hidayat, D. (2018). The use of realistic mathematics education in teaching the concept of algebra. Journal of Holistic Mathematics Education, 1(2), 104-113.

Thompson, T. (2006). Teaching for social mathematics: Exploring the collaborative role of social studies and mathematics educators. Social Studies Research and Practice Journal, 1(2), 272-283.

Traders, A. (1987). Three dimensions: A model of God and theory description on mathematics: The Wiskobas Project. Reidel.

Yuanita P., Zulnaidi H, & Zakaria, E. (2018). The effectiveness of Realistic Mathematics Education approach: The role of mathematical representation as mediator between mathematical belief and problem solving. PLOS ONE, 13(9), e0204847. https://doi.org/10.1371/journal.pone.0204847

Ulandari, L., Amry, Z., & Saragih, S. (2019). Development of learning materials based on realistic mathematics education approach to improve students' mathematical problem-solving ability and self-efficacy. International Electronic Journal of Mathematics Education, 14(2), 375-383.

Viskic, D., & Petocz, P. (2006). Adult students views of mathematics: Reflections on projects. Adults Learning Mathematics: An International Journal, 1(2), 6-15.

Wedege, T., Benn, R., & Maasz, J. (1998, July 1-3). ALM as a community of practice and research [Paper presentation]. ALM conference, Utrecht, The Netherlands.

Wedege, T. (1999). To know or not to know -mathematics that is a question of context. Educational Studies in Mathematics, 39, 205-227. https://doi.org/10.1023/A:1003871930181

Wedege, T. (2010). The problem field of adults learning mathematics. In G. Griffith & D. Kaye, (Eds.), Numeracy works for life: Proceedings of the 16th International Conference of Adults Learning Mathematics- A Research Forum (ALM). (pp.13-24). Adults Learning Mathematics (ALM) and London South Bank University.