Are we disconnected from the XXIst Century student?

This project is conducted as part of a Master's degree in mathematics at Université de Montréal under the co-supervision of France Caron (Département de didactique) and Yvan Saint-Aubin (Département de mathématiques et de statistique).

http://wiki.ubc.ca/Science:Math_Exam_Resources

is a digital educational resource for undergraduate students created mainly by a volunteer committee consisting of graduate students at UBC. We will first briefly demonstrate the wiki, its associated mobile application and present usage statistics. In particular, we will talk about how innovative use of MediaWiki technology allowed us to turn what started as an exam database into a year-round interactive study aid. We will then discuss how this online resource has the potential to transform how students engage with undergraduate mathematics. We conclude with a discussion of our current and future directions for research and how we believe that this innovation can change course design and curricula.

The Department of Mathematics and Statistics at Brock University adapted its undergraduate program in 2001 in a way that addresses the need mentioned by the EMS. In a sequence of three core mathematics courses, all mathematics majors and future mathematics teachers learn to use computer programming for simulation and investigation of mathematics concepts, conjectures, and real-world modeling. In this presentation, I will discuss the integrated teaching model used at Brock (students learn computer programming within the mathematics courses), including a short report of students’ views on the nature of these courses as well as their views on competencies developed (survey study, N=56).

European Mathematical Society (2011), Position Paper of the European Mathematical Society on the European Commission’ s Contributions to European Research [online]. Available: http:$//$www.euro-math- soc.eu$/$files$/$EMSPosPaper13$\_$03$\_$2011$\_$NP .pdf

In my presentation, I will present my reflections on the challenges posed by the availability of new technologies for some of our teaching and how we addressed it in some of our courses, including large service courses. I will also share my reflections on some of the differences between mathematics and other sciences which may be relevant for our discussions.

(*) The claims in this abstract are, perhaps, no longer true; the abstract itself is the result of paraphrasing mathematics education reports and papers appeared over the last 75 years. I will reveal what was said when at the talk–let’s say for now that some essential questions have not changed; they remain unanswered and mostly unaddressed.

My concern is that many students graduating from universities today are familiar with formal algorithmic procedures to solve mathematical problems while they are often unable to explain and justify them or connect them to more intuitive constructions because the students were never exposed to these ideas. \newline

I give examples illustrating that some old, elementary, yet insightful mathematical methods and facts remain effectively concealed from students studying mathematics today. I argue that while it is important for students to know modern approaches, their education should also include experiences highlighting preceding ideas related to these advanced methods. Building on a proper combination of modern and old ideas is essential for students to develop flexible thinking and use mathematics for modeling real life phenomena. Otherwise, they will tend to stick to procedural techniques and will not fully appreciate the results of modern approaches because of lost connections to old but enlightening mathematics.

"A fairly accurate picture of undergraduate mathematics is that, by and large, it is still dominated by the ‘chalk-and-talk’ paradigm, a careful linear ordering of course content, and assessment that is heavily based on final examination. Even the highly publicized ‘computer revolution’ has not really made a sweeping impact on mathematics. … That said mathematics in 1999 looks a lot more like mathematics in 1939 than is the case with any of its sister sciences." (p.64)

Furthermore, Hillel (2002) adds that, "Steen has written that ‘strong departments find that they replace or change significantly half of their courses approximately once a decade’ and ‘as new mathematics is continually created, so mathematics courses must be continually renewed’ (Steen 1992). These on-going updates to the curriculum can be regarded, in a sense, as ‘deterministic’ aspects of curriculum change, ones that do not put into question the purpose, goals, and means of undergraduate education." (p. 61)

In this mathematics education session, we will reflect and criticize on the present-day university curricula and think about possible directions for the near future.

Hillel, J. (2002). “Trends in curriculum” in The Teaching and Learning of Mathematics at University Level, D. Holton, Ed. Springer Netherlands, pp. 59-69.

Most first year students in Natural Sciences, Business and Education are required to take Calculus. For many of them, Calculus seems unrelated to their career ambitions. So, we must really ask ourselves, are there other potential avenues to get students thinking, investigating and problem solving in mathematics?

I will suggest course content, structure and objectives of a potential problem solving course. The course I am suggesting would be targeted to non-math majors and focus on solving problems strategies, frameworks and practice of open ended non-routine problems. I will also detail universities in Ontario that offer similar courses.

Reference:

Strother, S., Campen, J. V., and Grunow, A. (2013). Community college pathways: 2011-2012 Descriptive report. Retrieved December 1, 2013. from $\verb"http://www.carnegiefoundation.org/sites/default/files/CCP_Descriptive_Report_Year_1.pdf"$.