Mathematics, technology and curriculum: a complex interaction Frédéric Gourdeau Université Laval, Québec, Canada

Outline Our students – a brief description The doing of mathematics – a vignette (H. Bass) Providing experiences for students Technology : challenges and opportunities Resistance to change F. Gourdeau, SMC 2014

Our students Cegep : grades 12 and 13; calculus, linear algebra Engineering students Pre-service teacher education Mathematics major – Cegep teaching – Graduate work in maths or other subject area F. Gourdeau, SMC 2014

The doing of mathematics Hyman Bass (2011), A Vignette of Doing Mathematics: A Meta-cognitive Tour of the Production of Some Elementary Mathematics. F. Gourdeau, SMC 2014

A brief description : when we do mathematics, we… Question Explore Represent Look for structure conjectures or new questions. Consult, if we’re stuck: others, the literature, the web. F. Gourdeau, SMC 2014

Connect with other mathematics, through our research, reflection, analogies. Seek proof, to prove or disprove our conjectures. Often this proceeds by breaking the task into smaller pieces, for example by formulating, or proving, related, hopefully more accessible, conjectures, and showing that the main conjecture could be deduced from those. F. Gourdeau, SMC 2014

Can be opportunistic, letting the mathematics guide us if we see inviting trails. Prove, writing a finished exposition of the proof (if one is found), using illuminating representations of the main ideas, meeting standards of mathematical rigor, and crafted to be accessible to the mathematical expertise of an intended audience. F. Gourdeau, SMC 2014

Analyze proofs, which even if they are conceived of as a means to an end, are a product worthy of note and study, since the theorem typically distills only a small part of what the proof contains. Use our sense of aesthetics and taste, associated with words like elegance, precision, lucidity, coherence, unity. F. Gourdeau, SMC 2014

Reforming our curriculum For pre-service teachers, since the early 90’s – Emphasis on the doing of mathematics – Problem solving – Culture – Deconstructing packed formulae – Finding accessible answers to “why?” – And seeing when a “why” should be a “what” F. Gourdeau, SMC 2014

What helped to make it possible CMESG Few courses, did not impact of most Faculty Flexibility in our institutional rules People – Hodgson – Cassidy F. Gourdeau, SMC 2014

New technologies – Secondary school use it : it pushed us – Fits well in the “doing” – Presentation, team work: this has value However – Pre-service teachers: afraid of programming, and have used surprisingly little technology – Problems of assessment F. Gourdeau, SMC 2014

Reforming our curriculum For maths majors, in the early 90’s – Final year project – History of mathematics – Presentation Since – More on communication, some work as a program – Team work : very little F. Gourdeau, SMC 2014

Personal impressions Resistance to change in the curriculum – Mathematics is highly structured – Mathematical language is very compact, built on abstractions – Being lost in mathematics is so easy F. Gourdeau, SMC 2014

Personal impressions Resistance to a more important use of technology – Assessment of the work – Team work : who gets the grade – Hard work for “us” if we change Time, recognition – We are not used to be told how we should do things in class : give us the content, let us do the rest – We are not used to adopt a program approach F. Gourdeau, SMC 2014

Some successes R for engineers – Technology to teach technology Maple/Matlab – Important work in two service courses F. Gourdeau, SMC 2014

Math majors Prepare for graduate work and/or for teaching at Cegep More traditional approach F. Gourdeau, SMC 2014

Technology Maple, Geogebra, Fractint, Matlab, R Used in many courses, not as an objective but as a mean F. Gourdeau, SMC 2014

Thanks F. Gourdeau, SMC 2014