1 Mathematics in a Liberal Arts Program Riaz Saloojee Seneca College

2 Overview My background My background GAS program GAS program Math within GAS Math within GAS Reconceptualizing math within GAS Reconceptualizing math within GAS Overview of courses Overview of courses Successes/shortcomings Successes/shortcomings Example of a unit (graph theory) Example of a unit (graph theory)

3 My Background My previous graduate work was in mathematics My previous graduate work was in mathematics Current PhD is in math education Current PhD is in math education –Transition from secondary to college math Taught elementary (grade 5)* Taught elementary (grade 5)* And secondary And secondary Teaching math in GAS for last 5 years Teaching math in GAS for last 5 years

4 GAS Program General Arts & Science (GAS) is predominantly an arts articulation program General Arts & Science (GAS) is predominantly an arts articulation program Large increase in intake in past 5 years (currently about 1000 students) Large increase in intake in past 5 years (currently about 1000 students) Strong focus on humanities and liberal arts Strong focus on humanities and liberal arts

5 Math in GAS Students required to complete a math course in their first semester Students required to complete a math course in their first semester Placed in one of 3 math courses based on CPT results and math background Placed in one of 3 math courses based on CPT results and math background Math is (essentially) a breadth requirement Math is (essentially) a breadth requirement Terminal math course for 80-90% of students Terminal math course for 80-90% of students

6 Reconceptualizing Math within GAS 5 years ago – courses offered: fundamentals of math, basic algebra, intermediate algebra, calculus 5 years ago – courses offered: fundamentals of math, basic algebra, intermediate algebra, calculus Curriculum was a regurgitation of topics covered in high school (more of the same) Curriculum was a regurgitation of topics covered in high school (more of the same) Students were disinterested and viewed math as an obstacle/hoop Students were disinterested and viewed math as an obstacle/hoop High level of math phobia High level of math phobia

7 Began to ask: Began to ask: –Why are students required to take math? –Why this particular math content? –What is it we really want students to get from a one-semester, terminal course? Some answers: to foster a “mathematical way of knowing”; gain an appreciation of its cultural importance; (mostly) to engage in (to do) some mathematics of interest to students (to have that mathematical aesthetic experience) Some answers: to foster a “mathematical way of knowing”; gain an appreciation of its cultural importance; (mostly) to engage in (to do) some mathematics of interest to students (to have that mathematical aesthetic experience)

8 Hence, our point of departure from the traditional curriculum (luckily we had the support of a trusting (too trusting?) chair) Hence, our point of departure from the traditional curriculum (luckily we had the support of a trusting (too trusting?) chair)

9 Overview of New Math Curricula New courses are a “survey” of some topics in discrete math, combinatorics and number theory New courses are a “survey” of some topics in discrete math, combinatorics and number theory Content areas: Content areas: –Graph (network) theory –Voting methods –Number theory (intro to coding theory) –Probability –Game theory

10 Approach: Approach: –to engage students in meaningful mathematics through discovery, problem solving, and discussions –Problem-centred –Small group work –Strong emphasis on exploration, discussion and explanations –Greater focus on conceptual understanding than procedural competency These topic areas lend themselves nicely to this approach These topic areas lend themselves nicely to this approach

11 Successes/Shortcomings Much higher level of student engagement and interest Much higher level of student engagement and interest Levels the playing field (mathematical backgrounds) Levels the playing field (mathematical backgrounds) Importance of subject clearly evident (topics always related to current work and contemporary applications) Importance of subject clearly evident (topics always related to current work and contemporary applications) My increased enjoyment teaching this content My increased enjoyment teaching this content

12 Students have a rich experience and increased self-efficacy with mathematics Students have a rich experience and increased self-efficacy with mathematics –“I never thought math could be interesting or that I could be good at it.” (these are related) Shortcoming: Shortcoming: –Although focus is on “thinking mathematically” courses don’t necessarily provide content that students may need were they to transfer to technology- oriented programs

13 An example unit… GraphTheory