Mathematics in a Liberal Arts Program

Riaz Saloojee Seneca College 1

Overview

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

My Background

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

GAS Program

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

Math in GAS

    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 Math is (essentially) a breadth requirement Terminal math course for 80-90% of students 5

Reconceptualizing Math within GAS

    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) Students were disinterested and viewed math as an obstacle/hoop High level of math phobia 6

  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) 7

 Hence, our point of departure from the traditional curriculum (luckily we had the support of a trusting (

too trusting?

) chair) 8

Overview of New Math Curricula

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

  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 10

Successes/Shortcomings

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

 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: – Although focus is on “thinking mathematically” courses don’t necessarily provide content that students may need were they to transfer to technology oriented programs 12

An example unit…

Graph Theory

13