## New and Improved Algebra for Honours Mathematics

The Faculty of Mathematics made some big changes to the delivery of MATH 135: Algebra for Honours Mathematics beginning in fall 2015.

MATH 135 is a foundational course for students in the Faculty, yet too many were struggling to learn the material. Students’ needs and capabilities coming into university have changed. Modifications to high school curricula required a different strategy for the delivery of this course. The time had come to try something new to improve student outcomes and their intellectual stamina in learning mathematics.

In the fall 2015 term, 15 instructors led by Professor J.P. Pretti implemented a different version of the course for 1450 first-year students. By the end of the term, the median mark in the course was over 80% and approximately 90% of the students who had begun the course in September completed it with a mark of at least 60, allowing them to continue on to the next algebra course. All of this was accomplished while maintaining the academic rigour students expect at Waterloo.

MATH 135 is centered on proof, the defining property of mathematics. Proof defines the transition from high school to university mathematics. It must be thoroughly understood for students to be successful in their upper year math courses.

**What changed?**

Classes were smaller. Instead of 180 students, MATH 135 was offered in sections of just 60 students. Instructors got to know their students by name, and provide more one-on-one support during office hours. Smaller classes also helped the students to better connect and help each other. In-class participation increased, along with attendance. Instructors found that being able to call on the students by name made them more comfortable offering answers.

The classes met four times a week with their primary instructor, instead of the previous model of three times a week plus an hour tutorial with a teaching assistant. Lectures were designed so that there was time devoted to working through and discussing in-class exercises. This transition meant more preparation time for the instructors, but they were happy to see that the new approach worked. The students were pushed further, in terms of the difficulty of assignments and exams, yet showed a more solid understanding of the material.

MATH 135 moved away from a ‘sage on the stage’ model of lecturing to more active learning and student engagement. Instead of just listening to an instructor present the course material while they took notes, the students worked through problems in class. Spending this in-class time practicing proofs helps instill confidence. When students believe they can do it, they enjoy the material more and are ready to tackle even the most challenging assignment questions and exams.

In-class instruction was supplemented with a lively MATH 135 online discussion through Piazza. There were over 10,000 posts over the term for this course alone. The students weren’t just on Piazza asking for help. They were also chiming in to support classmates with questions, and offering insightful comments on the course material.

Increasing student engagement and active learning with these changes to MATH 135 was a very successful experiment. Not only were the grades better overall, but instructors noted that students seemed to show more interest in the material and to enjoy the course more.

MATH 135 instructors were pleased with the outcome of the course delivery transition, and they credit Professor J.P. Pretti’s leadership for its success. His collegiality and organization were noted by his colleagues, who also appreciated his trouble-shooting and clear direction.