Assessment Case Study - Math Inquiry Project
Ashley Weleschuk, Taylor Institute for Teaching and Learning
July 10, 2018
“Most students come in with some curiosity about what mathematics can be… This project gives them the opportunity to explore that” -Dr. Kristine Bauer
Dr. Kristine Bauer is an Associate Professor in the Department of Mathematics at the University of Calgary. She teaches courses on a variety of topics and levels. One course is Math 205: Mathematical Explorations, a course intended to survey a variety of topics in mathematics and its interactions with society. As this course is recommended for elementary education majors, they make up about half of the 100 students in the class each semester. Others come from a wide variety of backgrounds and majors. They take the course because they are curious about math, and want to explore it further. Kristine redesigned the course from a survey of unique math topics to one with a focus on case studies, applications, and mathematics communications. She teaches standard topics, but she uses popular media and specific cases to demonstrate their relevance. There are ongoing assignments in the course to help develop problem-solving skills, but Kristine also wanted to give students an opportunity for inquiry and exploration, so she introduced a large group project.
Most of the course topics are familiar to students from their junior high and high school math classes, but Kristine presents them in an interesting way. She was inspired by the textbook “Case Studies for Quantitative Analysis”, which connects different mathematical concepts to popular culture and different disciplines. While its examples are somewhat dated, she was able to follow the format for introducing the content to students. She has collected more current case studies outside of the textbook and uses them to analyze course topics. For example, while learning about functions, students read an article about how Pixar animated the main character in the film Ratatouille to make him sympathetic, rather than repulsive, even though he is a rat. They then have a group discussion about how simple functions to achieve certain shapes. After the discussion, students get to generate emoji faces using simple computer algebra packages they access online.
Their final project follows the same format. Students are put in small groups and asked to select a math topic and write a short chapter on it that could fit in the textbook. Their chapters include an explanation of the topic, sample problems, a related case study, questions, and an analysis associated with it. It is worth 50% of the course grade, but it is broken down into components that are due at different points throughout the semester.
Their first exercise is creating a team contract. Kristine forms the groups herself, to ensure they are balanced and diverse. Students start working together on in-class discussions and small activities right away. The contract is a written agreement that holds students accountable to their group members. This helps to prevent major disputes within groups, as they have specifically laid out tasks for each member to do. While this does not eliminate all team issues, it gives groups a starting point for discussion if problems do come up. It also gives students a chance to work on something together before starting their project. The first time Kristine taught the course, the team contracts were introduced before the teams had worked together at all, so they were not as meaningful and effective as they could have been. This year, since students already were getting to know one another, they were able to make their contracts substantive and useful.
The next component is a proposal of their topic and a related article. This is an opportunity for students to get feedback on their approach and thinking. Kristine finds it is a good way to make sure that all the groups start off in the right direction. The proposal is due a few weeks into the semester, so that students can start working on the project early and do not forget about it until the end of the semester.
Draft and Peer Feedback
Around two weeks before the due date, students bring a draft of their final product for another group to evaluate. Kristine admits that the peer feedback component was not as helpful as expected, mainly due to the project rubric. She tried to divide it into several sections and add as much detail as possible, but students were overwhelmed. Many did not even read it in its entirety so their peer feedback was not helpful. Kristine hopes that by simplifying the rubric and giving students more opportunities to practice giving feedback, this portion of the project will improve in the future.
Students submit their final product on the last day of classes. As previously mentioned, it contains a description of the mathematical concept, sample problems with solutions, the related media article, and quantitative analysis questions. They have a lot of freedom for the topics they choose, since math can be applied in so many different fields.
Students can divide the work in different ways, depending on the strengths and weaknesses of their group members. Some groups divide the work and each person does a separate component, while others collaborate on each section. Both methods are effective when students are committed and working together. Groups benefit from having so many different perspectives. Kristine recalls one group that chose a calculus topic for their project, despite some of the group members not having a calculus background. Those who knew the concepts wrote out the explanation and exercises, and those who did not were able to easily find gaps in their work if they did not understand it. This led to an incredibly strong final project.
Kristine is impressed by most of the student projects, although she does want to increase the focus on the mathematical concepts in the future. Students come up with creative and unique ideas for the project. For example, one group used the surface area concepts to compare the density of trees in Banff National Park in regular maps to topographic ones. Students are able to embrace their curiosity and interests while still applying math skills.
Students have good experiences in the course and give positive feedback. Kristine intends to keep making changes every year based on student feedback and her personal observations. She believes that courses are never static and that they will evolve over time. While she admits that the project was not perfect either time she ran it, she is very happy that she introduced the project and is excited to see how it progresses. She encourages other instructors to take chances and try new things in their courses, and to allow them to develop over several iterations.