MathEd Forum-Jan 25, 2025: Potential for Integrating Modeling in CÉGEP to Develop Critical Thinking

Summary

The speaker discusses the intersection of math modeling, critical thinking, and education, focusing on the impact of these concepts during the COVID-19 pandemic. They explore how math modeling was used in public health projections and its relevance in pre-university curricula. The speaker examines how critical thinking and math modeling are integrated (or not) into scientific and mathematical education, highlighting the challenges faced by math educators. Their research with eight math professors shows a gap in training and varying attitudes towards math modeling, while also acknowledging the difficulties teachers face with integrating technology and complex mathematical concepts into their teaching.

Takeaways

• 😀 The speaker discusses the importance of math modeling and critical thinking, particularly in relation to COVID-19 data and predictions.
• 😀 The speaker highlights the polarization between public health officials and political figures during the pandemic, and how it affected public perceptions.
• 😀 The speaker emphasizes the need for citizens to validate information from media sources using tools like critical thinking and math modeling.
• 😀 The curriculum for scientific tracks in pre-university programs (e.g., for medicine or nursing) does not explicitly address critical thinking or mathematical modeling.
• 😀 Critical thinking is often mentioned in humanities subjects, like philosophy and literature, but is less emphasized in the sciences and math courses.
• 😀 The speaker finds that math modeling is typically not covered in the scientific curriculum, though it is more often included in human sciences tracks, though in a limited scope.
• 😀 The speaker's research objectives include exploring how math modeling can integrate critical thinking into the math curriculum and understanding the relationship between math teachers and math modeling.
• 😀 Theoretical frameworks used in the study include the math modeling cycle and a framework of critical thinking competencies.
• 😀 The study revealed that many teachers were confused about what math modeling entails, often seeing it as a simple application rather than a complex process.
• 😀 Teachers were often not familiar with mathematical modeling in practice, despite having mathematical training, which led to a disconnect between theory and practice in the classroom.
• 😀 Some teachers, despite being enthusiastic about the real-world applications of math modeling, found it challenging to integrate technology and new methods, such as simulation tools like Insight Maker, into their teaching practices.

Q & A

What motivated the speaker to explore the role of mathematical modeling during the COVID-19 pandemic?

The speaker was motivated by the need to understand how mathematical modeling could help citizens critically assess COVID-19 data and media narratives. They wanted to bridge the gap between public health communications and public perception, particularly during polarized times.

How did the speaker distinguish between the roles of public health officials and political officials in managing COVID-19?

The speaker noted that while public health officials, such as those in Quebec, used scientific models to inform decisions, political figures were often perceived as driving measures for political reasons. This led to public confusion and frustration.

What are the two key tools the speaker suggests for evaluating public health data and decisions?

The two key tools are critical thinking and mathematical modeling. The speaker emphasized that these tools help individuals assess and validate the information presented, especially when dealing with complex situations like the COVID-19 pandemic.

What did the speaker find regarding the teaching of critical thinking and mathematical modeling in pre-university math curricula?

The speaker observed that critical thinking was not explicitly taught in most science-related curricula, with only a few exceptions in philosophy, French, and English literature courses. Moreover, mathematical modeling was largely absent in science tracks, even though it was included in some human sciences courses, but with a narrow focus on simple optimization problems.

What were the speaker's research objectives in examining mathematical modeling and its integration into math curricula?

The speaker aimed to explore whether mathematical modeling could help integrate critical thinking into math curricula and to investigate the relationships between pre-university math teachers and mathematical modeling, including their familiarity with and perceptions of it.

How did the speaker use theoretical frameworks to guide their research on math modeling?

The speaker used two theoretical frameworks: the math modeling cycle developed by their professor and a framework on critical thinking, focusing on competencies and subcompetencies. They also explored teachers' perceptions of knowledge using a concept that categorized knowledge into epistemic, identity, and social dimensions.

What methodology did the speaker use to gather data on math teachers' perceptions of mathematical modeling?

The speaker conducted interviews with eight math professors, which included two meetings. The first meeting aimed to understand their relationship with mathematical knowledge, while the second involved modeling activities and debriefing discussions to identify challenges and successes.

What were the key findings from the speaker's research regarding math teachers' understanding of mathematical modeling?

The research revealed that many teachers lacked formal training in mathematical modeling and often viewed it as a simple application rather than a process. There was also confusion about the role of modeling in math education, with some teachers associating it more with rigorous proofs than with critical thinking.

How did teachers' attitudes toward mathematical modeling vary in the study?

The study found two types of teachers: identity-driven teachers, who viewed modeling as oversimplified and disconnected from real math, and epistemic and socially-oriented teachers, who saw the value in real-world applications of math but acknowledged their lack of training in modeling.

What challenges did the teachers face in integrating technology and mathematical modeling into their teaching practices?

Teachers struggled to integrate technology like the Insight Maker simulator into their teaching. Despite some interest in modeling activities, many found the mathematical concepts involved, such as differential equations and numerical methods, too complex and challenging to teach effectively.