{"id":5730,"date":"2025-10-28T14:52:22","date_gmt":"2025-10-28T14:52:22","guid":{"rendered":"https:\/\/deliberativecitizenship.org\/?p=5730"},"modified":"2025-10-28T14:52:24","modified_gmt":"2025-10-28T14:52:24","slug":"critical-points-and-critical-thinking-discernment-through-multivariable-calculus","status":"publish","type":"post","link":"https:\/\/deliberativecitizenship.org\/deep\/critical-points-and-critical-thinking-discernment-through-multivariable-calculus\/","title":{"rendered":"Critical Points and Critical Thinking: Discernment Through Multivariable Calculus"},"content":{"rendered":"
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The Deliberative Pedagogy (DeeP) Faculty Collaborative<\/a> consists of faculty from Davidson College and other higher education institutions who are committed to learning and implementing new ways to improve and deepen the quality of their class discussions. These faculty come from a wide array of disciplines and backgrounds to study and discuss deliberative pedagogy methods, share their ideas and questions with one another, and work to embed deliberation in their classrooms. In this special blog series, members of the Collaborative describe and reflect on their experiences developing and teaching their deliberation-involved courses.<\/em><\/p>\n\n\n\n

By May Mei (2024-25 Deliberative Pedagogy Collaborative Faculty Fellow)<\/strong><\/p>\n\n\n\n

I think every mathematician cringes when approached with the sentiment that “Math is great because there’s one correct answer so you’ll know when you get there and you’re either right or you’re wrong.” Nothing could be further from the truth! Some processes might be imitable, but mathematics is about truth and beauty, creativity and rigor. Especially in the age of generative AI, I wanted to tell students: You have more answers than you know what to do with. This class isn\u2019t about finding answers, it\u2019s about deciding which of the many answers in front of you is better.<\/p>\n\n\n\n

My multivariable calculus class met an hour\/day for four days\/week. Every Monday was dedicated to deliberation. In the first half of class, students started with a quiz. This consisted of two standard questions in multivariable calculus with solutions (either former student solutions or answers from ChatGPT). The prompt was “You have received two problems with solutions. They might be completely accurate or wildly false. Your task is to evaluate these solutions. Are they mathematically correct? Are claims supported by evidence? Is the writing cogent and persuasive? Is notation used appropriately?” Students submitted a written assessment about the strengths and weaknesses of each of the two solutions. In the second half of class, there was a deliberation on their proposed responses.<\/p>\n\n\n\n

I will confess, the students had a hard time deliberating. Because the solutions they were engaging with weren’t embodied by someone in the class, it was hard to get them to feel like they were in dialogue with an answer. After trying out a few different models in the first few weeks of class, we settled on a popcorn reading of the solution with each student responding to that part in particular. This is perhaps closer to a discussion than a deliberation, but it is where the class settled.<\/p>\n\n\n\n

A learning outcome of the course was to “Engage students in the act of discernment: Deciding which of many answers in front of you is better and mounting a convincing argument as to why that is the case.” I started the class off with the first chapter of Why We Argue (And How We Should).<\/em> There, the standard philosophical definition of knowledge as a justified, true belief was presented. Students weren’t confused about what it meant to believe something. And when they were asked for justifications, they said things like “it’s in the book” or “you said it.” But when it came to what it meant for something to be true, they once again said “it’s in the book” or “you said it.” They had a hard time with the notion that I, their professor, or even the entire community of mathematicians could be wrong.<\/p>\n\n\n\n

Over the course of the semester, I saw my students engage deeply with their relationship with authority and to develop their own voice and confidence in their assessment. Here are two sample student responses on a reflection that asked for self-assessment of progress towards the learning outcome of discernment:<\/p>\n\n\n\n

Student 1: “I definitely improved on this aspect. When I first took my first quiz, I never said anything was wrong because I wanted to believe it was right because it was put in front of me. But I have definitely gotten better at understanding why there is a correct answer and not believing everything in front of me.”<\/p>\n\n\n\n

Student 2: “This is difficult for me because there are many ways to work through problems so it\u2019s hard not to believe someone else’s work\/explanation even if it\u2019s done in a different way than I would do it. I did get better at this and learned how to back up my argument.”<\/p>\n","protected":false},"excerpt":{"rendered":"

The Deliberative Pedagogy (DeeP) Faculty Collaborative consists of faculty from Davidson College and other higher education institutions who are committed to learning and implementing new ways to improve and deepen the quality of their class discussions. These faculty come from a wide array of disciplines and backgrounds to study and discuss deliberative pedagogy methods, share their ideas […]<\/p>\n","protected":false},"author":1275,"featured_media":5731,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[24],"tags":[],"class_list":["post-5730","post","type-post","status-publish","format-standard","has-post-thumbnail","category-deep","entry"],"jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"jetpack_featured_media_url":"https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7.png","rttpg_featured_image_url":{"full":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7.png",2025,2025,false],"landscape":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7.png",2025,2025,false],"portraits":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7.png",2025,2025,false],"thumbnail":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7-180x180.png",180,180,true],"medium":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7-300x300.png",300,300,true],"large":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7-1024x1024.png",1024,1024,true],"1536x1536":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7-1536x1536.png",1536,1536,true],"2048x2048":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7.png",2025,2025,false],"mini-thumbnail":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7-75x75.png",75,75,true],"team-member":["https:\/\/deliberativecitizenship.org\/wp-content\/uploads\/2025\/10\/2023-24-DeeP-Collaborative-Series-Instagram-Post-7-600x600.png",600,600,true]},"rttpg_author":{"display_name":"May Mei","author_link":"https:\/\/deliberativecitizenship.org\/author\/may\/"},"rttpg_comment":0,"rttpg_category":"Faculty Posts<\/a>","rttpg_excerpt":"The Deliberative Pedagogy (DeeP) Faculty Collaborative consists of faculty from Davidson College and other higher education institutions who are committed to learning and implementing new ways to improve and deepen the quality of their class discussions. 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