August 27: When Group Work Fails -- Group projects are lauded for their ability to teach students various skills important to professional work, including communication, management, and planning. But not all group work is successful. In some cases, members of a group may put in less work or no work at all. This week, we read a summary of literature from social psychology on this topic and discuss strategies to combat this phenomenon. --Myers, David G. "Many Hands Make Diminished Responsibility." Exploring Social Psychology. 6th ed. New York: McGraw-Hill, 1994. 203-08. Print.
September 3: Social Pressure and Group Projects -- Research dating back to the 1950s has demonstrated how difficult it is for an individual to withstand social pressure. In some instances, social pressure can quell correct ideas in favor of incorrect ones. This week, we read an article describing this phenomenon (observed in the laboratory) and discuss strategies to guide students away from it. --Asch, Solomon E. "Opinions and Social Pressure." Scientific American 193.5 (1955): 31-35. Web.
September 10: Group Projects Done Right -- Group projects can, of course, be done well... even in a mathematics classroom! This week, we consider ideas set forth in Assessment Practices in Undergraduate Mathematics by the MAA and discuss if they could be used in our classrooms. --Gold, Bonnie, Sandra Keith, and William A. Marion. "Assessment in the Individual Classroom." Assessment Practices in Undergraduate Mathematics. Washington, DC: Mathematical Association of America, 1999. 134-45. Print.
September 17: Would You Like Some Help? -- Sometimes people are altruistic and sometimes they are not. An ideal class environment is one where students work together and help each other, but what factors lead one person to help another? This week, we read a summary of social psychology literature on this subject and discuss how these findings apply to the classroom. --Myers, David G. "When Do People Help?" Exploring Social Psychology. 6th ed. New York: McGraw-Hill, 1994. 385-93. Print.
September 24: Do As I Say, Not As I Do -- Mathematicians may profess a set of values that differs from what is inferred by their actions. This week, we discuss a paper that looks at discrepancies between what mathematicians value in proofs versus how they teach them. --Lai, Y. & Weber, K. (2014). Factors mathematicians profess to consider when presenting pedagogical proofs. Educational Studies in Mathematics, 85(1), 93-108.
October 1: How Mathematicians Gain Conviction -- Mathematics is often thought of as a discipline that gains certainty by deductive reasoning rather than empirical or authoritarian evidence. In practice, however, this may not be entirely true. This week, we read a paper on this very topic and discuss if we teach the practice of mathematics honestly. --Weber, K., Inglis, M., & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49(1), 36-58.
October 8: How Mathematicians Use Examples To Understand Proofs -- Everyone knows mathematicians use examples to explore conjectures... except for many undergraduate students. This week, we read a paper that details how mathematicians use examples when exploring a conjecture and discuss its implications for undergraduate education. --Lockwood, Elise, Amy B. Ellis, and Eric Knuth. "Mathematicians’ example-related activity when proving conjectures." 16TH Annual Conference on Research in Undergraduate Mathematics Education 1 (n.d.): 16-30. Web. 20 Aug. 2014.
October 15: A Uniform Standard for Evaluating Proofs? -- Courses as basic as Calculus incorporate proofs. Is the mathematical community consistent in how it evaluates such basic proofs? This week, we read a paper that explores different standards used by mathematicians and discuss if there exists a uniform standard by which we judge proofs. --Inglis, M., Mejia-Ramos, J.P., Weber, K., & Alcock, L. (2013). On mathematicians' different standards when evaluating elementary proofs. Topics in Cognitive Science 5(2), 270-282
October 22: Opportunities for Theoretical Thinking -- The majority of lower-level curriculum provides little in the way of theoretical assignments. Is it, however, possible to incorporate activities that encourage high-level thinking in 100- or 200-level curriculum? This week, we read a paper that explores this issue and we consider if its suggestions could be realistically incorporated into the classroom. --Challita, Dalia, and Nadia Hardy. "Providing calculus students with opportunities to engage in theoretical thinking." 16TH Annual Conference on Research in Undergraduate Mathematics Education 1 (n.d.): 16-30. Web. 20 Aug. 2014.
October 29: Preparing Students for Calculus -- Last week, we considered ways of preparing calculus students for higher-level classes. This week, we consider what it takes to adequately prepare students for calculus. --Judd, April B., and Terry Crites. "Preparing students for calculus." 16TH Annual Conference on Research in Undergraduate Mathematics Education 1 (n.d.): 96-105. Web. 20 Aug. 2014.
November 5: Proficiency to Mastery (Week 1 of 3) -- For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we read the description of proficiency from Adding It Up. --Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. "The Strands of Mathematical Proficiency." Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy, 2001. 115-35. Print.
November 12: Proficiency to Mastery (Week 2 of 3) -- For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we consider if students are proficient based on results summarized in Adding It Up. --Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. "The Strands of Mathematical Proficiency." Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy, 2001. 136-55. Print.
November 19: Proficiency to Mastery (Week 3 of 3) -- For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we read about Mastery from How Learning Works. --Ambrose, Susan A. "How Do Students Develop Mastery." How Learning Works: Seven Research-based Principles for Smart Teaching. San Francisco, CA: Jossey-Bass, 2010. 91-120. Print.
December 3: What is "True" Understanding? -- What exactly is mathematical understanding and when has a person achieved it? Although it may seem clear cut, further thought on the subject may convince you otherwise. This week, we read an article that attempts to tackle the ambiguity of "true" mathematical understanding and discuss our experiences (both as students and as teachers). --Sfard, Anna. "Reification as the Birth for Metaphor." For the Learning of Mathematics 14.1 (1994): 44-55. Web.
December 10: Metaphors for Learning -- We often understand fundamental ideas like learning through metaphor. This week, we read an article that discusses two kinds of metaphors employed and argues that both are incomplete without the other.
--Sfard, Anna. "On Two Metaphors for Learning and the Dangers of Choosing Just One." Educational Researcher 27.2 (1998): 4. Web.
January 17:Planning for the Semester
January 24:Quizzes and Homework - Quizzes and homework are commonly used, but what are the benefits and are they different? (Paper)
January 31:Efficacy of Online Homework - How effective is online homework? Could it help lower-performing students? (Paper)
February 7:Teaching with Applications - How effective is it? Should we do it? If so, how? (Paper)
February 14:Teaching Study Strategies - How can we teach and incentivize students effective study strategies? (Paper)
February 21:Implicit Theories of Intelligence - Students' theories of intelligence can effect their performance. How can we effectively respond to this? (Paper)
February 28: Math Anxiety and Memory - Math anxiety is ubiquitous. What are the challenges anxious students face and how can we respond? (Paper)
March 7:The Instructor Matters - The most important aspect of the learning experience is the teacher. What are some important practices in your teaching? (Paper)
March 14:No Seminar
March 21: Articulating Math - The ability to articulate math is just as important to student success as knowing mathematical procedures. How can we successfully incorporate writing into a math class? (Paper)
March 28:Mathematical Thinking of Objects - We can think of mathematical objects structurally or operationally. True understanding of math requires the learner know both. Is that the case in our classes? (Paper)
April 4: Creativity and Mathematics - Many of us would argue that math classes do not contain creative elements despite the fact that mathematics is a subject requiring a great deal of creativity. (Paper)
April 11: Teaching Approaches versus Classroom Practices - We may characterize our teaching style one way but find that it actuality, it is described in another way. (Paper)
April 18:Research Problems of Post-Secondary Education - The majority of education research is conducted at the K-12 levels; however, do these findings translate well into post-secondary classrooms? (Paper)
April 25:No Seminar
May 2: No Seminar
Fall 2013 Topics
September 6: Negative Positive Messages -- Is there such a thing as a "bad" positive comment? Explain. Video
September 13: Student-Teacher Relationships -- What role do you, as an instructor, play in a student's life? Video (Further Reading)
September 20: The Art of Test Writing -- What are your goals when writing a test? How do you achieve them? Video
September 27: Grading Philosophy -- What messages are we communicating through grading? Explain. Video
October 4: Visualizing Thoughts -- What visualizations do you use to facilitate thinking? Video, (Further Reading)
October 11: Metacognitive Thinking -- How do you encourage metacognitive thinking in your students? Video (until 11:09)
October 18: Collaboration-- How important is collaborative/group work in learning math? Video
October 25: Underrepresented Populations in Math -- How do you maximize the success of all your students? Video (Further Reading)
November 1: Learning Disabilities -- Why do we provide special accommodations for ODS students? Explain. Video
November 8: Setting the Tone -- What are your goals for the first week? How much does it affect the rest of the semester? Video
November 15: Homework that Works -- What do you believe is the purpose of homework? How do you achieve that? Video
December 6: Syllabus Writing -- What are your Dos and Don'ts for syllabus writing? Paper