Math 148 Teaching Practicum

Texts

Robin Pemantle, Creating Your Own Teaching Community, Notices of the AMS 67 (2020), no. 9, 1354-1356, link
Colin Adams, Why do we teach?, Notices of the AMS 66 (2019), no. 7, 1045-1047, link
Bianca Viray and John Voight, The Value of Mathematical Storytelling: Our Perspective on Giving Talks, Notices of the AMS 70 (2023), no. 6, 928-931,
link
Ravi Vakil, The "Three Things" Exercise for getting things out of talks, website
Steven Krantz, How to Teach Mathematics, Third Edition, AMS 2015 (available on Canvas)

Weekly Schedule

Updated April 27, 2025.

Week	Date	Topics	Reading	Work
1	Mon 31 Mar	Introduction. Good/bad learning experiences. Affective vs. cognitive aspects of learning. Course planning. Setting learning goals. Why teach?	Teaching Community Why teach? Storytelling	"Teaching goals" short essay. Course creation: brainstorm topics.
1	Fri 04 Apr	Lecture schedule. Learn from lectures. Features of good lectures. Why lecture?	Three Things Krantz, Preface, 1.1-1.5
2	Mon 07 Apr	Web/Canvas course page design. Syllabus design. Problem set design. Learning outcomes. Why mathematics?	Krantz, 2.11	Complete course syllabus and webiste.
2	Fri 11 Apr	Course fine-tuning and workshopping.		Complete course syllabus and webiste.
3	Mon 14 Apr	Lecture 1 (Ben Si). Post-lecture discussion: first day introductions, lecture section titles, sufficient pausing after asking the class a question, pausing lecture to answer a student question, vagueness tolerance, writing distinct symbols on the chalkboard, be prepared for "depth" questions.		Upload original lecture notes to Canvas. Upload revised lecture notes to Canvas. Problem Set 1
3	Fri 18 Apr	Lecture 2 (Will). Post-lecture discussion: friendly daily introductions, answering questions with a smile, differentiating common math letters on board, pulling back student question answer to the whole class, sprinkle some fun reach/connections into the material, highlighting "vague idea" material, consistent notation, coordinating speaking with writing, mentioning relevance of earlier questions and lecture material, careful of long proof sketches.
4	Mon 21 Apr	Lecture 3 (Michaela). Post-lecture discussion: delineating the end of a proof, anticipating and structuring in opportunities for expanding outward, layout of algorithm statements and completeness proofs, making sure examples don't contain unnecessary accidents, knowing 1/3 of what you are presenting on, should the formal statement come before or after the illuminating example, knowing where your audience might appreciate a generalization or outward expansion, looking at all students in the room, rounding out the end of a lecture.		Upload original lecture notes to Canvas. Upload revised lecture notes to Canvas. Problem Set 2
4	Fri 25 Apr	Lecture 4 (Ben Sh). Post-lecture discussion: use a content review moment as an opportunity to add depth to the material, don't be afraid of making fun of yourself, stepping back from the board often to face the class, transparency in vagueness or delayed details "just keep with me here," the old addage "tell them what your about to tell them, then tell them, then tell them what you just told them," the cost-benefit analysis of providing overviews, injecting history to help motivate the next topic, writing out connecting sentences, and the importance of sectioning.
5	Mon 28 Apr	Lecture 5 (Ben Sh). Post-lecture discussion: some trivial banter at the beginning can break the ice, the art of "flagging up vagueness" and not letting it go too long, simplying textbook presentations to their barest essentials for what you need may take a bit of work, a history lesson can really liven up a transition to a new topic, the importance of constantly pointing back to earlier material in the class.		Upload original lecture notes to Canvas. Upload revised lecture notes to Canvas. Problem Set 3
5	Fri 02 May	Lecture 6 (Michaela). Post-lecture discussion: the importance of blackboard space management, don't leave huge swaths blank while cramming material into other regions, thinking about the time dedicated to the review material, colored chalk is good for highlighting but when the colors contains too much meaning it does not translate to the student's notes, emplying a surprising example as motivation for a transition to a new topic, history or anecdotes that involve "local" people hit home especially well a bit of a break for questions to indicate a major topics shift, being careful to keep symbols distinct, use of second person "you" in addressing class (as opposed to "we") might complicate the attempt to foster a feeling of mutual discovery, thinking through common questions and confusions ahead of time.
6	Mon 05 May	Lecture 7 (Ben Sh). Post-lecture discussion: getting people involved early in the lecture helps break the ice, don't try to hide the tricky points by speeding through them, presenting material as to invite questions and having prepared answers, a small break can be helpful before launching in a difficult proof or section, reviewing lecture ahead of time for repeated parts that could be handled once and for all, the importance of maintaining humility while remaining confident in your knowledge.		Upload original lecture notes to Canvas. Upload revised lecture notes to Canvas. Problem Set 4
6	Fri 09 May	Lecture 8 (Will). Post-lecture discussion: setting the stage versus jumping right in, when a student asks a question that only the instructor may understand the instructor should reinterpret/repeat the question aloud to the class with the answer, "did everyone catch that?" after student comment, the art of placing material on the board to be saved for later, find and highlight connections to previous lectures, titling in multi-step processes or algorithms, preparation leads to confident answers, distinguishing symbols redux, alerting the students to the fact that instructor is moving to a nonconsecutive board to make space, careful with "0" as number or vector, history as buffer for new topic, if horizontal lines are used to break up sections make them sufficiently long, end the lecture with a bit of wrap-up and not too suddenly.
7	Mon 12 May	Lecture 9 (Will). Post-lecture discussion: don't count the class out with "don't be worried about everything that's coming next..." just make it work, often we can further simplify the textbook's presentation to the particular context of the course, the hardest part of math is knowing what is trivial and what is hard (which changes as you learn), always explain new notations and new font scripts, sometimes writing something is faster than saying it then feeling the need to say it again, it can be good to selectively throw the textbook under the bus.		Upload original lecture notes to Canvas. Upload revised lecture notes to Canvas. Problem Set 5
7	Fri 16 May	Lecture 10 (Ben Si). Post-lecture discussion: humble introduction poking fun at onceself can be a good way to break the ice, good to list alternative texts if going off-piste, distinguishing symbols redux, explain pictures that you draw, make sure to define terms that might be nonstandard or new, talking is good for verbal intuition but keep in mind that little of it makes its way into students' notes, be careful for overloading "x" as a variable and as a value, think about the right ordering of "Theorem" "Proof" and "Example" for the case at hand, similarly with "Criterion" "Recall" "Conclusion" "Theorem" for motivating a theorem, don't add too much to an existing drawing, writing out questions can be a good way of setting up what's coming next, instructors usually rush when they are low on time and feel that they still have lots to say, sometimes writing too much intuition down can be counter-productive.
8	Mon 19 May	Midterm exam discussion.		Upload original lecture notes to Canvas. Upload revised lecture notes to Canvas. Problem Set 6
8	Fri 23 May	Lecture 11 (Ben S). Post-lecture discussion: a purposeful "wait a second, let's back up here" can be a good way to get people engaged, having the presence of mind to know when you are BSing answers, profusely thanking students for correcting your board mistakes, pointing out links to homework or midterm problems is great, appropriate use of colored chalk, careful to use same conventions as homework when setting up examples, don't necessarily need to get too detailed about writing out intuition, distinguishing symbols redux, time management and practicing, pacing is important.
9	Mon 26 May	No class: Memorial Day!
9	Fri 30 May	Lecture 12 (Michaela). Post-lecture discussion: appropriate use of mathematical notation versus writing out in English words is context dependent, condensing material for review, talking through a point or setting up what comes next while erasing a board (if you can do it), careful with using nonstandard symbols, a well-timed example can speak many words, having some flexibility to skip some topics if time is short, knowing/preparing more material than you are coming is so important, ending the class on a high note!
10	Mon 02 Jun	Wrap-up. Final reflections.

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