Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis. This week students learn about power series and the fundamental theorem of algebra (Rudin pp. 83-86). Authors: This recitation was developed by Joel B. Lewis, Craig Desjardins, Todd Kemp, Mia Minnes, Mohammed Abouzaid, Peter Speh, Kyle Ormsby, and Susan Ruff. Communication objectives: Be aware of the tools available for placing LaTeXed labels on figures, using LaTeX to create slides, managing bibliographies. Be aware of the challenges of giving slide presentations vs chalk talks. Recitation Kyle Ormsby created a beamer slide presentation on creating beamer files,

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Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis (18.100C). This week students learn about the Taylor series and the Stieltjes integral (Rudin pp. 120-127). This recitation is often combined with Recitation 9 on proof structure. Authors: This recitation was developed by Craig Desjardins, Joel B. Lewis, Todd Kemp, Mohammed Abouzaid, Peter Speh, Kyle Ormsby, and Susan Ruff Communication objectives: Students should begin to develop an awareness of proof elegance as well as an appreciation for revision (even correct proofs can be improved). Recitation: This recitation varies each term depending on instructor inclinations. Some

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis (18.100C). This week students learn about completeness and sequences and series (Rudin pp. 42-43, 47-69, 71-75). Trouble spots for students at this point in the term may include properties of continuous functions. Authors: This recitation was developed by Craig Desjardins and Joel B. Lewis based on a suggestion by Susan Ruff. Communication objectives: Choosing when to write conceptually and when to write formally. Recitation The following topics were addressed in class discussions: Should conceptual explanations &/or examples be given before or after formal statements? Discussion

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis (18.100C). This week students learn about completeness and sequences and series (Rudin pp. 42-43, 47-69, 71-75). There’s an exam next week on the first third of the course. Likely trouble spots for students at this point in the term include infinite series and preparing for the exam. Authors: This recitation was suggested by Susan Ruff. The description of the recitation below is by Kyle Ormsby. Communication objectives: Formulating precise questions; informal oral communication (communicating to learn) Recitation “We held a question discussion during this recitation.

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis (18.100C). This week students learn about compact subsets of Euclidean space (Rudin pp. 38-40). Likely trouble spots for students at this point in the term include how much detail to include in proofs; induction; Heine‐Borel is only true for Euclidean spaces. Students have been writing proofs in their problem sets since the beginning of the term. Authors: The proof-by contradiction handout was developed by Todd Kemp; the guiding-text handout was developed by Susan Ruff, the homework assignment is by Hans Christianson, Craig Desjardins, Joel Lewis,

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis (18.100C). This week students learn about countability and metric spaces (Rudin pp. 24-35). Likely trouble spots for students at this point in the term are negation, multiple quantifiers, abstractness of metric spaces, and “higher infinity.” Authors: The recitation was developed primarily by Todd Kemp. Communication objectives: Translating among mathematical concepts, mathematical language, and notation. Making tables and including figures in LaTeX. Recitation & Assignment: Most of the recitation is devoted to working in small groups on a worksheet on order of quantifiers. Other brief topics

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis. This week students learn about uniform convergence (Rudin pp. 150-154). Authors: This recitation was developed by Susan Ruff. The software engineering research is joint with Michael Carter, the case study is by Les Perelman, and the Active Listening story is by Fisher, Kopelman, and Schneider. Communication objectives: Communicate professionally Recitation: This recitation has three parts, a summary of research into the professional communication skills needed by software engineers, an explanation of one of those skills (active listening), and a case study from industry of (un)professional

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis. This week students learn about integrability and the fundamental theorem of calculus (Rudin pp. 128-136). Possible trouble spots for students include multiple quantifiers, formalizing concepts, and uniform continuity vs. convergence. Authors: This recitation was developed primarily by Joel B. Lewis, Craig Desjardins, and Susan Ruff Communication objectives: Analyze the rhetorical context of a communication and design the communication appropriately. Recitation Pair or small-group discussion: How would you explain the mean value theorem to a physics major who’s asking for help in a required math class?

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis (18.100C). This week students learn about the Taylor series and the Stieltjes integral (Rudin pp. 120-127). This recitation is often combined with Recitation 9b on proof elegance. Authors: This recitation was developed by Craig Desjardins, Joel B. Lewis, Todd Kemp, Mohammed Abouzaid, Peter Speh, Kyle Ormsby, and Susan Ruff Communication objectives: Structure proofs (and collections of statements) to help readers follow the logic. Recitation: This recitation varies each term depending on instructor inclinations. Some topics covered include the following: Claims, lemmas, propositions, theorems, corollaries, etc.

Read more →Context: This lesson plan is from a weekly communication recitation that accompanies M.I.T.’s Real Analysis (18.100C). This week students learn about differentiability and the mean value theorem (Rudin pp. 103-110). This recitation revisits concepts that were introduced in the second recitation. Authors: The recitation was developed primarily by Joel B. Lewis and Craig Desjardins. Communication objectives: Translating among mathematical concepts, mathematical language, and notation; with particular attention to how changing the order of quantifiers changes the meaning. Students worked in small groups on the following task: Give some examples of f: R–>R having each of the following properties. A function

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