Mathematics Educators Weekly Newsletter - Thursday, February 26, 2015

Mathematics Educators newsletter

Top new questions this week: How can I discourage proof by patchwork? I have a student who is working in their spare time on proving or disproving a conjecture of the form $$\exists x.\forall y.\phi(x,y).$$ Right now their strategy is to construct an $x$ and then show ... proofs graduate-education students-mistakes computer-science   asked by forritari 10 votes answered by ssdecontrol 4 votes Name the heuristic: exploiting the legitimacy of the questioner As a child, I made frequent use of a particular 'trick' in order to make short work of many different problems. The general form is to be presented a question which wants a definite (numerical) ... mathematical-pedagogy problem-design problem-solving   asked by NiloCK 8 votes answered by Benjamin Dickman 8 votes An intuitive derivation of Taylor polynomial coefficients I'd like to introduce Taylor polynomials by generalizing the linear approximation of a function $f(x)$ to a quadratic approximation. The linear approximation formula $L(x)=f(a)+f'(a)(x-a)$ of $f(x)$ ... calculus concept-motivation taylor-polynomials   asked by Jared 7 votes answered by NiloCK 4 votes How can I convince students that Fourier series are useful? Main question: Calculating the coefficients of a Fourier series can be difficult and time-consuming. How might a student be motivated/convinced to go through these (potentially tedious) details? Are ... undergraduate-education calculus mathematical-pedagogy concept-motivation series   asked by matqkks 6 votes answered by KCd 5 votes "Probable" vs. "Likely"; Choosing the Appropriate Word In some school textbooks, before introducing the probability as a number between $0$ and $1$, the words "likely", "More likely", "less likely" etc. are used to indicate the likelihood of an event. ... textbooks probability writing   asked by Behzad 6 votes answered by nickjamesuk 7 votes How to intuitively explain the role of transistors in boolean logic? Boolean logic is easily explained using truth tabels, but the underlying hardware is rarely mentioned in the same class. I would like to explain boolean logic from the point of view of actual ... undergraduate-education   asked by Sparkler 2 votes answered by Toscho 1 vote Greatest hits from previous weeks: What is a wise reaction to a silly question? I like students' nice questions too much (sometimes much more than their nice answers). It shows that they are thinking on what I am teaching and I am successful to make them curious about the ... classroom-management general-pedagogy class-participation   asked by Saint Georg 11 votes answered by Andrej Bauer 33 votes Real life examples to motivate the study of linear functions Some years ago I used mobile phone or internet rates (for example, with basic fees and a given charge per minute or by data volume) to introduce and motivate the study of linear functions. However, ... secondary-education reference-request concept-motivation functions   asked by Julia 11 votes answered by Sue VanHattum 7 votes

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