Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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May we permit identities to be established by equivalent equations?

A trigonometry text like Sullivan's Algebra & Trigonometry often has a prohibition like this (Sec. 7.3): WARNING: Be careful not to handle identities to be established as if they were conditional equations. You cannot establish an identity by…
Daniel R. Collins
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Arguments against multiplication by 'stacking'

A 8th grade student I was working with recently was faced with squaring 37 in a problem that they were working on. The student stared down the numbers for some time, and then came up with some slightly incorrect answer. I put my own pencil to the…
NiloCK
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Inspirational Mathematics Books for Teenager

My daughter is in 6th grade. She likes mathematics, i.e., she likes to learn mathematics at school, is also good at what she has learned at school and is rather quick at picking new things. However, she is currently only limited to text books, which…
user2219907
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What is the difference between "numeracy" and "number sense"?

Is there a difference between numeracy and number sense, or are they synonymous? In my language they are often both translated to the same word (tallforståelse). I'm thinking that perhaps numeracy describes a competency, while number sense is more…
Dag Oskar Madsen
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Styles of visualization in geometry

Some people talk about visual thinkers and non-visual thinkers, but I am interested in a contrast within styles of visual thinking. There are people who readily visualize complicated flow charts and other diagrammatic graphics for information, but…
Colin McLarty
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Greatest common divisor applications

What are some real-life applications of gcd? I am looking for a motivating way of introducing this topic in an elementary number theory course.
matqkks
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What is the pedagogical justification and history for using mnemonics to teach order of operations?

There was previously a question/rant here on MESE about why so many are still using the PEMDAS/BODMAS/BIDMAS/BEDMAS mnemonics to teach order of operations. The question was deleted (still viewable by 10K+ users), but there were some comments and an…
shoover
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"Good" and "Bad" student intuitions when teaching and learning mathematics

I'm a college math/science tutor and I'm really interested in STEM education. I'm currently starting work on a project I hope to present in a couple of months at a tutoring conference and I was wondering if you could point me in the direction of…
Jorge Medina
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Planning high school workshop on Goldbach Conjecture

So I'm doing a mathematics education extension for my current undergraduate maths course, and for one bit of the final assessment we're asked to create a detailed lesson plan on the (strong) Goldbach Conjecture - that any even number is the sum of…
Adrian Hindes
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How to incorporate optional higher level mathematical content in an Engineering Maths course?

Our department teaches two very large first-year "Mathematical Methods" courses (600-ish students) to Engineering students. The syllabus is dictated by their (future) needs and covers a huge array of topics, but none to any great depth. For…
Gordon Royle
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Why are proofs by contradiction counterintuitive?

And how to make them intuitive? We are tasked to prove $P \implies Q$. So we assume $P$ and are trying to prove $Q$. We assume not-$Q$ ($\neg Q$) and derive a contradiction, establishing $Q$. There is something counterintuitive about this. To…
Joseph O'Rourke
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Is there any advantage of plotting graphs using traditional paper and pencil method?

Why don't we discard the traditional pencil and paper method of graph plotting in high schools and for freshers at colleges since there are many electronic devices doing the graphing? And please where do I get citation on studies that show students…
Mafuyai M.Yaks
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Everyday Example Problems for Solving Linear and Quadratic Equations

I am going to teach some grade 9 students about solving linear and quadratic equations. I am looking for a question from every day life (of a teenager) or a puzzle which is hard to solve without using algebra. There are of course loads out there in…
Larry
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Importance of exercises for learning mathematics

For me it seem to be obvious that exercises and exercise courses are important for undergraduates to learn mathematics and skills like finding a proof or writing it down. Was there any research showing that exercises are necessary for math education…
Stephan Kulla
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Effectiveness of multiple-choice versus short answer questions

I want to know if there is any research on whether students' learn better by answering selected response (multiple choice) questions than constructed response (written) questions. My gut feeling is no. Well-structured written questions bring out…
Mark Fantini
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