# Tag Info

Accepted

### Why are induction proofs so challenging for students?

The following list comes from a combination of reading various research articles and my own experience helping students in my Maths Learning Centre for the last seven years. Some reasons why ...
• 8,735
Accepted

### Why do inequalities flip signs?

I'm slightly concerned that Is there a mathematical reason (like a proof) of why this happens? is a purely mathematical question, but since you write "we just warn students" I will assume that ...
• 18.2k

### Why are induction proofs so challenging for students?

In my experience, the biggest issue is that students don't have a clear grasp of quantifiers, so they don't see the distinction between "for all n P(n)" and "consider an n such that P(n)". This leads ...
• 11.3k

### How can I explain why we need proofs to someone who has no experience in mathematical thinking?

More fun than equations are patterns that seem to hold. Put a dot on a circle, connect it to all the other dots (none yet), there is 1 region. Second dot connects to first, two regions. Third dot ...
• 18k

• 28.3k

### Math Proofs - why are they important and how are they useful?

I am an engineer. Proofs are important to "get" engineering, but are not directly used. I see three aspects of learning proofs as important: Logic, Process, and Ontology. Logic is the ...
• 280

### Uninsulting way to say "this will eventually be easy"

Perhaps not pointing out that the obvious steps are obvious but that the insights are insights. I believe students don't feel bad for not seeing the "magic steps" by themselves, so pointing out that ...

### How to use false theorems or proofs?

I would not recommend putting false proofs onto the board unless you immediately (within the same class period) point out their falsity, and make an assignment to find it. For smaller mistakes that I ...
• 18k

### Why are induction proofs so challenging for students?

As someone who took math courses but does not teach, I would claim that inductive techniques are taught with two rather separate approaches: A step-by-step recipe to take a problem that tells you to ...
• 1,175

### Should my 8th graders see a proof of the Pythagorean Theorem?

If you are in the United States, at a public school, then you should explain a proof because this is one of the common core state standards: http://www.corestandards.org/Math/Content/8/G/B/6/ I ...
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### Algebraic Solving and Uniqueness Proofs

Be careful here. You're teetering close to the edge of checking whether the student has guessed your solution to the problem rather than whether the student has solved the problem. This is easy to do,...
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### Why are induction proofs so challenging for students?

Logic foundation In my opinion, the only way for anyone to really understand induction is to really understand the logical structure behind it. So a prerequisite is a complete grasp of working in ...
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Accepted

### Proofs that make theorems less clear

"A well-chosen example illustrates ... and is entirely convincing." For me, all of what is usually called "generic proof" satisfy your criterion. Consider the Euclidean algorithm for finding the ...
• 4,314