# 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 ...
• 8,707

### How to explain Monty Hall problem when they just don't get it

For some reason, the 'extend it to 100 doors and eliminate 98' explanation doesn't make it any clearer for me. Rather than talk about probabilities as fractions, I explain it this way: "If you ...
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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 ...
• 18.1k

### 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 ...
• 17k

• 10.4k
Accepted

### Is there any evidence about the effectiveness of "table proofs" in pre-college mathematics education?

The two-column proof form has been the dominant mode of presentation for proofs in secondary geometry in the United States for most of the past century. You ask about its effectiveness; unfortunately,...
• 16.1k
Accepted

### Inability to work with an arbitrary mathematical object

I'll focus on question 2 from a perspective of "maybe the right thing to think about is: what happens in the students' minds while they read this question?" When you say "Suppose $A⊆R$ is nonempty ...
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### Why do some linear algebra courses focus on matrices rather than linear maps?

Welcome Kostya! The mapping view is definitely important, but I don't think it's supreme. For me here's how I think about it. There are three ways to think about (basic) linear algebra: As a theory of ...
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### How to explain Monty Hall problem when they just don't get it

There isn't any sure-fire method of explaining anything, and especially in math. But specifically in the case of the Monty Hall problem it has been proven by extensive experience that many individuals ...

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

I think the main problem students have with induction proofs is that the ordinary direct proof works by reducing a statement with unknown truth value to one that is known as true. The bulk of an ...
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