Mathematics is indeed discussable

Jephian C.-H. Lin

https://hackmd.io/@jephianlin/mathematics-is-indeed-discussable

Mathematics is disgusting discussable!

About me

Jephian C.-H. Lin 林晉宏
National Sun Yat-sen University
Applied Mathematics

Experiences

• Overseas: Calculus, …
• EMI in Taiwan：Machine Learning, Linear Algebra, …
• Superior Teaching Award (NSYSU, 2021)
• EMI Faculty Institute (ASU, 2023)
• Promoting EML in the University EML Environment (British Council, 2020)
• Flipped Learning 3.0 Certification (Official 2020)

Outline

• Challenges: competency? interest?
• Active Learning:
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  teach \(\rightarrow\)
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  learn
• How: rapport \(+\) clear instruction

Are you happy with the current outcome?

Why Mathematics?

• Math is useful
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• Math trains your mind
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Essense of learning — real story

A function \(f(x)\) is continuous at a point \(c\) if …

Textbook version:

for any \(\epsilon > 0\), there is \(\delta > 0\) such that
any \(x\) with \(|x - c| < \delta\) also satisfies \(|f(x) - f(c)| < \epsilon\)

Student version：

\(\epsilon > 0\), \(\delta > 0\), \(|x - c| < \delta\), \(|f(x) - f(c)| < \epsilon\)

How to make the content fun?

fun

Theory ––––––––––––––-> Applications

Fun \(=\)

Active learning \(\neq\) self learning

https://www.youtube.com/watch?v=ZQ12ESNoy5k

https://www.youtube.com/watch?v=_L8roj-8HfM

• Video 1 by Jephian Lin: teaching only
• Video 2 by Eddie Woo: teaching \(+\) learning

Any questions?

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  no questions
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  don't understand, don't want to ask
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  I don't know where I don't understand.

Group discussion

• groups of 2 –>
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• groups of 4 –>
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  Image Not Showing Possible Reasons

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• unexpected answers
• free-rider

What happens?

• Charisma
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• Fluent English
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• Logical delivery
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rapport \(+\) clear instruction

\(=\)

Mathematics is discussable!

Clear instruction

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  to get to NSYSU, there are three routes, the one on the left takes longer but has beautiful views, the one in the middle is the easiest and the shortest, the one on the right is winding, bumpy, and not recommended, you may make a choice on your own
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  go straight

ICQs

Instruction Checking Questions

Where are we going at the next intersection?

CCQs

Concept Checking Questions

If you would like to enjoy the beautiful views, which route would you choose?

Rapport

The first clas is IMPORTANT!

Not your fault…

• clear instruction
• rapport
• students
• classroom
• course content

But there are rooms for improvement –> PDCA

Sharing my experiences

First class: Build the mindset

• M istakes make you smarter.
• A sk questions.
• T hink carefully.
• H elp each other.

We are bound to learn together.

First class: Scaffolded self instroduction

• How are you?
• My name is _____ .
• My major is _____ .
• Assign the group.
• ChatGPT: Please tell me some applications of linear algebra in _____ .

Activities: Run the definition

Activities: Collaborative computation

• Each group get a different exercise.
• The final answer depends on each group's result.

\({\bf u}_1 = \begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}\), \({\bf u}_2 = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}\)

\({\bf v}_1 = \begin{bmatrix} 5 \\ 9 \\ 13 \\ 17 \end{bmatrix} = c_1\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix} + c_2\begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}\)

\(c_1 = ?\), \(c_2 = ?\)

Activities: Yes-No jigsaw

• Is this set linear independent? Case of yes
• Is this set linear independent? Case of no

Why we need so many teachers?

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  Push students to work hard
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  Image Not Showing Possible Reasons

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  Motivate students to learn more
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  Image Not Showing Possible Reasons

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  Offer customized advice based on the needs

Be a student again

If you got a chance to learn the subject again, how would you learn it…?