Diving into the rabbit hole of AI

Neil Marshall has recovered from his roles in:

• Teaching
• Moderating (and he apologises for the pedantry.)
• Curriculum development
• Professional Development

But still has a keen interest in what is going on.

Starting out

I was prompted by Charles Fadel ( more of him later) to explore key mathematical ideas that have changed the world.

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I came across Stephen Hawking’s book God Created the Integers: The

Mathematical Breakthroughs That Changed History

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I asked chatgpt.com to summarise the key points for me., and then had an extended conversation with it.

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The next few slide shows the sequence of prompts I put into Gemini during the conversation

• Summarise the ten key points of God Created the Integers: The Mathematical Breakthroughs That Changed History
• Summarise any discussion of graph theory.
• Explain how graph theory was important in the development of AI.
• Which of these could be taught in a high school mathematics lesson?
• I would like two examples of how social network analysis could be taught in high school mathematics
• How could we show students how Facebook uses centrality measures?

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Out popped two detailed and good lesson plans to use network theory to investigate relationships between Facebook friends.

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Lightbulb moment

Using AI I can quickly (10 minutes or so) link important “earthquake” discoveries in mathematics with our secondary curriculum and find engaging, interesting contexts to use in teaching and learning.

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The full details of the conversation with chatgpt are available in a pdf available after the workshop

Next step?

What else could I use this for?

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I was prompted by this news item on RNZ.

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https://www.rnz.co.nz/news/national/528813/ai-use-in-nz-schools-i-just-put-in-a-prompt-and-spark-some-ideas

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Lets find out where this group is.

Have you used AI tools?

1. I’ve embraced them and encouraged others to do so too
2. I use them almost daily
3. I use them occasionally
4. I’ve played around with them a bit
5. I have never used them

Examples of Free AI ChatBots

ChatGPT

Google Gemini (also generates images)

Poe

Windows Copilot

Bing Search (in Microsoft Edge)

Khanmigo - from Khan Academy - targeted at teachers

Free AI Research Assistants

• https://researchrabbitapp.com/ for visualising networks between papers and suggesting relevant ones
• https://www.perplexity.ai/?login-source=oneTapHome for surfacing potential papers, as it actually provides the citations (most of the time, still hallucinates so be careful)
• https://elicit.com/?redirected=true is OK but again maybe just as a better Google scholar search
• https://www.semanticscholar.org/

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Thanks you Anna Fergusson for these links.

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Using AI to Increase Productivity

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These next slides whizz through a few ideas I have had - you might like to try them as we go.

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Non-teaching tasks that absorb teacher time

• Writing emails to students and parents
• Writing newsletters or blog posts
• Narrative comments for student reporting
• Writing letters of recommendation
• Discipline referrals
• Reading IEPs
• Entering grades
• Building teacher evaluation portfolios
• Managing data in spreadsheets

Prompting AI - Data Management

I want a sheet to calculate the difference between two cells, only if the cells contain data

=IF(AND(NOT(ISBLANK(A1)), NOT(ISBLANK(B1))), A1 - B1, "")

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Prompting AI - Emails Home

Write three generic emails home for parents that I can personalize.

Version 1 is for a student who tries hard in math but is struggling. This student would benefit from meeting with a teacher during a private study period for target support.

Version 2 is for a student who isn't putting forth their best efforts in math class. This student needs to prioritize learning math. I have confidence they can do it, but I need them to try harder.

Version 3 is for a student who has shown growth in math. This student has been working hard and is improving. This student needs to keep working hard, but their efforts are starting to pay off.

Prompting AI - discipline referral

Write a discip;line referral.for me to give to the Dean. Kyle got very angry in class, threw his books on the floor, swore and walked out of the room.

Prompting AI - request a promotion

Write a letter to my Principal for me, applying to be the assistant head of mathematics.

Teaching tasks that absorb teacher time

• Planning lessons
• Generating practice problems
• Creating rubrics
• Writing assessments
• Giving feedback
• Grading
• Differentiating lessons
• Catching up students who were absent
• Reflecting on prior lessons for future improvement

Prompting AI - how could I teach this boring stuff?

What specific lesson suggestions do you have to improve student performance on tasks like this?

1. Focus on understanding the basic rules of exponents.
2. Practice with applying the rules to simple problems.
3. Introduce challenges that gradually increase in complexity.
4. Encourage students to explain their thought process.
5. Relate exponents to real-world applications such as calculating growth rates of populations or the intensity of light.

Digging Deeper

What real world applications apply here?

• Areas and Volumes: Exponents are used to represent areas and volumes of squares and cubes.
• Growth and Decay: Bacteria growth can be modeled using exponents, where the zero exponent rule (a⁰ = 1) represents the initial amount of bacteria and negative exponents can show a decrease in bacteria due to a disinfectant.
• Signal Strength: Signal strength often weakens with distance following an inverse square law. This can be represented with exponents using the quotient rule (a^m/aⁿ = a^m-n). As the distance from the source increases (represented by the exponent n), the signal strength (represented by am) weakens (gets divided by a value greater than 1).

None of these are as complicated as the examples I wanted students to simplify. Are there any real world examples at this depth?

Finding real-world examples that directly mirror the complexity of advanced exponent simplification problems can be tricky. Often, real-world applications involve a combination of these rules rather than a single problem showcasing them all.

Takeaway: Maybe I should rethink my choice of problems to use to assess knowledge of exponent properties.

Prompting AI - Data Analysis

I asked students to reflect on their critical thinking. Their responses are below. What themes do you find in their responses?

I used my knowledge to criticize our own ideas and develop our product further in order to see improvement

I showed how I was a critical thinker by how I used my time

I used my teachers ideas and my own to create photos that others may not think of doing.

I critically thunk today by understanding the perspectives of others and considered their ideas.

Even though I am relearning old concepts again new ideas through those concepts have been flowing through my mind and it is interesting to see how my ideas mix with other people's ideas.

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Here are some themes I found in your students' reflections on critical thinking:

• Using knowledge and ideas to improve
• Problem-solving and decision-making
• Analysis and evaluation
• Communication and collaboration
• Personal growth

Prompting AI - Rubric Creation

Help me create a rubric for this task

Prompting AI - Solving NCEA problems

Try taking a screenshot of an NCEA external problem and ask AI to solve it.

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I found it was excellent for pure mathematics, less so for some of our statistics.

Prompting AI - Quiz Generation

Write a 10 question quiz to assess student understanding of the distributive property with negatives.

Prompting AI - Unit Structure

I need to teach a unit on the sine and cosine rules. Please outline the unit lesson by lesson, describing the topics and key ideas to be addressed each day.

Please set some problems in a context relevant to high school students.

What might you try to use AI for now?

Poll thing.

Ethical considerations

The MoE has published advice about the use of AI for teaching and learning.

https://web.archive.org/web/20241007084024/https://www.education.govt.nz/school/digital-technology/generative-ai/

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NZQA has publish guidance about the use of AI and internal assessment practice. It is towards the end of this newsletter, February 2023

https://web.archive.org/web/20240517212557/https://www2.nzqa.govt.nz/about-us/publications/newsletters-circulars/emaillink/february-2023-1/#e9308_heading1

Charles Fadel

He is a disruptor in mathematics curriculum development and is well respected in OCED and PISA circles

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Check out his website: https://curriculumredesign.org/

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Read the free chapter on AI and consider buying the book for your Principal to read: https://curriculumredesign.org/our-work/education-for-the-age-of-ai/

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I have been privileged to work with him and thank him for is ideas on the content of this workshop.