Teaching Math Processes with AI

TL;DR

(Instructional Guidance, Transcript, and Prompts below)

Why AI Helps With Learning New Math Processes

Students need to understand mathematical ideas, but true understanding comes from applying those ideas. To apply them, students need clear processes. AI can help teachers introduce, model, and guide students through these processes so that they eventually grasp the deeper concepts.

The example used in the transcript is quadratic equations, although the same approach works for any math topic, from fractions to calculus.

Step 1: Explain Why the Process Matters

Before students are asked to struggle with a new process, they need to know why it is worth learning. AI can generate student-friendly explanations about the value of specific mathematical processes and provide real-world applications that make the content relevant.

For quadratic equations, common examples include projectile motion, business modeling, and environmental simulations. Teachers can select examples that match their students’ interests.

Step 2: Provide Clear, Step-by-Step Instruction

AI can generate detailed, student-friendly steps for solving a mathematical problem type, along with examples that apply those steps to meaningful real-world contexts. These examples serve as the teacher’s direct instruction and help demonstrate each part of the process.

By tailoring the examples to topics like sports, gardening, finance, or other areas students care about, teachers can make the learning more engaging and accessible.

Step 3: Create Guided Practice Resources

AI can also build instructional tools such as worksheets that include:

A problem for students to solve
A sample problem that demonstrates the process
A three-column structure that shows the steps, the sample solution, and space for the student’s own work

This format combines guidance, modeling, and independent practice in a scaffolded way. Over time, students can transition from supported practice to solving problems on their own.

Conclusion

AI allows teachers to generate explanations, examples, and guided practice materials quickly, freeing them to focus on instruction and student support. With repeated practice using these generated resources, students can steadily build both procedural fluency and conceptual understanding.

Teachers can repeat this process across many mathematical topics to help students master new skills efficiently.

Teacher Take-aways

Pedagogical and Instructional Implications

A successful approach to teaching new mathematical processes begins by establishing relevance. Before students engage with unfamiliar procedures, they benefit from understanding why the process matters and how it is used in meaningful real-world situations. Providing contexts that reflect students’ interests, such as sports, personal finance, or environmental examples, supports motivation and helps students see mathematics as a practical tool rather than an abstract requirement.

Explicit instruction and modeling are essential when introducing a new process, . Teachers should present clear, step by step guidance and walk through a parallel example while thinking aloud about key decisions and common pitfalls. This approach makes the underlying reasoning transparent and reduces unnecessary cognitive load for learners.

Guided practice should follow direct instruction. A structured format, such as a three-column organizer, can help students connect the general steps of the process to a worked sample and then to their own attempt. This scaffold supports students who are new to the procedure and makes it easier for teachers to diagnose where misunderstandings occur. Over time, these supports can be intentionally faded as students gain fluency, shifting from direct teacher modeling to independent problem solving. This represents a gradual release of responsibility that aligns with how students build procedural confidence.

Formative assessment is integral throughout this progression. By reviewing students’ work within the scaffolded structure, teachers can identify specific breakdowns, address misconceptions quickly, and adjust instruction as needed. Written reflection or explanation of what a solution means in context also helps students connect procedures to concepts and deepen their understanding of the underlying mathematics.

These strategies also support differentiation. The same instructional sequence can serve whole class instruction, small group work, or enrichment for students ready to move ahead. By varying the complexity of tasks while maintaining a consistent structure, teachers can provide accessible entry points for all learners while still offering challenge where appropriate.

AI Support and Use

Teachers can use AI to streamline and strengthen each phase of effective mathematics instruction by generating explanations, examples, and scaffolds that align with sound pedagogical practice. AI does not replace instruction. Instead, it supports teachers in delivering clear modeling, meaningful contexts, and structured practice.

AI can assist teachers in the following ways:

Establishing relevance: AI can generate age-appropriate explanations of why a mathematical process matters and provide multiple real world applications. Teachers can select or refine examples that match their students’ interests, such as sports, gardening, design, or finance, making the learning more engaging and purposeful.
Providing clear procedural modeling: AI can produce step-by-step instructions for any targeted process, written in language accessible to the grade level. This supports direct instruction by giving teachers a clean, consistent explanation they can model aloud and annotate during class.
Creating meaningful, varied examples: AI can generate worked examples that follow the exact steps of the procedure. These examples can be tailored to different contexts or adjusted for different learner groups. Because teachers can request multiple versions quickly, they can offer diverse representations without extensive preparation time.
Designing scaffolded guided-practice tools: AI can build structured resources such as three-column organizers that include the steps, a completed model, and space for student work. Teachers can request versions with different problems, increasing opportunities for supported practice while maintaining a stable structure.
Supporting gradual release: AI-generated materials can be easily modified to fade supports. For example, teachers can request organizers that remove the sample column or the step list as students gain proficiency.
Assisting with formative assessment: By producing multiple parallel versions of the same type of problem, AI allows teachers to give students quick checks for understanding. Teachers can then compare student work across versions to identify patterns of errors or areas that require reteaching.
Differentiating instruction: AI can adjust problem complexity, contexts, or numerical values while preserving the same instructional structure. This enables teachers to match tasks to student readiness without creating separate materials from scratch.
Used strategically, AI reduces planning workload and frees teachers to focus on providing feedback, monitoring student thinking, guiding discussions, and supporting deeper conceptual understanding.

Full Transcript and Prompts

Let’s talk math instruction and specifically how can we use AI to help us to teach kids new mathematical processes and the steps for solving problems.

There is a strong argument to be made that students need to understand mathematical concepts. They need to understand what the numbers mean and how they’re taken apart and put together and how they interact with each other, and all of that, which we call numeracy.

However, mathematical concepts can really only be understood when they are applied. They can only be mastered when students are able to apply them. And to apply them, they have to have a process. So the real question is “How can we use AI to help us teach new processes to students?”

Here we’re going to use the example of the quadratic equation, but we could put anything in there, honestly. We could put in fractions, we could put in division, multiplication, multiplying fractions with different denominators, all the way up through calculus, and so forth. There’s a process.

So how do we get AI to help us to teach it to students and help students to master it so that eventually they get to understanding the concepts behind those numbers.

So here our example is quadratic equations. We’ll put in whatever we need to put in for our content, whatever it turns out to be, and a little bit of context teaching eighth grade students.

First Part: Explaining Importance

We’re going to try to answer the big question first, which is “Why bother? Why should my students learn this? And how is this process used in the real world? What are the real world uses of the process?”

If we’re going to ask kids to struggle with and try something new, we have to give them a reason to do it, right? So that’s really what this first part is about.

It’s the beginning of our direct instruction to students as we help them to master these new mathematics processes. So here, eighth grade students, why? And what are real world examples? So let’s just see if our AI can help us to answer that question for students.

Prompt

I teach 8th grade students. Why should my students learn the process to solve problems with quadratic equations? What are real-world uses of this process?

All right, what do we have? They should learn how to solve it because of these reasons. Why should they learn it? What do they get out of it? And so forth. And once they have mastered it, here are some ways that it’s actually used.

Projectile motion, which is, you know, how high does the ball go when you throw it, how long until it lands, and how far does it go. And business and technology and environmental modeling and so forth. So, there are some real uses for this process.

What we can do is figure out which of these areas students might be interested in, and we can use that in the next step of our instruction. So, let’s take a look at the next step. That’s simply the introduction for students. Now, let’s introduce the steps for solving the problems.

Second Part: Modeling the Process

What do I need as the teacher? I need step by-step instructions. I need to know first this, then this, then this, then this, and I need some examples that I can use, some real world examples that I can use to show students how to use that process.

Prompt

I need step-by-step instructions for solving quadratic equations.

First, provide the instructions, and

Second provide 2 relevant real-world examples that follows the instructions step by step.

Here I’m could modify this prompt to say real world examples using sports or using agriculture or using finances or whatever the case may be, whatever is relevant to the students. Here in this example, I’ll just leave it up to the AI to pick some for me, and that’ll be fine. But I think you’re going to want to tailor it a bit more around the interests of your students.

So, I need instructions, and I need to see how those instructions are applied in the real world.

All right, here’s a clear, student-friendly explanation. That’s the formula, and there’s the equation. Now, how do we solve it? Step one, step two, step three, step four, step five.

And now that I provided an overview of the steps, let’s walk through it with those examples. Basketball is thrown. Its height in feet after t seconds is modeled by this formula, and there’s my example. So there’s one good example right there.

The area of a garden. There is another good example. Something very tangible that the students could recognize and visualize in their heads, as well, and how it’s done. So, very nice.

This is all direct instruction. Obviously, this is what I’m doing for the class, whether the whole class or a small group or maybe I’ve got some students who are advanced beyond the prior content and they’re ready for the next step. Well, here is the next step for them.

Okay, but it’s still this is direct instruction. This is me modeling and providing the examples and demonstrating the process. Eventually, we need to turn it over to the kids and we need to give them a chance to try it themselves, but with some guidance and some modeling and some support that they can use on their own problems.

So that brings us to our third prompt.

Part Three: Guided Practice

Prompt number three is: let’s create an instructional resource, a tool, a worksheet for solving this type of problem. And frankly, at this point, I could have said for solving this type of problem, so I won’t have to keep typing quadratic equations over and over again.

So, what do we want it to look like?

At the top, I need a problem the students are going to work out for themselves. And I need a sample problem, which will be the model or the demonstration that they can follow. Then I need three columns.

Column one, give me the steps.
Column two, use that sample and walk through the steps as a model.
And then column three, a place where students are putting their own work on the problem that I want them to solve as well.

So let’s do this. I’m thinking that because it’s the first time for these students, they’re not ready to just go out and do it independently. “Here are the steps. Off you go. Follow them.”

Rather, “Let me guide you through with an example so you can see where the numbers actually go as you walk through the steps.”

Prompt

Provide a worksheet for solving quadratic equations. At the top, place the problem for students to solve and a sample problem, and then create 3 columns.

Col 1= instruction step.

Col 2= sample problem step.

Col 3= place for the student to write out the step for solving the actual problem.

And we’ve got that copied. So let’s get our AI to create this resource for us.

And one, two, three. So date, time, all that kind of stuff. The problem to solve. So this is what the kids will work on. When will the ball hit the ground? Okay. and a sample that will be used to model. And then finally, here’s where they’re going to do their work.

We’ve got column one, the instructions. We’ve got the instruction applied to the sample. And now we’ve got the place for the students to do their own work. They can simply follow the instructions. They can follow the example that’s provided as they’re plugging in their own numbers.

Now, eventually we’re going to move from this to instructions and their work. And finally we’ll just give the problem and we’ll have them do their work which they will turn in.

We’ll take a look at it and see whether or not they’re mastering the process and can do it independently. But at the onset here they need guidance and they need some modeling. So that middle column provides it for them very, very nicely, and, oh, some extensions.

What do the solutions to this problem mean in real life? Explain it in a sentence or two.

Now, one thing that I might do at this point to say “Prepare this as a Word download with formatting,” which it will do.

Conclusion

The nice thing is I can do this over and over again all day. I can give them multiple versions of this with different problems to solve at the onset while they’re first getting their hands into how to do this.

And it’ll take a moment to think finally, but it eventually will give us a nice sheet that we can then print, copy, and put in their hands to work on in their small groups.

And that is how we can use AI to help us teach kids new mathematics processes.

I hope you found this useful. Take care.

Transcript Outline

Outline of Video Transcript: “Teaching Math Processes with AI”

Introduction: Using AI in Math Instruction
1. Purpose of Discussion
  - Explore how AI can help teach students new mathematical processes.
  - Focus on teaching both procedural steps and conceptual understanding.
2. Importance of Conceptual Understanding
  - Students need to understand what numbers mean and how they interact.
  - Numeracy comes from applying mathematical concepts through processes.
3. Main Question
  - How can AI help teachers teach new processes and help students master them?
  - Example focus: quadratic equations (but could apply to any topic such as fractions or calculus).
Part One: Introducing the Concept and Real-World Relevance
1. Purpose
  - Engage students by explaining why learning the process matters.
  - Connect mathematical processes to real-world applications.
2. AI Prompt Example
  - Prompt: “I teach 8th grade students. Why should my students learn the process to solve problems with quadratic equations? What are real-world uses of this process?”
3. AI Response Highlights
  - Reasons for learning include understanding motion, business, and environmental modeling.
  - Examples: projectile motion, technology, and business applications.
4. Instructional Use
  - Teacher identifies areas that interest students to connect the lesson meaningfully.
  - Sets up the context for introducing problem-solving steps.
Part Two: Teaching the Process with Step-by-Step Guidance
1. Teacher Needs
  - Clear step-by-step instructions for solving quadratic equations.
  - Relevant, understandable examples for students.
2. AI Prompt Example
  - Prompt: “I need step-by-step instructions for solving quadratic equations. First, provide the instructions, and second, provide 2 relevant real-world examples that follow the instructions step by step.”
3. Example AI Output
  - Provides the quadratic formula and numbered steps for solving equations.
  - Example 1: Basketball thrown into the air (projectile motion).
  - Example 2: Finding the area of a garden (geometry application).
4. Instructional Context
  - Teacher models and demonstrates the process using examples.
  - Used for direct instruction—whole group, small group, or advanced learners.
  - Goal: move students toward independent problem-solving with guidance.
Part Three: Creating Instructional Resources with AI
1. Purpose of Resource
  - Provide students with structured practice using guided worksheets.
  - Encourage gradual independence in problem-solving.
2. AI Prompt Example
  - Prompt: “Provide a worksheet for solving quadratic equations. At the top, place the problem for students to solve and a sample problem, and then create 3 columns:
    - Col 1 = instruction step
    - Col 2 = sample problem step
    - Col 3 = place for the student to write out the step for solving the actual problem
3. Worksheet Features
  - Top section: includes a sample and a student problem (e.g., “When will the ball hit the ground?”).
  - Three-column layout: step instructions, modeled example, and student workspace.
  - Encourages guided practice before independent problem-solving.
4. Teacher Follow-Up
  - Eventually move from guided practice to independent application.
  - Assess student mastery and understanding through completed worksheets.
  - Optional extensions: ask students to explain the meaning of solutions in real-world terms.
5. Practical Benefits
  - AI can quickly generate multiple worksheet versions with new problems.
  - Teachers can prepare formatted downloads for classroom use.
Conclusion: Using AI to Support Math Instruction
1. AI as a Teaching Assistant
  - Provides explanations, examples, and customized resources.
  - Supports both conceptual understanding and procedural mastery.
2. Benefits for Teachers and Students
  - Helps differentiate instruction for varying levels of readiness.
  - Allows teachers to focus more on guiding understanding and less on content creation.
3. Final Thought
  - AI enhances teachers’ ability to help students learn new math processes effectively.
  - Encourages real-world connections and independent problem-solving skills.