AI–Powered Solutions: Bridging Math Misconceptions with Scaffolded Questioning

A practice we have been following for several years in the middle school maths department is taking a Follow-Up Worksheet to class after a review or an exam to tackle common misconceptions. Our goal has been to frame questions that encourage students to reflect on their thought processes and understand the correct approach to problems. While designing these worksheets was once a time-consuming task—requiring us to think deeply about students’ minds and craft precise questions—AI has now streamlined the process, making it faster and more efficient than ever.

Below is an example of a prompt and my leading ‘conversation’ with ChatGPT. The transcript of the chat is attached for those interested, but to summarize:

• I gave a prompt about a Grade 8 quadrilateral problem and asked me to target a misconception where students mistakenly identified the quadrilateral as a kite.
• ChatGPT provided questions to first target the misconception and then leading questions to help students find the correct answer.
• I then asked it to refine the questions to encourage deeper thinking, so ChatGPT adjusted the sequence to help students reason through the problem without giving away key steps.

Now, here is the detailed transcript of the chat. Do note how ChatGPT refines the leading questions. Initially, I was not fully satisfied with its first set of questions. After clarifying my expectations, ChatGPT quickly adjusted its response to better align with my needs, ultimately providing a strong sequence of questions.

User(me): Following is a question from Grade 8 Quadrilaterals. Several children wrote the answer as a kite. First target the misconception the children displayed that it is a kite and form a leading question to address that. Then, frame leading questions to help students arrive at the correct answer.

If the angles of a quadrilateral are in the ratio 1:2:2:1, then the quadrilateral is a

1. Rhombus b. Parallelogram c. Kite d. Isosceles Trapezium 

ChatGPT: The misconception that the students displayed here is assuming that a quadrilateral with angles in the ratio 1:2:2:1 can be a kite. However, a kite has one pair of opposite equal angles, and the other angles are typically unequal, not in a 1:2:2:1 ratio.

To address this, here are some leading questions:

Targeting the Misconception (Kite):

1. “What do we know about the angles of a kite? Do both pairs of opposite angles have a specific relationship?” Expected response: “A kite has one pair of equal opposite angles, but the other two angles are different.”
2. “Does the angle ratio 1:2:2:1 match the property of a kite’s angles?”Expected response: “No, a kite doesn’t have angles in that ratio.”

Leading Questions to Arrive at the Correct Answer:

1. “What is the sum of the interior angles of any quadrilateral?”Expected response: “360 degrees.”
2. “If the angles are in the ratio 1:2:2:1, how would you express the angles in terms of a common variable?” Expected response: “The angles can be written as .”
3. “Can you write an equation for the sum of these angles?”Expected response: “Yes, ”

4. “What does equal when you solve this equation?”

1. Expected response: “60 degrees.”
2. “What are the actual angles of the quadrilateral once you substitute the value of?”Expected response: “The angles are 60°, 120°, 120°, and 60°.”
3. “Now, based on the properties of quadrilaterals, which type of quadrilateral has two pairs of equal angles and one pair of parallel sides?”Expected response: “An isosceles trapezium.”

These questions guide the students from addressing their misconception about kites to determining the correct answer, which is an isosceles trapezium.

User: I like the questions to target the misconceptions. However in the leading questions to arrive at the correct answer, “What is the sum of the interior angles of any quadrilateral?” I feel is a giveaway. Can you add a question before that so that some students can think of this themselves?

ChatGPT: You’re right; it’s helpful to guide students towards discovering the sum of the interior angles themselves. Here’s a modified sequence of leading questions:

Leading Questions to Arrive at the Correct Answer:

1. “What do you know about the sum of angles in a triangle? How might this help us with a quadrilateral?” Expected response: “The sum of the angles in a triangle is 180 degrees, and a quadrilateral can be split into two triangles.”
2. “If you split a quadrilateral into two triangles, what would the sum of the angles in the quadrilateral be?”Expected response: “The sum would be 180° + 180° = 360°.”
3. “Now that we know the sum of the angles in a quadrilateral, can you express the given angles in terms of a common variable based on the ratio 1:2:2:1?”Expected response: “The angles can be written as .”

The remaining questions were the same as in the response above.

This adjusted approach encourages students to think about how to derive the sum of angles in a quadrilateral, fostering deeper understanding.

User: No, that’s not what I meant. They do know that the sum of angles is 360. Why should they think about this step at all? That is given the angles of a quadrilateral are in the ratio 1:2:2:1, why should they think they have to find the sum of angles?

ChatGPT: Thank you for the clarification. If the students already know that the sum of the angles in a quadrilateral is 360°, they should still be guided to realizewhyfinding the sum of the angles is relevant in this problem. To address that, I’ll adjust the flow to lead them into thinking about using the ratio to find the actual angles.

Here’s a revised sequence:

Leading Questions to Arrive at the Correct Answer:

1. “If the angles of a quadrilateral are given in a ratio like 1:2:2:1, what information can this ratio tell us about the actual angles?”Expected response: “The ratio tells us how the angles compare to each other, but not the actual angles.”
2. “If we want to find the actual angles, what do we need to know in addition to the ratio?”Expected response: “We need to know the total sum of the angles.”
3. “What is the sum of the angles in any quadrilateral?”Expected response: “360 degrees.”
4. “Now that you know the sum is 360° and the ratio is 1:2:2:1, how can you express the angles using a variable?”Expected response: “The angles can be written as .”

The rest of the questions were the same as above.

This sequence ensures that students realize they need to find the actual angles from the ratio and why it’s relevant to solving the problem.

This exchange highlighted the importance of clear communication and the adaptability of AI in enhancing our teaching practices.

AI is transforming the way educators approach teaching, offering personalized learning paths and effective tools to address student misconceptions. How is AI being used to enhance learning in your classroom?

#AIinEducation #MathEducation #EdTech #ScaffoldedLearning #StudentEngagement