MathematicsMathsMiddle schoolKey Stage 3
How to support productive struggle in math
Productive struggle in math is the effort students spend making sense of a problem that isn't clear to them yet. This guide gives three steps to support it, and a free ratios activity where Sparky asks a question after each mistake instead of giving the answer.
Jemel Fanfan | Founding Member at Flint
"My students are able to engage in interactive lessons that challenge them without overwhelming them. AI has made it easier for them to understand concepts by providing immediate feedback, allowing them to learn from their mistakes in real-time."
Rooban Arumugam, Lower School Math and English Teacher at SJK(T) SelamaWhy this matters
In one grade 7 class, a student finishes the ratio problems in five minutes and waits for more. The classmate next to her sets up every proportion upside down and gets 5⅓ cups of flour where the recipe needs 12. The first student learns nothing new, the second practices the same mistake ten times, and the teacher has to wait for quiz day to find out.
What productive struggle in math looks like
Productive struggle is the effort students spend making sense of a math problem that isn't clear to them yet. NCTM lists supporting it as one of eight effective teaching practices: give students time to struggle, and ask questions that move their thinking forward without doing the work for them (NCTM's Principles to Actions, summarized by the Colorado Department of Education).
- Give each student a problem that is a little hard for them
- Ask a question instead of fixing the mistake
- Give feedback right after each answer
A teacher with 30 students can't raise the level for every student who is ready and ask the right question about every mistake while it's fresh. Sparky, Flint's AI tutor, does it in each student's chat.
One ratio problem, practiced by two students
Both students are in the same ratios and proportions practice, and Sparky opens both chats with the same question. Each student has their own chat, and the problems after the first one depend on their answers.
Eli
Sparky
Eli
Confident.Understanding check
Eli
3/2 = x/8, so x = 12. 12 cups.Sparky
Eli
I don't know where to start.Sparky
Eli
1/25 = 3.5/x, so x = 25 × 3.5 = 87.5 miles.Sparky
Moved up a level, then solved it with one hint
Zoe
Sparky
Zoe
Okay, I think.Understanding check
Zoe
2/3 = x/8. 3x = 16, so x = 5.33 cups.Sparky
Zoe
3 is the flour and 2 is the sugar, so I flipped the first ratio. 3/2 = x/8, and x = 12.Sparky
Found the flipped ratio and fixed it
Eli gets a harder problem as soon as he solves the first one, and when he's stuck, Sparky gives the smallest hint instead of the answer. Zoe hears right away that something is off, and Sparky asks her to find the mistake instead of fixing it. The students and chats are examples we wrote for this page. The activity's guidelines tell Sparky to do both.
See who is stuck and who fixed their own mistakes
Sparky grades each chat against your rubric. The activity page shows who needs help right now, what the class does well, and what to practice next.
Example activity page
After a class finishes the ratios and proportions practice
The school and students are made up for this page. In this example, most of the class handles unit rates, and the area to practice is keeping each ratio in the same order.
Set up the activity for free
The ratios and proportions practice is in Flint's public library, with Sparky's role, guidelines, greeting and a rubric already written. Open it, select Use activity to copy it into a free Flint account, and move it to a class. Every student gets their own chat with Sparky, and the activity page fills in as they work. In the activity's Preview tab, select Try session myself to test the activity as a student before you assign it.
For grades 4 and 5, replace the list of levels in Guidelines for Sparky with your own unit. For example:
Example guideline
Levels, in order: 1. Equivalent fractions on a number line. 2. Comparing fractions with unlike denominators. 3. Adding fractions with unlike denominators. 4. Fraction word problems. When an answer is wrong, ask the student to find the mistake instead of correcting it.
For more math activities, see Flint for math.
Other use cases
See all use cases →MathematicsMathsMiddle schoolKey Stage 3
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How to teach adding and subtracting integers with temperatures: each student fills in a week of ski resort temperature changes with Sparky, gets a hint when they combine the numbers across zero, and moves to a harder day once they're right. Free activity.
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How to teach algebraic expressions
How to teach algebraic expressions from a real situation: each student writes an expression for money they earn, tests it in a spreadsheet in their chat with Sparky, and finds their own mistake when the totals stop matching. Free activity.
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How to teach amplitude and frequency
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