Helping children to think for themselves

Remember Engelmann’s premise that the mind is lawful? He further explains: “What humans learn is perfectly consistent with the input they receive.”

To get people to learn something, then — whether it is to read, divide fractions, or explain the cause of tsunamis — teacher models have to prioritise one thing above all else: getting kids to identify and internalise that law.

Previously, we talked a lot about how not to do that. Don’t under-explain, or kids will be confused. Don’t over-explain, or kids will likewise be confused, and also, it will take forever and rob kids of the practice time they desperately need.

So how do we effectively, eloquently, and simply propel students towards academic laws in just a few minutes?

We think that three basic teacher moves from Teach Like a Champion are good tools for getting this right, and they all hinge on getting kids to shoulder the thinking.

1. Cold Call: Don’t Do Thinking That Kids Should Do

It’s two-step equation day, and 2x + 5 = 15 is on the board.

We know that kids have learned to balance and solve one-step equations. If they already know that, then the teacher does not need to point out that this equation looks different than ones they’ve seen before. In fact, if the teacher does point it out, kids have already missed one opportunity to be on the lookout for the first of a few important laws in this lesson: solving this equation takes two steps.

Instead, a teacher could write on the board…

  1. 2x + 5 = 15
  2. x + 5 = 15

…and ask: “How is equation A different from equation B?” A pause for students to think, then, “Akeyo?”

Akeyo is in the hot seat, but more importantly, so is everyone else. Cold calling sets the expectation — in what should be a positive, energy-driving way — that kids should be ready to answer at any point in time. To be ready to answer at any time, you need to be thinking at every point in time.

The cold call is one of the simplest ways to ensure that every kid in the room is thinking. Not watching the teacher think, not listening to the teacher say things, not looking out the window, but getting down to the work of identifying 2x + 5 = 15 as a two-step equation.

Used throughout a model, this is a powerful way to make kids think, not watch (best case) or literally not watch (worst case). The cold call works well especially for “what’s the next step?” questions, ensuring that kids are actively solving a problem and internalising the laws that govern each step.

2. Turn and Talk: Don’t Do Thinking That ALL Kids Should Do

Thankfully, Akeyo answers the question correctly and the other kids can sigh with relief. Not for long, though. Another quick cold call: “What do we normally do to solve for x?” gets some version of “use the inverse operation to get X by itself.”

This is where we need to lock in this law, and give kids the opportunity to articulate and apply that process to a new context. Enter the turn and talk.

“How do we remove positive 5 from both equation A and B? Tell your partner.”

Now, every kid in the room has to explain how to balance the equation, and in so doing, actually solve the first step of the two-step equation without a teacher short-circuiting the thinking process. A teacher circulates and actively listens, a signal to all students to remain on-task and be ready to explain. With tight classroom management, we should only be about 90 seconds into this thing.

Another quick cold call for the answer, keeping kids accountable for having verbally done the math, wraps with this on the board:

2x + 5 = 15

2x = 10

3. Everybody Writes: Don’t Do Work That Kids All Should Do

It’s time for the teacher to say the next important law: 2x means 2 times x.

Assuming that a major key of this lesson is about balancing with opposite operations, not shortcutting to: “5 x 2 = 10, x is 5,” here is where we need to tap into what kids already know about algebra.

Eight more cold calls, call it 90 more seconds:

“What operation sign came before 5?”

“We used the opposite operation to remove 5 from the left and balance the right. What’s the opposite of addition?”

“What does ‘2x’ mean?”

“What is the opposite operation of multiplication?”

“What number do we need to divide from 2x to isolate x?”

“If we divide 2x by 2, what’s the quotient?”

“Now x is alone; how do we balance the other side?”

“What is 10 divided by 2?”

As the answers to these roll in, the teacher captures the steps on the board:

2x/2 = x

10/2 = 5

x = 5

(Or, the answers don’t roll in perfectly as scripted. Instead of hitting the panic button, here is where swift, simple articulation of the rules keeps the learning on track. “No, the opposite of multiplication is division. Shania, what is the opposite of multiplication? Everyone, what is it?” And keep moving. You lost 20 seconds, maybe.)

Now it’s time for everybody to solve a two-step equation, start to finish, and thereby crystallise the process and rehearse the laws.

The teacher writes a new, analogous equation on the board: 3x + 3 = 21, and sets pencils to paper. The teacher can circulate as the class solves independently, spot misconceptions (“Pili, we can’t subtract 3 from 3x to isolate it. What operation does 3x mean? What is the opposite of multiplication?”), and know what rule or rules students need to rehearse before practicing this independently.

Delivered tightly, this model should should take no more than seven minutes. In the entire model, there was one sentence of teacher explanation. It was the new rule for two-step equations: 2x means 2 times x.

With these three moves, we’ve not only kept the model tight and effective, but we’ve done everything we can to ensure that all kids are actively learning from it. In this set up, independent practice is not an abrupt drop-off into “now it’s your turn to think, good luck!” but a seamless continuation of what kids have been doing since the moment class started — just incrementally harder, deeper, and hopefully interleaved.

By setting up a teacher model for maximum student thinking, all parts of the lesson teach students to think for themselves.

About the author: Katie Cella is an Instructional Design Director at Bridge International Academies.

Click below to read more blogs