The Hidden Power of Estimation

Let's talk about an area of maths that we ALL use everyday, is critical for developing mathematical understanding – yet, is barely mentioned in the curriculum (not to mention, poorly covered by most resources)…

Estimation.

Let's talk about estimation.

Why bother with estimation?

If you open up a typical textbook or worksheet, this is what you'll see:

How a typical textbook or worksheet presents estimation.
How a typical textbook or worksheet presents estimation.

What do these communicate to learners about the value and purpose of estimating? According to many textbooks-

  • Estimation is dry & mundane
  • It's a skill to be drilled.
  • There's no clear benefit of estimating over SOLVING.

Yet, surely there's more to it than this?

When asked: ‘Why bother with estimation?', here's what a group of teachers had to say-

Christine: A lot of the time you don't need the exact answer
sarina: Because we use it!
Anthony: It can help validate answers
Samantha: Gives a sense of what a reasonable answer may be. When to go back and work out the problem again
Sarah: Students need to be able to make sense of their answers
Naomi: Extremely useful practical skill
Bernadette: Helps with checking reasonableness of answers
David: It's good to have a feel for how big and small numbers can be.
Thomas: It helps us to check answers
Cindy: It helps to check if your answer is reasonable.
Rhiannon: supports understanding the reasonableness of ones answer
Andrew: It values everyones particular insights and strategies
Peter: Its a way of evaluating the reasonableness of an answer
Rabia: Quick decision making would require estimation
Danijela: it moves the focus away from precision and towards developing strategies
Katies: Helps know if your answer could be correct

(What else would you add?)

Across these teachers' responses, you might have noticed some themesp. Estimation helps learners to:

  • get a ballpark direction for a problem they're solving
  • think about strategies
  • check the reasonableness of answers.

Let's look at some of these ideas more closely…

What does estimation offer maths learners?

Estimation is a skill you can develop – BUT it's also so much more. (Otherwise those typical textbook questions would be bang on.)

Here are three valuable ways that students benefit from meaningfully using & practising estimation on a regular basis-

1. Estimation builds understanding

Having a ballpark figure provides learners with a general direction. For example:

  • Should my answer be in the hundreds or thousands?
  • Are we talking metres or kilometres?
  • Am I looking for a larger or smaller number than what I started with?

Using this information, the question learners might then ask themselves is: Given where I'm roughly heading, what's an approach I can take?

Later, that ballpark figure also helps learners to see if their answer is vaguely reasonable. Instead of just reaching an end point and moving onto the next question, the learner's in a position to ‘sense-check' the answer for themselves – the answer has become meaningful.

2. Estimation builds curiosity

By asking learners to have a say – and to, therefore, get invested in what they're doing, estimation:

  • builds curiosity about what might be,
  • carries us into the realm of possibility, and
  • suggests that imagination has a role in maths class.

Why does this matter?

Consider what learning without curiosity means:

  • disinterest,
  • apathy,
  • switching off.

Learners in this position will enter a classroom, go through the motions and then leave, without any second thought to what's just passed.

Curiosity drives learners to find out more and to enrich their own understanding of the information in front of them.

Curiosity is essential for a desire to learn.

3. Estimation builds confidence

Hand-in-hand with curiosity, is confidence.

Quite often, maths is hyper-focussed towards getting precise answers. If learners don't see themselves as capable, then they will quickly shut down.

The effect? Without a sense of confidence, learners will close themselves off to the much broader field of mathematical knowledge that exists beyond school and that can enrich their life.

Estimation gently re-adjusts our attention, by inviting learners to have a go – without the pressure of needing to be ‘right'.

This first step, importantly, paves the way for testing ideas and taking mathematical risks. These are essential strategies for ongoing learning and managing mathematical challenge.

None of this will happen unless…

Now, we need to remember one essential component to all of this: Estimation WON'T build understanding, curiosity or confidence WITHOUT a meaningful context.

What does that mean?

A context for estimating:

  • can be real or imagined,
  • must support a greater goal, and
  • make sense to the learner.

In other words, students need relevant background knowledge to estimate. For example: If we don’t know what furlongs are, how can we estimate the number of furlongs in a marathon?

In summary:

Estimation is more than just a skill to develop. When used & practised in a meaningful context, it builds-

  1. Understanding
  2. Curiosity
  3. Confidence.

Join the Conversation

2 Comments

  1. I agree with all the aspects of why ‘Encouraging estimation’ should be the soul behind the lesson plans.
    Well summarised.

    Can we not bring it into the curriculum ?

    1. That’s a very good question.

      The Australian curriculum has proficiency strands (fluency, understanding, reasoning and problem solving) which underpin all curriculum content. I suspect this is where estimation would fit best as well.

      In saying that, because estimation works in service of other things (like understanding measurements), it’s then harder to pin down for something like curriculum documentation.

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