By Jen McAleer, posted May 8, 2017 —

Estimation is a difficult skill for many people. Take Andrew Stadel’s question from his NCTM 2017 presentation: How long is a dashed line on the highway? See the image below.
 

 

I asked my students the same question; this is a breakdown of their estimates:

1–2 ft.: 20 percent

2­–3 ft.: 40 percent

3–4 ft.: 15 percent

4–5 ft.: 15 percent

5–6 ft.: 5 percent

6–7 ft.: 5 percent

Over 7 ft.: 0 students

 

Much to my students’ surprise, the actual answer is between 10–12 ft.

 

Estimation is a practiced yet often undervalued skill in the mathematics classroom. Too frequently, we use estimation as an isolated practice at the end or at the beginning of class and generally spend only two to five minutes on it. An estimation activity is viewed as something fun that gets students involved, but it is often not discussed beyond “Yea, you were close!” Estimation can be much more. Presenting an estimation activity should be an opportunity to refine and make our estimating skills more precise.

In my school, we have pushed to have estimation be a part of our daily routine. In many classrooms that I have visited, I have noticed that the estimation activity is simply a warm-up and is disconnected from the mathematics the students will be learning. When we consistently disconnect estimation, students will not connect the value of using estimation when performing more precise mathematics. No wonder we aren’t good at estimating.
 

We are constantly robbing our students of opportunities to jump into mathematics using what every child has: intuition. Some students have better estimation skills than others, but providing opportunities for students to discuss how they approach estimation is important and necessary in our classrooms. We must make time for these types of exercises, and these opportunities should not be brief or an activity rated “correct or incorrect.” Talking about possible approaches to a task and refining these approaches is just as important if not more so.

One conclusion we have reached at my school is that not all estimation activities should revolve around finding the amount of candy in a jar. Note: Never ask a student to take a wild guess; you will get answers ranging from 1 to 1,000,000. In fact, to ask for a “wild guess” oversimplifies the process and meaning of estimation. It is not a bad estimation task, but it should not be the only task. Estimation questions that deal with time, distance, and volume, for example, are just as valuable and allow students to see the connection between mathematics and the world around them.
 

Estimation activities cannot be done in isolation within a math class. They should be part of the conversation of mathematics and should lead to the discovery of efficient ways to mathematize the world. They cannot and should not be relegated to five-minute warm-ups or exit ticket exercises in which the reward is whether the student is right or wrong. We need to find the time to do these tasks thoughtfully and carefully in the classroom.

In my next post, I will be discussing best practices for how to implement estimation into your classroom.

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Jen McAleer is the head of middle school mathematics (grades 6–­8) at the Carroll School in Lincoln, Massachusetts. The Carroll School serves students with language- based learning difficulties who also tend to struggle with mathematics. McAleer has been teaching middle school for ten years and has a passion to give all students a voice in mathematics and provide them with opportunities to be and feel successful working with higher-level content, despite their struggles with procedures and computation.