Math, Personal

Today I made a mistake – and that’s okay.

Last night, my students completed their notes on “Estimating Irrational Roots”.  As a part of these notes, the students fill in a number line (which I obtained via another teacher or TPT or online – I can’t remember) with decimals and square roots.  By doing this, the students can see where the imperfect square roots fall in relation to the perfect square roots, integers, and decimals.  It’s a great activity because it is a great visual on a new and complex topic.

On this number line, there are tick marks to represent the integers, decimals, and roots.  The tick marks at the top of the number line represent the integers and decimals, the tick marks at the bottom represent the roots.  Now, this is where I am going to get a bit mathematical on you.  The √2 = 1.41 and the √3 = 1.73.  If you look at the chart, the tick marks are not accurately represented.  Honestly, I completely missed this.  It isn’t that I don’t know how to mathematically calculate square roots but it is that I did not check my resources to ensure they were accurate before giving to my students.  I should have checked my resources, especially resources I did not make myself, to ensure that they are accurate.

One of my students caught this mistake.  It was definitely one of those “Oh no” teaching moments.  It’s one of those moments that can make or break a teacher because you really have four options on how to handle the situation:

1. Tell the students they are wrong and ignore the situation.
2. Get upset and frustrated then blame someone else for the mistake.
3. Own up to the mistake and scratch the activity.
4. Own up to the mistake and create a learning opportunity.

So, which option would you choose?  More importantly, how many times have we all been guilty for not choosing the best option?

Quite frankly, Option #1 and #2 never came to my mind.  I’m willing to own up to my mistakes.  It’s definitely a frustrating situation, but it’s my own mistake and I do not have anyone to blame myself.  If I am being very honest, I would say that Option #3 has always been my default.  I’ll own up to my mistake, tell the student’s I will give them a new copy of the activity, and move on.  It’s not a bad option – but it isn’t the best.

Today, I chose to go with Option #4.  Own up to the mistake, but don’t just move on.  Create a learning opportunity because it is what is best for students.

Option #4: Own Up to the Mistake and Create a Learning Opportunity

As soon as I realized that the activity was incorrect, I saw a learning opportunity.  I realized that if the students were able to correct the number line and input the correct ticker marks for the roots, they would have an even greater understanding of the estimating irrational roots.

Step #1: Lead Students to the Mistake

• The first thing that I did was help the students understand the mistakes within the activity.  I asked them to find the square roots of the irrational roots for the first few lines and compare the square roots to their location on the number line.  They quickly realized that this was inaccurate.

Step #2: Assign Each Group a Portion of the Number Line

• Instead of having each student complete the number line individually, I assigned each group a portion of the number line to complete on the
whiteboards.  By doing this, I was even able to differentiate instruction and assign more difficult portions of the number line to my higher students and easier portions to my struggling students.

Step #3: Gallery Walk for Missing Portions

• After each table completed their number line, I had the students complete a gallery walk of the entire number line and fill in the remaining portions of their number lines.

After we finished the activity, several students commented that they had an even greater understanding of estimating irrational roots now that they had fixed their incorrect number line.  It was amazing – they actually enjoyed correcting the mistake!

My mistake turned into their success.

Like I mentioned earlier…I made a mistake – but that’s okay.

It’s all in how the mistake is handled.  Do you give up?  Move on?  Get frustrated or angry?  Or, do you grow from it?  Do you find a learning moment – for yourself and students?

This is a part of a set of blog posts from the Transparency: Real Stories from a Real Classroom series.

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