One Math Test. One Math Question.

This January I was particularly frustrated with the way I was teaching math.

I had one foot in the traditional textbook method and another foot in an unknown black hole, where I didn’t really know what I was doing.

I knew my practice needed some reform, as I could see the lack of engagement and challenge in my student’s eyes.

Everything changed when I started integrating some Robert Kaplinsky problems into my practice. If you are unaware, Robert Kaplinsky is a math education expert who has offered a myriad of free math problems for a variety of grade levels.

I was blown away by the number of mathematical competencies and math thinking that would occur in a single problem that he made. This is what led me to think about how a strong problem like this could potentially be used to assess my student’s mathematical thinking.

Why do my students need to answer thirty questions when I could just ask them one?

Out of this thought, and inspiration from Robert Kaplinsky, my one question test was born.

Now, I understand what you’re thinking. If there is only one question, it better be one heck of a question.

I agree.

A math teacher needs a degree of artistry to compose a question that weaves a variety of competencies into one scenario. Luckily, I had lived a very similar scenario that lent itself incredibly well to the unit my sixth graders were studying (decimal multiplication).

The scenario was as follows:

I (personally) do not listen to a large variety of music. However, all of my friends have Spotify Premium subscriptions. After hearing their raving reviews of how awesome it was, I had to justify whether paying $9.99 CAD (I’m Canadian) a month was worth it for me and my music taste.

My one question test.

I personally needed to estimate how many albums I would buy in a year, calculate how much Spotify would cost in a year (with the one month you get free), and justify whether the total cost is worth it.

In those four sentences alone I’ve described a scenario where a student must estimate reasonably, multiply & add decimal numbers, and justify & explain mathematical reasoning.

Those are the exact competencies I was looking to assess in a 30 question test, except the students did not need 30 questions to prove their proficiency.

On another note, a one question test does not take the hours of marking that a 30 question test can take, thus making the teacher workload a lot simpler. Often 2–4 questions of a traditional math test can be extended word problems. If this one question test consists of only a single word problem, the marking time is minuscule compared to the traditional way.

To cap it all off, the test isn’t even marked out of a total, it’s assessed by a rubric with math competencies. I love this because then I do not have students begging me for half marks to bump up their grade percentage. Either they are not meeting expectations, approaching expectations, meeting expectations, or exceeding expectations.

Under each competency, I ask a question to help with assessment clarity. This helps my students understand what is being assessed, but the questions also help guide me as I mark the test. These questions help me look for certain elements in their math explanation.

I used the following rubric:

Wait, what if the students don’t understand the problem?

Good question. A student who does not understand the single problem on a single problem test is in quite a bind.

A test like this takes scaffolding. While the scenario on the test was brand new, we had done word problems in practice that dealt with gym subscriptions or Netflix sign up costs. All of these problems had similarities to the test.

Because of the scaffolding done in earlier classes, all of my students understood the concept of the problem and were able to jump into the question, at least to begin.

Furthermore, I had a meticulous outline for the problem-solving. Students had to outline the question they were answering, the data they had in the scenario (or didn’t have), a plan for solving the problem, their final calculations, and a written justification.

This structure helped students understand how to start and how to go about solving.

In addition to the scaffolding, I set up a desk near the back of my classroom with a sign that said “Free Help.”

I wanted to encourage my students to ask questions instead of embracing a fixed mindset and being stuck. I never gave them the answer or revealed the process, but I would help clarify anything they asked, free of charge.

My favourite quotation from the math test class was when a student asked, “does it affect our grade if we go for help?”

I replied by saying, “Nope, it’s free!” and I pointed at the sign.

I can’t know for sure, but I think the free help, used or unused, put a number of students at ease. There can be a lot of pressure with a test in general, let alone when there is only one question.

Even after the scaffolding, and the “Free Help,” I did have a handful of students who finished the test approaching expectations (as it is with nearly any test).

For these students, I organized a time where they were able to peruse their submitted test and correct their mistakes or errors. I understand that on a traditional test they would potentially have other questions to help show their math thinking, so I see how another attempt at this problem can be warranted.

I returned the test with minimal feedback. At most, I told them that they had made a calculation error, an estimation error, or a justification error. From there, they needed to find their mistake. After this extra time for correction, I found it quite clear to see who was able to correct themselves and meet expectations, and who was not.

Was the test too easy for the “math genius” students?

I have three students in my class who seriously pride themselves in their math abilities. I have a feeling that all three of them will be disappointed with their mark.

These students are exceptional at traditional math, meaning their math abilities are often limited to copious computation. A real-life scenario with a number of moving parts requires more creative thinking than the isolated computation they are used to.

I’m thrilled by this because these students were challenged.

I’m looking forward to fostering a growth mindset with these students, as a fixed mindset can quickly set in when a subject area becomes simple or easy.

Where do I go from here?

After reflecting on this process, I am looking forward to future math tests. I personally loved this form of assessment and will likely use it for my next math unit.

The major pros were the following:

1. Providing an engaging & real life task

2. Creating a challenging problem for all math learners

3. Avoiding tedious assessment for the teacher

What would I change next time?

I am not convinced that I have come up with a perfect way of working with students who completely misunderstand the single question on a one question test. If I’m honest, this time, I was willing to cross that bridge when I got there, but I could see it being potentially more frustrating in the future.

This idea, in many ways, is a work in progress, but it’s something I’m willing to continue to work on, and something I’m willing to continue to refine. I’m a relatively new teacher and I’m looking forward to future growth in my math assessment.

If you’re interested in this form of assessment at all, I’ve made my test available for free on my Teacher’s Pay Teacher’s store or you can find me on twitter @MrRileyDueck.