How do we know when students are proficient with a math skill? While there are many measures of proficiency in mathematics, what really matters is whether or not students can solve a problem when the problem is in front of them. Our best hope as teachers is to help kids develop the curiosity, the critical thinking, the content knowledge, the stamina, and the desire to solve whatever math problem they face.
While I keep this hope in the forefront of planning and assessment, I noticed that my fifth and sixth graders were not showing these traits when it came to the quizzes I gave. For many, it was just a quiz, and if they could get enough points, they could pass and be done.
Math should be joyful and challenging, yet this cycle of assessment was neither. What if the way we measured mastery actually told us what kids know? And what if kids were a little bit excited about showing us their stuff?
A solution presented itself when I discovered this problem-solving framework. The structured format helps kids work through challenging problems in a way that scaffolds their thinking. What if I adapted this framework and gave kids one question to solve instead of a traditional quiz?
I grappled with the fairness of having just one chance to show proficiency. Traditional assessments offer multiple chances, but when there are many problems, kids can score enough points to pass without really knowing the math. One fair question, on the other hand, is a way for kids to show what they know without taking up too much class time or awarding points for the sake of points. I give one such quiz per unit, which comes to about one every three weeks.
While a one-question quiz seems like a simple assessment, research and planning are required to make it work in a way that is fair to teachers and kids.
5 Necessary Steps to Implement a One-Question Quiz
1. Curate standards-aligned, challenging, and fun problems. For obvious reasons, kids should not all solve the same problem. Rather, you’ll need a hefty bank of problems that align to the standard being assessed. You can find problems in all the usual places: Illustrative Mathematics tasks, the Achieve the Core Coherence Map, or even the curricular materials you already use.
Keep in mind that no one wants to solve a boring math problem, so the problems should also be fun. When I’m selecting problems, I tend to revise them and get a little silly with names or scenarios that relate to our school. Generally, I gather questions daily as I’m planning my lessons, so selecting the best ones takes less time. To get a fair and robust bank of questions, it takes me one to two hours.
2. Sort the problems into levels of difficulty. Once you’ve found several problems and slightly adapted them to fit the criteria, it’s important to sort them into groups. Which of the problems will challenge your go-getters, and which have friendlier numbers for kids who need more processing time?
Make three to five groups of problems that can be given to the three to five levels of need in your class. I print them on different colors of paper, and I never keep the colors consistent because I don’t want kids tracking themselves or their peers into ability groups. Here is the problem bank for our unit on data analysis.
3. Adapt the framework, and create a rubric. While the problem-solving framework mentioned above is great, it does not serve all standards. For each unit, I adapt the framework a little to reflect the math we are learning. It’s important to maintain some sections for each quiz. Always ask students to estimate before they solve, and always have them defend their answers and show their calculations.
It’s essential to have a clear understanding of what mastery requires. Our school uses a four-point grading system. Students can exceed, meet, approach, or not meet expectations. Doing the math accurately and defending their thinking is meeting expectations. How can you have students exceed? Do they need to make an additional graph? Create an equivalent expression? Solve using a different method?
When explaining this to students new to our school, I tell them that exceeding expectations is a 95, meeting expectations is an 85, and so on. Connecting the grading scale to a system that is familiar helps students and their families alike. Whatever grading scale you use, think this through before you give the assessment and explain the system to students.
4. Consider safety nets. With just one question on the quiz, it’s only fair to offer some support. An easy way to do this is with a checker. Once a student has solved their one question, they find a classmate with the same color question but different problem to serve as their checker. All students serve as checkers, and the job of the checker is to look at the work and decide if it’s correct. They are forbidden to tell the correct answer but are allowed to say that something is wrong.
The teacher can help the checkers by creating questions on the framework for them to answer. Once the checker is done, the student can revise their work and submit it for a grade. It’s important to explain to everyone that the checker is human, so mistakes might be made. Having students check for those who have a similar level of question helps prevent situations where the checker is unsure of the accuracy of their classmate.
A benefit of the checker system is that each student is required to apply their understanding of the math to a second question, which generally reinforces the standard. Reminding students of the possibility that the checker could be wrong does highlight the need to double-check the work both before and after it’s checked. In situations where a checker has led a classmate astray, I generally intervene before the final grade is rendered.
Another safety net that I offer is retakes. If a student does not meet expectations the first time around, they are encouraged to practice a little more and try again later that week.
5. Reflect on results. The first time we tried this, many kids did not meet expectations. This was demoralizing for all of us, but it forced kids to reflect on their own understanding of the standard. They practiced and tried again, and most were able to meet expectations.
While we know that grades are not motivating, we know that success is. A positive outcome of the one-question quiz is that kids work hard to meet or exceed expectations. This means they are using curiosity, content knowledge, stamina, and desire to solve interesting math problems. They also become better collaborators and better participants in mathematical discourse. Rather than simply giving answers to each other, they’ve changed their language to say things like “Look at that again” or “I like your approach in solving this problem.”
The one-question quiz requires a lot of teacher preparation and student commitment to trying. However, I believe it’s an accurate and fair assessment of whether or not students have command of the standards learned in class. Perhaps more important, it creates a collaborative community of mathematicians in the classroom. Shifting the focus from grades to understanding and problem-solving is the ideal outcome and well worth the investment of time.
