I anticipated this would be the most challenging task, but before we could tackle it, we discussed our favorite candies. This positive mood set the stage for active engagement. Even usually hesitant students talked through strategies with their partners and participated enthusiastically.
Gauging Math Learning and Retention:
Using Performance Tasks to Move Beyond Standardized Testing and Unit Assessments
Written By: Andrea Knepper, 7th-grade teacher, VT
How can we tell if our math students retain learning throughout the school year? Standardized testing is not a good measure for all students, and even curriculum-provided unit assessments aren’t always effective. So, what other methods can we use to gauge learning and retention?
This school year, I used Exemplars performance tasks to evaluate what skills and strategies my 7th-grade students had retained and strengthened. During the last two weeks of school, I asked them to complete three Exemplars tasks focused on two high-leverage concepts: proportional reasoning and operations with signed numbers.
Specifically, I wanted to know about a handful of students who struggled to master grade-level concepts. These students participated in class, completed their work, and spent time with an interventionist. I wanted to capture their cumulative understanding.
Not So Fast
“Snails must not like mango and papaya!” “I used to have a pet snail.” “Why did they measure the snails’ improvement in different ways?” This buzz filled my classroom when I presented the Exemplars performance task “Not So Fast.” In this task, students compared the racing speed of three snails, calculated changes after diet and training, and determined which would win the next race. I selected this task to observe how students interpreted a graph, applied percent and fractional changes, and used rates to determine race times. After about 10 minutes of lively discussion, students eagerly applied their mathematical reasoning. Conversations demonstrated their understanding of mathematical concepts. For example, one student realized we needed to compare the snails’ speeds in inches per minute, while another shared different methods to calculate a 50% increase.
As students worked through the problem, I saw them successfully using the skills I aimed to observe. Surprisingly, even those who hadn’t shown proficiency on the unit summative assessment were able to calculate percent changes and fractional decreases, despite not formally working on these concepts for months.
Benji’s Allowance
“Benji should stop making bets with his friends.” “For having a $15 allowance, Benji spends a lot of money!” “How can we know what the transactions were? Are we supposed to guess?” These were some comments as my students tackled the Exemplars performance task “Benji’s Allowance.” This task involved adding and subtracting positive and negative numbers—a particularly challenging concept for many students. In addition to looking for evidence of proficiency, I wanted to practice the Exemplars’ Three Reads strategy.
To ensure all learners would be able to access this text-heavy problem, we made sense of the problem together. First, we read through the problem to understand the situation. During the second read, we identified the questions we needed to answer. Finally, we carefully read the problem section by section, marking important information and discussing possible solutions.
My gradebook showed that about two-thirds of the students were proficient on the integer operations unit summative assessment. My observations during the Benji’s Allowance task revealed students confidently asking and answering each other's questions and finding accurate solutions.
The Last Day of School
“What is your favorite kind of chocolate candy?” “Where are they shopping? These are good prices!” “Who gets to have the extra candy?” We were almost to the last day of school when I asked students to work on this task. The problem is about giving out candy so there was some extra excitement when we looked through it as a class. I chose this task to evaluate students’ ability to work with fractions, ratios, and proportions. In “The Last Day of School” task, students used survey data to calculate how much of each type of candy should be purchased for the entire student body and determined the number of bags and total cost.
"Even usually hesitant students talked through strategies with their partners and participated enthusiastically."
Some partners were stuck on how to use the small sample from the survey to determine how much would be needed for the whole school. I overheard talk of multiplying the results to match the total number of students, scale factors, and ratios. Someone mentioned the “constant thing we used when we were learning about writing equations”; I helped them out with the more formal terms, “constant of proportionality” and “equations for proportional relationships.” Students found they had multiple tools to work on this problem.
This Exemplars task, along with the previous two, allowed me to feel confident that the majority of my students were ready to build on their learning next year in 8th grade.
What Makes Exemplars Tasks Different?
"Observing my students work on these Exemplars tasks was eye-opening."
Observing my students work on these Exemplars tasks was eye-opening. I wasn’t doing anything different; students were working with partners as usual, yet there was a level of engagement and confidence not present in my usual curriculum-based lessons.
They were excited to solve the problems posed by the tasks. The concrete situations provided a context for students to apply their learning. The familiar contexts also allowed them to make predictions about their answers and evaluate whether their solutions made sense.
Most importantly, Exemplars tasks allow for multiple strategies to be employed so most students have an entry point. As I worked through the tasks personally before presenting them to the class, I found at least three ways to begin working with each problem. Watching students work on the tasks, I observed some using other strategies I hadn’t thought of.
When students felt stuck or thought the task was too challenging, we discussed what strategies they were confident with. Whether students wanted to use tables, models, an organized list, graphs, or anything else, we used that strategy to get started.
For students seeking a greater challenge, we extended the problem by asking them to confirm their findings using another strategy before tackling the differentiated questions included in the task. Some students were so interested in having different solution methods lead to the same answer that they set out to find as many ways to solve the problem as possible.
Reflecting on the use of Exemplars performance tasks throughout the school year has provided valuable insights into student learning and retention. Unlike curriculum-provided assessments, these tasks offered my students engaging, real-world problems that required them to apply their mathematical skills in meaningful ways. The excitement and confidence I observed in my classroom were clear indicators that students were not only retaining concepts but also deepening their understanding.
As educators, it’s crucial to seek out and implement assessment methods that truly capture student learning. Exemplars tasks have shown me that when students have the opportunity to engage with challenging, relevant problems, they rise to the occasion and demonstrate their capabilities in ways traditional assessments often miss.