Performance-based math tasks in Teach to One: Math ensure that students apply their knowledge to solve problems using real-world scenarios. Integrated over multiple sessions, TTO’s math tasks are designed to dive into the conceptual, procedural, and applied understanding of multiple mathematical skills, and to explore the connections between these skills. Guided by teachers, working collaboratively with their peers, and grappling with the math independently, students work through the task, which culminates in a final performance-based assessment in which students must demonstrate their applied understanding of the connections between the learned math skills.
From shopping sprees to pedestrian malls, below are examples of TTO’s performance-based math tasks in action.
Developing Pedestrian Malls
Elise Lake’s class hadn’t even started yet, but that didn’t stop her students.
Lined up outside Lake’s fifth grade classroom at Columbus Magnet School (Norwalk Public Schools), the students were buzzing about the upcoming session. They had one more day to put the finishing touches on their business plans for a pedestrian mall. The next day, they’d be presenting their plans to investors.
The performance-based math task calls for students to design a pedestrian mall that included storefronts, restaurants, and other attractions like water fountains and play areas. As developers, their jobs were to create plans that analyzed and depicted the growth of stores and earnings over a number of years.
As part of the project, students also had to create a graphical analysis showing annual growth and provide a written explanation for how to define a coordinate system and locate points using coordinates.
Inside the classroom, students quickly found workspaces and got started. On a rug in one corner of the room, two students were creating a computer-generated map of their pedestrian mall and planned to project them on a whiteboard for their presentations the next day. Another student was creating a 3-D Map out of cardboard cutouts. Ms. Lake, the teacher, circulated between small-group tables to check on each student’s work and answer questions.
Using Exit Slips Data
Down the hallway, Misty Hofer facilitated a discussion to kick off her task session that day. Before they dove into their projects, which called for students to design an advertising campaign for a shopping spree at a store, Ms. Hofer corralled them around a rug to reflect on the previous day’s Exit Slip results. A large number of students didn’t pass, she explained, and she wanted to reinforce the task’s math concepts and project requirements before moving forward. In this case, students were learning how to find unit rates, solve problems using constant rates, and use ratio reasoning to convert measurements units.
Each student could choose what kind of a store they wanted to develop the campaign for, and Ms. Hofer asked them to think about their favorite places to go. “McDonalds!” a student called out. “Would an ice cream store work?” said another student.
Nodding, Ms. Hofer then had the students talk about the different items sold in their stores and how much they would cost. They’d have to include those details in their final demonstration to show how they calculated the unit rates.
The teacher-led discussion may have been unplanned, Ms. Hofer later explained, but it was necessary to ensure the students would get the most out of the project.
“Project-based tasks are probably the most difficult [modality] for educators to implement because there is a tendency to want to stick with what is recommended in the TTO task teacher guide and not deviate,” Ms. Hofer said. “But the guides are really just recommendations and customizing the projects is the best way for getting students to apply what they’re learning.”
Tasks for High School Algebra
Across town, at Norwalk High School, students in Kevin Cosgrove’s Teach to One Algebra class were also wrapping up a performance-based task session. For these students, the skills they were learning were:
- How to solve multistep equations with rational numbers and;
- Analyze and solve verbal problems whose solution requires solving a linear question in one variable.
For this performance-based task, students work in a picture framing shop and need to mat and frame some artistic photographs. The problem in this scenario is that they don’t know which ones need to be framed – all you have are notes about dimensions and perimeters from when the customer dropped off the photograph. To figure out the right ones, the freshmen had to sketch and label their drawings, and write out equations that give the perimeters of the framed pictures.
Toward the end of the session, students were spread out across the Math Center, with some working on tables and others standing at the front using the whiteboards as an easel. Every student has to develop their own task projects, but there are opportunities for collaboration. One of the students standing, Brenna Dominick, was almost done designing her poster to present the next day.
TTO was different at first, says Dominick, and it took time getting used to the movement to and from different areas of the Math Center for each learning modality. Cosgrove agreed that it took a while for him to get used to the new structure, but everyone—the teachers and students—have adjusted and understand what’s expected of them. Now, he says, the self-pacing aspect of the program has meant that some students are “learning skills that no other algebra class in the school has learned. The exposure to skills is so much broader than what you’d normally get.”
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