Introducing DOK 4 Math Performance Tasks
“Mathematics excitement looks exactly the same for struggling 11-year-olds as it does for high-flying students in top universities — it combines curiosity, connection making, challenge, and creativity, and usually involves collaboration.”
-Jo Boaler, Professor of Mathematics Education at Stanford University
Quality math instruction goes beyond building mathematical literacy—it should serve to create mathematical thinkers. A mathematical thinker approaches relevant mathematical problems with excitement and confidence in their own math skill set.
The Importance of Productive Struggle
Math teachers across the country are faced with the challenge of pushing student thinking to apply and extend mathematical concepts without frustration and discouragement. Doing so requires teachers to cultivate a positive culture around problem solving that promotes the application of math skills in real-life contexts at Strategic and Extended Thinking levels (DOK 3 and 4).
The shift towards more complex math doesn’t mean teachers are simply teaching math that is superficially “harder”; they are using new teaching methodologies that promote creative problem solving, collaboration, and exploration. However, in order to effectively do that, teachers are faced with the challenge of figuring out how to make those activities engaging and exciting AND designing them in such a way that they are open-ended enough for students to engage in productive struggle.
New Math Performance Tasks Engage Students in Productive Struggle
We are proud to introduce a beta preview of math performance tasks in Goalbook Pathways that help teachers facilitate productive struggle that pushes students to solve complex problems that actually matter. The themes that our content designers settled on excite students by validating their interests and engaging them in socially relevant content.
All of the math performance tasks currently available prioritize these markers of complexity:
- They have several possible paths to a solution.
- They are multidimensional, thus requiring students to connect multiple mathematical processes to be successful.
- They require students to engage in domain-specific discourse to solve problems and justify their reasoning.
- They engage kids in a high-interest topic worth struggling for.
- They are accessible to multiple levels of students with built-in low floor high ceiling access points.
The Hidden Connection Between Steph Curry and Pythagoras
We understand that the engaging topics don’t necessarily drive the excitement; the engaging topics paired with the fact that students are acting as mathematicians to solve real problems is what ups the excitement around solving complex math problems.
A middle school example, that is already being taught in some of our partner schools, requires students to calculate the approximate distance of an NBA star Stephen Curry’s buzzer-beater shots using the Pythagorean theorem. The task goes far beyond giving students a word problem that includes his name and a set of arbitrary values that they need to use to find an answer.
Students get to APPLY mathematics, which is vastly different than simply DOING it.
They must work together to utilize diagnostic data from actual player estimates and a video recording of the shot as well as a diagram of a regulation-sized court and their knowledge of the Pythagorean theorem. Equipped with that knowledge, they can create a plan of action that will result in a well-informed approximate distance of the shot.
One of the best aspects of this task is the fact that there is no single right answer! In fact, there isn’t even one way to solve the problem—there are myriad possibilities for tackling it. This means teachers are truly evaluating the thinking that students are engaging in by reviewing the math and the justifications that they come up with.
Another performance task has students do a statistical analysis of the resegregation of schools. The implications of their work is directly connected to their experiences as students, and the math that they’ll engage in mimics applied mathematics in real life professional/research contexts.
Check out our DOK Performance Tasks and get your students excited about math by following the links to the beta preview below:
- The Water We Eat — 6th Grade Ratios and Proportional Relationships
- Hurricane Relief — 7th Grade Functions
- Steph Curry’s Shot — 8th Grade Geometry
- Still Segregated — HS Algebra 2 and Statistics
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