Embedded Files
The story of math at Polaris is further expounded upon in the Education Week article, "From Abacus to Algebra: Growing Young Mathematicians".
Mastery
Mastery
The first dimension of student achievement—Mastery of Knowledge and Skills—examines students' ability to apply their learning, think critically, and communicate clearly.
Since our initial EL Education credentialing five years ago, Polaris has intensely focused on EL Education's Core Practice 15: Teaching Mathematics, which states: "Teachers choose challenging curriculum and generative problems that will enable students to discover the mathematical concepts behind algorithms and procedures. They engage students by asking them to grapple with complex problems independently and to discuss and critique each other’s strategies. Students learn to reason abstractly and quantitatively, to model real-world situations mathematically, and to construct and critique mathematical arguments."
As a school, we developed a vertically-aligned problem solving block centered on Cognitively Guided Instruction (CGI), which is designed to build students’ natural problem solving ability and draw out their inventive strategies as well as deepen their comprehension of word problems and complex mathematical situations. During problem solving, students independently grapple with complex tasks and use discourse to articulate their mathematical thinking with peers.
Below, our portfolio will evidence the following:
Polaris students continuously show remarkable mathematical growth through problem solving and discourse.
Polaris students continuously show remarkable mathematical growth through problem solving and discourse.
Problem Solving & Discourse
Problem Solving & Discourse
Until 2013, Polaris taught math by having students follow rules rather than understanding the intricacies of how math works. We were not alone in this kind of teaching - this was (and often still is) the norm for math instruction across the country (cf. The New York Times article Why do Americans Stink at Math?).
With our student achievement growth stagnant, we decided to pilot new mathematical teaching strategies based on Cognitively Guided Instruction or CGI (based on the work of Thomas Carpenter et al.). Teachers learned that students move along a trajectory of algebraic thinking—from direct modeling to invented algorithms—that prepares middle school students to deeply understand rational numbers and algebra.
To utilize this framework, teachers first determine where students are on the trajectory, creating daily independent grapples that engage students in rigorous problem-solving. These tasks are directly followed by student-led discourse that collaboratively reveals students' current understanding and new insights from the grapple. Teachers facilitate robust math conversations where all students explain their thinking to their peers (cf. 5 Practices for Orchestrating a Productive Math Discussions and Ensuring Mathematical Success For All Students).
These two practices—problem solving and discourse—have transformed our students' ability to understand how math works at deep, conceptual levels.
To see examples of these practices, reference the Student Math Work (above) and Student Discourse Videos (below).
Math Video 5.m4vMath Video 3.m4vMath Video 1.mp4Student Growth
Student Growth
Polaris students grow faster in math mastery compared to their Chicago Public School (CPS) peers and at the national level, evidenced by the NWEA Measures of Academic Progress. This remarkable growth is a major factor in our continued CPS Level 1 rating (q.v., Polaris' School Quality Rating Reports). Additionally, Polaris students report they engage in dramatically more rigorous math instruction compared to their CPS peers, illuminated in the University of Chicago's 5Essentials school climate survey.
Balanced Math
Balanced Math
Come see our students and teachers in action at EL Education's first math-based Site Seminar!
Serving as a model of problem solving and discourse, the embedded video (left) shows Ms. Iehl's third grade class developing a conceptual understanding of the commutative property of multiplication.
While problem solving and discourse are paramount to our student success, these practices fit within a larger curricular framework we have coined Balanced Math.
To learn more about the entirety of math at Polaris, the two documents linked below provide an overview of our Math Vision and Math Components.
Mastery
Polaris students continuously show remarkable mathematical growth through problem solving and discourse.Mastery
Polaris students become more ethical people through ongoing reflection.
Polaris students are active citizens; their authentic, personal voices are heard in high-quality work that connects academics to real-world issues.
At Polaris, we have dramatically improved our strategic planning process and shared leadership practices that have allowed for focused, sustainable school growth.
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