Courses Designed For High School Students
Pathways curriculum materials are complete course resources including student workbooks with comprehensive lesson investigations, homework, and online lessons and repeatable practice. The materials also include a teacher support system based on the latest research on how students learn key mathematical ideas and how instruction can support the development of students’ mathematical thinking and problem solving abilities. Our materials promote conceptual understanding and procedural fluency by promoting reflection on repeated reasoning. Students in Pathways courses acquire a renewed confidence in their ability to make sense of ideas and develop meaningful formulas to represent patterns and relationships.
Precalculus
Pathways Precalculus prepares students for calculus with a coherent approach grounded in covariational reasoning and rate of change. Students are given ample opportunities to conceptualize and model dynamic relationships and learn to approach novel contexts by first identifying and describing patterns in how the values of two quantities change together. Recognizing similarities and differences in these patterns across a variety of contexts motivates conceptualizing function families and exploring the properties of different functions. Similarly, a focus on rate of change throughout the course is a unifying theme that helps students see connections across lessons and units as well as giving them a strong foundation for beginning calculus. Note that our Precalculus materials have been used successfully in both honors and non-honors course levels.
Algebra II
Pathways Algebra II is a flexible course that prepares students for either precalculus, trigonometry, or statistics. Similar to our precalculus course, Pathways Algebra II is a coherent approach grounded in covariational reasoning and rate of change but with a stronger emphasis on building students’ fluency in algebra. Students are supported in conceptualizing and modeling dynamic relationships with particular attention paid to seeing connections between multiple representations of these relationships. In particular, students build powerful personal meanings for the algebraic statements they generate and work with as well as the meanings for the operations they perform. Depending on question selection, Pathways Algebra II can serve as a non-honors curriculum or a more rigorous honors-track curriculum.
Geometry [Under Development]
Pathways Geometry weaves together three key ideas to form a coherent, interactive, and engaging exploration of geometric concepts. Transformations and their properties form the course’s foundation, with congruence, similarity, area, volume, and other ideas built from properties and consequences of performing sequences of transformations. Constructions are developed alongside transformations as ways to accurately reproduce figures and transformations, making constructions feel like natural extensions of daily discussions and not disconnected processes to memorize. Finally, students are encouraged to explore geometric figures and generate hypotheses to test and ultimately prove rather than always being asked to prove theorems the teacher and textbook gives to them. This shift makes the process of generating proofs or providing counterexamples a natural consequence of making conjectures and not an esoteric exercise.
Algebra I
Pathways College Algebra is a flexible course that prepares students for either precalculus or alternative paths such as business calculus, statistics, or finite mathematics. Similar to our precalculus course, Pathways College Algebra is a coherent approach grounded in covariational reasoning and rate of change but with a stronger emphasis on building students’ fluency in algebra. Students are supported in conceptualizing and modeling dynamic relationships with particular attention paid to seeing connections between multiple representations of these relationships. In particular, students build powerful personal meanings for the algebraic statements they generate and work with as well as the meanings for the operations they perform.
Secondary Mathematics [Integrated Approach]
Pathways integrated curricula (a combination of Algebra I, Geometry, and Algebra II taught over three years) is built from our Pathways Algebra I, Geometry, and Algebra II courses with the same focal points and philosophy. [Secondary Mathematics I and Secondary Mathematics II are mostly available now. Secondary Mathematics III is under development.]
Custom Courses
Pathways developers can (and frequently do) create custom courses for each site. Customization can range from minor modifications to the table of contents or adding additional skills practice to generating new lessons and homework for topics not currently included in a course.