Pathways Online Courses
Pathways turn-key online materials are designed to support asynchronous mathematics courses. Some sites alternatively use the online course materials in flipped course settings, as supplements to more traditional courses, or as co-requisite lessons for students who need more support to be successful in their mathematics courses. The online courses include cognitively-scaffolded lessons that focus on students taking an active role in constructing new knowledge, homework, quizzes, assessments, videos, and interactive applets.
Typically the turn-key courses are integrated into a Canvas shell to make it easy for students and instructors to access the materials and connect with school gradebooks and learner management systems. Sites not using Canvas typically access the course materials through custom iMathAS shells.
Pathways Online Course Features
Conceptually-Oriented Lessons
Each course includes online lessons linked with in-class investigation lessons printed in the Student Workbook. These lessons are designed to actively engage students in constructing personal meanings for important lesson goals.
Students are not asked to passively watch videos that demonstrate disconnected algorithms and then mimic what they see. Instead, students interact with dynamic applets and answer carefully scaffolded questions so that the mathematical ideas unfold naturally and sensibly. If students struggle, feedback and hints are programmed to support them in making sense of the problem so that they can be successful.
Integrated Dynamic Applets
Online lessons include integrated interactive applets to help students visualize and explore mathematical relationships they are asked to model.
Research indicates that many students do not conceptualize variables as representing the value of quantities when those values can change, and that students must conceptualize quantities and relationships for themselves if their mathematical models are to be meaningful to them. These dynamic applets support students seeing variation in mathematical contexts and help them visualize the quantities and relationships critical to generating meaningful models.
Repeatable Practice and Assessments
Online homework is included that corresponds with the online lessons, and repeatable skills practice is available to allow students to improve their procedural fluency. Online assessments are also available that provide students and their teachers with immediate feedback on their progress.
Short Conceptual Videos
Lessons are supported with short instructional videos that help motivate mathematical ideas, clarify connections between ideas, lessons, and units, and help students ensure they are making sense of the lesson’s key ideas.
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.
College Algebra
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.
Intermediate Algebra [Under Development]
Pathways Intermediate Algebra focuses on addressing key conceptual foundations students need to be successful in college algebra, various STEM fields, and in everyday life. The course supports students in conceptualizing mathematical relationships and communicating information about those relationships through various representations. Exploring and modeling dynamic situations helps students develop powerful images of variation and covariation, the meaning of variables, and the meaning behind the structure of expressions and algebraic statements.
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.