Who We Are
The Pathways writing, research, and professional development team is made up of mathematics educators and education researchers committed to operationalizing the latest research on mathematics teaching and student learning into classroom resources and practices that improve the quality of students’ learning experiences.
Piloting of Pathways materials began in 2006, and since then we have continually revised and refined our approach to lesson design, contents, and professional development training based on research results, student performance, and feedback. Tens of thousands of students and instructors have benefited from using Pathways materials, and we look forward to impacting many more!
Pathways History
The following is a brief history of the Pathways project and curriculum materials.
Phase 1
Pathways began as a professional development training program for secondary mathematics and science teachers with the primary goal of impacting students’ classroom experiences and improving their success and persistence in STEM fields by improving teachers’ mathematical knowledge and teaching practices. Furthermore, to the extent that teachers’ knowledge and practices shifted, to understand how and why those changes occurred (or did not occur). The hope was to produce a research-developed, refined, and tested model of in-service professional development for secondary mathematics and science teachers.
Participants enrolled in graduate level coursework to increase their understanding of key mathematical ideas (covariation, quantitative reasoning, meaning of function, etc.). Participants also participated in professional learning communities (PLCs) to promote reflection about personal understanding of mathematical ideas and student thinking relative to those ideas.
Phase 1 Goals
- Improve teachers’ understanding of foundational mathematics & science ideas and connections between ideas (including covariational reasoning, function reasoning, etc.).
- Improve teachers’ reasoning abilities and STEM habits of mind (problem solving, scientific inquiry, engineering design).
- Improve teachers’ content knowledge for teaching, e.g., the processes and complexities of acquiring understanding of key ideas.
- Support teachers in reflecting on and modifying their classroom instruction.
- Understand the impacts of these on students’ learning.
Key Findings
- Teachers’ understanding of important mathematical ideas increased, but there was a high degree of irregularity in teachers implementing problem-solving skills in their daily lessons.
- The research team discovered that a focus on “speaking with meaning” (Clark, Moore, & Carlson, 2008) in classes and PLCs corresponded with larger shifts in PCA scores for teachers and teachers self-reporting greater understanding of ideas, more attention to student thinking in lessons, and an improved ability to articulate their course goals when communicating with parents, students, and administrators.
Challenges remained that restricted the impact on student learning, including (i) that teachers felt constrained in their ability to shift their teaching goals due to limited high-quality curriculum resources, (ii) that they struggled to reconcile new ways of thinking about mathematics with traditional approaches they had used in their past experiences, (iii) that teachers did not have the daily support needed to help them enact new images of the role of the teacher (“stand and deliver”) and the role of the student (“memorize and practice procedures and solution algorithms”) in their classrooms, and (iv) that some teachers did not have the confidence that students could learn and work with the same meanings that they developed in the professional development settings.
Phase 2
Phase 1 demonstrated that teachers needed dedicated support in order to implement what they learned in the professional development setting in their individual classrooms. Teachers rely heavily on curriculum materials to drive the focus and content of their lessons, and their current curricula were inadequate in helping them implement new learning goals for students. We hypothesized that a coherent, cognitively-scaffolded curriculum aligned with the learning goals emphasized in our professional development trainings would help teachers make positive shifts that would impact students’ learning experiences. We began with Pathways Precalculus, a course that could be simultaneously piloted in both secondary mathematics and university classrooms and eventually branched out into prerequisite courses for precalculus.
Phase 2 Goals
- Develop, pilot, study, refine, and scale up a conceptual, cognitively-scaffolded curriculum to improve teachers’ classroom resources (the Pathways curriculum materials).
- Continue focused professional development to help increase teachers’ conceptual knowledge of the mathematics they teach and make new connections, including scaling up the Pathways Professional Development Model.
Key Findings
- We observed significant shifts in most teachers’ mathematical understandings. The Pathways curricula proved to be educative materials, meaning that teachers learned new mathematics and new pedagogical approaches through the act of teaching with the materials.
- We also observed significant shifts in students’ mathematical understandings, passing rates, and persistence in STEM.
Work in Phase 2 demonstrated that the most effective instructors (i) have a deep understanding of important ideas in the course and connections across topics, (ii) routinely gather evidence of student reasoning to model students’ meanings and reach based on those models (they decenter), (iii) develop a degree of ownership over the in-class materials, and (iv) are supported by effective local leaders and have administration-level support at their site.
Phase 3
Phase 2 demonstrated that the course materials and professional development model were effective in helping teachers grow and improve both their knowledge and instructional practices as well as supporting better learning outcomes for students. However, we also discovered time and again how challenging it is for departments and sites to embrace the learning goals and approach in the Pathways materials compared to using more traditional materials. Phase 3 (our current phase) involves better understanding how to scale up reform efforts like Pathways across diverse sites with their own unique needs and concerns.
Phase 3 Goals
- Continue to scale up use of the curriculum to new sites and new faculty at existing sites.
- Study the scaling and implementation process in greater depth to understand the processes and attributes of the innovation associated with sites considering, piloting, locally scaling, and sustaining Pathways use.
- Continue to develop new courses and new course resources based on what we’ve learned.
Key Findings
- Piloting and planning for early success was critical in helping sites adopt and scale Pathways materials.
- Focused and ongoing professional development support was key to Pathways’ success at each site that sustained its use.
- Instructors who repeatedly use the Pathways materials evolve in their mathematical understandings and teaching practices.
Work in Phase 3 shows that scaling curricular innovations is challenging, but when successful provides significant benefits to both instructors and students.