■ 145 ■ Proficiency-Based and Problem-Based Instruction: Mutually Supporting Moves or Contradictions? Nicole Rigelman, Portland State University, Oregon P roiciency-based and problem-based teaching and learning are two instructional approaches that can appear to be at odds with one another in the mathematics classroom. For instance, while the instructional move of clarifying and sharing learning intentions with students (Black and Wiliam 1998) that is advocated in a proiciency-based approach may improve student achievement, the way a teacher employs this move may diminish the cognitive demand of the problem-based task, a key component of a problem-based approach. Students’ dispositions can also inluence the implementation of proiciency-based and problem-based instruction. If a student’s focus is on meeting the criteria in a proiciency-based approach merely to address “What do I need to do to get an A?” and not on “How can I show you what I know?” it can be challenging to draw out mathematical thinking and problem solving—important components of a problem-based approach. his chapter suggests that teachers who use proiciency-based and problem-based learning as mutually supporting are able to engage students with problem-based tasks to support learn- ing, and that they are also able to use tools, such as rubrics, not only for grading but also for supporting teaching and student learning. Providing students with examples of a range of student work shows what quality work looks like and supports students in understanding clear, high expectations. When students use these tools to guide self- and peer-assessment prior to the teacher providing growth-focused feedback, the tools support students during learning as opposed to merely being used summatively. hus students understand that assessment and learning are ongoing and the student is actively involved in both processes. ■ Background “Proiciency-based learning refers to a system of instruction, assessment, grading and reporting that is based on students demonstrating mastery of the knowledge and skills they are expected to learn as they progress through their education” (Great Schools Partnership 2014). he goal of proiciency-based teaching and learning is to ensure that students learn what they are expected to learn. Many educational stakeholders ind proiciency-based teaching and learning attractive in that it can provide a more ine-grained analysis of a student’s strengths and areas for improvement. It can also provide the opportunity for more detailed feedback on a student’s work. Instead of receiving a holistic grade or score on a ■ CHAPTER 13