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      Your Work and Your Story

      Your work as a teacher of mathematics tells a story over time. That story, steeped in the decisions you make year after year, eventually becomes your career. Along the way, you must decide which parts of your journey are the most important to pursue so that your daily effort and toil can make a difference in the mathematics learning of the students you teach.

      Gaining clarity on your vision for mathematics teaching improvement will result in helping your students achieve greater agency and ownership over their learning as the school year progresses. One of the best benefits of working in a community with peers is the benefit of belonging to something larger than yourself. There is a benefit to learning about mathematics from each other, as professionals. It is often in a community that we all find a deeper meaning to our work and strength in the journey as we solve the complex mathematics learning issues we face each week of the school calendar, together.

      Thus the mathematics assessment and intervention, instruction and tasks, and homework and grading vision of the Every Student Can Learn Mathematics series features a wide range of research-affirmed voices, tools, and discussion protocols that offer advice, tips, and knowledge for your PLC at Work–based collaborative mathematics team.

      As a teacher and leader of mathematics, your daily work and actions tell a story. That story reveals itself through your collaborative actions with colleagues around three important aspects of your daily work.

      The Story of Your Mathematics Assessment Design and Intervention Routines

      Your successful assessment story uses the essential standards for each mathematics unit to drive the assessment process in your school and uses those assessments for effective mathematics intervention. The research of James Popham (2011) and others highlights highly effective mathematics assessments designed to expect student participation in a reflect, refine, and act cycle of learning; and more important, to support students to take ownership of the learning process.

      Although this may sound complicated, it is primarily a matter of refining your current mathematics assessment story and effort into a more efficient routine that looks something like this: design high-quality mathematics assessments, score (grade) samples of student work on those assessments together, pass quizzes and tests back to your students for an analysis and response to errors (students reflect and refine), and require your students to take action on the standards they have not yet mastered (students embrace and then act on their errors).

      The Story of Your Mathematics Instruction Design and Lesson Routines

      Through your experiences as a mathematics teacher, and your deep dive into the research on how students learn mathematics, you examine closely the educational research in the mathematics profession and find the right criteria for K–12 mathematics lesson design.

      The elements of effective instruction are certain. Yet, those criteria are not prescriptive. That is, the research provides the freedom to act and teach mathematics within the well-defined boundaries of those criteria. As a mathematics teacher, leader, or school principal, you lead the way in describing how a student formatively reflects, refines, and acts when using the lesson-design criteria. In doing so, you will discover that the most effective K–12 mathematics lessons present a story of student perseverance and engagement during the lesson.

      That story includes great lesson openings through prior knowledge and vocabulary work development. The story then moves to great lesson development using tasks that show a balance of lower- and higher-level cognitive demand and a balance of whole-group and small-group discourse as part of a sustainable formative-feedback process. The story ends with great lesson closures that students lead. Can the students provide evidence they have learned the standard for that day?

      Most likely, many of these lesson-design elements are already a part of your effort. It must become your intent to bring efficiency and clarity to your use of each of these lesson-design criteria.

      The Story of Your Mathematics Homework Design and Grading Routines

      There are two additional mathematics issues your team must address: (1) homework and (2) grading. These two very difficult topics tell a story about your professional work as a mathematics teacher or leader.

      When it comes to designing mathematics homework, there are many noisy voices and experts claiming advice. You can help your team cut through the noise and find the best wisdom for these important K–12 mathematics issues. In doing so, your story shows that you understand mathematics homework and grading routines through the lens of Mathematics in a PLC at Work. The criteria for a highly effective homework, grading, and design story expect students to reflect, refine, and act as part of the learning process.

      Whether it’s basic number sense or calculus, you answer the questions, What is the best we know about the meaningful design elements of homework assignments, the scoring of those assignments, and the effective use of those assignments in class? and How does research inform the idea of homework?

      When you lead the process to achieve these answers, you will realize you cannot ignore the role grading can play in inspiring students to learn mathematics—or in destroying their desire to learn mathematics. To that end, we decided to provide the best wisdom we could to help you tell a story of efficient and effective grading routines in mathematics, designed to inspire student perseverance, effort, and engagement in learning all year long. Although you may view grading as a back-burner issue to student learning, you realize that grading eventually becomes part of your required work.

      This reaches beyond the role of teachers. As we examined poster papers from an initial brainstorming day, we also found that we had quite a few mile markers for mathematics coaches, team leaders, and administrators. This serves as a reminder that there are many leaders pulling the mathematics teacher collaboration story forward, and so we made the decision to also provide meaningful tools and support for mathematics coaches and leaders.

Common Unit Assessment Formative Process Evaluation