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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

Use this tool to evaluate the current reality of the mathematics assessment process quality for your grade level or course. Unlike in other evaluation tools written into the Every Student Can Learn Mathematics series, the six criteria present in this team discussion tool are somewhat linear. Meaning, your grade-level or course-based team should identify areas to improve in your team’s formative assessment process in the order the criteria are listed.

In some sense, this tool reveals why it is so important for your students to take common unit mathematics assessments that your teacher team writes. It is in the action students take on your mathematics assessment feedback (scoring), the nature in which they embrace their errors, and then your subsequent coordinated team effort to design equitable quality interventions that this tool will significantly impact every student’s mathematics learning.

Formative feedback requires intentional team planning to determine the essential learning standards to be assessed and create common unit assessments that reveal student thinking and learning. From the data revealed through student work on the assessments, your team can plan for students to reflect and set goals for continued learning. You can also plan for how your students will re-engage in learning through the shared intervention opportunities your team provides.

The intent of students analyzing their performance on the end-of-unit assessment is to help each student build responsibility for his or her own learning. Although each student takes ownership of his or her individual progress toward each of the essential learning standards, students may still work together to meet those standards. Students can work together when your team provides equitable feedback to students, regardless of which teacher students have.

Student goal setting during and at the end of each unit helps them to see what they learned well and what they still need to learn. Such collaboration with peers and this ownership of learning engage students more deeply in the learning process and provide evidence for each student that effective effort built on the reflect, refine, and act cycle of learning leads to improved mathematical understanding and success.

Common Assessment Self-Reflection Protocol

Use the self-reflection team assessment protocol as a survey for each member of your team. Then, use your responses for a subsequent discussion with each member of your grade-level or course-based mathematics team. Share your personal unit-by-unit assessment practices and routines with one another. You can use each team member’s responses to find initial common ground for your collective mathematics assessment work. Discuss your responses and, as a collaborative team, reach consensus and determine how you will build your common assessments and how you will use those assessments to support formative student learning routines.

Assessment Instrument Quality Evaluation Rubric

A great place to begin your initial work as a professional learning community team in mathematics is the collaborative design and writing of your common unit assessments. DuFour et al. (2016) describe the importance of using common assessment instruments this way: “One of the most powerful, high-leverage strategies for improving student learning available to schools is the creation of frequent, high-quality common assessments by teachers who are working collaboratively to help a group of students acquire agreed-on knowledge and skills” (p. 141).

Creating common assessments to use during and at the end of each unit ensures equity in the rigor of the mathematics problems used for the assessments. It will also help your team to backward-map your instruction during the unit as you prepare the students for the expected and required rigor. Ideally, your team should create these common unit assessments before the unit begins.

You can use the eight criteria in this evaluation rubric to determine the quality of your current common unit assessments. A rating of 1 has a description attached and would be considered poor performance with these test criteria. A rating of 4 indicates your current common assessments act as an exemplar in these criteria we could all learn from. Regardless of your self-rating, make it a team goal to keep improving the quality of your unit-by-unit mathematics assessments.

You should also note that, if you do not collaborate to become a 4 in each category, the first four mathematics assessment design criteria listed here often create places of great inequity in your mathematics assessment process and professional work. Perhaps the most important are the identification of and emphasis on essential learning standards, the balance of higher- and lower-level-cognitive-demand tasks, the variety of assessment-task formats and use of technology, and the appropriate scoring rubric. Yet, these are also the most limiting aspects of many mathematics unit assessments—both during and at the end of a unit.

Mathematics Intervention Program Evaluation Tool

The third critical question of a PLC at Work expects your team and school to develop a robust response to the question: What will be our response when students do not learn the expected standards for each grade level or course? You can use this evaluation tool to rate and evaluate the quality of your response to intervention and learning using evidence based on a recent common unit assessment.

How do your current mathematics intervention programs score? You should expect to develop an intervention program that scores 4s in all five of the intervention criteria. Which of the five criteria for a high-quality mathematics intervention program are currently part of your collaborative team practice? What do you need to do to strengthen your mathematics intervention program?

Each of the five criteria is necessary for continued student learning when a student has not yet learned an essential learning standard, as evidenced by the end-of-unit common mathematics assessment. The challenge is to create an effective system that allows students to engage in the intervention, while simultaneously practicing the essential learning standards for the next unit.

Intervention Practices

The questions on this page aim to help you and your team understand one another’s perspectives related to your systematic Tier 2 interventions as a team. In other words, how does your team respond when common assessment data, during or at the end of a unit, reveal some students have learned the essential learning standards and others have not? Your professional response as individual teachers and as a teacher team reveals your current beliefs about the need for interventions and the plan for making those interventions effective.

The intent of your mathematics interventions should be to provide students with the additional time and support necessary to learn your grade-level or course-based essential learning standards.

Instructional Framework and Lesson-Design Evaluation Tool

The true purpose of any mathematics lesson is to maximize student engagement, communication, and perseverance during the lesson based on the tasks you have chosen. The tasks you choose must help students learn the essential learning standards for the current mathematics unit of study.

Your daily lessons should provide an opportunity for your students to reflect, refine, and act during the lesson. You should expect your students to use the mathematical tasks you have chosen and the formative feedback you provide during the lesson to refine their errors in the process of learning the mathematics learning target or standard each day.

You and your team can use this lesson-design evaluation tool to evaluate the quality of your current mathematics lessons. It will help you identify areas of strength and areas for lesson-design growth as you assess the strengths and weaknesses of your current instructional planning for mathematics. These six research-affirmed lesson-design elements also provide an instructional framework for highly effective mathematics lessons every day. Some of these elements may already be present in your daily planning; you just need to work with your other team members to brainstorm and share creative ideas about how to most effectively implement the criteria.

Other criteria may not yet be present in your lessons and only score a 1 or 2 using the evaluation tool. You can decide how to adjust your daily lesson design to better impact student perseverance and learning in your mathematics classroom by improving on these non-negotiable aspects of the mathematics lesson. Your daily lesson-design preparation throughout the school year has a certain rhythm to it, and these six lesson-design criteria can serve that.

Protocol for Team Analysis of the Mathematics in a PLC at Work Lesson-Design Tool

Mathematics in a PLC at Work Lesson-Design Tool