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Mary Rack, Mendocino High School, CA

As a member of the assessment writing team that met in Sacramento in July, I have dubbed us the Assessment Week Warriors. Working in teams by course, we were able to choose what we felt were the priorities for the week. Different course teams chose different areas of focus, but we all realized that writing quality assessment is a difficult, enlightening, and creative task. To help us get started, Judy Kysh presented some strategies for creating assessment tasks for students.

First, Judy suggested we ask students to show more than one way to solve a problem. For example, a student could use the rewrite, look inside, or the undo strategies to solve the equation (x – 7) 2 = 9. Different strategies create flexibility in math thinking.

A second strategy for creating an assessment task is to ask students to “Pause, Think, and Describe a Strategy”. Judy suggests a teacher should ask students to “Tell what the problem says and tell what you are going to do” before solving the problem. An example of this strategy is to ask students to identify the operation, and how they will “undo” the equation, all before solving. For example, given the equation (1/3 ) x =7, students should identify the operation, and use a full sentence to describe it, such as “The x is multiplied by 1/3” or ”x is multiplied by one and then divided by three.” For the “undo,” students might state “Both sides are divided by 1/3” or “Both sides are multiplied by the reciprocal, 3”. And lastly, the question “Why do you divide both sides by 1/3?” or “Why do you multiply by 3?” gives students an opportunity to communicate to their teacher mathematically, justify their thinking, and in a class discussion, critique the thinking of others.

The “Work Backwards” strategy gives students an answer such as x = 5/8, and asks students to write an equation that will take at least four operations to solve, that will give that answer. Another “Work Backwards” assessment task could ask students to write two pairs of linear equations: one set of equations that intersect at a specified ordered pair, and another set of equations that are parallel lines.

Judy’s other ideas include asking students to give an example of a mathematical concept, asking students to identify and explain errors in a solution, and confronting points of confusion students have about different math concepts by asking them to justify their solution and use multiply representations to justify their reasoning. This last one became known simply as Points of Confusion problems, or PoCs.

Buoyed by Judy’s suggestions, we set to work. Within our room, writers would talk about “Judy-fying” our problems so we could learn more about our students understanding. Due to the flexibility of the structure of the week-long assessment writing project, we were encouraged to think our tasks through, communicate our ideas to create an exemplary assessment product that would be accessible to diverse or marginalized groups of students, engage all learners in STEM related real-life problems, and assess the CCSS content and practice standards.

Our week closed too quickly. But I was happy to note that the teamwork was very similar to the teamwork we facilitate in our classrooms. We were independent learners using discussion and questioning to discover and experiment in a cooperative learning environment where we viewed, listened, responded, reflected, edited, problem-solved, summarized, and reinforced effort while producing our assessment tasks.

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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.