CPM’s Position Paper on Homework

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Karen Wootton, Director of Curriculum and Assessment

CPM believes that homework is an opportunity for students to individually practice skills and deepen their understanding of concepts. Because of this, CPM authors have taken care to purposefully place each homework problem correctly within the course to support one of CPM’s guiding principles, mastery over time. Looking at the homework, headed Review & Preview in the text, you will most likely see one or two problems related to the day’s topic, a couple problems on topics from a few weeks ago, and a few problems on topics from possibly a few chapters ago. This is called mixed, spaced practice, or interleaving. The research is clear on this: learning is improved when the practice is spaced over time, rather than being massed, or happening all at once and then left behind. Topics and skills are revisited again and again through the homework. Each time, the questions grow in depth and complexity, topics are presented with different representations, as well as connected to other areas of mathematics.

Homework assignments allow teachers to formatively assess their students’ ability to demonstrate mathematical skill, understanding in writing, and growth, as well as the quality of work. The spaced practice of the Review & Preview sections allow students to demonstrate growth over time and progress toward mastery. CPM recommends that teachers do not spend time grading every homework assignment for correctness. CPM believes that one of the best ways to prepare to teach a CPM course is to work through all the assigned problems. Teachers who do so create solution sets for homework checking as an added benefit of thorough preparation.  Teachers should provide these solutions for students to check their work which allows students to take responsibility for their learning. By reviewing detailed solutions, students can correct any errors, and determine if they need to see the teacher for additional help or clarification, or to feel confident that they have mastered the concepts and skills. Homework is an opportunity to practice outside of class. Errors are to be expected and not penalized. Every effort should be made to help students understand that homework is for their benefit and to improve learning. Doing homework problems gives students an opportunity to self assess their readiness and preparation for individual assessments.

Because CPM feels that doing homework should support student learning, there are two pieces of information that students, parents, and teachers should all be aware. First, there are only a minimal number of homework problems to do each night. This is purposeful and CPM does not expect teachers to supplement the homework problems with additional worksheets or problems from another source. Students will get the necessary practice through the mixed, spaced practice that continues throughout the year. For example, when students first learn how to factor trinomials, there might be only two problems for homework that night on factoring trinomials. However, over the course of the next several weeks and months, the students will end up doing well over one hundred factoring problems, far more than the “1 – 30 odd” many teachers assign in a more traditional massed approach to homework. Second, CPM provides online Homework Help free to anyone with internet access. Within the eBook, next to each homework problem is a link:

which will take the student to the hints and suggestions for solving the problem. For students who do not have an eBook, all Homework Help can be found by going to CPM.org and selecting the student’s text from Textbook Resources then choosing Homework Help from the menu on the left.

Homework Help is designed to support a task that is done outside of the classroom with no teacher oversight or support. The variety of assistance that Homework Help provides is appropriate to the purpose of homework, that is, to practice and deepen understanding. Therefore, students will not find simple answer statements in the Homework Help. Rather, hints, suggestions, and references to previous problems are offered. A student may choose to rapidly click through all the hints, and then copy the answer. (Some problems do not have the answer.) Of course this is not what we would want students to do, but most students use Homework Help as the support it is intended to be. CPM believes it is important to let students know that Homework Help is available, free of charge, and students should use it to help them learn, not to copy answers.

Every school and every district has its own policy on homework and how or if it should be graded. CPM believes it is the school’s or district’s duty to have a policy on homework and the assessing of it that is readily shared with students, parents, and teachers. CPM believes that homework falls under the heading of formative assessment and should therefore be used accordingly.

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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.