Help Parents Understand CPM

Community/Public Relations Icon

Dr. Tom Sallee, Davis, CA

Most parents want their children to do well in school and they are usually willing to trust the teacher. But because CPM does not teach in a familiar way sometimes parents become nervous for their child.  After talking to lots of parents, I have come to believe that much of the conflict comes from a mismatch of expectations about what mathematics is.

I first came to understand this mismatch while reading the book The Psychology of Learning Mathematics by Richard Skemp, especially chapter 12 (this chapter is available separately at https://www.skemp.org.uk).  Skemp pointed out that for many (most?) people, to “know mathematics” means to be able to know when to apply a rule or to replicate an algorithm and to do it properly.  Then you know this little piece of mathematics.  (Skemp calls this “instrumental understanding.”)  For example, if you know the fact that you divide fractions by “invert and multiply,” you know that part of math.  In contrast, if all you know is the rule, but not why the rule is true (Skemp’s “relational understanding”) most college instructors (certainly including me) would say you know only the beginning.

Notice that if “knowing math” just means knowing the rules and procedures, then lecturing seems effective.  If you want students to know a specific rule and be able to use it today, then explicitly tell them the rule, and let them practice many examples.  Ask them to use the rule the next day and they can probably do so.  Everyone is now happy:  the teacher has taught the rule; students have learned it and the parents know that their child can use the rule.  Success!  This happy result will probably last a week but, too often, not a month.

To oversimplify a long history, the assumption has long been that if you know the rules, then in general these rules will get you by, and the brighter students will create the unified understanding necessary to advance for themselves.  However, a German report about the 1997 TIMSS study found that students were less likely to learn either math or science if they had a lot of routine practice homework.  Grappling with the ideas was more effective than lecture and practice in the long run.

CPM is about long-term learning—not regurgitating for tomorrow’s test.  CPM starts from the assumption that understanding the big picture will help students develop the rules as an integral part of the interconnections they learn.  In practice, there is a continual interplay between understanding rules and understanding the larger concepts and each reinforces the other.

To learn this way means serious intellectual effort.  And serious thinking is harder than memorizing.  Many centuries ago Ptolemy asked Euclid if learning geometry could not be done more easily and heard the reply, “There is no royal road to geometry.”  The same is true today—not  only for geometry but for algebra and every other part of mathematics.

It is understandable that parents want to make school easier for their children.  It is too bad that easy ways are rarely effective.

You are now leaving cpm.org.

Did you want to leave cpm.org?

I want to leave cpm.org.

No, I want to stay on cpm.org

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.

Edit

Building on Instructional Practice Series

This series contains three different courses, taken in either order. The courses are designed for schools and teachers with a minimum of one year of experience teaching with CPM curriculum materials. Teachers will develop further understanding of strategies and tools for instructional practices and assessment.

Building on Equity

In this course, participants will learn how to include equitable practices in their  classroom and support traditionally underserved students in becoming leaders of their own learning. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for implementing Chapter 1 that creates an equitable classroom culture and curate strategies for supporting all students in becoming leaders of their own learning. Follow-up during the school year will support ongoing implementation of equitable classroom practices.

Building on Assessment

In this course, participants will apply assessment research to develop methods to provide feedback to students and to inform equitable assessment decisions. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

This professional learning builds upon the Foundations for Implementation Series by improving teachers’ 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 rigorous, team-worthy tasks with all elements of the Effective Mathematics Teaching Practices.