# Help Parents Understand CPM

#### 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.

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# 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.