From the Innumeracy Files

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Mark Cote’, CPM Project Manager

In 1988, John Allen Paulos published a revealing and poignant book entitled, Innumeracy – Mathematical Illiteracy and Its Consequences. In his message filled with riveting examples and sadly humorous anecdotes, Paulos painted a troubling picture of American society’s struggle with the meaning of number. This is a story about one such struggle.

For many families, taking on the high school to college transition can be a challenging undertaking. Those that have the financial resources are able to hire private counselors to offer guidance and help with the lengthy application process. In general, the typical private counselor has a wealth of experience with America’s post-secondary world, is highly educated themselves, and takes great pride in providing excellent professional service to their clients.

Most members of the college counseling community belong to both regional and national professional organizations that offer a wonderful network of local experts who are virtually always on call. With blogs, webpages, and a listserv at their fingertips, counselors have a small army of in-the-know colleagues who are available to exchange information and address the most difficult questions that crop up in the ever changing college admissions landscape.

With any large group of people sharing a common occupational calling, varying levels of expertise exist. Overall, you will find private counselors to be very hard working and exceptionally skilled at helping young scholars fulfill their dreams of getting in to just the right school. And in most cases, facility with number is no problem, as the job often requires collecting and interpreting large amounts of data. But every now and then a math challenge comes up. Just as the world of university entrance requirements may seem mysterious to us, certain applications of statistics and probability can be confounding to them. These perplexing situations become public knowledge when they are presented in the form of questions sent out on the listserv to thousands of members of the national association.

Such a question was recently broadcast to the college counseling community. Sometimes the inquiries posted are thought-provoking and informative. On occasion, others are humorous jabs at the often ridiculously complex testing and admissions process. Many are routine. Then there are those that leave you scratching your head and wondering, “How is it possible that the American school system produced a highly educated person that does not know the answer to this question?”

A short time ago, a counselor made the following post: “I don’t understand what went wrong. I’ve done the math and this just doesn’t make any sense! I had my client apply to 10 universities that each had about a 10% acceptance rate. He didn’t get into a single one! I mean come on! With a 100% chance of being accepted, he’s got to get in somewhere! What’s going on here?!?!”

Fortunately, the collective body of counselors were too polite to post any snarky replies, and one kind soul offered to help untangle the math in a private chat.

So as you can see, we have plenty of work to do as we continue our mission to help lift America out of the throes of innumeracy. Have you come across any instances of innumeracy lately? If so, please send a synopsis of the article, advertisement, media occurrence, or classroom incident to for the next installment of “From the Innumeracy Files.”

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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.