Teaching Mixed-level Classes with CPM

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Gail Anderson, Lansdale, PA  gailanderson@cpm.org

It all started when a bright young freshman in my geometry class asked me “Why don’t freshmen get some sort of bonus for being in a sophomore level class?” I explained to him that he is gaining the chance to take college level math classes while he is in high school, which is a great advantage for him. But that got me thinking. The freshmen in this class were generally the ones at the top of the curve, in fact, they were often bored with the material which the sophomores (and some juniors) in the class needed more time to process. Because our school is small, we cannot offer separate honors classes as a means to differentiate for each of the math classes. I wanted to motivate all of the students in this class to work hard, not just the ones who needed to work hard to survive.

And so, our embedded honors math program was born. Our CPM math classes provided the perfect setting for this idea to work. Students were already used to working in teams; it was really a small leap to differentiate by teams and teach an honors level at the same time. We already had learning support students embedded who were supported differently from the rest of the students. Being able to circulate and meet with every team several times during every class period meant I was able to direct the work of different teams to different levels and different expectations. With the added weighting for honors students, the higher-level students accepted the extra requirements and demands placed on them in class, and they no longer raced through the problems so they could get their homework completed during class as well.

Here is how it works at our school. Students may sign up for the standard or honors (weighted) courses, and then they are put into whatever class section fits their schedule best, which means always a mix of students in each class. We offer this option for algebra, geometry, algebra 2, and during the first semester of AP stats as an embedded “intro to stats” course.  We typically have 4-8 honors students, 10-20 standard students, and a couple learning support students in a section (although for statistics, it tends to be more 50% intro and 50% AP). Our class sizes range from about 15–27 students. Students may opt to switch in or out of honors any time without making any disruptions to their schedules. Because of the higher demands of the honors section, we only allow switches in to happen during the first six weeks of school, but students may switch out any time. We encourage any student up for the challenge to give the honors class a try, and we are able to support them if they find out they have bitten off more than they can chew.

The introduction and closure to each lesson apply to the whole class. The daily homework assignments are the same Review & Preview sections. The classwork problems assigned may be the same, or additional problems may be assigned to honors teams to provide them with additional challenge or depth. (I generally write all of the problems on the board, so only I know which ones I expect only honors students to get to. This encourages everyone in the class to keep moving and try the tougher problems as well.) Honors students are assigned more in-depth chapter projects in place of the review assignments (closure problems) assigned to the standard students at the end of the chapter. Honors students also work on quarter-long research projects to allow them to explore additional topics, such as non-Euclidean geometry, the Golden Ratio, or applications of quadratics. We have one mandatory lunch time meeting each quarter to discuss these projects. Honors students are frequently called upon to present their work to the rest of the class, which allows all of the students at least an exposure to these rich topics or the tougher problems they may not have been able to complete in class.

I have found that some chapters work well when I seat my honors students in separate teams, while other chapters benefit from mixing students in heterogeneous groups. This has the advantage of giving all students a chance to meet and work with other students of varying levels. It becomes clear to all the students that everyone makes mistakes and we all really do have something to offer. And we can all learn from each other.

Is our system perfect? Of course not. It is challenging on occasion, especially later in the year, to prevent some students from just listening to the honors students and not challenging them in their responses. It is challenging to prevent them from giving in to the temptation to just copy work from the “smarter kid.” Since our focus is depth, the honors students do not cover as many new topics as they might in a section devoted to students with exceptional skills. They do have to be relatively self-motivated to push themselves beyond what the majority of the class is doing. It takes more teacher prep time to design lessons with multiple access points and expectations. But the advantages of the great cross-pollination we get in the heterogeneous classes, as well as the scheduling ease, have outweighed the disadvantages for us. If you would like to see the contract we use for students choosing the honors track, and a sample of the enrichment assignments I have written for geometry, you can find Honors Geometry Philosophy and Policies (gdoc). Feel free to email me if you have more questions about my experiences with mixed-in honor classes.

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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

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.