Success in math is all about your mindset. Having a growth mindset and believing you can learn anything if you work hard instead of a fixed mindset where you believe you are either good at math or not, will be important for success in school and life. Your brain is a muscle that gets stronger at math by practicing math.
Students do not arrive at your classroom door with the same background knowledge or readiness, so you are constantly required to differentiate instruction. There are general notes and suggestions in the “Universal Access” section in the front matter of the Teacher Edition. You will find specific suggestions for differentiation of instruction within the “Lesson Activity” notes or in the Universal Access section at the end of the teacher notes for many lessons. These notes include questions to ask students when they need a nudge to move on with the lesson and extension questions for students who need more challenge. Asking well-crafted questions is one of the best ways to differentiate instruction, so prepare a set of questions as a resource. Include some questions to check for prior understanding, some to help students explain their thinking, and some to extend thinking. Be prepared to ask individual students within teams to respond to these questions depending on their depth of understanding or their need for help in attaining a basic understanding of the concept(s).
In some lesson notes you will find a discussion of typical points of confusion, common misconceptions, or anticipated errors and suggestions for how to address them along with information about the core problems and any extension and enrichment problems. Each lesson lists the core problems that all students need to complete, but which students do the non-core problems in your classroom may vary from day to day.
When more than the lesson notes and student textbook is needed you should refer to the Universal Access document in the front of the Teacher’s Edition. This document lists and discusses various strategies to use with various learners’ needs. The last few pages of this resource address literary support strategies.
Do you have teams that work at different paces? Some teams are working quickly, while others are stuck? A strategy that can help is called a Swapmeet and is the focus of this week’s tip.
This week make a conscious effort to see that everyone records their work. Sometimes teachers and/or students get the impression that by assigning the role of a Recorder/Reporter, there is only one person in each team who is responsible for recording the work that is done with the problems in the lesson. This is NOT the intention of the role. The Recorder/Reporter’s job is to make sure that everyone in his or her team records his or her own work.
Why is it so important for all of the students to record their work? There is research out there that supports the importance of recording your work. There is more about the writing process and brain function that shows the brain works one way when students explain their thinking aloud and another way when students explain their thinking on paper (using math symbols and words). Students form deeper understanding when they are able to explain their thinking both orally and on paper. If students work without speaking with their teammates or do not record their own work on their own paper, they are missing the full process of learning the mathematics deeply. Find a way this week to increase the expectations you have for what students record on their papers.
Note: There are some instances when we want the whole team to work from and complete one paper, but this is not generally the case.
Note: When you want team ideas, solutions, and work shared with the whole class, you can call on the Recorder/Reporter to share or summarize the work of the team.
This week make your study team and teaching strategy focus Teammates Consult. This strategy is especially helpful if some of your students are not committed to the team approach. It is also a good strategy to use if you find students are consistently slow at getting started with the lesson.
Teammates Consult (Pencils in the Middle)
During the CPM summer and school year workshops the mentors model many study team and teaching strategies. However, once the school year begins, it is easy to overlook the various options. The editors of the Core Connections series made it easier for you to use them by making suggestions for using specific strategies in most lessons. By using the suggested strategies you will build confidence and expertise with them and become proficient in assimilating them into your daily practice. The strategies are useful to focus the responsibility for working as a team and for learning mathematics on the students.
This week consider using a Huddle. A Huddle (calling up a person from each team and talking with all of them) is effective as well as versatile because it can be used to get a problem started, pass out materials, tell the students something you forgot to talk about as you discussed the lesson, correct a common error you notice, or get feedback about what different teams are doing (what problem are they on, what strategy they used, what answer they got, etc.). For example, if you want students to carefully check their work, you can call a Huddle and have each team representative share his or team’s strategy and answer. A Huddle can initiate a closure activity by asking questions and summarizing the lesson with each team representative, then having them go back and do the same thing with their team.
Be creative in deciding which member of a team to call to the Huddle. You may use Team Roles or Numbered Heads or have the person with the most siblings, the oldest or the tallest come up. If you have a specific student in mind (perhaps you want to use the Huddle to encourage a certain person’s participation) then simply call on the team role that person holds. You may want students to bring up their book and/or paper and pencil for a Huddle. Your challenge this week is to use a Huddle every day for different parts of the lessons. Have fun with it, save time with it, and see how responsible your students can be when you put them in charge of information for their team!
In CPM workshops the mentor teachers are often asked how to plan for days when a substitute will teach your class. By this point in the year your teams should be functioning reasonably well, so they should be able to complete most lessons with a substitute present. But this type of teaching may be entirely foreign to substitutes and you will need to help them understand their role in a classroom of teams. Make sure that the substitute understands that they are to circulate, keep the teams/students on task and monitor progress. Providing substitutes with a list of team norms and classroom expectations is a must. Avoid starting a new chapter or using a lesson that is just one big problem. If you must leave the class with such a lesson, use the existing “further guidance” section, if there is one, or create similar questions/guidance for the class to use. Team assessments or the closure problems from a chapter are also good activities that a substitute can supervise.
It is okay, and not unlikely, that your students may learn something new without you there. Have them each write you a note at the end of class (or to start the next class) about what they learned and use the notes as formative assessment tools to help you decide how to proceed. CPM teachers often note that a day with a substitute teacher does not seem to create a gap in the students’ learning as much as it keeps the teacher from knowing how the students processed the lesson from that day. Talk to your students about their increased responsibility when you are not there to help them. They might just impress you.
How do you typically plan for each lesson you teach? Whenever possible it is best to first do all of the problems from a given lesson using the student book (without answers visible). This will help you see the problems from the students’ point of view and help you to anticipate any areas where students will have questions. As you work through the problems make a list of some questions of your own and your predictions regarding common misconceptions. Next read through ALL the teacher notes including the objective of the lesson, the core problems, the suggested lesson activity, possible study team and teaching strategies, and closure. Now you are ready to complete your planning. Put in time limits for each portion of the lesson to serve as a guide and do your best to follow them. However, watch for instances where your predetermined time slots may need adjusting. Without a planned pacing guide, sometimes strong students will go too fast and ignore the deeper questions, while students who take longer to do their work will, if given the opportunity, take the entire period to do one problem. The more you practice timing out a lesson, the better you will be at scheduling a lesson to fit into the time allotted. Nonetheless, you will always need to be sensitive to the needs of each class.
If this is your first year teaching the course we strongly suggest that you follow the lesson as it is written. Once you have taught the entire book and are comfortable with the overall objectives and content, you can use your professional judgment to adjust the lessons as needed. Creating simplified versions of the problems or turning them into “worksheets” instead of following the lesson as written is not recommended. It often stripes the lesson of the thinking and exploring that is the basis for conceptual understanding and that fosters long-term retention of ideas. Nevertheless, CPM does understand that working with the students requires some flexibility. Carefully monitor the work of your students during class and adjust your plans as needed while making every effort to implement the program with fidelity. Have fun listening to your students’ thinking and watching them learn math!
One way to start a new year (calendar or school), semester or chapter is to make a commitment and concerted effort to try something new. If you have not used teams consistently, make a commitment to do so. If you have not used team roles, try them. If you have not used a study team strategy, try one.
An easy place to start is with Reciprocal Teaching. Have each student find a partner (it could be their elbow partner or someone from another team). One member of each pair pretends that the other was absent and explains something that they learned today. Then have the partners switch roles. This is great for vocabulary review. When teaching someone else, students are able to consolidate their thinking.
You have established good classroom norms from the very beginning, but you must continue to revisit them throughout the year. Remember:
S Start promptly.
P Peer support expected within each team.
A Assignments due each day.
R Respond to teams rather than individuals.
C Circulate. Circulate. Circulate.
Your tip this week is a reminder about how important it is to circulate around your classroom effectively and often while students are working. We can easily get in the habit of just responding to whatever hand comes up first rather than completing our purposefully designed circulation routes.
It is ok to tell a team, “I will be there once I am finished talking with the teams I haven’t checked in with yet.” Often teams will work out the problem they thought they needed you for while waiting for you to complete your rounds. Make it a goal to visit each team at least twice per class and to physically join them and ask a few target questions about their work. While circulating notice your pattern. Is it always the same path? Do you cover all sides of a team or always pass by the same students? Keeping things varied can help keep students on task and give you a clearer assessment of how teams are functioning and how individuals in the team are developing. Keep a list on a clipboard (perhaps using your seating chart) of which team you visit, which student(s) you talk to, what questions you ask, and which problems you have discussed. These notes can help you identify your circulation patterns. In addition, they can help keep you organized and provide valuable formative assessment information.
Often we are unaware of our own habits and behaviors as we circulate. If possible, ask a colleague to come in and observe your circulation in class and give you feedback about it and perhaps questioning techniques as well. An alternative method is to set up a video camera and tape a class for later viewing. Try to focus on the math as you circulate and listen carefully to your students. It is both informative and exciting to hear all their ways of thinking!