What is the Aspirin for the Headache?

Instructional Practices Icon

Karen Wootton, Director of Curriculum & Assessment, karenwootton@cpm.org

In his session several years ago at an NCTM Annual Conference, Dan Meyer posed the question “If math is aspirin, how do we create the headache?” The session focused on intellectual need: how can we make doing the math the obvious next step? How can we make students want to know the math needed to solve the problems they are working on?

This headache-aspirin analogy helps to frame many issues. For example, if the headache is It snowed two feet last night! then the appropriate aspirin is Today is a snow day! Or, if the headache is In every team I have one student who jumps in and takes over before the teammates have a chance to even think about the problem! Then a possible aspirin is Use a Teammates Consult to allow everyone some thinking time before students start to solve the problem. 

Sometimes it is beneficial to use this analogy in the reverse direction. If the aspirin is The teacher dominates the first 10 – 15 minutes each day to go over the homework problems, what is the headache? If the headache is All students come into class confused on all homework problems then this might be the appropriate aspirin. Although, if all students come into class confused about all homework problems, maybe a better tonic would be to rethink the classwork that led to that homework or to rethink the homework itself. 

In our current climate, there are many headaches and I wish there was one aspirin that would cure them all. Teachers are challenged with in-person classes, hybrid classes, and online classes, and students are struggling with the effects of this as well. Some perspective: a current 7th-grade student’s last complete normal school year was when the student was in 4th grade. (In the current 7th graders’ 5th-grade year, schooling stopped in March, the student then spent all of the 6th grade in virtual classrooms, and now if this year, the 7th-grade year, is in-person, it has been a while since the student has experienced a normal school year.) Students are struggling to adjust, teachers are being asked to do an incredible amount of work, and in many cases, schools are short-staffed. 

During difficult times, we might want to look for simple solutions. I have an ache? I can take aspirin. But maybe the pain is better addressed another way. It is understandable to employ remedies during difficult times that might not reflect best practices. Remember your values. When you can, go back to those best practices. 

Recently some different aspirins have surfaced. Perhaps you are using these tonics as well and might have a different headache you are trying to solve. I hope these discussions will have you consider your headache and tonics carefully. 

Aspirin 1: I must print out all the classwork and/or Review & Preview problems and copy them into packets if my students are going to do the problems!

Historically, there have been issues with students, classwork, and homework. If someone had the solution by now for ensuring all students would complete all the assigned problems and do the needed practice, we would have heard about it. There are many issues that lead to students not doing their assignments and teachers can never assume they know the reason. It might be they have to tend to younger siblings as soon as they are home or they dash off to a job after school, work very late, and are tired during class the next day. Maybe the student does not have a home life conducive to doing homework even though they may want to. It might have been necessary during the past year of virtual school to support students at home without a book with printed copies. While printing packets of classwork and Review & Preview problems with added space to work might seem like an appropriate aspirin, will that cure the headache? 

Consider if the tonic may have unintended consequences. Certainly, one solution to a broken arm is to amputate the arm. But, that would not be a reasonable approach. Part of schooling is to prepare students for life, and life has obstacles. Are students better served by teachers and parents trying to remove all obstacles that are before them? Or would students be better served if they are taught how to navigate those obstacles? 

Let’s go back to the original headache of students not doing the assigned problems. If the root cause of the headache is that students do not have paper to write on, packets are an appropriate aspirin. If the root cause is that students are disorganized, an appropriate aspirin could be to teach students to use a book and a notebook efficiently. It is unlikely that once they leave school, students will routinely have problems presented to them neatly with space to fill in a solution, so it is worth carefully searching for an appropriate aspirin before heading to the copier.

Aspirin 2: My students need me to go over the homework problems at the start of class before we can begin the new learning.

Each teacher might have their own headache they believe they are solving with this response. It might be worth the time to question and reflect on the headaches you believe exist. Does every student need to see you work the problems or are only a few benefiting? If it is only a handful of students, does it make sense to have every student sit through it? Do your students need you to do the problems or is this a habit? Can this need (headache) be remedied in another way? What if students found at their tables a solution sheet, with every problem worked out correctly and students began there? What if the habit was that as soon as students enter, they take out their homework and discuss the assignment with their teammates, comparing their responses to those on the solution sheet? Could many questions be efficiently answered this way? 

While some school districts require teachers to grade homework and record something in their grade book, we strongly encourage districts to change this policy. Homework is an opportunity for practice. Students should not be graded on their practice! Accountability can come from checking that the assignment is complete without spending time grading every problem. 

Aspirin 3: Before each test, my students need to have a practice test, so they know what the test will be like and what will be on it.

Is the headache low test scores? Is the headache teacher bias, thinking some students need the practice test? Perhaps the test is not covering the appropriate topics. The problem with having students rely on practice tests is that the process encourages students to memorize how to do certain types of problems rather than focusing on understanding the math. 

Students should know what will be on the test, but that does not mean they need to know the wording of every problem. As an example, suppose a teacher is about to give a chapter test on Chapter 5 of Core Connections, Course 3. The teacher should let students know that on the assessment they will need to solve more complicated equations (that probably include the Distributive Property) including solving equations that contain more than one variable for a particular variable, they will need to solve a system of equations by identifying the point of intersection from the graphs, and they will need to write equations in y = mx + b form, and use that form to graph the equation (without using a table). And that’s it! That covers the test, lets students know what they need to know, and then it is up to them to review these things. While the teacher’s job is to support students, the onus for learning is on the student.

By providing a practice test, you might be smoothing the path immediately before the students but you are not supporting them for future learning. Students need to learn how to study, how to think about what they have been learning, make connections to past topics, and connect new topics. This is more challenging than doing a practice test, but that is a good thing. According to a recent Edutopia article, “Challenging tasks spur the production of myelin, a substance that increases the strength of brain signals.”

Aspirin 4: I put all the topics from the chapter on the test to make sure I assess everything for a grade, but students failed! 

Assessment for learning over time is a tough adjustment. It is even more difficult during times of interrupted learning. While the Suggested Assessment Plan in the Teacher Edition offers guidance on when and on what students should be assessed, this information is based on when a topic was introduced and how much time students have had to meaningfully engage in the topic. Some topics are introduced in a chapter but students will not meaningfully engage with the topic enough times to be assessed on it until a chapter or two later. If problems are routinely skipped, then students might not have sufficient practice with a topic. The Suggested Assessment Plan is just guidance. You know best on which topics your students are ready to be assessed. Ideally, you have listened to the team discussions, observed student work, and have seen enough student work so that you have a good idea of how your students will do on an assessment. 

If you learn, via your circulation and listening, that your students are proficient at graphing using slope-intercept form, you do not need to put a question on an assessment on this topic. It might be that instead, you ask a deeper question, like What does this slope represent in this context? It is not necessary to ask an assessment question about every topic students see. Use your best judgment. 

Sometimes teachers need to rethink when they ask questions, how they ask those questions, what questions they ask, and how they score the responses. 

Support students when grappling with difficult things, but remember to do what is best and not necessarily what is easiest. Sometimes because of the situation, we need a quick and easy remedy. Let’s not let these quick and easy things become permanent habits unless they are what is best for student learning.

Have you seen other aspirins and wondered what the headache might be? Do you have other remedies you would like to share? Consider continuing the conversation. CPM pays $100 if we use your article in one of our newsletters. 

You are now leaving cpmstg.wpengine.com.

Did you want to leave cpmstg.wpengine.com?

I want to leave cpmstg.wpengine.com.

No, I want to stay on cpmstg.wpengine.com

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 Content

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.