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Mark Coté, CPM Project Manager

In fall 2015, some 20 million students attended the first day of classes at American colleges and universities, according to the National Center for Education Statistics.  Among them are many with learning differences who cleared extra hurdles to earn a letter of admission, including those with autism spectrum disorder.  At this moment, future collegians and others who plan a different post-secondary pathway are enrolled in a CPM course.  What can we do as math teachers to help remove a few more hurdles?  Read on!

First, know that diligent research efforts coupled with a desire to develop a more consistent and scientifically accurate standard for diagnosis led to recent landmark changes in the definition of autism.  The umbrella term autism spectrum disorder (ASD) may include students with autistic disorder, Asperger’s syndrome, childhood disintegrative disorder, or pervasive developmental disorder.  General indicators for ASD include a tendency toward communication deficits, such as using and interpreting speech literally, responding inappropriately in conversations, and misinterpreting nonverbal interactions.  Additionally, students with this disorder may struggle with changes to their daily routine or in their physical environment.  They may also perseverate on tasks or exhibit repetitive behaviors that reach beyond what a given situation requires.

As is often the case, a deficit from one perspective may be an advantage from another.  In her book Congratulations!  It’s Asperger’s Syndrome, Jen Birch* (with ideas from Cathie S.) offers several positive aspects of ASD gleaned from her own first-hand experience.  You may find that one or more of the following positive characteristics are exhibited by a student with ASD:  the ability to think creatively with pictures, pleasure in repetitive activities coupled with an intense focus, an eye for detail and delight in noticing specific structure, a unique perspective on problem solving, a passion for one’s interests, and exceptional honesty – they have trouble understanding and engaging in trickery or deception.

 Adhering to the slogan “More Math for More People,” CPM teachers want every child to get the most out of their mathematics classroom experience, including those with autistic spectrum disorder.  Parents and experts in the field agree that to make this happen, it takes cooperative planning, a good dose of structure, and the understanding that every student with an ASD has a unique set of needs.    
The following general classroom practices are beneficial for all students, and especially helpful for those with ASD.

  • Maintain a positive, can-do attitude about the learning potential of all students. 
  • Create an atmosphere of inclusion and provide support in the least restrictive way possible.
  • Employ a daily agenda for instruction that is predictable.  
  • Establish simple, fair expectations regarding behavior and practice consistent treatment for everyone.
  • Offer advanced notice about all changes in the daily routine, such as an assembly, substitute teacher, and alterations in the daily schedule.  Depending on the student, you may need to use a written or other visual reminder of the change.
  • Frequent and accurate communication between the teacher and parent (or primary caregiver) is very helpful.
  • Most importantly, allow zero tolerance for any harassment, bullying, jokes, putdowns, etc.

The core principles of the CPM curriculum and the structure of the CPM classroom provide an excellent foundation for all students with learning differences.  Additional suggestions for students with autism spectrum disorder include the following.

  • Plan ahead for success.  If possible, meet with the parents, special education teacher, and school counselor prior to the start of school.  Learn all that you can about the student’s unique needs, individual learning styles, particular strengths and weaknesses, and intervention strategies that have worked in the past.  Make adjustments in workload expectations as necessary.  Discuss any behavior concerns and develop a plan for an unobtrusive classroom exit to a “safe place” if social pressure, stress, or confusion become overwhelming.  The plan should also include a protocol for “re-entry” when feelings of order and control return.
  • Working in teams can be quite challenging for a student with ASD, as learning to interact with other students is often a more complex task than learning the math.  A key component is to allow the student to select the level of team interaction that they are comfortable with and to be prepared for daily changes in preferences.  Think “mastery over time” when providing the following options.
    1. Seat students in a location that provides easy access to the teacher, especially at the beginning of the year.
    2. Employ a variety of team building activities that promote relationship development, allowing the student to determine their level of participation.  Even watching others engage in this type of social behavior is beneficial.
    3. Designate an isolated seat that students can move to when they feel the need to work alone.  This option should always be available to the student.
    4. Offer the option of “preferred pairs” as a stepping stone toward teamwork.  Working in pairs may need to happen for a short period of time, even as little as five minutes.  Allow the student with ASD to select a partner, or ask a mature and understanding student who has a calm, soft-spoken demeanor to work with the student.
    5. While some students may gradually grow comfortable sitting with larger groups, understand that teams of four may never be an option for others.  Learning to work with a partner, even for short periods of time, should be considered a significant achievement and possibly a milestone in social development.  A variation within a group of four is to allow interaction with a single, pre-selected member of the team, with no pressure to join a group discussion.
    6. If you decide to try a more randomized approach to forming groups for class work, select a strategy that prompts inclusion.  If your class involves pairing off or choosing partners, either draw numbers or use some other arbitrary means of pairing.  Ask an especially kind student if he or she would agree to choose the individual with ASD as a partner before the pairing takes place. Plan ahead so that the student with ASD ends up with a partner.
    7. Of course, feedback provided in the form of participation quizzes needs to reflect the unique circumstances involved in a given team.
  • To support daily instruction, provide students the option of simply responding to math problems verbally if writing is an overwhelming task.  When presenting material, use visual cues such as drawings or written words to augment an abstract idea.  You may also need to use shorter sentences to get a concept across.  Modify assignments as necessary to optimize engagement.  This may involve scaffolding the more involved problems from the text, offering graphic organizers for complex material, and simplifying instructions.  As you visit the team during circulation, present questions in a written format as well as verbally.  Consider all team and individual presentations to the class optional for the student with ASD.  Offer short, engaging breaks that involve physical activity every 15 or 20 minutes.
  • Many students with ASD are meticulous and will spend an excessive amount of time on a single problem, particularly on homework.  Early in the year, establish a limit on their work time (with parent approval).  One strategy is to have the student start with the last question in the Review & Preview and move forward until the time limit is reached.  Clearly there should be no penalty for incomplete homework due to time constraints.
  • Many teachers have found that summative assessment in the form of tests are not necessarily a good reflection of what the student actually knows.  Level of mastery seems to fluctuate daily and depend on the student’s current emotional status.  Consider the variety of formative assessment options as mentioned in the CPM teacher’s edition.  If they do participate in testing, allow toolkits, notes, homework, and other resources that help reduce stress.  Also, extended time on tests and a providing a reader (school staff member) may prove beneficial.  Many may wish to take team tests individually.
  • Avoid issuing consequences or punishment for something that the student has no control over.  Some may engage in disruptive self-stimulating behaviors (or other types of calming behaviors) that can be triggered by a variety of circumstances.  Again, have a designated spot in the room that the student can retreat to, or employ the exit strategy that was discussed with the parents.    Remember to offer praise for accomplishments and avoid punitive feedback about behavior.  Typically, misbehavior is a result of trying to cope with confusing or frightening situations, so do not take it personally.
  • Be aware that normal levels of auditory input can be perceived by the student as too much or too little.  Monitor and adjust class volume as necessary and maintain a calm, moderated speaking voice when addressing the class or teams.
  • Consider environmental changes such as removing “visual clutter” from the room or seating changes if the student seems distracted or upset by objects in classroom.
  • Many students with ASD are learning new communication skills in a special education classroom just before or after they are learning math in yours.  If possible, visit the student’s support class to learn how social skills are being taught.  In an ideal situation, students have the opportunity to see models of good teamwork, practice constructive interactions, learn to share ideas and take turns during discussions, and acknowledge what a team member says before disagreeing or taking the conversation in a different direction.
  • If at all possible, avoid idioms, double entendre, and sarcasm when speaking since many people with ASD interpret speech literally.  Do not rely on body language or facial expressions to convey an idea.
  • They may be challenged to relay important messages to their parents about school events, assignments, school rules, etc.  If you send a note home, be sure to follow up with an email or phone call.  Continue this practice until you know that the student has mastered the skill.
  • For some students with ASD, statements work better than questions.  For instance, “Yes,” would be considered a complete response when asked “Can you defend your answer for part b?”  Instead, offer the statement, “Defend your answer for part b.”
  • Assume nothing when assessing skills.  For example, the individual with ASD may have a proficient understanding of algebra, but may not be able to make simple change at a cash register.  The student may have incredible recall about books she has read, speeches she has heard, or sports statistics, but may not be able to remember to bring a pencil to class.  Uneven skill development is a common occurrence.

Embrace the opportunity to work with all students.  My students with autism spectrum disorder were a delight to teach.  They brought a new level of richness to the social fabric of the classroom, and were some of the most outstanding problem solvers I ever had the privilege of knowing.

Thank you to the following CPM teachers who contributed ideas for this article:  Jennifer Ard, Kathy Borst, Erin L. Kenney, Pat King, Katie Lamon, Leigh Ann Leugers, Laura Ratliff, Mark Ray, and Cam Wong.

*Jen can be contacted at

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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.