**(Note added 1/11/2018 – this article, more than any other, is getting daily traffic on my blog. It ‘s now the second most read article on the blog behind It’s AP ex(sc)am time again!. I’d appreciate it if readers would leave a comment below about how they were referred to it and what their interest is in CPM math. Thank you!)**

This article was prompted by the comments of a parent to my last blog article. Those comments were made on Nextdoor, not on this site. (The Nextdoor link will only work for local residents who have Nextdoor accounts.)

Referring to the new math curriculum “pathways” or course sequences from 6th through 8th grades, the parent said:

I would add that these new pathways and CPM curriculum (2014) were unveiled with promises that they would provide a deeper and more comprehensive math program. My observation is that this curriculum is more confusing and less comprehensive. I have two daughters who enthusiastically take Math at RSM and who can explain how little material is covered in CPM textbooks and what a superficial foundation they provide in math.

RSM is “The Russian School of Math,” a private organization with an office in San Mateo and many other locations across the U.S.

The CPM (College Preparatory Math, www.cpm.org) mathematics textbook series is used in many classes at Aragon High School (as well as some other SMUHSD schools such as Hillsdale HS). According to Superintendent Dr. Joan Rosas, it was also adopted by SMFCSD middle schools to align their curriculum with the high school curriculum.

I first used this math series when I taught 9th and 10th graders at George Washington High School in San Francisco, and have tutored many local students who are using these textbooks in class. I should also note that the unfortunate CPM precalculus textbook trial two years ago at Aragon was the motivation for my starting to blog, first on Nextdoor.com, and then at this site.

Although many teachers will say that CPM is the best mathematics series that they have used, I have very mixed opinions about it and am NOT an unabashed fan of the program as I will detail below.

A Google search on “opinions on CPM math” may interest you and will display the experiences of many other communities.

**The CPM Math Program**

CPM spans middle school to high school math, previously stopping at precalculus, but lately including Calculus AB and BC textbooks. The program strongly encourages group work over individual study.

Students are typically placed in groups of four in their classroom and are given defined roles within their group: “Resource Manager,” “Facilitator,” “Recorder/Reporter,” and “Task Manager” (see the beginning of any CPM textbook for details if you are interested in what these roles entail).

CPM literature frequently mentions that in the “real world” people work in teams, and therefore CPM aims to teach and facilitate collaborative learning. Many teachers have told me that students are more engaged with the CPM math curriculum than with any other series that they have tried. Students have active discussions about the material and work on group problems in class versus passively listening to lectures, taking notes, and only working actively when they do homework alone after school.

As long as the program works in this manner this is definitely a strong positive in its favor. Mathematics is definitely learned by working problems actively rather than watching a teacher do them on the board. It is also a major plus to work problems in class, when others are around to offer a helping hand, instead of finding later, when starting the homework at home alone, that one didn’t understand the material.

A typical CPM lesson works as follows. Each textbook section begins with a series of guided questions that lead students to discover a new math concept if they answer the questions correctly and in order. Often these guided questions are quite clever and well-designed. The books do not simply explain a math idea and and then provide worked examples to imitate, as do traditional math texts. Students work with their groups to solve the set of problems and learn the lesson that the section intends to teach.

Teachers are supposed to move around the class from group to group, answering questions from each group and making sure that students are on task. Lecturing is kept to a minimum. This is in agreement with the “learning by doing” philosophy. Current teaching practice tends to denigrate lecturing, calling a lecturer a “sage on the stage,” with the implication that lecturing stokes the ego of the teacher instead of really instructing the student.

As I have found with many ideas in education, such theories work great when one has motivated students who actually do the work. If the student groups are well-structured, the better students help those in their group who struggle with math, and everyone benefits. The good students benefit because, paradoxically, there is no better way to learn a subject than to teach it. The less mathematically-inclined students get help from their peers, which is often less intimidating than asking a question from the teacher.

However, if a teacher has a class of mainly lower level students who have not done well in math previously, the CPM method can become problematic. Putting pre-teens or teens who “hate math” into groups results in a major “classroom management” challenge for a teacher. The group conversation is often on any popular teenage topic other than mathematics when the teacher is not watching!

Again, if a group is able to finish the guided questions, then they learn the lesson for the day. In a poorer class, however, the teacher often has to answer the same questions repeatedly for each group and may eventually decide to stop the class and lecture for a while on the topic.

During the one-year CPM precalculus trial at Aragon, two school years back, one of the teachers tended to lecture at the beginning of each class. That teacher’s students were appreciative of this lecture effort while those in classes where the teachers followed the standard self-discovery prescription were often frustrated. In fact I had one student, who was totally upset with a teacher’s “hands-off” approach, comment to me, “Don’t they get paid to teach??!!??”

CPM basically is a set of pre-made math lessons which alleviates a lot of lesson planning for teachers. A motivated teacher can use these lessons as PART of a good curriculum as I will explain further below. Unfortunately this also means that a burned out teacher can use the CPM program as an excuse to coast. The lessons are spelled out in the book, the students are supposed to do the work themselves, so “get in your groups, open your book to section X, and do problems Y to Z” is the very minimal teaching effort required.

Typically, the group problems in the first part of each section take up most, if not all, of a class period. The second part of each textbook section is a set of problems (with no additional explanatory material) entitled “Review and Preview.” These “review” problems are typically assigned for homework. Hints for the homework problems are online at the CPM website, and Aragon teachers frequently post answers online. The “review” problems include some additional practice on the ideas just learned in the guided questions section, but also include review problems from earlier textbook sections. This practice of frequently returning to older topics in each new section is called “spiraling.”

*[Aside: The spiraling concept can also come into play on CPM chapter tests, i.e., the chapter 4 test will include problems not only from chapter 4, but also from chapters 1, 2, and/or 3. This can turn a chapter test into what is basically a mid-term or final exam. On the plus side, the constant cycling back can really reinforce the material. On the minus side, students can feel really stressed as the tests can cover much more material than traditional chapter tests.]*

The “Review and Preview” homework section may also include “thought” problems (called “preview” problems) on topics that students have not even encountered yet. The purpose of such questions is probably to see if a student can discover the solution to a completely new, challenging problem on his/her own. Unfortunately, “preview” questions tend to confuse all but the very best students.

**Critique of CPM**

Having now described how the “Review and Preview” section works, I must next note its most serious drawback. I have seen many instances where the “Review and Preview” section offers only minimal additional homework practice on the lesson just learned and then “spirals” back to problems from earlier sections picked in a rather random fashion.

Too often I have tutored students who are just beginning to master a new concept when the homework diverts them back to earlier topics without cementing the knowledge just learned. I then have to use other sources or make up my own problems to help the student.

Traditional texts give a far greater number of practice problems than CPM. They usually have solutions readily available to odd-numbered problems and have worked examples, both of which allow a motivated student to do extra work if they still don’t understand a concept.

This is much harder to do using the CPM series. In my experience a teacher who decides to use CPM needs to give students supplemental practice problems. If one has to find this extra material, then one needs to be convinced that the CPM guided questions are so good that it is worth this extra trouble, instead of simply using a different textbook.

One must also strongly believe in the value of the self-discovery process. “Self-discovery” as a teaching method is not universally accepted, and I address the issue of self-discovery versus fully guided instruction further below.

In summary, the biggest problems with CPM are the lack of explanations, worked example problems in the textbooks, and insufficient practice problems. The first two omissions are by design because each group is supposed to discover the concepts through the guided questions. Worked examples would circumvent this process.

However, if a group does not “get” the topic and fails to complete the guided problems in class, they are left with nothing to explain how they should do the homework! Essentially the student has a textbook with only questions and little or no explanations. This is a significant problem in classes with weaker math students and with students who are absent from class. They have nothing to refer to at home unless the teacher puts additional material on the Web. However, this means the students have to navigate to other sources instead of just being able to use their textbook.

The CPM books do have small boxed highlight sections called “Math Notes,” usually in sections of the book beyond the section being studied that day, that try to summarize the important points. These sections are very concise and also do not contain worked examples as do traditional math texts.

Another learning problem can arise because many schools use the cheaper paperback version of the CPM books which are split into two volumes. The index is in the second of two books, and the student may not have book 2 during the first part of the year. Only the hardback version is a single volume. Lack of an index makes it difficult to look up particular concepts when one is “stuck.”

**Critique of the Self-discovery Methodology**

**Finally, and the most important learning issue in my opinion, the self-discovery method tends to work better on easier concepts such as Algebra 1. As one moves up the math hierarchy and ideas become more complex, self-discovery becomes increasingly time-consuming and inefficient.**

I think this was a major reason why the CPM precalculus experiment at Aragon failed, and why at least one of the teachers had to revert to lecturing.

In fact I presented the teachers at Aragon with an article from an American Federation of Teachers journal critiquing “self-discovery” methods when I met with them early in the 2014-2015. I warned them early in the school year, first by emails and then in a face-to-face meeting with math department staff, the principal, and a vice-principal, that the CPM experiment was in grave danger of running off the rails. I believe the principal had evidence of this too, which is one reason why the meeting took place. The precalculus students that I tutored that year were clearly struggling significantly more than in years past when a traditional textbook was used.

The article I gave Aragon staff was the in Spring 2012 issue of American Educator, vol. 36, no. 1 and it was a through review of numerous educational research studies including academic references. The article concluded:

Research has provided overwhelming evidence that, for everyone but experts, partial guidance during instruction is significantly less effective than full guidance.

To date, I have no indication that anyone at the school ever took the time to read this article unfortunately. If the article’s conclusion is true (I think it is, and the research in this article has the great advantage of correlating closely with common sense unlike many teaching fads), this is a damning condemnation of the CPM methodology.

The fact that CPM now has textbooks for Calculus AB and BC makes me shudder. This would raise self-discovery to the highest level of complexity in high school math. I would be extremely concerned if any of the SMUHSD schools adopted those books.

**Research Supporting CPM**

Having discussed the CPM methodology and its pros and cons, one might still wonder what kind of research does CPM tout to promote their program? If one takes the time to navigate through the cpm.org website, one can find a section detailing research studies behind the CPM program.

Much of the research is older, probably in part because the standardized STAR test base was discontinued with the adoption of Common Core. However it is interesting to look at one of the later studies from 2013 in 8th grade and high school.

The methodology of this study is very flawed, however, because it appears to only take the results of school districts that CPM knew used their books and compare them to statewide averages. There is no controlling for differences in, e.g., demographics between districts that adopted CPM and the state as a whole. **Nevertheless, there is no indication that schools using the CPM series did any better (or worse) than the STAR test state averages in Algebra 1 and Geometry and only slightly better in Algebra 2.**

This might not seem too bad until one realizes that our local schools have always prided themselves on scoring significantly ABOVE the state average! Why would they want to adopt a series that only delivers average state test scores, particularly when we know how pathetic state math scores have been??

The illustration below shows California STAR math scores (% scoring proficient or above) from Grade 2 up through Algebra 2 for years up through 2012 before the state terminated this test in favor of newer Common Core testing. As one can see, there was a downward slide in math scores from 4th grade through high school in 2012.

Passing rates of 35%, 32%, and 34% are not benchmarks that I would want to use for marketing any product that I developed!!! Why would one adopt a program if this is the research used to promote it??

In fact, I learned from an administrator that CPM was tried in the SMUHSD years ago, long before Common Core was a glimmer in anyone’s eye, and was abandoned by all high schools except Hillsdale! The group work encouraged by Common Core appears to be resurrecting it from the dead.

**Postscript**

One final aside which I did not mention earlier as it is a lesser, but persistent, irritant for many parents: students in CPM classes also engage in a practice called “group tests.” All four students in a group work collaboratively on a test. At the end of the period, the teacher randomly picks one of the group’s four test papers, grades it later, and then assigns that grade to everyone in the group.

The first time this happens during the school year, some of the groups will have a paper selected from the weakest student in the group, and everyone in that group might end up with a bad grade. During subsequent group tests, the better students in the group will frantically check that everyone’s test papers have the same answers, so that they do not “get screwed over” a second time. Parents tend to shake their heads incredulously when they learn about this practice, and I can’t blame them.

However, I don’t see that this has to be an essential part of a CPM class and could be eliminated if a teacher so desired. Of course, this would require grading four times as many tests… However, I always thought that the purpose of a test was to assess what a student knew, not what his/her group can gin up and copy in a hurry…

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I have used two “discovery” programs. Neither was effective in comnprehensive, deep study , college prep settings because the students do not get enough information, skills,etc to be ready for calculus, nor were they effective with non-college bound who could care less about math and were more interested in mechanics, plumbing, electrical, cowboying, football, or anything else except math. Reading challenged students also struggle if they try at all. Not just a bad choice, but a serious mistake. What blows me away after teaching math for 45 years is that many think that students cannot “discover” discuss, work together, and a pile of other things if they are in a traditional math class. I have seen all of those things in traditional classes and have had great success in sending student into the scientific world.One of the last I taught is now an MIT graduate. His class did all of the things discussed above, BUT A TEACHER HAS TO BE CAREFUL ABOUT WHEN AND HOW MUCH FOR ANY PARTICULAR CLASS.

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Thanks very much for your comments. I have been getting a lot of traffic on this article recently and have been curious how people are finding it. The “referrer” stats on WordPress don’t seem to work very well. Would you mind telling me how you discovered it?

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David, Thank you for this post!

I’m a 27 year veteran math teacher. Unfortunately the district where I teach is “piloting” CPM in Algebra I and already considering it for geometry and algebra 2. There hasn’t even been enough time to collect, let alone analyze data from the supposed “pilot” but here we go forging ahead with dataless decision making.

I think you hit the nail on the head in observing that “The group work encouraged by Common Core appears to be resurrecting [CPM} from the dead.” I’m SO glad that I began my career years ago, but I am still very concerned about opportunities for students in the future.

The tutoring boom will surely continue as long as CPM is keeps creeping in…

Thanks again

and best wishes!

Lisa Jones

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You’re welcome, Lisa. I hope the article will be of use to you!

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This is a wonderful write up of all the issues I have with CPM.

I’m a 17 year old junior going through pre-cal right now. I’ve never been extraordinary at math, but I rarely got anything below a B. I always understood all the concepts and by the time finals arrived, I was confident I would pass.

However my pre-cal class uses the CPM textbook, and I simply cannot deal with the level of confusion I go through every day in that class. I feel like I’m getting no guidance whatsoever, and my only option is to get a math tutor, which is something I’ve never had to do. One of my best friends who’s now attending NCSSM had to retake precal because he simply couldn’t grasp the concepts she was teaching.

My teacher is also quick to assume I’m simply slower when compared to the rest of the class. She’s constantly singling me out, asking if I’m doing alright and if I need help. Besides being embarrassing, it just feels insulting. I just want one day where I can sit alone and take notes to study later.

And I can’t turn to my classmates for help either. They’re either way ahead of me and just give me answers so they can move on to the homework for that night, or stutter over themselves trying to explain a concept. Which isn’t their fault, they’re certainly now the ones expected to know how to teach.

To top it off tests make up 65 or 75 percent of our grade, and they’re some of the hardest tests I’ve ever taken, compounded by CPM. Luckily we’ve done one of the group tests, but I’m sure there will be more.

I’m not really sure how to express the problems I have with CPM to the school admin. Of course they’re not going to rollback a program they spent money on to train teachers and buy textbooks. So I feel like I’m just doomed at this point.

Thanks again for writing this.

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Danny,

I really sympathize with your situation as I have seen students in my location in similar situations.

Even though I work as a tutor and am essentially arguing against my own business, not only CPM, but much of the AP curriculum almost forces students to get tutors to survive. This gives yet another advantage to students from wealthier families which runs counter to the public school idea of equal opportunity.

When I went to high school back in the late 60s and early 70s, tutoring was almost unheard of. The curriculum was such that a good teacher could explain it well and students could master it without resorting to expensive after school fixes.

I hope you can find some help, but you might also consider getting your parents and other parents in your area to read my article. If enough of them get upset and complain to your school district, perhaps the system can be changed?!??

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Mr Kristofferson,

Thanks for taking the time to so lucidly explain your thoughts and concerns with this teaching approach. I suspect that the reason you are getting so much traffic is because concerned parents, including me, are looking to combat the “kool-aid” tainted view presented by school administrators when they embark on this social experiment.

In our case, the Birmingham (MI) Public School district has decided to roll this out despite the unequivocally dismal responses from students in the pilot(s) over the last year. Parents are justifiably irate because our schools consistently rank at the top within Michigan and this clearly does not advance learning as purported.

We are fighting. Parents are rallying to reverse this, but at this point the outcome is unclear.

Thanks for the well thought out and insightful perspective.

Steve

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Thanks for taking the time to write your comments above, Steve. Glad that I can be of assistance. You might be interested in another article on my blog in a similar vein entitled “Never Trust Educational Experts (or Me)! It details my local struggles with the education system.

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Hi David! I am part of the Birmingham (MI) parents that are fighting the administration. I, along with 4 other moms, started a FB group titled Concerned Birmingham Parents, please check it out. Have you found, in your research, any other states in recent years that students have been negatively affected by the CPM program. We appreciate your blog and quoted some of your research in our presentation to the board. Thank you for your hard work. Ashley

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Thanks for your comments, Ashley. Unfortunately, I do not use FaceBook for a variety of reasons which I will not elaborate on here.

In the 8th paragraph of my article there is a hyperlink in the following text:

“A Google search on “opinions on CPM math” may interest you and will display the experiences of many other communities.”

That link should lead you to other communities’ experiences, and I would not be surprised if variants on that Google search might uncover more.

Best of luck with your efforts!

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PS – What grades/math classes is the CPM series being considered for?

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