First of all, I should say that I am not getting paid by CPM in any way (except for in the free sample books that they’re happy to send out to anyone who asks). I’m about to give it a pretty freaking positive review, tainted only by the melancholy of knowing a superior. CPM, if you want to *start* paying me after reading this post, that would be fine. riley@larkolicio.us.

College Preparatory Mathematics (CPM.org) has a boring name but the most exciting lesson materials and curriculum I’ve ever seen. Now, I’m only 26, everyone, so you might skip the shakers and go straight for the salt *mine*, but I have been using sample lessons from CPM’s algebra 2 and calculus books for the better part of two months, and I am literally moved to extol the benefits I’ve seen to each of my 118 readers. Bulleted, for your convenience:

- The sequencing is beautiful. It makes so much sense. In big ways, like “teach derivatives and antiderivatives together,” and also in small ways, like “finding the derivative of a logarithmic function will be a great way to practice implicit differentiation,” and also in tiny ways, like “think about this, and then this,” and then as often as not I see my kids beaming with pride and excitement at their discoveries. CPM is very well thought out.
- The teacher’s manual tells teachers what the authors were thinking, which allows you to be flexible. It tells you which problems are most important, and which ones are important for topics coming up soon, so if you want to skip a topic or lesson, you know what you can drop and what you can’t. If you have an awesome lesson idea, the teacher’s manual helps you figure out how to swap the CPM lesson out and swap yours in without missing something that will be essential later.
- The books are really lesson plans. The courses include homework, assessments, and classwork. They include materials for each lesson. There is literally a full, well-explained lesson plan for each of like 160 days of class. Purchasing the courses gives you three free days of professional development (re. how to work with CPM materials) and it gives your kids free access to solutions and additional practice online.

It’s this third bullet that has me in an existential crisis. This is why I haven’t been writing much lately: I’m not doing much lesson planning! CPM has done all of the work I used to do, and they’ve done it better. They’ve tested their materials on thousands of students and hundreds of teachers over the course of the last twenty years (or so? I don’t actually know, sorry). How can I presume to add anything to this after 5 years of teaching by myself? I haven’t even been taking good notes, for crying out loud! These books have been a huge hit to my (admittedly distended) ego for the last couple of months.

One of my coworkers really put this crisis into perspective for me. She said, as if this were obvious, that I’m supposed to be a teacher, not a curriculum developer. My immediate reaction, which scares me retroactively, was that there is no distinction – this is what I’ve been doing for all five years! Thinking about what’s important to teach my students and then figuring out the best way to teach it to them! That’s what’s so fun! Right?

But imagine this drastic role change: it is my job to deeply understand math and to guide my students through lessons created by people who have spent WAY MORE TIME ON IT THAN I CAN EVER SPEND IN MY WHOLE LIFE. It’s my job to support my students, encourage them, lead them to additional resources or work to fit their interests into the class. It’s my job to assess their progress and support them in failure and success. It’s my job to show them the habits of successful and happy intellectual adults. It’s my job to deal with schedule hiccups and individual circumstance to give the students the smoothest experience possible.

*It might not be my job to figure out what is important for my students to learn, or how they will best learn it. *Holy fuck.

One of my first reactions to this realization was, “well, I’m in the wrong job. I want to work on curriculum.” But I’ve been ceding entirely to CPM in my Algebra 2 class for over a month now and the increased depth I’ve attained in my relationships with students during class is satisfying in a new way. I’m hoping my school will officially adopt CPM for Algebra 2 and Calculus next year, so I can start from the beginning of the year next year, and I can really give it a shot. But you might see significantly fewer posts from me about the totally rad new lesson idea I’m developing. Because maybe teachers don’t develop lesson ideas!

Oof. This idea still shakes me. It’s so radical.

PS: Teaching is taking less time than it ever has before, btw. Pretty nice side effect.

I’ve been looking at the Algebra I and PreCalc books and thinking kinda the same thing…

I have taught at a school that expected elementary teachers to create their own science curriculum based on a list of objectives. At the time I thought it was foolish to have individual teachers recreate the wheel when there were so many great curricula available. Since then I have noticed a trend in math education away from textbooks toward more teacher prepared material. I again wondered why. Teachers have enough to do without having to create their own curriculum. We are cheating our students if we don’t make use of the best resources that are available and that includes excellent, well-researched textbooks.

Well put, Lisa. I was certainly one of those teachers eschewing my text in favor of lessons I spent hours and hours creating myself. Frankly, considering my old text, I think I was right. I wonder how much the movement away from text books reflects a desire for progressive math ed. A “math classes have been historically bad, so let’s throw out the history” kind of thing.

Don’t give up hope of doing curriculum development. You’ve just discovered a great new resource, and right now you’re finding out all of the things it does really well. It’s cool, it’s exciting, and you’re learning from CPM ways to teach that you hadn’t thought of. But give it a couple of years, and all of the CPM stuff will be in your brain, and you’ll have so many more great ideas in your toolbox, and you’ll start creating stuff for your classes again, I bet. They’ll just be better things, because of all of the new ideas you’ve learned!

A good textbook does help a lot in teaching. Part of the impetus for teacher-created materials was the insistence of so many schools on using really, really bad textbooks.

Following a good text is not bad teaching, but I agree with Lsquared that if you find yourself drawn to curriculum development you’ll find ways to improve even good textbooks. When you do find an improvement to a good text, share it with the publisher of the text—that is one way that the good books get better. (There’s not much point in sharing improvements to bad texts—they are usually better off being trashed than being tweaked.)

You mean, there’s a reason I feel like I have to do the work of two women? Dag.

Thanks for the reminder, LSquared and Kevin. There is the fact that CPM books have my kids learning entirely within our classroom, which is at odds with my teaching philosophy (and my school’s for that matter). I’ll have to find ways to adapt these lessons to fit some of my broader, more holistic vision.

@Kate: I know, right? Since using more CPM materials I’ve been, like, reading novels and *watching movies* some evenings. And there was this weekend where I didn’t do ANY WORK. Did you realize that was allowed?

You bring up many good points, Riley. Is it realistic for a single person to create quality assessments on a regular basis, provide timely feedback (grade, score, record, write comments, whatever) and then plan for the assessment-driven next steps in instruction? No wonder so many teachers go insane: the textbook tests are mediocre, but they use ‘em anyway; the textbook tests are awful, so much time is spent (at the expense of another area…typically for me, thinking about the next day’s/week’s instruction) creating new ones from scratch.

I want to teach, assess, re-teach and plan at a high level on a regular basis, but sleeping, eating and spending time with my wife also take up some time every 24 hours.

Great post.

Riley, I had the same epiphany with Spanish textbooks when I was mandated to use them for beginning levels a few years ago. After working through the textbook for a year, I realized that I had wasted time reinventing the wheel in other situations without a textbook, and probably did a less thorough job. During that time, I had sort of looked down my nose at them as something that would stymie teacher and student creativity and passion.

I almost hate to admit how much I love the textbooks, mostly because they sequence everything together so much better and have supplemental materials that make assessments so much easier. Yes, time-saving is HUGE thanks to them.

That said, it seems that students have enjoyed equally activities from the textbook as well as things that I have supplemented out of my own brain and gotten from other teachers. Sometimes it’s nice to just have something to go from in the textbook and just create a different format for it– adding movement, or turning it into a collaborative Google Docs activity, or improvising on the delivery and rationale for the activity in a fun way, or changing the content on some things altogether because it fits a cultural component that I’m more of an expert on.

I met two of the textbook developers last year at a conference. I was pretty enamored, even though they were salespeople– who had been teaching for YEARS. They seemed to have enjoyed teaching, but have enjoyed just as much the puzzle of how to sequence learning and decide on content. I am glad those people do what they do (though I regret how big and influential several textbook companies have become), and I’m glad for mentoring from other professionals who taught before me.

In fact, one thing I love is that my textbook has improved my storytelling ability. Many teachers/curriculum developers were paid to write very clever stories in Spanish that go with the textbook curriculum. Some are better than others, and I have selected some for class with the result of 100% engagement and raucous laughter. When would I have the time to create stuff like that? I have never cultivated a storyteller’s mind, until now. My time is spent on the delivery, the fun part. It has helped me focus on using my knowledge of how my students learn and figuring out how best to deliver content or help them discover knew knowledge and insights.

Yes, utilizing a textbook has helped my students and me have a pretty fun year. It has also helped me differentiate for students in the same classroom, by having students work more independently with different texts and ready made materials.

I’m a CPM fan myself. I taught the original series (Math 1, Math 2, etc.) for three years, then moved to a different school and supplemented with CPM materials until I got the Connections series for Alg1, Geo, and Alg2 for my sixth year. If I were to add a fourth bullet to your list, it’s that CPM is a non-profit and the materials are very cheap compared to traditional textbooks. (It’s also why neither of us should expect any kickbacks for promoting CPM.) I’ve never been that comfortable with salespeople, so I greatly appreciate the vibe I get when talking to CPM reps at state and national conferences compared to the people from big publishing houses.

That said, CPM isn’t perfect. No textbook is. The supplemental assessment materials you mentioned are certainly time-savers, but I still think the default suggested tests could use some work. (And the resources I had didn’t have default tests for Geometry, for some unknown reason.) Also, all the “extra practice” supplements reflect a strict, behaviorist, repetitive drill approach. Without starting up the math wars here, it would be nice to have extra practice that also included a more constructivist approach. It would more closely match the style of most of the lessons, be useful for remediation in small groups, and give the teacher more choice depending on his/her perceived needs of the student. But what’s probably most important is that you’ve found materials with which you’re comfortable using and modifying. Fighting your curriculum is no way to teach.

Best of luck to you and I’ll be following!

How well does CPM fit in with standards based grading (à la Dan Meyer etc)? I’ve switched to that from my traditional testing, and I’m very, very happy with the increased student ownership and targeted data. However, I’m pretty unhappy with my lecture based lessons — very ready to make a change, but totally unsure how to go about it. I was at a conference several months ago and a CPM rep showed us the very structured “Guess and Check” method that they teach the kids — wow. So are any of you using CPM and SBG?

I think CPM has a nice built-in structure for setting up standards based grading. For example, chapter 5 of CPM Algebra Connections contains the following chapter outline:

Section 5.1: Using algebra tiles and generic rectangles, you will develop a method to rewrite products, such as (3x-2)(4+x). Then, continuing the solving focus of Chapter 3, you will study how to solve one-variable equations containing products and how to solve multi-variable equations for one of the variables.

Section 5.2: Here you will continue your study of proportional situations started in Section 2.2. You will develop algebraic techniques to solve proportions and continue to build intuition about what makes a relationship proportional.

If the descriptions of the sections are too broad, you can also refer to the lesson objectives listed in the teacher guide. For the same chapter (all lessons are 1-day lessons):

5.1.1: Exploring an area model

5.1.2: Multiplying binomials and the distributive property

5.1.3: Using generic rectangles to multiply

5.1.4: Solving equations with multiplication

5.1.5: Working with multi-variable equations

5.1.6: Solving equations without manipulatives

5.2.1: Setting up and solving proportions

5.2.2: Practice with proportions

5.2.3: Applying proportions

If those are too narrow or repetitive, you could certainly lump several together. Either way, the objectives for each CPM chapter are made quite clear and would provide an easy-to-follow framework for setting up standards based grading.

Hi Riley!

I very much appreciated your review of the Calculus text I co-wrote. (I was unclear which CPM Algebra 2 text you referred, so I’m not sure I was involved in the development of that text. There are two — Math 3 was published many years ago, and more recently Algebra 2 Connections, which I helped co-write, but really was the work of Evra Baldinger and Judy Kysh) In your blog, I recognize within your review a very insightful reading and appreciation of the mathematical storyline (what you refer to as the sequencing). This is how I view mathematics curriculum – as a story with mathematical characters that develop and change over time, and interact with each other in various settings. During the development process, we (the writers) tried to develop plots as well, intentional moments when we tried to have students anticipate what will happen — moments of aesthetic wonderment that hopefully propelled students to figure things out and reach closure. I know it may sound corny, but thinking about mathematical development this way (in my opinion) led us to focus on trying to create better mathematical stories.

I wanted to point out that these texts were written by teachers – I was in the classroom when the Calculus course was “hatched,” as it were. The main difference is that we were a team of teachers (much strength in numbers) each with many years of doing exactly what you described doing — only there were many of us to bounce all these ideas off of and we gave up many of our summers to do it. I don’t think any single one of us should compare our work to that of large groups with copious time.

I hope that you will continue to interrogate curriculum – that is, look at it for its potential, use it to help you develop the math story you want to tell, and change it when you have a better story! If our texts help you focus more time on supporting students to be more successful and to help them love math, our goals have been met.

Cheers!

Leslie Dietiker

CPM Director of Curriculum and Assessment

Riley-

I’m glad to hear your positive take on CPM. I was very positive and actually pushed my department into adopting CPM until I started teaching it and got a bit frustrated. I just started writing a blog and am reflecting on this. Do they use Algebra Tiles in Algebra 2? I got frustrated with those.

We used algebra tiles to visualize “completing the square,” which worked really well. That was the only time.

What didn’t you like about the tiles? How were they being used?

The tiles got tedious, we used them for learning about combining like terms (that was fine) but then we got into these expression and equation mats and “legal moves” it was tedious to draw the tile representations and the tile work was a lot more work than just distributing, combining and solving. My students were already pretty comfortable with adding and subtracting integers.

As a parent who has to watch her child suffer through “group assessments”, neglect in class by the teacher, confusing aimless texts, incorrect answers on the CPM homework help website, and an almost total lack of actual instruction…replaced by “discovery” exercises…I was very unhappy with CPM. I do not know one student at our high school that is thriving with CPM. All the kids we know are lost, failing or cheating their way through it. The school however seems to think it is a miraculous curriculum. Until I realized that th purpose of CPM is to reduce teacher effort and satisfy the teacher’s needs I could not understand how anyone could endorse this terrible curriculum. It has cost me at least 100 hrs of tutoring to replace the missing instruction for my son so he does not fail and drop out of high school. For us, CPM has been a nightmare.

I agree completely. CPM is non-math. The kids neither learn to be curious problem-solvers (because CPM insists on the most absurd, unintuitive, counterproductive and rigid problem-solving routines), nor structured, skilled algebraists (because CPM fails to give most tried and true algorithms). It is a bad joke. At Berkeley High (we are in Oakland), the academic programs gave up on CPM and the non academic programs use it; nobody who wants to learn math goes into these programs because of it. Some local private schools use it, too, and it serves neither the strong students nor the weak.

It is simply not math.

When I ran CPM in my classes my students were more likely to follow curiosity into actual investigation. CPM almost never required them to think in one particular way – the guidelines and discussion steps it leads them through often got them to see things in _multiple_ ways.

You said “It is simply not math,” but I can’t agree. I think CPM is some of the first real math – the creative, internal formation of numerical structure – that students ever do in schools. Traditional math education, with only algorithms and lectures and other external entities, is simply not math. Math must be constructed in the mind of a student, BY the student.

David and Frazzled Factorer, I believe that the math programs at your schools are not serving your students well. There are lots of reasons that students get under-served by math classes, including curriculum. In this case, I have to suggest that it’s something besides the curriculum – as a math teacher, with a degree in math, who kept meticulous records about student achievement before and after CPM, I am telling you that CPM simply can help students learn math.

As an owner of a tutoring company, I have to agree with you. CPM is horrible. We have dozens of students coming to us every year because their teachers are extremely LAZY and don’t teach anything! Perhaps that’s not what CPM intended, but quite literally, teachers are handing books out to these groups and saying, “Here, go figure this out. I’m going to be back here. Don’t ask any questions.” You might as well have a babysitter, not a certified math teacher, in the room. Not-for-profit, written by teachers, whatever. This curriculum is extremely low quality!!

Elizabeth – I agree with you. Maybe this text works well for a teacher who is thoroughly familiar with it and planning his lessons around it, but from the standpoint of a tutor who has to come in and fortify the weak areas, the CPM books I have seen are not helpful. I will say that I have only been exposed to the Algebra I and Algebra II texts.

I spent an hour today with a student who was preparing for his first Algebra II test. We ended up putting the book aside and having discussions about the concepts we thought he might be covering instead. I felt as though he absorbed some of the information well, but that he is still shaky on some Algebra I ideas that would be useful to have down. He took Integrated Algebra I, which used CPM’s Algebra I text. He has also taken Integrated Geometry.

I am not a fan of CPM or “integrated” math, and would advise parents to put their kids on the “traditional” math track if possible. Maybe I just had good math teachers, but I never thought that their methods were overly boring or difficult to follow.

I agree I HATE CPM. Having the students discover how to do math on their own and from their peers is a terrible way to “teach” math. Let teachers teach math not coach the students in their self discovery of math.

I just got a sample of their precalculus book at a conference and was looking for reviews/opinions on them from the world at large. I was drawn to it because I’m trying to integrate more small group work into my precalculus class and honestly hate the book we’re using now. I am constantly making up my own stuff, but find that I keep having little mistakes or things that just don’t work out as I intended and it’s frustrating. I’ve just looked at the logs/exponentials chapter so far, and I assume it’s a little brief partly because they probably do it more in depth in algebra 2, but the kids at my school would need a more in-depth treatment. I think a lot of the problems look good though, and certain sequencing things make sense.

I went through the exponentials chapter with my precalc class, and was surprised by the depth of the connections the students were making. I added a bit of my own material to flesh it out with computer-aided graphing (Geogebra), but was generally pleased!

I’m in a district that has been using CPM for over 10 years. From what I see it has not done well. The advanced students get it but many/most? of the rest don’t. Though maybe the high end kids aren’t either because 2 kids I know were told to change out of engineering in college because their math wasn’t good enough, even though they did well in CPM math in high school. My own kids always ended up having to do the work for the groups. They hated it. Teachers might love it because they see wonderful, new connections forgetting that they already knew the math topic when they started. Only about a third of our tenth grade students are proficient on our state math test. CPM doesn’t prepare kids for the rapid, fluent math required for the ACT or the reasoning required on the SAT. I think some of the CPM activities are great as supplements but really the books are mostly a collection of activities. The 2008 Final Report of the National Math Advisory Panel recommended Computer Assisted Instruction. That’s the best way I see to personalize instruction and meet students exactly where they are.

Thanks for your response, Liz! I certainly didn’t have a lot of long-term data and it’s possible I was so enamored with the connections students were making that I was devaluing the skills of being able to add, subtract, etc QUICKLY and FLUENTLY.

It’s great that they see why subtraction works, but maybe it’s more important that they can subtract.

There are a number of contradictory studies out there. Before we chose to adopt CPM we found enough studies supporting it that it seemed like a responsible choice. I could believe that a lot depends on the implementation, too. I had a degree in math and was a real stickler for details, precision, and responsibility in each student – it’s not hard to imagine a teacher without the skills and passion to run CPM as carefully. It’s not even necessarily about the teacher – if administration chooses CPM *for* teachers, but doesn’t supply the requisite motivation and training, I could imagine it flopping.

Thanks again!

Riley

I’m wondering what’s happened with your use of CPM since this post. I am a CPM user and am looking for collaborators.

Cheers

Hi Jeff,

Two years ago I left teaching to create a tool for teachers. I ended up loving CPM as much as I raved about in this post, but I’m afraid I don’t have many long-term tips.

Thanks for writing! Check out the main CPM site for collaborators – they (at least used to) have a forum for CPM teachers to share questions, strategies, etc.