Starting this September, nearly every Algebra teacher in New York City is expected to follow a new curriculum called ‘Illustrative Math.’ This is part of a $34 million investment in a program called ‘NYC Solves’ which aims to improve math instruction and, consequently, math test scores.

At a press conference, Chancellor David Banks explained that this shift to a uniform curriculum is needed because “Schools all over the city, even on math, were just kind of doing their own thing,”

Before getting into the details of this curriculum and what my issues are with it, it is important to look at the recent history of math initiatives in New York City.

What students have to learn in the different grade levels is something that has evolved over the years. Generally what happens is that textbook companies update their books to reflect the different priorities and then teachers use those textbooks. In the 1950’s elementary school math was mainly about how to calculate with fractions, decimals, and percents, for example. But if you look at a 4th grade math textbook now, you will see some basic statistics and interpreting pie charts and bar graphs. You will also see problems that allow students to use calculators to do problems that are less about calculation and more about thinking about what exactly needs to be calculated. New York City teachers have generally been using textbooks that come from a very short list of approved books so it isn’t really true that math teachers around NYC are all doing their own thing. There’s a state test to prepare for and there are a list of topics that have to be covered and there isn’t so much room for doing your own thing.

Every Chancellor tries to improve math instruction. I remember about 20 years ago, the new thing was called ‘The Workshop Model’ which was a way for students to have more opportunity to experiment and to make their own observations and conclusions about math before the teacher tells them how to do it.

Then, about 10 years ago, after the Common Core standards were adopted by New York, there was a new bunch of textbooks that were updated to reflect the new priorities and New York City started pushing teachers to use a standardized curriculum called EngageNY which was an adaptation of something called Eureka! Math published by Great Minds. Part of the reason NYC chose this curriculum was that it had gotten stellar marks from an organization called EdReports, a Gates funded nonprofit, which reviews math curricula and grades it on various metrics. No other math curriculum came close to Eureka! on the EdReports summary. (Though EdReports methodology was questioned by some of the other publishers.)

I was not so impressed by EngageNY since most of the lessons were too long and there wasn’t enough opportunity for students to practice their skills. EngageNY was a K-12 curriculum and an issue at the time was whether it was possible to have all students switch to it or was there an issue with 8th graders trying to do it when they hadn’t done the 7th grade EngageNY the year before. But they rolled it out anyway and teachers had to adjust and try to use those materials as best as they could. Sometimes this meant supplementing by teaching topics that were needed as prerequisites. Sometimes this meant leaving out lessons or shortening lessons that were too long.

So EngageNY has been around now for long enough for us to know that it didn’t result in math scores improving. And now EngageNY has been scrapped and NYC has adopted a new curriculum, Illustrative Math, that has been touted as the best with a perfect score in every category by none other than the same organization, EdReports, that gushed about EngageNY.

Ironically, in the most updated EdReports review of Eureka! they give them pretty low marks.

What EdReports will say about Illustrative Math 10 years from now is unknown. But one thing that I do know is that Illustrative Math will fail to raise test scores for many of the same reasons that EngageNY failed.

A funny thing about EngageNY and also this new one, Illustrative Math is that the lessons are all freely available on their websites. I suppose that for extra money you can get various assessments and supplemental materials but I’m wondering how much of the $34 million is going to Illustrative Math and how much is going to internal people working on implementing it.

I’ve spent a lot of time going through the Illustrative Math Algebra lessons this summer and thinking about this. I’m hoping that my insights will help all those thousands of teachers to find a way to navigate this new directive. I also hope that Math supervisors and principals who are the ones who will be directing the teachers will read this and get some context to help them lead their teachers in a way that won’t be counterproductive.

Problem #1:
Illustrative Math is not aligned to the NY State Algebra Regents

Illustrative Math has a lot of topics that would never be on the Algebra Regents. An example is how they begin the course with students looking at statistical scatter plots and differentiating between bell curve shapes and other types of distribution. While this is a kind of interesting thing, it isn’t even something that comes up on the NY State Algebra II Regents. There are other topics, like rewriting exponential expressions in equivalent form (like changing interest rate from annual to monthly) that are part of Algebra II two years later, but not needed in Algebra I. There are two days of teaching the statistical concept of standard deviation which is on the Algebra II Regents. Then there are other things that are on the Algebra I Regents but aren’t part of Illustrative Math at all, like things with sequences and series. The current Algebra Regents is kind of a weird test that sometimes is more about reading than it is about math and sometimes about trying to interpret some real life situation into math language. I could imagine a new Regents exam that would be based on the Illustrative Math course and maybe that would be a good test, but the reality is that the effectiveness of this course is going to be based mainly in whether Regents scores go up or not and unfortunately this topic list, if followed faithfully, would likely make Regents scores go down.

Problem #2:
Illustrative Math requires that students have already mastered prerequisites that NYC students have not.

The Illustrative Math Algebra curriculum seems to assume that the students are already very familiar with a lot of Algebra. A big thing in Algebra is when you solve what’s called a ‘linear equation’ like 2x+1=11. This is a staple of Algebra and if a student does not master a problem like this, there is no way he or she can go very far with using equations like this to analyze real world situations. But I challenge any math teacher to look through the first six lessons of unit 2 and find where students would master and practice this ‘bread and butter’ skill. This is supposed to be the heart of solving equations, a fundamental skill and it is lost in a vague idea about rewriting equations and then there’s a lesson about graphing kind of thrown in the middle of all this. I think maybe the idea is that students who have been through the 8th grade Illustrative Math will have already learned how to do basic Algebra equations, but that won’t be the situation especially next year. I think that if a New York student truly knew all the math that Illustrative Math assumes they do in the beginning of this course, they would already know enough to get a passing grade on the Algebra Regents on the first day of the course.

Problem #3:
The Illustrative Math lesson lack ‘levity’

Students generally do not look forward to coming to math class. So a math teacher has to be aware of this and find a way to ‘sell it’ so that students want to learn it. This means that a math teacher often has to be, at times, entertaining. It is the only way to get kids to pay attention. This entertainment factor needs to be be baked into the lessons. There simply must be something fun about it. It can’t just be that we expect kids to get excited because there are multiple ways to solve the same quadratic equation.

Even though this is not one of the categories that EdReports uses to gauge the quality of a math curriculum, they should. Because without some kind of fun energy, students will tune out of lessons that are too ‘serious.’ And any teacher looking through the Illustrative Math lessons will see that these lessons lack that component. They just don’t have much ‘heart’ (again, this is hard to measure, but a teacher knows it when they see it).

Here are some examples of what I mean:

The very first activity of the curriculum, Unit 1 activity 1 is this:

Only in some imaginary world are students going to get excited by this question. This is an example where the correct answer is “Who cares?” And this is supposed to be the ‘hook’ that gets kids excited to learn about this topic.

And here is the first activity from the second unit:

Again, this is not something that would grab an actual student’s attention. It is the kind of thing that maybe the author of the lesson thinks will inspire kids but it is actually a really dull opening activity. Throughout this course the ‘voice’ of the lessons is like this. It is boring yet the authors aren’t aware of how boring they are.

Problem #4:
Illustrative Math Algebra is geared toward the wrong audience.

If I was in charge of a district where most of the students were getting about 80% correct on the Algebra end of year tests, this might be a very good curriculum for getting students that extra depth and getting the average from 80% up to about 85% or even 90%. But that is not what we are dealing with here in NYC.

If you look at the state data you might think that 56% of the students in NYC are ‘proficient’ on the Algebra Regents. But if you look more closely at the data you will see that 35% of the test takers only passed with a ‘level 3.’ And if you look more closely to see what it takes to get a ‘level 3’ you will learn that there is a massive curve on the Algebra Regents. Actually you only needed a raw score of between 27 and 51 out of 86 which means that you only needed between 31% and 51% of the possible points to be scaled up to passing the Regents.

So to me, the percentage of students actually ‘passing’ the Regents is about 21% of the students overall and, for Black and Latino students it is about 11%.

So the Illustrative Math lessons that assume that students are already pretty good at math and that students just need math to be more challenging for them are going to lead to a lot of frustration for students and for their teachers too.

I know that there is an adage that students will always rise to the level that you challenge them with. As nice as that sounds, a talented teacher knows how to craft lessons that are challenging but not so challenging as to make students totally confused and dejected. I feel like telling anyone who says that students always rise to the challenge and that teachers need to not hold students back to try to teach a week’s worth of material in one day and see how that goes for them. They will have to spend the next two weeks trying to undo the damage that they did that one day. This is true for adults trying to learn things too. When people go on their Pelaton bikes, they choose a program that is just the right level for them. If it is too hard you are going to get discouraged. And kids are even more like this. They want to learn but they don’t like the feeling of utter confusion and trying to digest too much. The idea that making the math harder is the cure for the low Algebra Regents is something that could only be believed by someone who never taught math before.

Problem #5:
Many of the ‘Problem Based Learning’ activities from Illustrative Math are not high enough quality

Illustrative Math is not a ‘bad’ curriculum. The authors obviously know a lot about math and they have a good sense of what topics are essential and how to connect topics together. Just because it is not appropriate for current high school students in NYC or, for a lot of reasons, most places, does not mean that there are not some good ideas in it.

For example, I like the way they utilize thought provoking questions to get students trying to really think about the essential problem they are going to learn about that day. Sometimes this is called ‘Problem Based Learning’ sometimes it is called ‘Inquiry Based Learning’ and it is something that over the years I have used very effectively. The way it works is that when the class starts, there is some question the students have to work on. It is not a review question but maybe something that they haven’t learned yet but that there are some hints to get them started.

I try to include this kind of thing in each of my lessons so that math becomes a bit of a mystery each day where there is a challenge which gets eventually resolved. Maybe 25% of a class period, I challenge students like this and give them time to ponder. Then during my actual lessons I try to sprinkle plenty of little questions, things to get them thinking more. There are some teachers who don’t do enough of this and you often hear that too many math teachers just show algorithms and that the students don’t get to think enough. On the other hand, there is such thing as too much of a good thing and in a class where they attempt to do this type of open ended exploration 90% of the time, it can lead to many students learning very little. I think I’d rather have my own child in a class where they do too little of this than too much.

An extreme version of this is a current math fad called ‘Building Thinking Classrooms’ by Peter Liljedahl where the author starts with a very good premise, that students are not thinking enough on their own in math classrooms, but then his solution is to create a classroom that is so student-centered that there is not obvious ‘front’ to the classroom – in theory students are working together and they are writing on their vertical white boards and the teacher is monitoring all this. This is a risky thing strategy to overuse, especially with students who are behind in their skills. Like everything in education, you need to have some balance in your methods. (Here is some skepticism about how valid the research is for the Building Thinking Classrooms philosophy.)

In my opinion Illustrative Math goes too far toward the Building Thinking Classrooms model. Some of the lessons seem to consist only of various prompts that students are supposed to go though and essentially figure out all the techniques themselves. (There is even a webinar on the Illustrative Math website where Peter Liljedahl is the featured speaker.) And many of the tasks are just OK so if a teacher is forced to use those, it can lead to a very inefficient use of valuable time.

Here’s an example of one of those warm up activities. I kind of think I know what they’re getting at here but even I’m not 100% sure. You can judge for yourself how many minutes you could see yourself pondering this question before you just dismiss it as a waste of time.

(In case you are curious, I suppose that the thing that students are supposed to eventually notice is that the black arrow has the same endpoint as the blue arrow and the same other endpoint of the green one so that this shows that -4 + 7 + 9 = 12. I would like to see a video of any class of math students in the country getting motivated by this prompt.)

And here is the way they suggest you teach a fairly obscure method of solving certain quadratic equations (which, again, would never be on the Regents for Algebra I or Algebra II). I’m familiar with this one so I appreciated that they even knew this technique but I defy Algebra teachers who are not familiar with this technique to try to follow this lesson.

Wrapping up

EdReports should have had in their grading metrics something about how likely it is that a curriculum would work if you tried to teach it to real kids. Again, it is not that these lessons are total gibberish. It’s just that there is no way they can be used effectively without massive adaptations.

In a Chalkbeat article they write about how teachers are concerned they will have to stick to some kind of pacing calendar where every teacher is supposed to be on the same lesson on the same day. But the article contradicts itself in two conflicting paragraphs:

“Education Department officials are holding teachers to a pacing guide, reminding teachers when they should wrap up units, according to communications reviewed by Chalkbeat.

Several educators said the pacing expectations are unrealistic and have made it harder to adjust to the new curriculum. An Education Department official said the pacing guide is “not a mandate” and teachers have freedom to spend longer on individual lessons if they need.”

So one official, at least, did say that the pacing guide is not a ‘mandate’ which means that teachers may not have to follow Illustrative Math 100% faithfully. But surely for $34 million they want this to be followed by some minimum percent. But what does that look like? I know it is hard to quantify but I’d say that this curriculum should be followed maybe 20%. This means that teachers try to incorporate at least some warm up activities that get kids thinking and anticipating. And maybe some of the ways that they develop some of the concepts in Illustrative Math are interesting and can be adapted. The question is whether something like 20% will be enough. I’m not optimistic that the NYC DOE is willing to give that kind of flexibility. What will the reaction be from the higher ups when teachers tell them “It is not possible to follow these lessons.” Will the DOE see it as just teachers complaining about change or will they trust that the teachers have their students’ best interests in mind?

Chancellor Banks addressed the idea of teacher autonomy in an interview:

“Banks, however, argues that as a citywide policy, curricular autonomy has produced mediocre and inequitable results.

“Everybody is not ready for that level of autonomy,” he recently told reporters. “Because if they were, we would have much better results than we have.” “

My concern is that some of the administrators who are directing those teachers, particularly the newer teachers, will insist that they follow the pacing calendar. Those administrators might not understand why it would be negligent for a teacher to try to follow this too faithfully. Surely if you take all the supervisors in the 420 schools that are supposed to use Illustrative Math next year and you sorted those administrators by what percent of Illustrative Math they want their teachers to try to accomplish next year, there is some administrator at the top of that list and the teachers who work for that administrator and the students who have those teachers are all going to suffer next year for all the reasons I outlined here.

I don’t fault Chancellor Banks for wanting to improve math scores and math instruction. The issue with the low Algebra Regents scores is definitely a symptom of something. Yes, teaching can be improved. Different strategies with encouraging more thinking are definitely needed. And maybe there is a better curriculum and collection of teaching strategies that can be started in the early grades so that by the time students get to 9th grade Algebra they can learn it from a curriculum like Illustrative Math. But to think that the main problem was that the Algebra curriculum was not standardized enough and was not hard enough is wishful thinking and short sighted.

I would love to hear from teachers who are switching over to Illustrative Math next year and to hear about what kind of guidance or directive they have been given for how to use these materials. Is your supervisor saying “We are all going to use this now (wink, wink)” or are they taking this thing really seriously like these are the 10 commandments brought down by Moses?

Unfortunately good intentions to improve math instruction is not enough. There needs to be excellent decision making and thinking through all of the ‘what can go wrong’ scenarios. It does not seem that the NYC DOE has thought that far ahead. It’s going to be rough.

[Note: Earlier in the summer Leonie Haimson did a great podcast about the issues with this new curriculum. She interviewed teacher Bobson Wong and researcher Tom Loveless https://talk-out-of-school.simplecast.com/episodes/nyc-new-math-curriculum-the-common-core-standards]