At the NCTM conference last year I attended a talk by Scott Baldridge, lead author of the Eureka math curriculum, which is also called EngageNY in New York. Education Week recently compared different math curricula to see which were truly ‘aligned’ to the common core and only Eureka math had top scores. Look at all the green blocks for Eureka in the infographic below!

We always hear from common core supporters, including even Randi Weingarten, that the common core is wonderful — it’s just that darned implementation that is spoiling its reputation. So if this Eureka math is the one that is the purest interpretation of the common core, well, then it surely will be superior to anything we’ve seen in the math classroom up until now.

After a few minutes of listening to Baldridge it was clear that he was a very passionate man who took a lot of pride in the curriculum that he and his team developed. It was also clear that he knew very little about crafting good lessons.

His master vision reminded me a bit of the kinds of things I would think about before I became an actual teacher and learned so much about pacing and about the sorts of things that get students motivated to learn and retain math.

Listening to him discuss what he accomplished last year, then reading some of the blog posts on the Eureka math site, and finally by delving into the famous EngageNY ‘modules’ that many teachers are using throughout New York (they can be downloaded for free, but the cost of making copies is so steep for some schools that it becomes cheaper to buy the books from Eureka publishing — wouldn’t ya know it?) I’m certain that this is a curriculum devised by amateurs.

First of all, some lessons are full of errors. Second, some lessons are unnecessarily boring, and third, some lessons are unnecessarily confusing.

I should note that I have not gone through every module in every grade. I also did not search through to cherry pick examples that were particularly bad. I just randomly picked some important topics to see how they covered them and either I just happened to find the only four bad lessons in my first four tries or there are so many flawed lessons in this project that randomly selecting a bad one is quite likely. It’s a bit like evaluating a singer and the first few songs you listen to are out of tune. How many more do you have to listen to before you can safely assume that this is not someone with a lot of talent?

Exhibit A is the first lesson in the first module for 8th grade, exponents. On the second page, they introduce the concept of raising a negative number to a positive integer. Every real math teacher knows that there is a difference between the two expressions (-2)^4 and -2^4. The first one means (-2)*(-2)*(-2)*(-2)=+16 while the second one, without the parentheses around the -2 means -1*2*2*2*2=-16. I have checked with all the math teachers I know, and none have ever seen -2^4 interpreted as (-2)^4. Yet, here all over lesson one module one for 8th grade EngageNY teacher’s edition, we see this mistake.

In the teacher’s edition for this lesson, they very clearly make this error in their solution to a True/False question.

“So what?”, you might be thinking. They are choosing to imply the parentheses. Isn’t this just a notational thing? Maybe, but there are two more oddities. The first is that the necessity for parentheses when raising a negative to a power is actually one of the two ‘Student Outcomes’ written at the beginning of the lesson.

The second bizarre part is that they are not even consistent since out of the twenty times that this concept is presented, eighteen times are incorrect while in two places it is correct.

So Tim is allowed to write it incorrectly, but Josie and Arnie are not. How is the student to know what he or she should do on this issue?

To make matters worse, these lessons have been up for two years and this error has not been corrected even though it would be quite easy to simply upload a corrected file to the website. Does this mean that nobody reported this to them? Or are teachers following this lesson because they are supposed to? Who knows. But it definitely is a bad sign when curriculum authors can make such a basic mistake. It is much more likely that we are dealing with incompetent curriculum authors than that it was just a careless error.

For an example of a lesson that doesn’t have any major errors in it, but is just a boring missed opportunity that actually isn’t even ‘aligned’ to the original philosophy of the common core, look at 8th grade module 4 lesson 15 which is titled: Informal Proof of the Pythagorean Theorem.

The Pythagorean Theorem might be the most famous thing in all of elementary math. Throughout history cultures from around the world have independently discovered and proved the curious fact that in a right triangle, the longest side is always equals to the square root of the sum of the squares of the two smaller sides.

I do appreciate that they want to begin the unit with an informal proof, of which there are hundreds. The one they chose to use was once that required a lot of computation and manipulation of symbols and would probably fall flat on a group of 8th graders.

(a+b)^2=c^2+4*1/2(ab)

a^2+2ab+b^2=c^2+2ab

a^2+b^2=c^2

It’s not that I don’t like this proof. I just think that if you’re advising the entire country on which visual proof of the Pythagorean Theorem to use, this, from a pedagogical point of view, is not the ideal one.

Here’s one that’s a bit more appealing and appropriate for 8th graders since it doesn’t require symbolic Algebra to explain:

Or maybe this one:

Also the pacing is off since in one lesson the teacher is supposed to guide the students through an involved proof of the theorem and then also do a bunch of questions practicing the theorem. This is too much for one lesson which will result in the students likely not understanding the proof or how to apply the theorem.

The examples remind me of something out of an old workbook from the 1960s. Since the triangles are intentionally ‘not drawn to scale’ this becomes a monotonous exercise with the exact shape where students don’t even have the opportunity to estimate what the answer is likely to be before calculating it themselves. This is a weak activity, for sure.

Something that hits close to home for me, literally, is the way that the first grade standards are being implemented. I have a daughter in first grade right now and it definitely frustrates me when she brings home math assignments that are developmentally inappropriate. In first grade, kids should be getting comfortable with numbers, measuring, telling time, things like that. In the quest for getting them ‘college ready,’ EngageNY along with other publishers like the Go Math curriculum that she is trying to learn from, have decided that first graders need to know tricks for doing mental math. Some of these tricks are developmentally appropriate, but some are not. An example of such a trick is in module 2 lesson 20. Read this ‘dialogue’ teachers are supposed to have with the students from the EngageNY lesson plan:

Have students come to the meeting area and sit in a semi-circle with their personal white boards.

T: (Write 13 – 9 = ___.) Solve and share with your partner what you did to get your answer.

S: (Discuss solution and strategies.)

T: Explain what you did to get your answer.

S: We made a 5-group drawing. à We used the take from ten strategy using fingers. à We made a picture in our minds. We just took away 9 from 10 and did 1 + 3. That’s 4.

T: Everyone, use the number path to show how you can count on to make ten first. Don’t forget to use two arrows to show your thinking.

S: (Solve by starting from 9. Arrows land on 10 and 13.)

T: What addition number sentence helped you to solve 13 – 9?

S: 1 + 3 = 4.

T: How is counting on the number path similar to using our real and imaginary fingers?

S: After we drop 9 fingers, we have 1 more finger left from 10 fingers. We then add 1 to 3 imaginary fingers. This is just like hopping 1 square to get to 10 and 3 more to get to 13. We had to add 1 and 3 both times.

I can only hope that many first grade teachers out there have the wisdom to quietly skip this lesson. Ironically, it is not even clear that this lesson is ‘aligned’ to the common core standards. The closest thing I could find in them for first grade is 1.NBT.C.4.

## Use place value understanding and properties of operations to add and subtract.

CCSS.MATH.CONTENT.1.NBT.C.4

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

I think that there are ways to meet this standard without forcing kids to have an unreasonable amount of mathematical sophistication. My issue isn’t simply that this way of teaching 13-9 is different from the ‘regular’ way. I’m all for new and improved ways of teaching things. In my own classroom many of my methods deviate from the ‘regular’ way of doing things. In one of my classes, recently, my students had to learn how to solve algebra equations using an obscure method invented in Egypt in 1600 BCE. I thought it was worthy of teaching because it was thought provoking to have students analyze the ancient method and see why it got the correct answer by comparing it to our modern method. I guess the difference is that I can distinguish between what sorts of non-standard methods are worthy of teaching and which are actually harmful to the learning process. The authors of EngageNY, unfortunately, lack such wisdom.

I recently started following the lead writer of Eureka math, Scott Baldridge, on Twitter and saw that they have a blog where some of their authors describe some of their revolutionary ideas. This post was about a presentation one of the authors did at the NCTM conference about a better way to teach one of the most fundamental topics in all of middle school math: slope. There are so many creative ways to teach slope in a thought provoking meaningful way. Even when I started teaching over twenty years ago there were many good resources for teaching this topic beyond just memorizing a formula. This resource from England published in 1985 is still a classic.

From ‘The Language of Functions and Graphs’

Yet in the post the author says that kids don’t understand slope because we have been just teaching it as a mindless rote formula. And her solution was to introduce it by relating it to a much more abstract topic, similar triangles. Any math teacher will cringe, reading that post. The following Twitter conversation happened:

Not surprisingly, I never heard from him again.

So next time you hear from a ‘reformer’ that the problem with the common core isn’t the standards themselves, but the way that some textbook companies have unfaithfully implemented them, remember this short examination of the ‘pure’ interpretation by Eureka math.

The word ‘Eureka’ was made famous in math as, legend has it, Archimedes ran through the streets of Ancient Greece, naked, shouting it after he solved a tricky applied math problem in the bathtub. I think if Archimedes were still alive, he would be lunging for some hemlock if he knew his famous catchphrase was being used to promote such an overrated product.

I thought Archimedes was yelling “I’m a streaker.”

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I think we’re all lunging for some hemlock, at least metaphorically.

Also: beautiful title.

This water-flow video of the Pythagorean theorem informal proof is a great resource…

While baby sitting for my grandchildren I had the opportunity to help them with their HW.

My NYS 1st grade granddaughter had work on subtraction. The subtraction was basic but reading the problem and trying to understand what they wanted was the difficulty. Then the twist was that the last problem wanted to know how many groups of 5 could be make from 20 students, not exactly subtraction.

My NYS 3rd grader had HW on polygons. Not only triangles and rectangles but parallelogram, trapezoid, octagon, decagon. Why they are dealing with these polygons in 3rd grade is beyond me. Where do they go with these polygons in 4th, 5th .. grades?

I found Eureka math and decided to check it out. Oh dear ! So boring and rigid, and unnecessarily complicated. This is NOT the fault of the CCSS.

I’m not crazy about Go-Math at all. I’ve watched it in action in the lower and middle grades, and it just swaps out rote memorization of various mental math strategies, for the old rote memorization of math facts. Also there’s their emphasis on word problems, often with above-grade level vocabulary, hurts the chances of English Learner students to master the material. But I’ve flat-out detested Eureka Math ever since I got trapped into trying to teach a lesson to a classroom full of Fifth Graders last spring. That thing was so damn confusing, and so unnecessarily, that I went home and printed myself out a copy from the website, just to show people the harm the Common Core standards are doing to our schools. I never showed it to anyone, but what they saw my point right away.

I’m not defending or attacking the CCSS-Math content standards on the whole. And I’m not clear on how Eureka Math’s errors, egregious though they are, condemn the content standards for math. Can you explain your thinking on that, Gary? What Scott Baldridge and his financial backers claim for Eureka Math is not the responsibility of the people who wrote the Common Core, any more than a brilliant lesson in any curriculum is necessarily to the credit of those folks.

That said, I’m hardly surprised that Baldridge isn’t being intellectual honest here. Ever try publicly criticizing a Khan Academy video? The True Believers come out in droves to tell you all the reasons that YOU are the problem. We’re no longer in the Age of Mathematics Education. We’re in the Age of Mathematics Education Propaganda. And I’m afraid that no one seems to have the market cornered on the bull.

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For the issue of -2^4 = 16 : Try Excel or any other spreadsheet. It’s consistently wrong in them. Presumably the “Math” writers don’t realise this.

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The 3rd, 4th, and 5th grade modules are exceptional. I have used them with students with great results.

I was teaching the 1st module for 8th graders and me and another teacher aide noticed that Eureka math is actually forgetting the parenthesis surrounding the negatives and fractions. It’s the oddest thing. At one part they tell students that they must have a parenthesis around these things, and on another hand they don’t bother fixing up their own worksheet….and these things are revised every year. I have also found that they arbitrarily add instances in their word problems that throw off the entire flow of the lesson. As someone who is not versed in teaching math, I work hard to prepare for it when I substitute. I ask math teachers who worked as engineers before and they explain things to me if I’m having a hard time. They often tell me that I’m actually good at this. So when I see a mistake, knowing full well I’m not trained to teach this, then there is something definitely wrong with this system.

Does anyone have suggestions for a decent math workbook? Textbook?

Gary: What would you recommend for a curiculum to a small school, not tied to common core or state testing? We went with Eureka because they said it wa all about discovery and stories in math. It is SO not, I teach a 1-2 split and the 2nd grade fires way too much information (Friendly tens, fast tens, which ten did you want me to do???) and moves way to fast for these young minds. We may still be able to cut our losses. Any advice on where to go from there would be great.

my apologies for the typos…

Singapore Math is the way to go (link below). I would suggest the Primary Math US Ed. I have been advising a group of classical charter schools concerning their mathematics curriculum and Singapore is hands down the best available from what I have seen. Also, I expect it to be available (and hopefully unchanged) in 10 years when CCSS is a thing of the past.

http://www.singaporemath.com/Primary_Math_s/21.htm

I am aghast that NYS used taxpayer money to purchase these math modules. It is an embarrassment and a terrible waste of money.

i teach the kinder math. I find it is very teacher centered and involves very little decent problem solving. I taught math in Vermont for 20 years and we wrote our own CCSS curriculum at our school. It was heavy on number sense and problem solving using real world examples. Eureka aka Engage NY bites.

I teach the kinder version as well and it’s all problem solving and number sense using real world examples so I’m confused that you think the opposite. As a former first grade teacher the k version of eureka has been amazing and has built a strong foundation for my students mathematical journey. I am amazed at what they are able to verbalize and show at this young age. They are truly conceptulizing math! I would check if you are implementing it with fidelity and not just skimming the lessons because you feel they aren’t good. Truly implement it as is and then see if it works for you.

Regarding the 13-9 problem in 1st grade: taking from the 10 is a strategy used in the Singapore curriculum, but it’s done with ten-frames and counters. It’s not taught as a “mental math” trick, but rather as an introduction to place value in computations. Students fill up one frame with 10 and the other with 3. Then the teacher asks if there are enough in the ten frame with 3 to take 9 away. They realize they need to go to the full ten frame to take 9 away and then add the 1 left to the 3. One of the most common errors students make with the standard algorithm in G2 and above in subtraction is to subtract a smaller minuend digit from a larger subtrahend digit in a particular place value. As a result of practicing the ten frames exercise, first with counters, then with pictorials rarely do I see students in later grades make this common mistake in the standard algorithm. They understand they need to “get a ten and regroup it into ones.” (There are other concepts that build on “taking from the ten” in later grades, but this comment would be too long.) Maybe this is the goal of Eureka, but they aren’t incorporating the concrete and pictorial experience and are going to the abstract too quickly. In any case, this comment is in defense of learning to “take from the ten” in first grade.

The proof of the Pythagorean Theorem in the Eureka math materials need not involve the algebra if squaring the binomial (a+b). Instead draw a second congruent square with side length of (a+b). This time draw lines parallel to the sides dividing the square into four parts: a square with a side length b, a square with side length a, and two rectangles with side lengths of a and b. Removing the two rectangles, you are left with area a^2 + b^2. In the original square removing the four right triangles, you are left with area c^2. Since the area of the two rectangles equals the area of the four triangles, one has shown that a^2 + b^2 = c^2.

Mr. Rubenstein,

Regarding the exponential notation errors in Engage NY… I DID write to them 2 years ago! However, since I am in Filer, Idaho; I’m sure they assume that I am an ignorant farm girl in Ohio…

Mr. Rubinstein, no one answered Cary Grimm’s question. Any ideas on a good teacher textbook for 5th and 6th grade?

Hi Nora, did you find anything?

Hello Leigh…I’m actually using Eureka Math…It’s not perfect but the 6th graders are doing really will with Ratios and Tape Diagrams and the 5th graders struggled with Place Value and Decimals at first but they’re now back on track. I majored in K-8 Mathematics for my Masters since it was my weakest subject so I truly look at the lesson in the textbook and add on and take away depending on where my students get stuck. I like the guidance that the textbook provides since I’m a new teacher teaching Mathematics as well as the fact that you can download the book for free through Greatminds.org since I teach at a very small school that has a tight budget. As for Singapore Math, I taught in China for two years and they used it for our students K-5 but most of my students were still struggling with Mathematics. I’m not sure that there’s a perfect textbook out there but I’m constantly working on playing around with my lesson plans on a daily basis.

Oh…and sometimes I have to go back and look at lessons from previous grades in order to explain the concept since many of the students are not familiar with the text as well as the fact that this is the first year they switched over to Common Core…

I did some coaching/consulting in a low-income, high-needs district last year that was just starting with the Eureka program. Based on what I saw and what many teachers had to say, it was a very poor fit. It presumes levels of literacy that such districts lack. Students in 9th-grade algebra were struggling mightily because there was a clear presumption that they had had the 8th-grade Eureka math program. And that raises another crucial issue for districts thinking about adopting a program for K-12: will it work with students who haven’t had it from the start? I am skeptical that many available books suffice to accomplish an entire K-12 adoption in one year (and that is a criticism that applies to not only the Common Core as well, but to ANY sweeping reform that tries to do everything at once in all grade bands).

Mathematics educators I respect highly who’ve had Eureka/Engage-NY for longer than the district I’m speaking about above were, in general, as contemptuous of it as is Gary Rubenstein. I can’t say that I saw much last year to counter that view.

The issue goes far deeper, in my view. Publishers try to seduce teachers and administrators in a host of ways, some of them ethically questionable. But all the little goodies aside, the siren tune they all play is “Buy our program and relax: it practically teaches itself. Teachers: you’ll never have to think! Administrators: test scores will soar no matter how poor your teachers might be or how little support they have. We’ve got the magic bullet right here, you betcha!”

And public education is increasingly structured to make districts and those working in them desperately need to believe such malarkey. And one hand washes the other, except that the kids and the communities who swallow the quick, big fix nonsense get screwed, as do many of those gullible, ignorant, and/or lazy educators, when the test scores DON’T, in fact, soar because no book has ever been written that could come close to repairing all the damage our inequitable society guarantees will have been done to these children before they first set foot in a schoolhouse door.

Our school used Eureka Math for one year (I taught 7th grade) — I ditched it halfway through the year; the next year I taught Algebra I and DID NOT use Eureka. Now we are being mandated to use Eureka throughout 7-12. I have looked over Module 1 for Algebra I and can sincerely say that I am in awe. The lesson on Distributive Property starts with a simple exercise of using 1, 2, 3, and 4 in combination to = the numbers 1-25. OK. Within one page, we are asking students to multiply binomials and binomials X trinomials ! WOW !! What a leap. It is like anything else — good lessons, poor lessons. It should be used as a resource, NOT a curriculum.

My district is using Eureka K- 5 for the first time this year. I teach 3rd. My colleagues and I are SO frustrated due to the fact that third grade begins with 3 lessons on multiplication, then jumps into division for the next few lessons. I understand that this helps the kids have more time with multiplication and division, but what I can’t understand is a lot of the rest of th equalities of the program. The pacing is too fast, the script is sad, the vocabulary is different and these kids have not had Eureka in years past. I agree it can be a resource, but shouldn’t be the end all and be all of our math program. I am also a special Ed co taught classroom and teaching it whole class does not work for MANY of my students. It is dreadful and frustrating. So sad because I love teaching.

I was offered the opportunity to start Eureka earlier than the district requiring it next year. I teach 6th grade in a middle school. I am trying to get on board and teach with fidelity. I am struggling because I am still on Module 1, not even through the middle when I should be almost through with Module 2. Some of it I like, such as all the word problems, however i am beginning to see my students really struggle with trying to learn all the different ways to solve them. They want to “hang their hat” on one way. My low level students are really struggling to remember how to do it. What I am searching for now is data that shows this curriculum really does work, and not from the company. Part of the no child left behind stuff I though and “race to the Top” was that districts would use material that was proven to be successful. (Maybe I am wrong). I just got my masters in curriculum instruction and technology so I question everything, curriculum wise. I am also looking for ways to make the lessons more exciting. I made videos for the first 13 lessons for module 1 as part of my internship this past summer,so students who miss my class can watch and catch up, or review them and understand better. It’s too early to tell if this was effective at all.

I did find that some of the ideas in Eureka (Engage NY) were from Singapore math such as tape diagrams. I’m going to keep researching to see what methods work for other countries and how it is that Countries like China keep scoring so high on the PISSA tests.

There’s simply no magic curriculum and no curriculum expert who knows your class, your students, their needs, as well as you do, let alone better.

Students who struggle with seeing mathematics from more than one viewpoint are generally those who simply try to memorize a set of meaningless procedures. When they start to see math as making sense, then they can quit relying entirely on memorization (or nearly so) and move towards seeing and using connections between big ideas (and smaller ones), patterns that emerge as one gains perspective and some mathematical maturity (a concept that shouldn’t be reserved only for mathematics majors or graduate students, let alone professional mathematicians).

I don’t have sufficient experience with Eureka Math to make any ultimate judgments about it, but I do find Scott Baldridge more and more annoying over time (I subscribe to his blog). There’s an arrogance that comes from him that really irks me. If that has permeated the teacher and/or student materials for Eureka, it’s no wonder that it’s off-putting to some people.

As for test scores and what the Chinese, Singaporeans, or other countries do, keep in mind that these nations have significant cultural differences from the US in a host of meaningful ways. I have found specific ideas and practices from various Asian and European countries useful in my own teaching and teacher-educator practices, but again, nothing is magic. You ultimately have to find things that work for you and your kids. Take a look at the excellent book MAKING SENSE:Teaching and Learning Mathematics with Understanding by Carpenter, Fennema, Fuson, Hiebert, et al. I think you’ll find very useful precepts for what we can and should focus on in math classrooms nationally.

You have no idea how insane the Eureka math modules are for kindergarten.

Just FYI, some of what you pointed out with the (-x)^n might have been a font issue. There are empty spaces where the parentheses would normally be seen, wider gaps than would otherwise be justified.

In looking through the PDF of this lesson, I see the parentheses; this also explains the unusual explanation of why Josie is incorrect.

I’m not saying I trust the Eureka curriculum, and there are many more examples of egregious mathematical and pedagogical errors, such as working on the SSA “ambiguous case” in Grade 7. But in this case, it might have been a very simple issue.