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.
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.