Dear Future Math Standards Writers,
I’m writing you this letter from the perspective of an educator who has worked as a math teacher and math teacher specialist for a public school district since 2003. I know that one day, maybe years from now, there will be a new set of math standards and I wanted to give you two thoughts to consider when writing whatever comes next.
Agencies such as the Center for Disease Control (CDC), the state of Florida, and the United States Navy use the Flesch Reading Ease formula to measure how easy an English language passage is to read. Scores from this formula range from 0 to 100 with scores between 0-29 considered to be very difficult to read. For reference, Time Magazine articles during the 2000s averaged a score of approximately 55, the nursery rhyme “Humpty Dumpty” scores a 79.7, and Florida deems an insurance policy “readable” if “the text achieves a minimum score of 45 on the Flesch reading ease test.”
Using this formula, as calculated by Microsoft Word 2010, the Standards for Mathematical Practice average a score of approximately 32. Scores are as low as 17.5 and 15.6 for Standards 2 and 5, respectively, making them especially difficult to read.
At this level of readability, it feels like you’re reading a language you don’t speak. As an example, here’s a single sentence from Math Practice 2:
They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.
If you got lost while reading that sentence, you’re not alone. Written in this manner, most people have to read the sentence again and still don’t understand what was read. I had to read Math Practice 2 over a dozen times before I started to figure out what it was really talking about. When this happens, most people will simply stop reading the standards.
This is obviously a huge problem. When I work with teachers across the country, I informally survey them about what percentage of them have actually read all eight of the Standards for Mathematical Practice. On average, around 10% to 15% say they have.
Someone might think that this implies that it is teachers’ fault because they are not making enough of an effort. I believe that is the wrong conclusion and is committing the fundamental attribution error. Let me explain.
Consider what happens when people vote on laws. Whether it’s an elected official or a citizen voting in an election, the vast majority of people vote on laws without having read the actual laws. At best, they read someone else’s summary of the law.
One explanation might be that everyone is lazy. Another reason might be that laws are often written in such a way that they are not realistically read and understood. Sometimes they are too long or use words few people understand. In reality, if the laws were more understandable, more people would read them. That is an issue that must be addressed if we want greater participation. Similarly, if the math standards were easier to read, more educators would actually read them.
It doesn’t have to be this way. Consider the English equivalent to the Standards for Mathematical Practice. The English Language Arts Anchor Standards are written using short and understandable sentences. Here’s one of them: “Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.”
Just because something can be written complexly, doesn’t mean it should be. A true measure of the future standards’ readability should be how understandable they are by as broad of a segment as possible. For example, wouldn’t it be wonderful if parents and students could understand the standards too?
UPDATE (11/10/2018) – Here’s my attempt at making more readable practice standards.
There will certainly be many opinions on what to deprioritize. However, I think that before you make a decision, I strongly suggest you spend the next 83 seconds watching this brilliant point from Conrad Wolfram’s TED talk beginning at 3:17 and going until 4:40.
As he mentions in his talk, we have to address the reality that we are spending significant time teaching students computation skills that they will rarely ever use because we have calculators and computers that can do it for them. Instead we should consider prioritizing things calculators and computers still cannot do. I’m not saying that we should never focus on computation. What I am saying is that we should consider making it less of a priority than it currently is.
I agree with this and would also add that they need to be published using the CASE format (imsglobal.org/case) for easy connections into edtech tools. Publishing standards in PDF form is the worst possible way. In addition, states should then create derivative frameworks if they like but the similarities would be automatically tracked. Really, it’s an equity issue to have wildly dissimilar standards (I’m looking at you Texas, Virginia, Alaska…). Teachers shouldn’t be scrambling to find materials that might work for their students. The better the focus the standards provide means we can all focus on writing amazing low floor highs ceiling tasks and encourage professional development of the standards that focuses on how to best teach them not how to read them! Bravo for the post Robert.
Thanks for the extra ideas, Brandon. The Common Core was definitely a step forward, but now it enables us to think about what steps might come after it. I also agree that in an ideal situation, it would be lovely if all states could agree upon a single set of standards as it would allow us to focus energy rather than making separate versions for slightly different sets of standards.
Thank you for this post. Just imagine if all our curriculum development, inservice and coaching time was not spent on debating translations. We might actually have time to talk about content connections and best practices.
That would be a wonderful place to be. Thanks, Leeanne.
I think enough time has gone by since their adoption that we can sit down and evaluate the standards and see what’s worked and what hasn’t. My understanding is that the CC itself was an attempt to resolve the “mile wide and inch deep” issue; perhaps they didn’t go far enough? Anyway, I’ve always believed that much of the multi-digit computation was overdone. I’ve been told it’s primarily to reinforce place value concepts, but I don’t know.
As far as making the standards understandable, I tried to do that here with the practice standards:
I like to know what things look like and I’m often confused by ambiguous language, and then find myself poring through the progressions documents, which also can be confusing. It also doesn’t help that the curriculum materials we use are themselves interpretations of the standards. Looking at a problem on a journal page I’ll ask myself, “Is that what the standards writers intended?” Again, I’m not always so sure. More clarity would be helpful. If we had it we could then, as Leeanne says above, concentrate on what we do best, the pedagogy part.
Thanks for starting the conversation.
Thanks Joe. I am definitely in favor of building upon the CCSS. I can’t imagine what kinds of political pressures everyone must have faced. I’m sure they had tight timelines and the need to get buy in from far too many people. So, compromises clearly must have been made.
In regards to the mile wide and inch deep issue, yes, that was the goal of their “focus” shift (http://www.corestandards.org/other-resources/key-shifts-in-mathematics/). I agree that in practice, it doesn’t feel like this was achieved.
Nice job with your practice standards explanations. As you mentioned, it becomes an issue of meaning being lost in translation as you synthesize so much information into something more readable. I’ve also found issues with most breakdowns of the SMP, which generally either means that I am mistaken or that the breakdown is too oversimplified. And all of this ignores the content standards and potential misinterpretation of those.
Again, much respect for the CCSS authors and what they accomplished. Just lots of hope for even better standards the next time around.
A while ago I did ask Bill McCallum about the idea of revising them. He basically said (on twitter) that they sort of set the standards loose and the States are the ones now revising etc… My problem is that if the States keep revising soon they won’t be too common which again, to me becomes an equity issue because now you have a more difficult time sharing curricular ideas across geographical boundaries.
Re: Priorities… I recall learning that the countries with some of the highest math scores teach fewer topics or strands in math Tha we do in Canada or the US. (Sorry, I don’t have a reference for that). The takaway being ‘depth, not breadth’. (I heard that little nugget from Nancy Karp, but whether she was the first to say it I don’t know!)
Hi Sarah. Yeah, I recall reading similar things though I also can’t remember the source. It might have been an article from Stigler and Hiebert from a long time ago. Either way, that is not surprising to me at all. If you ever track down the source, please let me know. I’ll add it to this post if I do.
William Schmidt from Michigan State University was the U.S. National Research Coordinator for the Third International Math and Science Study (TIMSS). It is my understanding that Schmidt coined the phrase “mile wide, inch deep” after analyzing the number of standards/concepts taught in U.S. math classrooms compared to the highest-performing countries in the study, particularly Singapore. See: https://www.chicagoreporter.com/math-teaching-in-us-inch-deep-mile-wide/ .
“There are too many content standards at every grade level. I understand that there is so much we want students to learn, but there is not enough time in the school year to teach every standard.”
The number of content standards likely will not go down until colleges stop requiring college algebra and calculus. That sounds like a pessimistic statement, but it is hard to argue with: many students are required to take college algebra and calculus, and in order to reach this standard, we have to shape the curriculum to get us there.
Part of this idea comes from something I read from Ben Orlin: https://mathwithbaddrawings.com/2016/03/02/why-the-math-curriculum-makes-no-sense/
That’s a great blog post. Thanks for sharing it. Clearly, as both you and Ben state, there are competing goals and requirements coming from a variety of sources that rarely result in achieving a great many of them. I’m not sure that I see colleges requiring calculus and algebra as my #1 offender, but I can see that it could be a problem in some situations.
If anyone subscribed to this post, I got inspired to show my ideas more:
Thanks for sharing this Brandon!
I’m glad you brought up the readability of the standards. The old standards were simple and understandable. The new ones (a re-written version of CC, which many states like mine adopted but re-wrote and re-numbered so that authorities could deny using CC) are an unreadable mess, just like CC! 67% of our state’s 9th and 10th grade first time test-takers fail the end-of-course test based on these unreadable standards, which I suppose means we’ve accomplished the goal of making Algebra 1 a nightmare for both teachers and students that will result in many of the kids never graduating from high school.
With regard to computation, I respectfully but vociferously disagree. Number sense went out the window when calculators replaced computational thinking. The students can’t estimate, can’t add negative and positive numbers, can’t multiply, can’t find common denominators, can’t factor, can’t do proportions, can’t understand how to convert units and can’t convert from percents to decimals. Obviously I’m generalizing: Many can, but most can’t. If they can’t do DOK 1 work then forget about DOK 3-4 and forget about the standards.
Two of the best lessons I learned in grad school were first, that a camel is a horse designed by a committee, and secondly, there is a supply and demand curve for policies: Policy demand is met by policy supply, so in our fragmented system with so many actors and so many agencies, what we really want (and get) is a plethora of policies on this and every other topic. No wonder the standards are inscrutable! BTW, this is why I teach math and not social science. 🙂 I want to give my students a love for mathematics for its own sake, and free them if just for a little while from the real world.
Thanks for sharing this. If you get a chance, check out this TED talk from Conrad Wolfram. He makes a point about the majority of K-12 Math Ed being on things calculators are already really good at with little time on the things calculators can’t do. He articulates these points beautifully.
Let me know what you think about this in regards to the part you “vociferously disagree” about.
I like how you took the stance of not getting rid of the Common Core standards entirely, but to change them to best fit everyone’s needs. I believe the common core standards have so much potential in becoming a great way to push our students to hit the highest standard possible to help benefit their learning. However, this potential is locked by the language in which these standards are presented, i.e the readability level of the standards, the redundant standards, etc. and need to be changed! Well written article and I thoroughly agree with your position.
Thanks Mike. The fact that the standards have been out for 7 years and educators STILL don’t know what they mean is a big problem.
Amen. I am hired time and time again to “unpack” the standards. When do we stop unpacking and start teaching?
It would be interesting to bridge the divide between people making the standards and those using them so that the impacts and realities were easier to understand.
In other words, everything I do makes sense from my perspective. It isn’t until I actually try to implement it that I get a better sense of the numerous shortcomings.
Amen, thank you for saying this. I agree completely!!
Thanks Sherry. This needs to be more obvious.
This is what the math TOSAs in my district have been saying for years! It would be so much easier to change math instruction if the list of standards was not so long.
Yes, there are just too many standards. You might like this blog post too: <