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.

 

Understandable Standards
The standards need to be phrased so that they make sense to as many people as possible. As I mentioned in detail in this blog post, the Common Core State Standards’ Mathematical Practices (as well as many of the content standards) are nearly unreadable.

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.

 

Prioritize
As the saying goes, “When everything is a priority, nothing is a priority.” 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. This leaves teachers with the awful choice between not spending enough time on key ideas or running out of time to cover everything. Something has to go and educators will be counting on you to make this tough decision.

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.

 

Conclusion
I don’t envy the challenging task you have ahead of yourselves. The Common Core State Standards were certainly over-politicized and I’m sure your task will be no different. It will be incredibly difficult to meet everyone’s expectations and come up with a solution that makes them all happy. I do appreciate the complex balance ahead of you and hope that you will consider the two points I made when reaching your decisions.
 
Sincerely,

47 Comments

  1. 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.

  2. 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.

  3. 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:
    http://exit10a.blogspot.com/2016/09/smp-scavenger-hunt.html
    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.

  4. 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/ .

  5. “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.

  6. 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.

  7. 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.

        • 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.

  8. 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.

  9. An issue I deal with is in interpretation. I interpret a standard one way and our director of curriculum another way. I also have to consider how Pearson, our state standardized test (the PARCC) creator interprets each standard. There has been much confusion on the 8th grade standard asking students to solve systems of linear equations algebraically (CCSS.Math.Content.8.EE.C.8.b) In my opinion the PARCC expects an Algebra 1 level of procedural fluency in using substitution and elimination, but I don’t think this is what the authors meant for 8th graders.

    • Yeah, systems of equations is particularly murky. We’ve had that conversation many times. In my own district, we decided that substitution and graphing would be part of 8th grade and then in Algebra 1 (or Integrated 1), elimination would be introduced.

      In general though, I feel like it would be beneficial to build in a process for how the standards can be modified, if only to make them easier to understand. As it is, there are no revision possibilities.

  10. Thank you for articulating this so eloquently. There is too much left to interpretation causing unnecessary anxiety for teachers and students alike. For every curriculum writing effort we must unravel and decode the standards for instruction. We ‘use this group’s interpretation’ or ‘that group’s interpretation’ while trying to decide is this what they mean?

    • Thanks Angelique. This really needs to be addressed at the standards level, because curriculum writers will get marked down if they leave anything out. So, it has to be the standards.

  11. I agree with you, thanks for taking the time to focus on these ideas and use data to back up your ideas. While I agree mostly about your part on computation, sometimes I think some parts of the computation help students in lower grades to develop math sense.

    • Thanks for the push back Patty. I’m far less qualified to speak on WHAT we should include in the standard and more about the reality that there isn’t time for all of it and that it has to be readable. So, your point is taken.

    • Ha! It’s waaaay easier to write some words on a blog post that few people will read than it is to actually make compromises with many groups and reach a compromise.

  12. I agree that there are too many standards, especially at the high school level. Even worse, most math teachers either think that they DO understand the standards or PRETEND that they understand them, because they fear they will be judged or given a bad evaluation if they admit their lack of understanding. In a culture where test scores are all that seem to matter, schools are not often safe spaces for teachers to admit a lack of understanding.

    I have chosen to focus on learning targets for my students in student friendly language, instead. I remember that Rick Stiggins once said that students can hit any target that is clear and stays still long enough. If its not clear for the teachers, how can it possibly be clear for the students!

    • Thanks for sharing your thoughts Pam. I definitely thought I did understand the standards. The reality has been though that the more math I learn, the better I can appreciate everything I still don’t know. I THOUGHT I was getting closer to knowing it all, but it really seems like the more I learn, the more I realize all I still don’t know.

  13. Robert, thanks for writing this, and I wonder if I may add a simple suggestion to the writer of future state standards:

    Just adopt the NCTM content and process standards. That is all.

    I teach at a private school, and we use NCTM standards for middle school math. There is plenty of time for interesting, in-depth conversations about big ideas when you don’t have to attend to and try to assess dozens of minutiae for each standard. The NCTM document Curriculum Focal Points helps teachers organize the learning around 3 or so main topics per grade, and shows how each connects to multiple branches of mathematics.

    Then, an additional plea needs to go out to schools and districts: Don’t accelerate! Let students go at the pace set by the standards. For students who need it, add support or enrichment as an extra math experience beyond the regular math curriculum instead of slowing down or speeding up. So many schools make the too-many-standards problem even worse by trying to cram all of prealgebra into grade 6 for the top 20 percent or so of math learners. And it goes too fast, and many kids get the idea they are “not a math person” because they can’t keep up, or they make it through but then drop out of the honors math track in high school because their foundational understandings in math are weak. We are in many cases undermining the success of students who might otherwise have enjoyed and done well at mathematics!

    • Thanks Gloria. I’m not super familiar with the NCTM content and process standards but I wonder if there are also too many of those content standards as well and if they’re easy to read.

  14. I don’t think the total number of standards taught in high school is too long, I just think for some strange reason we try to do too much in any given year and then repeat 80% of it the following year. I have taught algebra 2 for many years now and the only things I think I teach my students that they did not already see in some form or fashion in algebra 1 is logarithms, and perhaps rational functions. Why do I teach entire units in algebra 2 dedicated to systems of equations, and quadratic functions if the student already learned about these in algebra 1? Because the algebra 1 teachers were going so fast in their attempt to get to exponential functions and radical functions that no one (except perhaps a small number of the mathematically gifted) understand the material, or will remember what was taught.

    If I could write curriculum I would not do anything in algebra 1 other than make sure students understand what a function is, and how to solve an equation by isolating the variable. That is a very simplistic, high level description of what I think algebra 1 should cover. I imagine most algebra 1 teachers would think they couldn’t possibly spend and entire year on such limited topics but believe me, I can go into much greater detail. How many of your kids really understand domain, range, and the difference between discrete and continuous functions?

    • Clearly there need to be extended conversations about what is included and in which grade levels. My hope is to put this on standard writers’ radars so that they can be debated and reasonable compromises can be found.

  15. Conrad and YOU Robert WIll be the names in books like The History of Mathematics! Everything Conrad Wolfram says is correct but good luck changing anything. I was a teaching fellow at our local university for 2 years. The president of the school told me it was my goals to raise numbers of students passing the math section of the PPST . I knew the issue – math was being taught by mathematicians in the same style as The SMP are written. SO he asked me to write a new syllabus for the math courses taken in the elementary teaching math courses. All went well – those professors in the school of education agreed with me and were amazed at the few examples I showed them as to how math should change. Final approval was needed by the professors of math. They asked – where is the Cartesian product? where is truth tables? where is proving the properties ? Since they could not see beyond that and how to weave those higher math concepts into elementary math , the syllabus I wrote never came to fruition. New pre service teachers continue to come to us in schools not understanding how to teach elementary math. I believe until we get higher ed to change its focus – the way math is taught will never change.

    • You’re too kind, Janie. Thank you. I absolutely agree with what you described: the disconnect between those choosing what is taught and those implementing it with students. There’s so much status quo bias and we keep teaching things because that’s the way it’s always been done.

      I wish I had a clearer idea of how to break out of this cycle instead of lamenting it an a blog post that could be just as relatable in 20 years.

  16. True that! Like they say Rip Van Winkle will always feel right at home in a classroom! The good news is more people who carry weight – Bill Dagget – are starting to lament about the same issues! We need forward thinking University Presidents! Until then WE keep on advocating for change and make small strides. Happy mathing!

  17. Yes. I rewrite the standards in SWBAT form using language for students to understand to see if they meet those goals, why not have them in that format already? And MANY of the standards are really “butterflies” (nice to knows) and should definitely be stars, allowing true depth for the things that truly will help students…

  18. “ Just because something can be written complexly, doesn’t mean it should be.” TRUE! The writers need to consider their audience. The reality is that many elementary school teachers have not excelled in higher level math courses. This does NOT mean that they are unable to teach elementary content expertly with the proper guidance. While the practice standards are golden, they should be broken down by grade, or by BLOCKS of grades, at minimum. Teachers’ interpretations vary. Just because a resource has been downloaded often, does not make it accurate, as we know! I must state here, that teachers are doing the best they can, and they are seeking out content on the internet because they’re looking for help.

    • Joan, I was a math major at UCLA and focus on secondary mathematics and it STILL was hard for me to understand what the heck the standards were saying. It’s not a matter of elementary teachers’ ability levels.

  19. South Carolina is currently working on its math standards. I heard the state says they expect teachers to teach only 80% of them. The teachers in the room asked, “Which 80%?” Your note to prioritize is right on point. There are gaps of learning every year if we don’t prioritize which standards we ALL need to teach. Thank you for your letter.

    • Based on what you wrote, that is mind boggling to me. Why wouldn’t they just give you standards they thought could be taught… or mark the 20% as optional???

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