## Reflections on Teaching

### 3 simple questions for Common Core mathematics standards…

March25

In my last post, I said I would look at three questions about the new common core standards and how they play out for fifth grade in California:

1. How do they compare with the current standards (with no assumption that the current standards are working–they aren’t);
2. Are they too narrow, or too broad;
3. Are they developmentally appropriate, and are some of the exemplars appropriate for elementary.
This post will cover the mathematics standards. I’m going to start with a story from my professional life. I’m doing this even though Mr. Coleman (co-author of the ELA standards) insists no one give a “hoot” what I think, and further that I need to read the text itself, without biasing things with prior knowledge, I think that’s stupid. I think it’s really stupid that someone as well educated as Mr. Coleman would say that because let’s face it, most learning is gained by creating analogues between something new and novel, and what we already know.
My story is this, when I was in the classroom last we used a text from Saxon. It was heavy on procedure and computation, light on visuals, and completely devoid of any joy. Four years later, I return from the computer lab to the classroom, and a new mathematics text. It’s full of illustrations! It’s full of real-life examples! It sucks. I wrote a bit here. My point is this, I don’t like my state’s current math standards. They are way too broad, way too rigorous (to the point of not being at all developmentally appropriate), BUT just because they suck, doesn’t make any replacement the automatic answer to my problems. Let’s get this started…

### How do the Common Core mathematics standards compare with the current standards?

They are a little less bulky than the current standards my state has for the fifth grade. I read the fifth grade section, then did a text search if I couldn’t spot a current California state standard in the Common Core ones, trying to figure out when they would cover it.

Gone: They have lopped off computing percents of whole numbers (moving it up to sixth grade), and the use of variables in algebra (e.g., a + 3 = 10) is also moved to sixth grade, but they are still expected to deal with area and volume formulas. Computing averages (mean, median, mode) is also moved up to sixth grade. This seems to prove my sense that California math standards more closely resembled sixth grade standards in the rest of the country (since we had to use the sixth grade Saxon text — Saxon 76, I kind of knew that already). Integers are not mentioned until 6th grade.

Still there: The core of what they need to know is still addition/subtraction/multiplication/division (including long division) of decimals and fractions. In the current standards, the multiplication of fractions does not include mixed numbers, but for some reason our current text introduces them to this in fifth grade shortly after they first learn how do this with just fractions. To make it easier to manipulate those pesky fractions, they have to learn about prime factors. Unfortunately, they have no introduction to factors before BAM, they are hit with it in fifth grade. Our current text at least gives them factors in fourth grade.

### Are they too narrow, or too broad?

Hmm, well I’m not feeling that these are “streamlined” but they are lighter than prior standards. It’ll make it easier to hit a Proficient or Advanced band on test, as the kids who master the core standards of computing decimals and fractions, won’t have their scores dimed-down by bombing out on integers or computing percentages, etc. They are still expected to cover new material in five sub-domains at each grade-level; Operations & Algebraic Thinking, Number & Operations in Base Ten, Number & Operations—Fractions, Measurement & Data, Geometry. That is a lot of territory to cover, and I’m not thinking this close to a svelte Singapore-sized curriculum, but since I’m not finding a handy-dandy guide to grade-level standards for that country I may be off-base.

The one area that is going to be different in some states, is the section of the standards on Practices which are about how students should be “thinking” about mathematics. These are not grade-level specific and preface the content standards. California already has a sub-domain for Mathematical Reasoning (more on that at the conclusion).

### Are they developmentally appropriate, and are some of the exemplars appropriate for elementary?

I’ve noted that some of the “bump” ups in concepts that occur in the fifth grade standards that don’t have a lot of preparation (e.g., prime factors appear instantly, introducing both factors and primes together).

What about the exemplars? More attention has been paid to David Coleman (and his sure to get attention remarks) on The Hunt Institute Channel of YouTube than to the offerings on mathematics. Coleman’s at +12,000 as of publication of this post vs. under 3,000 for this video on the math standards. So far, the math part of the Hunt Institute YouTube channel is long on what we used to call “persuasion” and short on “explanatory” (citing the standards, but not discussing what that looks like in any sort of detail).  Perhaps it’s just as well, as they seem to be avoiding pushing instructional approaches like Mr. Coleman advocated. This shows that the folks on the math panel had at least enough experience with education standards in the past (NCTM anyone) to want to avoid more “Math Wars”.

I have to say…I am not impressed. The professor explains that with these new standards, students will understand that fractions are part of a whole, and they even show this by showing the illustrating the standard with fraction pie! Like we haven’t been presenting pie, cookies, pizza, and other “round food” to kids ad naseum for the last I don’t know how many years of math instruction.

Notice it is being presented by a professor of mathematics. His work looks impressive, but I’m not seeing any work on elementary math instruction on the googles. Glancing through his work on mathematics education, I’m seeing stuff mostly related to preparation for college, but not for kids before high school. I suppose this would make that pie diagram look novel and new, when it’s the same pizza we’ve thrown at kids for I don’t know how long, and it still isn’t sticking.

I’d be more impressed with these folks if they had bothered to include some elementary folks in the discussion, but they didn’t because the consortia is made up of suits and college folks and what they want is to have kids ready to do college-level mathematics when they leave high school, and roll the same standards down to kindergarten, simplifying them a bit along the way.  They start at where they want to be instead of looking at where kids are, and building up. They look at the standards from an adult perspective, with the same silos of sub-domains for each grade-level, just adding a little more complexity each year. What if numbers and math don’t fit into those silos for the kids?

People talk a lot about how Common Core breaks down the disciplines, etc. and you can see some evidence of that in this lesson shown in a first grade classroom where the kids are using writing, and analysis, and counting together. That lesson shows how the Practices part of the standards could play out in primary classrooms. The teacher appear to be using tables ala Singapore Math (I only have  a passing knowledge of that program — so correct me if I’m wrong about that). It is very hands on, and does involve exploration so is very age-appropriate. OTOH, my state has had a Mathematical Reasoning component in the standards since the 1990s, and all it does is have students doing contrived word problems with little real world application (something that one of the Common Core authors bemoans in a Hunt Institute video).

Given how we’re finding out that many exemplar lessons developed by outsiders in ELA do not match the standards, or the exemplars from folks who wrote the standards, I’m not going too get excited.  I’ve been teaching in a state that has tried to test this type of thinking for over a decade, but unless the assessment is done like this video, with a teacher asking questions of the student to assess learning rather than a paper an pencil test, I feel little progress will be made.  We’ll only know what we “must do” with these standards when the assessments roll out, because after all that has become our bottom-line whether we like it or not.

Other posts in this series:

For further review:

California Mathematics Standards

Common Core Standards for California

#### “3 simple questions for Common Core mathematics standards…”

1. Stephen Stukas Says:

I appreciate your insights.

2. Stephen Stukas Says:

I appreciate your thoughts and impressions.

3. Kathleen Tarrant Says:

Thank you for your comments. I especially like how you noticed there were no elementary teachers helping to develop the Common Core standards. It should have started at 1st grade and gradually try to develop this new curriculum year by year instead of throwing it at the students regardless of where they are. I am so frustrated with people outside of the classrooms making the decisions without input from those of us working with the students!
It’s nice to know someone else out there understands my frustrations!
I hope you have a good school year.