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Thursday, March 19, 2015

A Cautionary Tale: The Common Core is not Common

Hello friends, please, gather round the fire here while I tell you a tale of discovery, frustration, and utter confusion.  Mind the rocking chair, you don't want those fingers to get smooshed.

Some of you that follow my store know that I have been working all year on developing a full curriculum for the 4th grade Common Core math.  It is a lot of work, but I wanted each unit to be complete.  I wanted to create units where the teacher (or sub) has everything he or she needs to teach those standards effectively to their students.

 Just to give you a little background, I like to research states that implement the Common Core.  I compare what their expectations are to finalize what I put into my units.  This helps me make sure that I am interpreting and covering the standards correctly.

It really is sad that it is even necessary, but because of the sometimes incredibly vague wording of the standards, and the minimal examples that are included on the CC website,  it is good to check to make sure you are not alone in your thinking.

Honestly, everything was going pretty smoothly with following the standards.

That is, until I reached the decimals unit.  Okay, I thought, this is still numbers and operations, and until this point, it seemed that following the standards was pretty easy.  However, after doing some research between states I found a lot of discrepancies.

The standard in question was this: CC.4. NF.C.5:  Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Now, if you read that literally, you come to the conclusion that you are going to have the students adding fractions.  Look at the example, the vocabulary about using fractions "with denominator 10."  So, naturally you would believe that your students would be adding tenths and hundredths using the fractional form of these numbers.  Well, the Common Core apparently isn't natural, so no that was not the correct assumption.  "But, look at that example!" you might think..."it shows fractions, it says fractions.  Yes, you are correct, but you are not.

I was just as confused as you, I looked and saw some states adding just fractions (like I assumed at first).  Then, as I continued my research, I found states adding fractions to fractions, but also including decimals to decimals.  Okay, I mean, that makes sense, it is a decimals standard after all.  But then, I found states adding decimals to fractions.  By the time, my head was spinning.  How can I make this work?  I decided to write to the Common Core through their website/email and ask them.  Why not go to the source, right?

Well, a helpful lady named Ellen sent me an email back referring me to a forum about the Common Core standards.  In the referred post, seen here  a teacher had basically asked what I did.  They said there was disagreement in their school over whether it means fractions + fractions, decimals + decimals, or decimals + fractions.  Well, a  man named Bill McCallum, who I take must have a connection with the Common Core itself, said this, "The standards don’t regard decimals and fractions as different types of numbers between which conversions must be made, but rather as different notations for writing fractions. Note the language of the cluster heading above 4.NF.5: “Understand decimal notation for fractions, and compare decimal fractions.” Thus, students should see 0.57 as another way of writing the fraction 57/100. I think this means that the answer to all your questions is yes "

 My first reaction was, "What?  Why don't they just SAY that?"  I even wrote Ellen back suggesting that the examples on the site be broadened to give several examples, especially when the wording of it is considered vague compared to what is truly expected of the student.

Now, I hoped this would be the end of it.  That's just a speed bump considering all the standards I've covered already.  But alas, I just found another hair in the soup...

Measurement units, my friends.

Everyone has their own opinion on this, each state I've looked at seems to have their own take, and even my old math workbook we used (CC based) tells a different tale.  If you look at the previous years (2nd-3rd) in measurement you see that they learned to measure and estimate liquid volumes and masses using grams, kilograms, and liters.  Estimated length was used in 2nd with inches, feet, centimeters, and meters.  Time in 3rd also included telling time to the nearest minute.  Now, to show you where I'm going with this, here is the fourth grade standard pertaining to units of measure:

CC.4.MD.A.1 : Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Now, given what they already have covered in 2nd and 3rd, then reading the "added" units in this standard, you assume that CC isn't going to introduce them to units like tons, decimeter, miles, oh and ALL of customary capacity?  However, if you take a look around at the different states, they do include these.  Well, let me take that back.  Some include miles, some don't, but have all of customary capacity.  Others have tons, but no miles.  Decimeters?  Sure, in some is a proverbial nightmare of differences for someone who is trying to make a unit for any teachers going by CC standards.

 After checking the forum that was referenced to me for the decimal issue, I found nothing about particular units.  I did, however, find a complete (non)answer about using conversion tables.  A teacher asked whether students were allowed to use a conversion chart if they hadn't memorized all of the unit conversions.  This was the answer from our friend Bill: Well, the standard 5.MD.1 simply asks students to convert … it doesn't say whether they should memorize the relationships. That said, my own opinion is that there are some basic relationships that students should simply know, for example that there are 12 inches in a foot. It seems a waste of time to look this up in a chart when the human brain is already naturally adapted to storing such bits of information. Whether they acquire this by memorization or by repeated exposure is a matter of pedagogy, not specified in the standards. And the metric system is designed for ease of remembering.

So...yes, but no?  My favorite part was "It doesn't say whether they should memorize the relationships."  Of course it doesn't, because that would be TOO simple for teachers.  Then, we would miss all these glorious hours of needless research to find no answers to our questions because, it's not like teachers have anything else to do, right?  Come on, Bill here went to Harvard and has a PhD in math.  Even he doesn't exactly know what they want!

My conclusion?  I decided I'm going to keep these extra units in since most states and publications use them.  In my experience, my fourth graders always handled them just fine.  If teachers aren't sure what to do because normally they don't use them, they can use the conversion chart because Bill said so.  Or...did he?

Well, the fire is getting low, friends.  I better wrap up this tale.  So, the moral is, when you don't know what a standard's okay, no one else does either.  Despite the name, the "Common" Core is not common at all.

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