Let's take a look at an example of a math standard to see what this process looks like,

*CCSS Math Standard (Grade 4)*

*Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models*

The writers of the standards were going for clarity. They provided a lot of specifics, including exactly HOW the standard is to be taught which they promised they would not do. If they are going to take the time to detail how you teach a standards, you can bet they are going to test whether a teacher is using this method or not.

Picture, for example, that the assessment will ask the child to solve the problem 247x38. In pencil and paper math world, they would write the standard algorithm for this, mutliply the ones, the tens and the hundreds, add the totals and come up with the answer. In the rectangular array method noted above, they will be asked to fill in a chart like this:

For comparison, here is how California currently writes this standard.

*Solve problems involving division of multi-digit numbers by one-digit numbers.*

Simple, clear and it allows the teacher to use whatever method works best for her class and her district in order to get the standard across.

Teachers in Utah have begun unpacking the Common Core Standards. Here are some of their comments.

*I am a 3rd grade teacher at a Charter School in Utah. I am becoming very frustrated with Common Core, and I am starting to feel helpless, and feel that I am failing my students, which will one day affect me as they grow up and enter the workforce.*

*I attended the Math CORE Academy this summer and was told that Utah is not going to suggest a math book that will meet the new standards, instead I have to use whatever math book my school is using to create work for the students. It is incredibly difficult to teach the Common Core using Tasks with the math book we have, and I imagine it is just as difficult with any math book. First of all, it takes 2-3 hours to create a Task using a math book, I had to help create 2 at Core Academy. Secondly, the instructors encouraged us to leave out key pieces of information so that the students could construct their own knowledge.*

**I cannot imagine elementary students doing well in Algebra or Calculus after spending years learning that whatever number they come up with is correct.**I am frustrated that students are required to make a guess to solve the problem, and of course, they are correct, because any number they choose would work. They would then see that their classmates all chose different numbers, and yet all of the answers are correct? How confusing for an elementary student! I have decided to send these Tasks home as extra credit so that the parents in my class can see what to expect in the next school year. I am sure I will get many complaints that the problems are unsolvable, because important information has been left out! I believe that math has right and wrong answers, and that teaching students that any answer can be correct is foolish.Another teacher had this to say about the math standards.

*I just attended the Core Academy for math as an elementary teacher and was told for 4 straight days that the common core does NOT require math facts or the teaching of standard algorithms. I was taught how to teach solely using discovery learning or weird, unusable, at least with larger numbers, fuzzy math algorithms which actually make understanding place value unnecessary to solve problems requiring regrouping. What? I thought the core was supposed to help teachers REMEMBER to teach skills and standard algorithms …*

**I am devastated and do not even know if I can teach in Utah if this is the direction we are going…aligning ourselves with Washington state which is all discovery and has some of the poorest performing math students in the country…where they still believe Terc Investigations is great Curriculum. May the saints preserve us all.***There will always be the anti-memorization crowd who think that learning the multiplication facts to the point of instant recall is bad for a student, perhaps believing that it means students can no longer understand them. Of course this permanently slows students down, plus it requires students to think about 3rd-grade mathematics when they are trying to solve a college-level problem...*

*The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared. Avoiding hard mathematics with young students does not prepare them for hard mathematics when they are older.*

Combine these new standards, and all of the assessments that will come with them, with the fact that Race To The Top and NCLB have tied teacher tenure to student performance on assessments that will include things like the array above and you can bet that unpacking the standards next year may send some really good teachers packing.

The Common Core State Standards were sold as an improvement on many states standards and the public was told they would help kids. This was to happen by minimizing the differences in curriculum from district to district and state to state. What was never told, is that the CCSS not only dictate what must be taught, but how it must be taught. Your post is dead on.

ReplyDeleteThe state was given a waiver from NCLB. Maybe schools should receive a waiver from CCSS.

The composition of the standard is crucial. The array you have a screenshot of refers to the final clause of the standard, which states that any of these representations are ways to illustrate and explain the algorithm. The and/or construction emphasizes that students may deploy these to explain and illustrate the process of multiplication, but arrays are not required. What is required is that students be able to explain and illustrate multiplication.

ReplyDeleteHope that helps!

Mr. B - Such an array is a gimmick for teaching math facts. There have always been gimmicks for teaching math. A recent one is to teach the basic concept of addition by using manipulables. But this gimmick ignores the fact that, to really develop facility with addition, students must memorize a basic set of addition facts. I have a book at home that promised to teach you to do large multi digit math much faster. Most students are taught to do multi-digit addition starting at the ones column on the right and work their way left. This book's gimmick was to have you start at the largest digit on the left. This may allow you to start saying the answer faster because speak/read left to right, but the basic math does not change. The array above is just the latest gimmick and draws the focus to the process. The current focus on "envisioning" our math is what is leading to students in 4th, 5th and 6th grade still doing addition with their fingers under the table. They are focusing on the process as they were taught it with manipulables . We are de-emphasizing the necessary rote memorization of basic math facts. It looks like the new standard is sticking with that line of thinking.

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