Why does Common Core mandate fuzzy math?

June 10, 2013 16 Comments

Below are the standards for multiplication and division for fourth, fifth and sixth grade under Common Core. While the Common Core tests, like New York’s, require students to be able to do multi digit multiplication and division in fourth grade, the Common Core standards do not require the mastery of the standard algorithm until later. This creates a mandate that students learn “alternative strategies.” Here are the standards for multiplication:

EXAMPLES OF HOW TO MEET THE FOURTH GRADE ALGORITHM WITHOUT THE STANDARD ALGORITHM:

THE RECTANGLE METHOD (DIRECTLY BELOW) WAS ON THE SMARTER BALANCED SAMPLE TEST:

OR

THE CRAZY LATTICE METHOD FOR MULTIPLICATION:

Partial Products Method

In the Partial Products Method one takes the base-ten decomposition of each factor and forms the products of all pairs of terms. Then these partial products are added together. The student text does not recommend any particular addition algorithm for this second stage. In the example at right I’ve assumed traditional addition with carries done mentally, but an Everyday Mathematics pupil may well do that addition problem by the Partial Sums or the Column Addition method.Observe that the number of terms in the addition problem is the product of the numbers of digits in the factors.
               83
               27
             ----
  80*20  ->  1600
  80* 7  ->   560
   3*20  ->    60
   3* 7  ->    21
             ----
             2241

Lattice Method

The lattice method employs a grid of squares. One factor is written along the top, left to right, and the other factor is written along the right edge, top to bottom. In the example at right the factors are 83 and 27. Each square of the grid defined by the two factors is divided by a diagonal. The digits of the factors are multiplied pairwise and the two-digit result written down in the corresponding square in the manner shown. The result of the multiplication is then obtained by addition down the diagonals.
        8   3
      +---+---+
      |1 /|0 /|
      | / | / | 2
    1 |/ 6|/ 6|
      +---+---+
      |5 /|2 /|
      | / | / | 7
   11 |/ 6|/ 1|
      +---+---+
       14   1
     1,11,14,1
  -> 1,12,4,1
  -> 2,2,4,1
   = 2241

 

THE COMMON CORE STANDARDS DO NOT REQUIRE THE STANDARD ALGORITHM (BELOW) UNTIL 5TH GRADE. THE IDEA BEHIND THIS IS THAT IT WILL STUNT THEIR UNDERSTANDING OF MULTIPLICATION. I’M NOT JOKING. THEY ACTUALLY CALL IT THE SHORT CUT METHOD, NOT THE STANDARD ALGORITHM??

How about division? This what the Common Core standards include:

SO, WE DON’T REQUIRE OR TEST OVER THE STANDARD ALGORITHM UNTIL SIXTH GRADE, BUT REQUIRE DIVISION OF UP TO FOUR DIGITS BY ONE DIGIT DIVISORS IN FOURTH GRADE, AND DIGIT DIVISORS IN FIFTH?? HERE’S HOW TO DO DIVISION WITHOUT THE STANDARD ALGORITHM:

OR

Column Division Method

The column division method appears to be the traditional method, but implemented in a rather verbose manner, and presented in a way that constitutes a viable student algorithm only when the divisor is a single-digit number. The Everyday Mathematics 5th and 6th grade student reference books present it via a visualization as money sharing. In the example at right we divide 1220 by 7. We have one $1000 note, which can not be shared by 7 people. We change it to 10 $100 notes, giving us 12 $100 notes in all. With 7 people each gets 1 such note, and we mark the 1 above the dividend. This removes 7 $100 notes, leaving us with 5, which we convert into 50 $10 notes, giving us 52 such notes in all. With 7 people each can get 7 such notes, which we mark above the dividend. This removes 49 $10 notes, leaving us with 3, which we convert into 30 $1 notes, giving us indeed 30 $1 notes in all. With 7 people each can get 4 such notes, which we mark above the dividend. This removes 28 such notes, leaving us with 2. That 2 is our remainder, and the integer result of the division is read above the line.
       0 | 1 | 7 | 4
    -----+---+---+--
  7 )  1 | 2 | 2 | 0
     - 0
     ----+---
       1 |
  ->     |12
         - 7
         ----+---
           5 |
       ->    |52
             -49
             ----+---
               3 |
           ->    |30
                 -28
                  ---
                   2
  ans: 174 R2

 OR


Partial Quotients Method

The Partial Quotients Method, the Everyday Mathematics focus algorithm for division, might be described as successive approximation. It is suggested that a pupil will find it helpful to prepare first a table of some easy multiples of the divisor; say twice and five times the divisor. Then we work up towards the answer from below. In the example at right, 1220 divided by 16, we may have made a note first that 2*16=32 and 5*16=80. Then we work up towards 1220. 50*16=800 subtract from 1220, leaves 420; 20*16=320; etc..
     ------  |
  16 ) 1220  |
      - 800  |  50
       ----  |
        420  |
      - 320  |  20
        ---  |
        100  |
      -  80  |   5
        ---  |
         20  |
      -  16  |   1
         --  |  --
          4  |  76
  ans: 76 R4

THIS IS THE STANDARD ALGORITHM (BELOW) FOR DIVISION-NOT TAUGHT UNTIL SIXTH GRADE WHILE DIVISION OF MULTI-DIGIT NUMBERS IS REQUIRED ON COMMON CORE TESTS STARTING IN FOURTH GRADE.

Comments (16)

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  1. Barry Garelick says:

    Defenders of Common Core math standards (like Bill McCallum, the lead writer of the standards) will say that the standards do not prohibit teaching the standard algorithms earlier than the specified grade. For example, the standard algorithm for multi-digit addition and subtraction is required to be learned by 4th grade. He posits that teachers are free to teach it earlier. But who is going to do that when the standards for 2nd and 3rd grade require it to be taught via various place value “strategies”. Further, programs like EM and Investigations readily provide such alternative strategies in those earlier grades.

  2. Michelle says:

    Years ago, I assisted in a fourth-grade classroom using Everyday Mathematics as the curriculum. At first, I was “sold” because it was developed by the University of Chicago and deemed to be “cutting edge.” Who wouldn’t want such “advanced” learning for their children? In reality, it was a disaster. Students were regularly lost and confused and had not a clue as to how and why they arrived at their answers–if they arrived at them at all. The only students who “got it” were worked with intensely one-on-one and few, if any, had mastery of simple computation by year’s end. Since parents hadn’t been taught using this method, they were powerless to help at home. Most classroom days were spent watching students boil over in frustration. This type of math instruction does not work in large groups because it is developed by “educational experts” who have not the first clue as to the realities of the classroom environment.

    • M. Sibinovic says:

      Amen. The “new math” of the 70s was a disaster and eventually schools reverted back to “traditional” math instruction. I daresay the same will eventually happen with CC.

  3. Patrick says:

    Encouraging children to think, not just calculate, isn’t necessarily a bad thing is it? You can buy a calculator for only a few bucks now so the need to be proficient at calculating has been somewhat diminished. An alarming number of high school kids I tutor are completely incapable of comprehending the mathematical relationships defined here. This type of mathmatical thinking, not just calculating, is essential in technical fields. Instead of ensuring we can save our children the 3 bucks it takes to buy calculator, maybe we can help them get their minds to make these relationships on their own and save me from having so many kids to tutor.

    • Erin Tuttle says:

      I think most people would expect a well educated child in math not to need a calculator. Many ideas in math stem from these simple calculations which math textbooks have ignored in favor of concepts at the expense of many children having difficulties with higher level math. Learning calculations helps children to think and shape mathematical thinking.

  4. Brendan says:

    I’m a PhD Engineer. Math is a central component of everything I do – if I’m not using directly, I need to understand what is happening. The understanding these people are looking for won’t come until the children begin to mature. Teach ‘em the basics, and even if they don’t “understand” they can cope later. Don’t teach them the basics, and the ones who aren’t interested in the basics will never learn.

    This is a sad state for education… I’ve already begun to encounter this idiocy with my kids. I do my best to counter program them, for their sakes.

  5. Jim says:

    I have a Ph.D. in Physics, and I’ll be damned if I can figure out the last steps in the “lattice” method of multiplication. I’m sure if I spent more than 5 minutes, maybe I could, but really . . . this is multiplication we’re talking about! That lattice thing is more confusing than anything I have ever seen. The division methods aren’t quite as awful; at least they made sense to me rather quickly. Stick with the older, working algorithms, and leave this other nonsense to the educrats.

  6. Scott says:

    This is exactly why my children are being homeschooled. For example my daughter is now in 7th grade and is being homeschooled for the second year now because she was #1 bullied and the school did nothing(thats a different matter all together) and #2 she was so behind in math because nothing was explain to her and when she brought her work home it was “foreign” to us. Now that she is home she has come into her own and is excelling in math because she is learning the basics that should be taught not this new crap that most adults don’t understand. I learned math using the basic way and I turned out just fine.

  7. mark says:

    It is difficult to avoid the conclusion that an unwritten objective of common core is to displace/marginalize the role of parents in the educational process. Our son was literally punished for using “normal” multiplication and division (which we taught him this last summer in prep for his school year). Punished for getting the right answers, more quickly than the kids setting up strange lattices and long tables of partial quotients.

    There’s only on explanation for that. Someone wants kids looking to the omniscients in the government apparatus rather than their parents.

  8. Kevin Cook says:

    I have a granddaughter who was excellent in math until 4th grade. The multiplication and division concepts threw her into a loop. I tried to help her with traditional methods but she said what i showed her was “wrong” and the teacher would get mad if she did it the way I showed her.

  9. Eric ferguson says:

    Sick of common core, what a load of crap. I am on this website because of it my son getting a bad grade due to partial sums and fuzzy math. I taught him early in Kindergarten and 1st grade how to do math, even multiplication, and now they say its the wrong way. Dept of Education is pathetic. that is what happens when you get progressive dictators in office that in reality they know nothing.

    • Erin Tuttle says:

      Keep teaching him the correct method. We have a new post on our website that allows people to download images of the Common Core materials children are being instructed with in Indiana. Our hope is to compile them and show them to the IDOE and Governor Pence so they can see NOTHING has changed and none of our concerns were addressed.

  10. Erin Tuttle says:

    This has been tried before and it doesn’t work.

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