After reading the interview of Mitch Daniels in the New York Times, I was surprised that he claims the standards are only set goals for the kids to master and that it doesn’t prescribe the methods or curriculum, that is up to the local schools and teachers. He gave an analogy using the high jump:
“I always tell people if you go to a track meet and the high jump pit, one coach can teach the flop, and one can teach the barrel roll. And if somebody wants to do the old-fashioned scissors, that’s fine too. But we’re going to have one bar. You don’t let everybody set the bar where they want.”
I like this analogy, but it doesn’t describe what the Common Core accomplishes. Here’s how his analogy really looks under Common Core; Yes, there is only one bar set, but it’s lower than what many states had and way lower than our international competition. A coach could teach the flop, or barrel roll or scissor approach if they like. However, the jumper would be disqualified in competition if he used the scissor approach because it isn’t aligned with the new standards. The Common Core sets a uniform low bar while putting new technical requirements on the approach. The highest jumper might not win, because he used a traditional approach that is no longer allowed.
Within the standards there are several pedagogical approaches that are dictating how students are to learn mathematics. In fact, the writers of the CC math standards wrote documents for teachers, publishers and curriculum developers to use to implement the standards with the “letter and spirit” intended. This is why every Common Core aligned textbook is using the same strategies and curriculum to teach the standards and it absolutely tells teachers HOW to teach.
In the Progressions for the Common Core in Mathematics, the writers of the standards tell teachers EXACTLY how to teach math operations like addition, subtraction, multiplication and division. They give explicit directions how to teach it and be aligned with the spirit of the Common Core. Keep in mind that these same directions were given to the testing consortium that are formulating the items by which all teachers and students will be measured.
Here is an example of a standard for addition:
CCSS.Math.Content.1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Just by reading the standard it seems obvious certain methods are being required. Teachers do not have the freedom to use other methods and getting the correct answer will not be enough. Students must be able to use these methods in order to fulfill the standard. Taking a quick look at reform math textbooks like Everyday Math one can see these are strategies they use. Note that the traditional method of the standard algorithm is not mentioned here and is not an acceptable approach to meet the standard.
Not only is the standard itself a clear indicator of how to teach addition and subtraction, but writers of the math standards elaborate on the specifics in the Progressions of the Common Core Math Standards with pictures and details:
The standards and implementation documents continue to dictate methods through out the grade levels. Here are the some of the standards for performing operations in second, third and fourth grade:
CCSS.Math.Content.2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
CCSS.Math.Content.3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
CCSS.Math.Content.3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
CCSS.Math.Content.4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
CCSS.Math.Content.4.NBT.B.6 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.
I have put in bold the methods they are emphasizing. These strategies are the center point of the standards. In the Publishers’ Criteria, written by the authors of the Common Core, they write that these are the focus standards and should comprise 75% of class instruction time. They do not require a traditional algorithm to be used until later grades. Answering with the traditional algorithm will not be allowed as meeting these standards.
Here is an example of how teachers are suppose to teach 6X4 using these strategies and be in alignment with Common Core. This is also how they will be assessed.
Level 1: draw six sets of four objects and count them out.
Level 2: Skip count by six four times. Student will say the multiples of six while nodding head four times or using fingers to keep track of how many multiples.
- They recompose the factors to be easier to use. 4×6=4x(2×3)=(4×2)3=8X3. That’s three eight times, count by threes with the head nods. This is an example of using properties of operations to solve and the count by method.
- If the problem was 132+232. They would recompose the number to make 100+30+2 and 200+30+2. Add the hundreds 300, add the tens 60, add the ones 4, then add together. This is an example of using place value to solve.
I’m sorry, but that is looking pretty FUZZY. The child doesn’t know 6X4=24, but they require him to use the abstract properties of algebra like the Distributive Property, Associative Property and Substitution Property to solve the problem? This is for third grade. They are 8 or 9 years old. This abstract processing is unnecessary for kids this age.
Most people would say teach them the fundamentals and stop the romantic notions of eight year olds thinking like mathematicians. It just isn’t appropriate and it prevents them from gaining the early knowledge and practice they need with math facts.