1.3: How Did We Get Here?

A Brief History of the Creation and Need for Common Core Mathematics

Somewhere around 2007 to 2008, a few mathematicians got together and decided that students are not prepared for the 21st century. They spoke with physicists, engineers, business people and the like to figure out what the current student needs in this world of having all the information of the entire world in their pocket. Remember when people used to say “You need to learn this because you won’t be walking around with a calculator in your pocket”? Those days are gone forever. Today, with the right technology, anyone can solve complex equations (i.e. photo math) graph anything (see graphing apps, as there are many) or even ask google to do it for him or her.

However, what about analytical thinking and problem solving? The original reason why mathematics became a school requirement was to teach students how to think. Technology has not figured out a way to problem solve. That is where Common Core steps in. Yes, we are still teaching the basics. Fractions are not going anywhere, sorry. Nevertheless, we cannot use technology to solve problems. A computer still is stupid. Seriously. It follows the instructions, which comes from a human being. A human being needs to correctly give the instructions to the computer. Common Core challenges students to solve problems conceptually and discover the meaning behind the calculator. For example, think about dividing fractions. A trick that many people have learned is to change the division to multiplication and flip the second term. Then multiply. But why does that work? (We will explore this in Chapter 3.) Another example which Common Core wanted to stress is Mental Math. Make people smarter by forcing them to learn mental math tricks. Think about it, how do you train your body to run a marathon? You run a little bit each day and gradually improve your mileage and then gradually improve your speed. Your body is improving each day that you practice. The brain is the same. Work on mental math activities a little bit each day, and you are training your brain to be stronger and a better thinking. Math trains you to be smarter in general, which can help you master all other subjects.

The Impact of Common Core in Elementary School Mathematics

When Common Core first arrived it was daunting, from a teacher’s and parent’s perspective. Photos were floating around social media about bad math techniques. Parents and students disagreed on how to solve a problem. It was joked about in Disney’s Incredibles 3, where the Dad is trying to help his son do his homework and he becomes very frustrated that “they” changed math. The way subtraction is taught has changed. The way multiplication is taught has changed. The authors wanted students to understand the meaning behind subtraction and multiplication instead of just rote memorization. The biggest change was pushing down the curriculum. What students are learning now in elementary is around two years earlier than students before Common Core. Kindergarten is fully academic, no longer just learning to be social and learning how to play nice.

How has Common Core changed assessments?

The biggest change is having students complete Performance Tasks during their exam. The first part of an exam can be basic questions. The next part could have error analysis (find the mistake). There could be a matching portion as well. There are many methods to access students without having multiple-choice answers or simply asking to solve a math problem without any context to why. Then there are the Performance Tasks, which always show up on State Standardized Testing. A typical Performance Task starts with a situation, a more involved word problem. Students then have to go through a process of steps, answering questions along the way to eventually reach the overall question. There could be solving and graphing involved in the same Performance Task.

How has Common Core changed grading?

Another large change brought by Common Core is how teachers grade assessments. Before, we cared about the final answer. Right or wrong? If wrong, a teacher would look for ways to give partial credit. Now, we look at everything and assign points accordingly. For example, say a student is asked to perform a long division problem worth five points. Getting the right answer is one point out of five. HOW they got to the answer is worth four points. Did they move the decimal correctly? Did they subtract correctly? Did they make a mistake twice and ended up being lucky and getting to the right answer? Did they check their work by multiplying back?

Comparing the Old Traditional Standards to the New Common Core Standards: Kindergarten through 3rd Grade

The major change to 4th through 6th grade are more pre-algebra standards.

Information in the table is pulled from corestandards.org.

Table 1.3.1: Kindergarten

New: Common Core Standards	Old: California State Standards
Count to 100 by ones and 10s.	Count to 30 by ones.
Identify whether the number of objects in one group is greater than, less than or equal to the number of objects in another group.	Compare two or more sets of objects and identify which set is equal to, more than or less than the other.
Solve word problems that require addition and subtraction for problems with sums up to and including 10. Use objects or drawings to represent the problem.	Use objects to determine the answers to addition and subtraction problems.
Break numbers between 11 and 19 into two parts: 10 ones and some further ones. For example, 17 contains 10 ones and seven additional ones.	Not taught until 1st grade.
Put two shapes together to form a different shape. For example, place two triangles together to make a rectangle.	Not taught. New standard.
Moved to first grade.	Tell time and recite the days of the week.

 

Table 1.3.2: Grade 1

New: Common Core Standards	Old: California State Standards
Solve word problems that call for addition of three numbers whose sum is less than or equal to 20 by using objects, drawings or equations.	Replaces the old standard that required students to "commit to memory" addition equations with a sum of 20 or less and subtraction equations with a difference of 20 or less. Notably, the new standard does not require memorization.
Apply properties of operations (commutative and associative) as strategies to add and subtract.	New to 1st grade. The associative property (a + (b + c) = (a +b) + c) was previously introduced in 2nd grade. The commutative property (a + b = b + a) was not mentioned in the state standards for kindergarten through 3rd grade.
Determine the unknown number in an addition or subtraction equation. For example, 8 + x = 11.	New standard. Previously, students were not expected to find for "x" until after 3rd grade.
Given a two-digit number, mentally find 10 more or 10 less than that number, without having to count. Explain your reasoning.	Similar to the old standard that asked students to identify one more than, one less than, 10 more than and 10 less than a given number.
Tell and write time in hours and half hours using analog and digital clocks.	Previously introduced in kindergarten, although 1st grade students were also required to tell time to the nearest half hour under the old standards.
Eliminates previous 1st grade standards requiring students to understand weight, volume and the monetary value of coins, among other specific skills found in the old 1st grade standards. Also eliminates requirement that students memorize sets of numbers.	The old standards called for 1st grade students to work with weight, volume, classifying objects by color and size, estimating sums, committing math facts to memory, writing number sentences and understanding the value of coins.

 

Table 1.3.3: Grade 2

New: Common Core Standards	Old: California State Standards
Use addition and subtraction to solve one- and two-step word problems where the sum or difference is less than 100.	New standard. Multi-step word problems were not mentioned in the old standards for kindergarten through 3rd grade.
Easily solve addition and subtraction problems with a sum or difference of less than 20 in your head (7 - 4 = 3; 2 + 9 = 11; 14 + 3 = 17; etc.). By end of grade 2, memorize all the ways to add two one-digit numbers.	Similar to the old standard that required students to find the sum or difference of two, two-digit numbers in their heads (14 + 16 = 30; 12 + 5 = 17; 32 - 7 = 25). However, the old standard required students to add and subtract larger numbers.
Use addition to find the total number of objects arranged in equal rows. For example, if there are three rows of four, students should be able to add 4+4+4 to find the total, rather than counting each object. Students must also write an equation to represent how they found the total number of objects.	Replaces the old standards that focused on multiplication and division, which required students to do "repeated" addition and subtraction (2 + 2 + 2 + 2 = 8), form equal groups from a set of objects (sort eight blocks into four groups of two) and know the multiplication tables for twos, fives and 10s.
Explain strategies that can be used to make addition and subtraction easier. For example, for the problem 14 - 5 = x, a student might know that 15 - 5 = 10. Because 14 is one less than 15, the student could figure out that answer to the problem presented would also therefore be one less, or 14 - 5 = 9. Students should be able to use these strategies and explain why they work.	New standard. The old standards did not call for student explanations of specific math processes, nor did they call for specific instruction in developing strategies to add and subtract faster. Instead, a standard at the end of each grade level called for students to be able to "justify their reasoning" in general.
Understand that each number falls a set distance from zero on a number line. Use a diagram of a number line to find sums and differences of less than 100. For example, for the problem 82 - 17 = x, start at 82 on the number line and count down 17 spaces to determine that 82 - 17 = 65.	New standard. Common Core's focus on teaching children about the number line comes from research showing that familiarity with number lines improves mathematical performance in young children.
In a first introduction to the concept of area, students should understand that a rectangle can be made up of a grid of smaller squares. Count the squares that fit within a rectangle to find the total number of squares.	New standard. Fractions were introduced in 2nd grade under the old standards, but not in this format. Area was not introduced.

 

Table 1.3.4: Grade 3

New: Common Core Standards	Old: California State Standards
Students are required to solve two-step word problems using addition, subtraction, multiplication or division as needed.	Solve problems using two or more operations (addition, subtraction, multiplication or division), but does not specify solving word problems.
Understand that a fraction can be represented on a number line between zero and 1.	New standard. Previously, students were required to add and subtract fractions, but no mention is made of understanding that a fraction is less than 1.
Tell and write time to the nearest minute.	New to 3rd grade. Previously, this was a 2nd grade standard.
Measure and estimate liquid volumes and masses of objects.	Similar to old standard calling for students to estimate and measure the length, liquid volume and mass of an object.
Recognize that shapes in different categories (i.e. squares and rectangles) can share attributes (i.e. both have four sides) and that those shared attributes can define a larger category (i.e. quadrilaterals).	Similar to old standard calling for students to identify the attributes of quadrilaterals (i.e. parallel sides for a parallelogram, equal side lengths for a square), but with emphasis on how to sort shapes instead of on specific rules about shapes.
Multiplication tables are not mentioned in the new standards.	Previously, students were required to memorize the multiplication tables for number 1-10.