1. Learning progressions
The CCSS do a great job of building learning progressions through all K-12 grade levels so that each year students build on what they learned the year before and deepen those skills. One example is equations. In kindergarten through second grade, students use equations to represent addition and subtraction problems. This includes the decomposition of numbers in multiple ways (8 = 4+4 and 8 = 3+5), finding the missing number in an addition equation (3 + __ = 8), and writing equations from visual representations and word problems. In grades 3-5, these same ideas are extended to multiplication and division.
As students move into middle school, variables (x, y, z) are added to equations, and students use opposite operations to find the variable’s value. For example, students are asked to solve 3x + 4 = 8 for x. Students also learn equations in two variables where the result is a straight line graph (y = 3x - 2).
As students move through high school, their understanding of the concept of functions grows to include exponential (think money growing in your bank account), quadratic (functions that model the motion of an object being thrown in the air), and other types. This comprehension of math as it relates to real-world phenomena wouldn’t be possible without the basic understanding that the two sides of an equation are equal, which was established in elementary school.
2. Focusing not only on the how… but the why
I created this Wordle using the top 100 words in the CCSS math standards. The bigger the word, the more frequently it appears in the standards.
When this picture popped up, I was surprised at the sentence that emerged: “Understand problems using numbers and equations.” This is the foundation of the Common Core math standards. We want students to truly understand mathematics, not just be able to “do” it.
I also couldn’t help but notice the words that are not visible in this picture, such as do and compute. While there is a place in the standards for algorithms, such as putting numbers on top of one another and adding down, it’s not the focus. Other visible words that support the idea of understanding in this picture are explain, recognize, apply and represent. When students complete the progression of the standards, they will not just be able to do math but really understand it.
3. Developing 21st century skills
“Why can’t it just be done the way I learned?” is a question I hear often from parents regarding the CCSS. The fact is, our students aren’t growing up in the same world we did, and we owe it to them to prepare them for today’s society. Our students will likely be doing jobs that haven’t even been created yet!
So how do we prepare students for those jobs of the future? We teach them 21st-century skills such as problem solving, communication, and digital fluency. A colleague of mine, Rob Kriete, created an awesome visual representation of these skills for parents and teachers. The CCSS for math also include eight math practice standards (link is external) which are habits of mind embedded within the instruction of the content standards. These are not standards that can be checked off a list--like being able to solve an equation--but are skills to be developed across all grade levels. In these practice standards, students are asked to persevere in solving problems, construct arguments, critique others’ arguments, and use appropriate tools in problem-solving. Being able to do these things will prepare our students for success in college and careers--even the jobs that don’t exist yet.
Like I said before, no set of standards will ever be perfect. But I truly believe the CCSS for math are putting our students on the track for success in the world in which they live. That’s what we all want for our kids, right?
Lindsey Walborn is a high school math teacher in China Grove, NC, who has nine years of classroom experience and is working towards a M.Ed. in Curriculum and Instruction. She has been a math department chair and currently leads a learning community for teachers of Math 3. Lindsey is also a member of Center for Teaching Quality Collaboratory and works closely with Student Achievement Partners
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