One of the biggest roadblocks to a better understanding of Common Core mathematics standards is the aversion so many people have to math. Ask around, and more adults recall their old math class with disdain or outright revulsion than those who have warm and fuzzy memories.
Those same people, when asked to help their son or daughter with homework, are looking at new Common Core-aligned math problems and feeling sweat break out on their brow and the room beginning to spin.
“This is crazy math! It doesn’t look at all like the math I learned in school!”
Math is a language, for most of us a foreign one. There are expressions and statements in math, just like in our written language. And there is a mind-boggling vocabulary of mathematical terms. Like any foreign language, if you don’t know it, you can hear it or look it and be totally lost.
For our children, they are in the classroom learning that specialized language, a little bit each year. Common Core was designed that way, so the math studied in first grade creates a foundation for the math to be taught in second grade, and so on throughout the school years. This kind of stair-step approach allows students to master and build on critical mathematical concepts.
And it’s true, the math models being taught to our children today are not the same as how we were taught to solve problems when we were in school. That’s because Common Core seeks to correct a problem with curriculum that’s been around for a long time.
Math done right is very, well, mathematical. By definition, math is very precise, meticulous even. The problem is that math education has become disconnected and imprecise. State and national math standards have come and gone over the past 30 years. Often changes have amounted to simply reshuffling statements. If some standards were moved up to an earlier grade, then the new standards were considered “better.” The assumption was that the math in school curriculums was fine if it was only put together “the right way.”
Common Core succeeds in restoring the continuity of math education grade to grade, creating a progression that makes sense to students at each grade level, and prepares them to build on their understanding at the next grade level.
Kindergarteners learn counting basics and how to add and subtract within five, which creates a framework for first grade, when students learn to add and subtract in the 10s. Success with basic math functions leads to fractions in grades 3-5, then ratios, proportional relationships and equations in grade 6; then algebra, then college-level mathematics.
Let’s take a look at one strand of math education as it expands from year to year:
- In kindergarten, students learn and understand addition as putting together and subtraction as taking away from.
- In grade 1, students learn and understand the rules of addition and subtraction (for example, 5+2=2+5).
- In grade 2, students learn to solve one- or two-step word problems by adding or subtracting numbers up through 100.
- Third graders will learn, understand and be able to explain what it means to multiply or divide numbers. They know their times tables and can multiply one-digit numbers by multiples of 10 (such as 20, 30, 40). They can solve two-step word problems using addition, subtraction, multiplication and division.
- In grade 4, students are now adding and subtracting whole numbers up to 1 million quickly and accurately. Fractions have been introduced, and students are solving multi-step word problems, including problems involving measurement and converting measurements from larger to smaller units. They can also multiply and divide multi-digit numbers.
Laid out step by step, this illustrates a logical progression of understanding from grade to grade. At each level, students are learning terms (the language of math) and tools (Rekenrek, number bonds, paths, towers, tape diagrams, etc.) to help them understand. Looking at your child’s homework may seem foreign, but that doesn’t mean it’s wrong, just different. But different for a reason.
Common Core was conceived starting with the desired end results, the skills and abilities students need to succeed in college and careers in today’s world. The way students were taught in the past simply does not prepare them for these higher demands. The new standards were designed stepping backwards through the years, setting expectations of what students should know and be able to do at each grade level.
In mathematics, this means three major changes.
- Concepts – Teachers will slow down and dig deeper, concentrating on teaching a more focused set of major math concepts and skills. Students are allowed time to master important math concepts and skills in a more organized way throughout the year and from one grade to the next.
- Fluency – Like our spoken language, fluency in math is important too. An emphasis in Common Core math is the memorization of basic math facts so students can bring them to mind quickly and use them correctly to solve more complex problems.
- Application – Finally, students are expected to understand why the math works and be able to use it in real-world applications.
While it may look like Greek to most of us, and it can frustrate us when we attempt to help our children with their homework, it’s important to remember that there is rhyme and reason behind this “new math.” Common Core standards provide a grade-to-grade progression of math knowledge that really does add up.