This post is part of a series about the Common Core State Standards Initiative. Click here to view all of the posts about the Common Core.
The adoption of the Common Core standards in the coming years means change in how many instructors will approach teaching their students mathematics. David Coleman, a contributing author of the Common Core standards, describes these shifts in 6 terms: focus, coherence, fluency, deep understanding, application, and dual intensity.
The Common Core State Standards Initiative has taken an effort to reduce the number of topics covered in each grade, but to increase the time spent on each covered topic. This allows those topics to be explored at a much greater depth and it gives students a greater level of understanding. This focus is an attempt to combat the “mile long and an inch deep” approach to mathematics that has been active in the past.
This new level of focus creates priorities of what topics are necessary (such as the intensive focus in the image above) and which are optional. The required topics create a core of knowledge that is the basis of the more advanced mathematics. The Common Core authors believe that mastery in that core is the most essential part of math education, because spending more time ensuring an understanding of the basics will allow students to more easily and quickly understand the advanced topics in later grades.
The authors of the Common Core standards have made an effort to connect the topics from one grade to the next. For example: students learn to quickly add and subtract within 5 in Kindergarten. In first grade they expand this to 10 and then to 20 in 2nd grade. This means that they learn the basics in a young grade and then build on that foundation in later grades.
The students are expected to be able to do simple calculations quickly and accurately. By being able to do these simple calculations on their own it gives them the understanding of what is going on even when they move on to using calculators on more advanced calculations.
Rather than memorizing equations and formulas, students should learn the underlying math behind such concepts. Instead of simply plugging in variables into the formaula 1/2 × height × base to solve for the area of a triangle, students should understand why that is that formula for the area. This deeper understanding helps students apply math concepts to new situations that don’t fit problems that they’ve seen in the past.
A big part of learning mathematics is learning how to apply the mathematical concepts that you know. As David Coleman puts it “rarely in life is someone going to rip you off with, let’s say, a mortgage do they warn you to take out a calculator.” Not only is important to understand “how” to solve a problem, but also “when” and “where” that problem is relevant.
Dual intensity is really a combination of the previous shifts. It is important that students are able to fluently do the simple drills and calculations as well as being able to apply those concepts at a deeper level. While some teachers and learners favor one side or the other, technical or practical, the Common Core standards place weight in both fields.
What Does This All Mean?
For teachers this shift towards focus means the removal of some parts of their curriculum from previous years. In order to ensure mastery in the core knowledge time must be taken from other topics. However, the Common Core authors hope that by giving teachers some time outside of the intensive focus means that if a teacher thinks there is something that is important, but falls out of the scope of the common core then that teacher still has time to bring that something into the classroom.