There was no shortage of controversy about the Common Core State Standards for Mathematics (CCSSM) when they were introduced a decade ago, in June 2010. In actuality, most of the complaints were a reaction to some of the early classroom implementations of the Standards, and many of us involved with mathematics education research agreed with some of the objections.
The Standards themselves—there are exactly eight of them (listed below)— are precisely what the name suggests: standards, that set a bar as to what should be mastered in a mathematics education designed to prepare students for life in today’s world.
They are not a curriculum. Nor do they say how math should be taught. Yet, for the most part, it was those two implementation manifestations of the Common Core that raised hackles among critics. With hindsight, maybe the possibility that the initial implementation of the Standards could cause problems should have been considered in more detail and steps taken to alleviate the roll-out issues. But they weren’t, and we had to live through a rocky period of adjustment. But with the launch now well behind us, we can at least see clearly how the furor arose.
To implement the Standards in the nation’s schools, the schools and education authorities needed a detailed curriculum, backed up by teaching materials and a list of recommended classroom practices. And that was where many problems arose.
Before the Common Core, mathematics education was delivered by a system designed to prepare citizens for the pre-computer era, which meant fluent mastery at a range of basic computational skills was an essential prerequisite. All pre-CCSS math teaching was developed with that as a major goal. But today, every one of us carries around a mathematical power-tool in our pocket; the typical mobile phone has way more computer power than any room-filling computer in the 1960s and 70s, when the digital revolution started to take off. That changes everything.
By way of an analogy, in the early Twentieth Century, a revolution in transportation began, whereby people in the more industrialized parts of the world had to acquire an important new life skill: driving a car or truck. Today, if we want to go somewhere outside our neighborhood, we use some form of motorized wheeled transportation.
In the 1980s, an analogous revolution occurred in mathematics. Since the end of that decade, no math professional spends much, if any, time doing mental or hand computation any more, be it arithmetic, algebra, trigonometry, calculus, or whatever. Of course, the devices we have to hand do not, in general, operate on their own. Their safe and effective use requires a whole skillset. Just as is the case when it comes to driving.
The need to become proficient in being able to use mathematics to describe things accurately, to build things, and to solve problems is still as crucial as ever. What has changed, however, is the specific skillset required. Just as the introduction of the automobile meant the need for transportation changed from being physically able to walk (or bike) long distances or ride a horse or a horse-drawn carriage, to being able to control machines that carried us, so too the arrival of ever-more versatile and powerful digital math tools over the period 1965 to 1990 meant replacing the skill of mental- or hand-computation with the ability to control machines that do those computations for us.
That was the changed situation that led to the CCSSM. Here they are:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
More precisely, those are the Common Core State Standards for Mathematical Practice (CCSS.MP). The CCSSM website itself is a substantial document, that breaks down those eight MP principals into specific curriculum goals for classroom instruction, grade-level by grade-level. Teachers, education authorities, publishers, and other providers of educational resources can use them as a basis to design curricula and other products.
At first, the materials that were produced were very much a mixed bag in terms of quality. That’s hardly surprising, given the magnitude of the changes required to catch up with the revolution in mathematical praxis brought about by the digital revolution. But since those early days, now a decade ago, things have been improving, faster and better in some places than in others, and in due course the entire system should adapt.
In parallel with the development and rollout of the Standards, the nation had to develop assessments that can effectively measure the degree to which students, teachers, and local and state education systems meet the Standards. That is in some ways a much harder issue to tackle, and work is ongoing, but again, progress has been, and continues to be, made.
A major part of the problem is how we can assess understanding. For, what is many ways is the most significant aspect of adapting mathematics education for life in the digital era, is the change in primary focus from developing computational skills to one of understanding mathematics. The CCSSM acknowledges this major shift on the very first page, saying:
“These standards define what students should understand and be able to do in their study of mathematics. But asking a student to understand something also means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One way for teachers to do that is to ask the student to justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”
At BrainQuake, we had the CCSSM firmly in our sights through the entire design and development of our product.
Not the large matrix of specific classroom goals that fill the pages of the CC website; they were developed for classroom teachers using textbooks and other traditional educational materials. Though a number of educational game developers did create games that address specific classroom topics, we were aiming at more wide-ranging general problem solving and mathematical understanding issues, so our blueprint was the list of the eight CCSS.MP I presented above.
Since our products carve up mathematics education not in terms of specific basic skills but more general thinking and problem solving capacities, our goal was not “total coverage of the CCSS” in an item-by-item sense, but the development of valuable thinking and problem-solving abilities that apply across the board to all of CCSS mathematics.
In pursuing that goal, we automatically hit five of the eight MP principles full on:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
For the remaining three, it is up to the student, teacher, or parent as to whether to use our product in ways the impact those principles:
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
They certainly can be used to that end.
We also went through the exercise of producing a detailed mapping from each of our three puzzles (and other, related learning products we will release in due course) onto the entire CCSS grade-level standards. It cuts across those more detailed standards in terms both of content and grade level. For instance, each of the three main puzzles connects to standards at all grade levels. I’ll go into more detail about the connection between the BrainQuake app and the CCSSM in future posts.
Meanwhile, the Common Core just turned 10 years of age. As someone who has spent my entire professional career as a mathematician and math educator, both in universities and working for industry and various branches of the US government, an experience that makes me acutely aware how critical are the CCSS.MP to our nation’s future, let me wish the Standards a Happy Birthday! We need you!