I really believe that a major obstacle in making much-needed changes to public education – making it more personal, relevant, flexible, enjoyable… making it less boring and more likely to build literate, happy, employable and productive members of society… a major obstacle lies in the Common Core Math Standards and everything that causes us to cling to them.
I can’t prove these standards are bad for kids’ education. I can’t prove it because we measure the quality of a child’s education by how well they take a test according to these standards, and whether they eventually learn these standards well enough to graduate high school. We don’t tend to measure the quality of a child’s education by metrics that actually matter, but when we do, the measurements aren’t good. The achievement gap persists. Students report increasing boredom and disengagement with school as they proceed through high school. Students that attend college increasingly need remediation. Employers report a dearth of applicants with needed skills for jobs. Surveys of adult science and math literacy are depressing.
A thought experiment. If there were no math standards and no curriculum and no textbooks. Nothing. All math books and online curricular resources and all math teachers suddenly went away, and we had to figure out a way to teach children what they needed to be successful, confident, productive, empathetic citizens. What would we do? We had a similar thought experiment in our Education Reimagined cohort, and interestingly, not one of us suggested anything looking like the current state of mathematics learning. We thought of many ways to make mathematics interesting, relevant, creative, personal, even joyful.
There are undoubtedly math and numeracy skills that are fundamental for our students to learn. Maybe it would be a good thought experiment to start with the end in mind. What do literate adults need to know about mathematics?
What would be on that list? Here is my list. I put stars next to “advanced”, possibly optional, topics. Just an off-the-cuff list of what I am glad to know and what I wish other people understood about math. What are yours?
- Basic principles of addition / subtraction, especially mental math and estimation
- Multiplying and dividing, again especially mental math and estimation
- Doubling and halving mentally
- Percents and proportions (mental math and back-of-napkin techniques)
- Ratios and fractions
- Using technology for all operations above and testing reasonableness of answers
- Statistics and presentation / organization of data. Estimation, identifying outliers, using technology
- Making sense of very large/very small numbers and the proportionality of them
- Scientific notation
- Formulas – substitution into a formula, and writing your own
- Spreadsheets, data collection, visualization tools, and spreadsheet formulas
- Computer programming
- Logic and puzzles (*?)
- Personal finance – taxes, loans, interest, saving for goals, budgeting, shopping.
- Entrepreneurship and running a business. Profit/income/expenses.
- Strategy, game-playing *
- Simulation, modeling, making predictions. Taking a real-life situation and modeling it with bare-bones variables, with or without technology. Evaluating a simulation to determine if it’s valid. (*?)
- Measurement, units and unit conversions. Length, weight, volume, mass, area, speed, time. Making your own units when needed. Using measurements in: Food prep, sewing, crafting/DIY, gardening, home improvement, public transportation and auto care.
- Coordinate graphing – plotting points in 1, 2, and 3 dimensional space and making meaning from the graphs – creating your own coordinate axes and using them – xy and xyz. Applied math in 3-D design and automation.
- Trigonometry – sin,cos,tan and using these in 2D and 3D space for design *
I believe most of these skills can be taught in an applied way, relevant for students at whatever age they learn them, in the context of a project or experience. Students that enjoy learning math for the joy of pattern-finding, logic and thinking just for the purpose of improving one’s thinking could certainly dive deeply into theoretical mathematics. But there’s no reason all students would need to learn most theoretical mathematics. I think they could learn to find beauty, joy AND relevance in math and learn numeracy in an applied context.
Did I come close to your list? What did yours have on it?
For kicks, now go to the Common Core Math Standards website and browse through. This is the essential set of math knowledge experts deem that kids need to master by the end of each grade band. By the end of high school, to be college-and-career-ready, you should have mastered the whole thing. This is the low bar. Is that where you would have put it? Why or why not?
I have to tell you I find the high school standards outright discouraging. They are difficult to understand, even for me, a former engineer with a major in Computer Engineering and an almost-minor in mathematics. As a teacher, you have to search the far corners of your brain and your resource library to TRY and find a way to make many of those standards relevant or interesting. Kids don’t retain them after a unit’s over, let alone after a summer or a year or two. They don’t retain the math knowledge because it doesn’t connect to anything in their lives. There’s no purpose for it. Nobody in the “real world” actually interacts with math in the same way we do in a math classroom. As teachers, we know this about brain-based learning and we teach these stupid standards anyway.
Colorado is beginning a review process for all of its content-area standards, including math. I applied to be on the standards review committee, but didn’t make the cut. I started the lengthy process of giving feedback via the online system, but I’m embarrassed to say that around the submission deadline, I ended up swamped with things to do at school and in life, and I never turned in my answers. I did get a chance to talk with a representative from the CDE about the first review meetings, to ask him what kind of changes they were thinking of. Would Colorado keep Common Core? He indicated that we probably would, but the new standards would be better organized, easier to search and more useful for teachers.
This is ridiculous. They need to be gutted. We need to start over.