In our series on the Common Core State Standards for Mathematical Practice (CCSSMP), we’ve reached number six: Attend to precision. For students who communicate instantaneously by thumb-typing emojis, doing a task slowly and attending to detail can be maddening; as educators, we need to gently insist on the kind of sustained precision necessary to do a task well. Students complain when I mark them down for missing a negative sign, but “small errors” simply don’t fly in many professions. We’re hoping for pretty much zero errors from the people building our bridges, doing our taxes, and writing our laws. Math class is a great place to teach the attention to detail and scrupulous checking of work that make these endeavors successful.
This standard requires students to use accurate vocabulary. For example, kids often use the word “solve” when they mean “simplify,” which can imply conceptual misunderstanding. Math symbology is part of “vocabulary” as well—symbols like +, –, °, ≈, and ≥ are part of the language of math, and each has its own perils and pitfalls. CCSSMP6 asks students to “make explicit use of definitions.” What does that mean? Consider the definition of a parallelogram: a quadrilateral with two sets of parallel sides. This says nothing about opposite angles being congruent or diagonals bisecting each other; these are properties that can be derived once we’ve set the definition. Being clear about what’s part of a definition, as opposed to properties that follow from it, is a powerful understanding, creating a foundation that does not permit circular logic.
Another aspect of attending to precision is deciding just how “precise” is precise enough. When talking about the GDP of the United States, would you give an answer rounded to the nearest penny? Of course not; you’d say $17 trillion and be done with it. (You could even go with $16.77 trillion. This still allows for billion-dollar errors!) When measuring the distance between here and the nearest star, what unit makes most sense? Miles? Kilometers? Light years? When do we need to pull out the calculator and get an answer with six decimal places of accuracy, and when can we just wing it and get a rough estimate? These are life skills that apply to more than just math.
Here are some ways to address this standard with students:
- Be nitpicky about vocabulary. I used to be fairly lax on this, believing that as long as I could understand what a student meant, that was good enough. I didn’t want to intimidate kids with fearsome math vocab. I’ve since changed my tune. Math is about a universal, precise vocabulary, and the definitions and concepts build on each other. If we are informal and use shortcuts, the whole point of math—that it’s a logical structure built on a few foundational postulates—can be obscured.
- Require 100% perfection on selected problems, including rounding, units, and display of work. In this situation, let students recheck their answers as many times and with as many tools as they need; but to get credit, no errors can exist. This is certainly not necessary for all, or even most, homework and test problems, but the exercise of working through problems in exacting detail is rewarding and educational, and students can feel proud when they see what they’ve achieved.
- Have students make up their own units of measure to get an understanding of why units matter. Perhaps they can measure the length of the classroom in “Lydia’s arm lengths” or “Tyren’s shoulder widths.” They can discuss which units work best and debate the value of standardized units.
- Discuss very large and very small numbers with students. An infamous meme with a glaring math error went around the Internet recently; it described how much money each person would get if the Powerball lottery jackpot were evenly distributed across the US population. I saw lots of comments along the lines of “exponents are hard” and “big numbers scare me.” Big numbers scare me too, but we need to be able to differentiate between a billion and a trillion if we’re going to be informed citizens
Attending to precision is a skill that kids love to hate. Building facility with concentration and detail orientation can be a long process, but it ultimately pays lifelong dividends.