I know that Standard for Math Practice #6 calls for students to “Attend to Precision,” but what if we got it wrong by making it a practice standard? I think we go too far with this statement. I worry that our over-emphasis on precision is detrimental to student learning. I’m concerned we are being too rigid and exclusionary with this focus on precision.
Before you rush to email me to tell me that part of math is getting the right answer, let me tell you about some recent experiences I’ve had as a learner. Those that know me know that I have been trying to learn French through classes and apps for the past few years. This past year, I decided to really dig in. I wanted to finally reach a level of conversational fluency with French. But I hit several roadblocks:
- Typos. I’m regularly marked wrong (losing points) for every typo in my written work. For instance, I might forget the s at the end of a verb (like parler) in the second person conjugation (Tu parles). Sometimes, this is just a careless mistake. I do understand the conjugations of regular verbs. However, careless or not, I JUST DON’T CARE when it comes to my learning. I want to be able to speak and understand conversations in French, and in that language, parle and parles sound exactly the same. So my goal of communication is met the minute I speak it, whether or not I remember the s. Constantly being corrected over minor mistakes (often just careless) frustrates me and makes me want to stop learning. It makes me feel excluded and not welcome to continue the learning.
- THE Way. Sometimes, depending on the teacher or the app that I’m using, I am reprimanded for not saying it the way they want me to. I may not remember or fully understand the most elegant way to say something. So I may take a circuitous route to communicate the idea. I may need some gestures to aid in my communication too. It’s not always the prettiest, but if I were hanging out at a cafe in Paris, I would be able to get my point across. However, in “learning” French, I’m constantly getting the message (however conscious or not the teacher is of this) that there is only one correct way to say something. I need to learn the way. It feels very restrictive and alienating. I feel like I’m memorizing full sentences in isolation just so I can repeat back what is expected, rather than learning the words and concepts more generally.
- Details. When I write French, I often write without adding in accent marks. My defense: I’ve lived for 40 plus years writing in English where there are almost no accent marks, and on top of that, my computer and certain programs can make it difficult to add in accents. So I just skip them. However, this means I’m “not good at French” to instructors. No matter how well I can pronounce the words, spell the words, or put a grammatically correct sentence together, the whole thing is marked wrong if I forget that little flair above some letters. I understand that precise French would include these details, but I have no desire to be a French scholar. Again, I want to chat up some friends at dinner in Quebec, not write the next great French novel. My lack of elegance and the constant reminders about them send me the message that French is only for some privileged elite group. It is not welcoming, and it indicates that French is only for those who want to dedicate themselves to perfection.
So here’s the dilemma, my goal is to be able to speak and listen to others in French. However, my language classes and apps require that I speak, write, hear, read, spell, conjugate, live and die with precision. I want to be a functioning adult in the French world mais quand suis-je assez bien? And the message I keep getting over and over is that “you are not good enough” or “you do not belong.”
So I wonder and worry: how many students have we alienated every time we correct an error (taking off a point for each tiny error)? Or when have we sent the message that math is only for those who are “perfect” at it? How do we engage students and work with them to establish goals that meet their plans?
I want to live in a mathematically literate world, one where no one would dare say “I’m not good at math.” But at the same time not everyone has to be an engineer or physicist. How do we balance improving numeracy and fluency with also helping students to feel included?