On the culture of accuracy
At first glance, it seems unnecessary to explicitly state that we should all strive for accuracy. The word "duh" comes to mind. As in, "Of course accuracy is important, Robert." But it's not "of course" all the time, because our schools run the risk of indirectly condoning inaccuracy unless we directly discuss it.
One way to appreciate accuracy is to think of when the lack of accuracy occurs in our lives. How about within customer service, when one representative contradicts another, either in person or on the phone? Or when a product we specifically request to be a certain way turns out to be another? Let's rattle off a quick list where accuracy deeply matters within society: the food industry, car repairs, lifeguarding, personal finance, the legal system, medical issues, the military, construction, and caring for people with needs, such as children or the disabled. In the backdrop, we live in a political landscape that is rife with inaccuracies, as semi-true claims are made regularly and without flinching.
So what does a teacher do when a student hands in assignments with errors on it? In the spirit of imparting lessons that apply in life, I believe that the main priority centers on developing a shared culture of accuracy. This culture applies to both teachers and students (and parents.) From that point of cultural synchronization, we can formulate classroom models that transmit that culture.
We must create systems that nurture the human pursuit of accuracy. I say "human pursuit" because working towards accuracy is a challenging process. Humans undertake that process - and humans inevitably make errors. However if our processes are fluid enough, such that we can correct and learn from those errors, then our actions demonstrate the priority of striving for accuracy. It is within those corrective actions where we nurture this culture.
Striving for accuracy thus is embedded within my homework system. Students arrive to class and we go over questions they have on the assignment due that day. Other students or I complete those problems on the board, with accompanying explanations. The students who had questions are free to correct their work right on their papers before turning them in. In addition, the answers to all the odd-numbered problems are at the back of the textbook, for students to directly verify that they are doing their work correctly. Moreover, I am available during office hours for students to drop by and ask any questions they have.
Fascinatingly, many assignments still come in with mistakes. Even though the answers are in the book. Even though we went over them in class. And even though we have open office hours that go mostly unattended. Per assignment, I check three problems at random for correctness, as a way to streamline the process and not be personally overwhelmed by homework grading.
At first, some students are bewildered that I mark the grade lower on their assignment. Many students have been conditioned to "do their best" and believe they'll get full credit if they "just finished the assignment, even though they didn't completely understand everything." This is the culture we must change. What is their best, anyway? To me, someone's 'best' is doing everything possible to meet with me, on multiple occasions, to figure out what gives him or her difficulty. As educators, we send the wrong message when we blindly accept work that silently screams of the students' lack of understanding, without offering feedback on that work in return. Isn't the fundamental purpose of homework to learn more and achieve proficiency?
In fairness, teachers must commit to giving assignments that are reasonable in length, perhaps 12-18 problems for math, depending on the concept. And students must commit to learning the concepts within each of those problems. That is the intention of the assignment at its core. The undercurrent of this discussion is imparting a core value to them, that accuracy matters. I write that so many times, on so many assignments I grade, which I will continue to do as long as necessary. Accuracy matters; deep down they know this. Probably not even deep down.
Some of the most fulfilling feedback I ever received in my career has come recently, from the Algebra 2 students I had last year. Several of them have said that our Algebra 2 group from last year feels well prepared for their current math class. For me, as the person they directed their moans and groans to last year about my homework system (which I took in stride and with love), I glow at the knowledge that they are well prepared for this next level. I give credit to the notion of raising the bar of accuracy. They have learned to be unsatisfied with not knowing, compelling them to work towards filling in those gaps. Maintaining a high standard of accuracy is a culture that I passionately believe will serve them throughout their lives.