I have often wondered if teachers should have some form of a Hippocratic Oath, reminding themselves each day to *first, do no harm*.

Since the network of relationships in classrooms is so complex, it is often difficult to discern what we may do that causes children harm. Most of us have experienced the uncertainty of teaching, those dilemmas endemic to the classroom. Was it the right decision to stay firm on an assignment deadline for the child who always seems to misplace things, after giving several extensions? Or was there something more going on outside of the classroom that would alter that decision? Why did a student, who is usually amendable to playful teasing, suddenly storm out of the room today in the wake of such an interaction?

What I have arrived at is that there are levels of harm. The harm I describe in the previous examples can be recovered if teachers have *relational competence* — that is, the lines of communication are open with their students so that children can share and speak up if a teacher missteps.

What I am coming to realize is that mathematics teachers have a particular responsibility when it comes to doing no harm. Mathematics, for better or worse, is our culture’s stand-in subject for being smart. That is, if you are good at math, you must be smart. If you are not good at math, you are not truly smart.

I am not saying *I *believe that, but it is a popular message. I meet accomplished adults all the time who confess their insecurities stemming from their poor performance in mathematics classes.

Here is an incomplete list of common instructional practices that, in my view, do harm to students’ sense of competence:

**1. Timed math tests**

Our assessments communicate to students what we value. Jo Boaler recently wrote about the problems with these in terms of mathematical learning. Students who do well on these tend to see connections across the facts, while students who struggle tend not to. But if timed tests are the primary mode of assessment, then the students who struggle do not get many opportunities to develop those connections.

**2. Not giving partial credit**

Silly mistakes are par for the course in the course of demanding problem solving. Teachers who only use multiple choice tests or auto-grading do not get an opportunity to see students’ thinking. A wrong answer does not always indicate entirely wrong thinking. Students who are prone to getting the big idea and missing the details are regularly demoralized in mathematics classes.

Even worse, however, is …

**3. Arbitrary grading that discounts sensemaking**

Recently, a student I know had a construction quiz in a geometry class. The teacher marked her construction as “wrong” because she made her arcs below the line instead of above it, as the teacher had demonstrated. This teacher also counts answers as incorrect if the *SAS Theorem* is written as the *SAS Postulate* in proofs. Since different textbooks often name triangle congruence properties differently, this is an arbitrary distinction. This practice harms students by valuing imitation over sensemaking.

**4. Moving the lesson along the path of “right answers”**

Picture the following interaction:

Teacher: ** “**Can anyone tell me which is the vertical angle here?”

Layla: “Angle C?”

Teacher: “No. Robbie?”

Robbie: “Angle D?”

Teacher: Yes. So now we know that Angle D also equals 38˚…

That type of interaction, called *initiation-response-evaluation*, is the most common format of mathematical talk in classrooms. Why is it potentially harmful? Let’s think about what Layla learned. She learned that she was wrong and, if she was listening, she learned that Angle D was the correct answer. However, she never got explicit instruction on why Angle C was incorrect. Over time, students like Layla often withdraw their participation from classroom discussions.

On the other hand, teachers who work with Layla’s incorrect answer –– or even better yet, value it as a good “non-example” to develop the class’s understanding of *vertical angles* –– increase student participation and mathematical confidence. And, they are doing more to grow everybody’s understanding.

*What are other kinds of teaching practices that stand to “harm” students?*

I am sad to say that I know that all of these things, but especially #1 & #4, are happening right now in mathematics classes around my district, including those of my own children. Here are a couple of other’s that I would add:

#5: Teaching of answer-getting techniques and “rules that expire” which focus on the path to the correct answer at the expense of mathematical understanding.

#6: Adopting the latest educational trend for the wrong reasons or without adequate understanding, planning, and support. I know too many teachers who have adopted the flipped classroom model because they are frustrated that students are not completing homework assignments. Now, students watch (or don’t watch) videos at home, and complete the same “drill & kill” practice during class time.

#7: Grading practices that do not allow redo’s or retakes and emphasize compliance (i.e. homework completion, neat notebooks) over mastery of standards. Grades should reflect how much math students know – not how well they play the game of school.

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Thanks for putting these together. I am a Jo Boaler fan and you’ve already covered the main “reform” ideas that I strongly agree with, especially timed “math facts” tests, so I’m going to add a few more curmudgeonly ones.

#8: Having grades or a grading system depend heavily on factors outside a student’s control. Examples: tech-based learning without adequate or equal access to technology; a redo/retake system that depends on an adult providing non-routine transportation before or after school; heavy dependence on homework in a way that only students with lots of parent or tutor support will succeed at the highest levels. These send a damaging “you can’t succeed” message to some students.

#9: Lack of coverage of math standards for the grade or level being taught. I’ve seen teachers scrap 1/4 or more of the year’s material with the best intentions in the world, as they focus on getting kids “caught up” with some topics at the expense of others. Then the students hit the next grade missing crucial knowledge and they feel incredibly stupid and confused, especially if other students were taught the material that they never saw. This can especially be an issue in a child’s first year at a school (6th and 9th grades in my district for most students, for example, or any time for children who move). This problem is one of the main reasons I support Common Core.

#10: Letting students stay so much in their comfort zone that they don’t go through the struggle of learning new problem-solving methods, models, or techniques. For instance, I’m fresh out of a fraction unit with my sixth graders and had to watch myself for the tendency to let them use visual models for everything without nudging them toward more numerical techniques also. It is so fantastic that they understand and use visual models, and I promote them too, but I draw the line when they insist on trying to solve 18/35 x 7/27 with a picture. Similarly, I’ve had algebra students who got so comfortable with using Guess & Check with great facility that they really didn’t want to learn how to set up and solve equations, which are (after you learn them) a lot easier to use and more powerful.

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These are all really great points. Our surveys say that math is typically the least favorite subject – and, unlike all other least favorites, because “it makes me feel dumb” (instead of “uninteresting work” or “don’t like my teacher”). I think most of these harms relate to that issue but i think #4 is arguably the worst because day after day the ability to quickly see the right answer is what’s prized.

In genuine problem-based learning math and science classes (as well as in English discussions) the questions are of course typically designed to generate varied answers and the need to explore each answer with some arguing. So, i would add “Endless quick factual questions” to the description.

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I was lucky, I had great teachers growing up. But I was one of those students sitting in math class who frequently ‘checked out’ of a lesson because other students were able to shout out the answer before me. I wasn’t allowed the opportunity to feel satisfied by solving the puzzle or answering the question myself in my head first. Because I wasn’t as quick, I felt that I wasn’t as smart as the other students, so I lost interest. I think as teachers, we do a disservice to some of our students who need more time to process if we take away those opportunitites to think the question through.

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I like your term “relational competence”! My research (and yours) demonstrates that relational competence and content learning are mutually constitutive. In other words, relational competence is not an add-on that is separate from PCK (or MKT). We may act as if the way we teach math content is neutral, but it is always coming from a cultural standpoint and positions us and our students in particular ways with respect to issues of power, intelligence and overall competence.

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I think it’s going to be my next study — all of this is thinking aloud as I develop my frameworks. Thanks Vicki. Nice to “see” you here.

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I would add “not penalizing for practicing” when it comes to quizzes. For many years now, I give quizzes, have the student mark their own, but don’t count them for marks. Allow kids to make mistakes without them counting them against them. Quizzes are mere snapshots of one’s learning. I did go farther with this and not count HW, either. I abandoned this after 2 semesters, though. My weak grade 10-12s were not mature enough to just do the HW anyway. Overall, test results dropped when HW was optional.

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I’ve been pretty horrified over the last year by what experts who should know better do in the name of developing a growth mindset. Lecturing teachers and students about a growth mindset is no more effective than lecturing students about mathematics! Emotional intelligence and experiential modalities are required. I’m so glad you are considering studying this. Great post.

– Elizabeth (@cheesemonkeysf)

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Wonderful post! In my opinion we inflict some the greatest emotional and psychological damage on our students through our complicity in the administration of high stakes standardized tests. The genius of the corporate reform movement, and the testing-industrial complex it represents, is that it can only function with our complicity. Thus we become morally compromised by our behavior, and agents participating in our own destruction. Chris Hedges has written forcefully about this, for example here:

http://www.truthdig.com/report/page2/why_the_united_states_is_destroying_her_education_system_20110410

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How many teachers do you think would go out of their way to deliberately harm a student though? I’m not against an oath as you are suggesting, but I think that often we are not aware of the harm we are doing because we don’t know all the circumstances involved (and we never can).

Also, you give the example of a question being marked wrong for using the word ‘postulate’ as opposed to ‘theorem’. How many maths teachers actually know what the difference is between the two? If you are following a markscheme, without knowing what the difference is, it might as well be the difference between 4.5 and 6.5

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I think you are right. But I see students decide school is dumb or meaningless over these trifles. My point is not to vilify teachers: I agree people do not become teachers to hurt children. My point is that sometimes things that are just par for the schooling course can inadvertently push students away.

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I really enjoy this article but I have to disagree with something said in comments. I am a big fan of giving students homework points for effort. I have found that many of the checked out students or ones who think they are dumb won’t do homework because “I will just it it wrong anyway”. By giving points on homework for effort it values the struggle for understanding not the mastery but that is what homework is designed for. Mastery should be shown in other ways (usually testing and projects but not always). The key is that you have to balance those points. No one passes my class by homework alone.

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