Reflection inspired by Meaningful Quotes

So, a blog post from Prof Ilana Horn (found on twitter @tchmathculture) came across my reader last week. It was titled ‘First, Do No Harm’ (you should head over here to read it) and this caught my eye for a number of reasons. The first is that one of my proudest moments in the sprawling world of internet interactions came when Tina Cardone (on twitter @crstn85  or over at her blog here) grabbed a quote from me to use in her magnificent Nix The TricksThe following quote, a comment I made about the use of the dreaded FOIL acronym, is the one she used in an earlier version of her terrific book.

I would say, then, that it is not reasonable to even mention this technique. If it is so limited in its usefulness, why grant it the privilege of a name and some memory space? Cluttering heads with specialized techniques that mask the important general principle at hand does the students no good, in fact it may harm them. Remember the Hippocratic oath – First, do no harm.

I’m excited whenever I see a new post by Prof. Horn, but this one grabbed my eye by its title. Little did I realize that her post would be itching my brain for days at a time when I have little spare space or energy. We’ve been engaged in fall term finals at my school. Otherwise, I would have responded sooner.

Prof. Horn lays out some common practices that do harm – at different levels – to students and to their chances of increasing their competency in the math classroom. I’d like to respond to a couple of them and try to gather the wisdom of the internet (or at least the minuscule portion of the internet that will read this post!)

  1. Timed math tests – Prof Horn links to Prof Jo Boaler here and says that our assessments communicate to students what we value. I could not agree more with this statement about assessments. I speak to colleagues about this all the time. If we say to our students that we value thought and process but then give them multiple-choice tests where points are all or nothing, then the students quickly figure out that we do not mean it when we say we value process. What we do is FAR more important than what we say in this arena. Years ago I read a powerful essay about assessment written by Dan Kennedy (you can find that essay here.) I found many of Mr. Kennedy’s arguments to be powerful ones and I remember that my primary takeaway was that we should assess what we value and we need to value what we assess. I tell my students that I want them to be able to tackle novel problems. That they need to be able to tie together ideas we have worked with and apply them in a new context. I often give problem sets for HW that require them to remember from past lessons and from past courses. I tell them that I don’t necessarily expect everyone to get these problems completely correct, but that I think it is important that they grow as problem solvers. If I never put problems like this on graded assessments, then my students would quickly sniff out the fact that I don’t really value that process very much. However, what also has to go along with that in a graded assessment is a willingness to pay careful attention to their work, a willingness to reward thoughtful work with meaningful partial credit, and some careful feedback either on their written work or in a group setting when papers are returned. (This feedback question is also burning my brain thanks to a recent series of thoughtful posts by Michael Pershan over at his blog on twitter you can find Michael @mpershan – I hope to draft something meaningful soon in response to these thoughts!) The belief that I have that is challenged by Prof Horn here is the idea of speed or efficiency being valued highly. I think that I want to argue that efficient problem solving is a skill I want to value and one that I want to reward. Where this gets tricky is that I know that there are certain problems – meaningful, valuable problems – that just do not lend themselves to quick solutions. How do I balance the desire to see my students think and wrestle with new contexts with the desire to reward efficiency and cleverness? I also teach in a school run by the bell system (I’m certainly not alone there!) and I need to think how to work within that system. I tell myself that I balance the points on my tests so that the diligent student who has gained increasing mastery of facts and skills can still earn a respectable grade even if they fail to connect the dots on the novel problems. This only comforts me to a small degree. I know how much grades serve as motivators (and de-motivators) for my students. I know that a student who feels that s/he has worked hard can walk away from an assessment feeling defeated and incompetent simply due to failing to finish one problem. I know that students can convince themselves that their hard work was for naught and that maybe they just are not cut out for this particular challenge. I’ve been at this a long time now and I still do not have a satisfactory answer and Prof Horn’s post really brought that home to me again. What do you say wise readers? Is it reasonable/valuable/important to reward those clever students who can solve novel problems more quickly than their peers? Should this be a valued skill? If it is, then I believe it should be assessed somehow.
  2. Not giving partial credit – I agree 100% with this point. As a teacher of two AP courses, I feel that part of my task is to help my students be ready for the format and the peculiarities of the AP test in May. Most of my students choose to take these tests and for those who are not yet seniors, they feel that their test scores can help/harm their chances to get into the college of their choice. What this means is that I incorporate multiple-choice questions into their assessments. Now, if I tell them that I value process, how can I feel good about MC questions? Well, I don’t. I have dealt with this two ways and I am not thrilled with either of them. Sometimes I simply value each MC question at such a low point total that mistakes will not have a great impact on their grades. The other way I have dealt with them is to decide what the most reasonable incorrect answer is and give partial credit for this mistake. I am not happy with either path. Any wisdom from others who deal with the (sometimes) reality of MC questions?
  3. In the comments section there are some additions like this one – Grading practices that do not allow reassessment. Again, I am wrestling with this and I have blogged about this. In my two AP classes, where I am the only instructor, I allow retakes on unit tests for anyone unhappy with their grade. I have averaged the two grades. I have read some powerful arguments against this from the SBG crowd, but I cannot find a place where I am happy simply waving off performances. I may get there one day but I am not there yet. I am not at all happy with myself or with my students about the current retake policy I have. I hope that I can construct a more meaningful one by the time our winter term starts in December.

So many thoughts rattling around my brain. Thank you to Prof Horn for agitating me with her blog post. Thank you to her commenters for furthering the conversation. Finally, thank you to anyone who reads this and helps to continue to refine my thoughts and practice.

What Do I find Interesting? – How Can I Help my Students Answer this Question?

One of the joys of my engagement in the interweb of math teacher bloggers (some of whom I stumbled across my self many of whom I have discovered through the MTBoS challenges) is that I feel my brain tickled and challenged. One of the most consistently challenging of the bloggers is Michael Pershan and he has recently been writing a series of posts about what he finds interesting. Kind of math-y in general, but also just musings. I used to think that success as a math teacher might be measured by running into a student after college and having him/her still be able to answer, say, a trig question about oblique triangles. Luckily, I grew out of that and have a different idea of what success might mean. I have a story from a former student (Chris S.) that I think is apropos here – and I apologize if it seems like I am patting myself on the back here, trust me when I say that there are many students who don’t see their experience with me the way that Chris did. For a few years, I was living in NJ a mere 35 minute express train ride into Penn Station. On days when I was off work but my wife was not, I would often head into Manhattan. Chris was working there at the time doing some high powered financial advising. He was one of the more brilliant kids I’ve ever taught and I have kept in touch with him since he graduate in 1994. So, one day we are having lunch and he is recalling a particularly thorny data analysis problem he had been wrestling with. Much of what he detailed was over my head, but it was great to sit and listen to him so passionately recalling a struggle. He said that his boss, let’s call him Ned (I don’t recall his actual name), helped him with a major breakthrough. He said that one morning – after wrestling with this problem for over a week on and off – he told Ned that he needed to take a long lunch and get out from under this problem. He came back a few hours later and Ned had made an important advance on the solving of this problem. Chris then said to me, “Jim, Ned kind of reminds me of you – he just asked some questions of the data that I did not think of asking and this allowed me to finally solve this problem.” I still get kind of chocked up thinking about this day. He did not say that he remembered a certain lesson or a success on his AP test. He did not say that he remembered having fun in my class, but I think he did. He did not say that he thought of me as a caring teacher, but I think our ongoing relationship says that he does think of me this way. No, what I took away from that conversation was that I challenged him by asking questions he did not think of. What I inferred (maybe this is just optimism on my part) is that he finds this to be a positive trait. He was speaking with admiration about his boss. Now, I know for sure that Chris is a smarter person than I ever have been and I know that many of my students fall under this category. But what I hope that I can convey is the value of questions. Many times in the classroom these are restricted to a mathematical context, but I want my students to develop an appreciation of a good question and develop the habit of asking good questions about the world  around them. There is a quote I found in my reading years ago when I was a student and it is a quote I share with my students. I have not found the correct citation for it, so I apologize for not being able to give credit where it is due. Here is the quote:

Genuine enquiry is an important state for students to recognize and internalize as socially valid. Consequently it is an important state for teachers to enact. But it is difficult to enquire genuinely about the answer to problems or tasks which have well-known answers and have been used every year. However, it is possible to be genuinely interested in how students are thinking, in what they are attending to, in what they are stressing (and consequently ignoring). Thus it is almost always possible to ask genuine questions of students, to engage with them, and to display intelligent directed enquiry. For if students are never in the presence of genuine enquiry, but always in the presence of experts who know all the answers, then students are likely to form the impression that there is an enormous amount to know, and that experts already know it all, when what society wants (or claims to want) is that each individual learn to enquire, weigh up, to analyse, to conjecture, and to draw and justify conclusions.



One of the amazing librarians I work with found the citation for me. You find the whole text at

The author is John Mason