Tag Archives: Tina Cardone

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.

Professional Growth in a Connected Age

I’ve been teaching for a long time now. It makes me feel old when I realize I am in my 27th year in the classroom now. I joke with my students that I have been teaching longer than any of them have been alive. When I started teaching the predominant models of professional development were the inservice days at school where the school administrators decided how we needed to grow, the weekend workshops or summer workshops that I would scramble to find funding for, or the one or two day workshops that would cause me to miss school. It’s a different world now. I know I’m preaching to the choir if you are even reading this but this world of twitter, of blogs (both writing them AND reading them), of online simulcast workshops, or improv EdCamps, the list goes on. In this day in teaching I am fully convinced that if you want feedback and you want connections to help you think about your craft and to expand your toolbox – if you really want it – there is an ocean of resources at your fingertips. Literally (since I’m typing this right now!) at your fingertips. Not all of it fits everyone. I know that I am still wrestling with the timing and pace of my twitter feed, but I think I’m getting better at it and I KNOW I’m growing as a result of it. I spent a long time reading blogs, then commenting on blogs before I felt confident enough to launch my own. I have two kids at home so I know how tight time can be, but I also know that the past two Saturdays (that I blogged about separately here and here ) where I spent a combined 16 hours out of the house were worth the time and effort. Luckily Mrs. Dardy is kind and flexible and supportive of this pursuit.

I’ve been thinking quite a bit about this, about how different my life as a teacher is in the past few years. I’ve been in regular communication with one of my former colleagues, Gayle Allen. Gayle (@GAllenTC) hired me seven years ago when my family left Florida and we landed in New jersey for a while. Gayle is a remarkable, energetic thinker and was a great boss. She and I have been engaged in a long conversation about professional growth and one of the results of this conversation is an article that got posted today over at a website called Getting Smart. I know that I am not unique in this journey, but I also know that there are still many of our colleagues who have not taken this plunge. Some because they are not interested in doing so, some because they don’t know where to start. I’m pleased to be able to give shout outs of thanks to Dan Meyer (@ddmeyer) and to Sam Shah (@samjshah) through that article and I’m pleased to be connected again (even if we are nearly 3000 miles from each other) with Gayle.

This summer will see a trip to OK to take part in TwitterMathCamp. This would not have happened if Tina Cardone (@crstn85) had not reached out to me and asked me to join in on the fun. This summer will see me finish an in-house Geometry text for our students. This project would never have happened without the encouragement and advice of Jennifer Silverman (@jensilvermath). This summer will see me work on plans to help a brand new teacher in our high school take the leap from teaching Algebra I in the middle school to teaching Honors Precalculus for the first time. All of these experiences will help me grow as a professional. 27 years at it now and I feel like I still have an awful lot to learn. I hope to be smarter this time next week about this craft than I am right now.