A String of Good News

Our school year ends early, we graduate the day before Memorial Day here. So, I have had some time to unwind AND to look ahead to next year. I’ve been thinking about my new Discrete Math text, problem sets for my AP Calculus BC class (thanks to inspiration from Lisa Winer (@lisaqt314)), and my upcoming trip to TMC where I will be hosting a brief session to discuss how to develop communities similar to our MTBoS back at home.

Recently, I received not one, not two, but THREE pieces of good news that has happily distracted me a bit from thinking about the fall.

Last summer I led a session at the Pennsylvania Teachers of Mathematics summer conference. I gave it the dramatic title Escaping the Tyranny of the Textbook and it is essentially my love note to the MTBoS community. The goal of the presentation was to have any participants in the session leave the room feeling empowered to write their own curriculum or to learn better how to crowdsource curriculum that is tailored for their classrooms. I was pretty happy with it but I know it needs to be punched up. What better motivation to improve something than to put yourself in a public position where you need to be up in front of people all over again? So, I sent proposals to two upcoming conferences and I learned in the past few weeks that I was accepted to both of them! I will be presenting at the fall conference of the Pennsylvania Association of Independent Schools in October and I will be presenting at ECET2NJPA in September. I am flattered that my proposal was approved by each of these conferences and I am excited to meet some new folks to expand my circle of colleagues even more.

Our school started a STEM initiative shortly after I arrived here in 2010. The first director of the program has decided to step down in large part due to other responsibilities that she has since taken on. She has put the program on firm footing and when he school announced this opening they committed to having a director and two associate directors. I received the great news last week that I will be one of the associate directors of the program. All of our freshman take a STEM class that was designed by the program director and some of our students. They created some lovely iBooks that are still works in progress and that I feel a kinship to since I created our text for Geometry in a similar fashion. We have been hosting guest speakers, alumni, panels of regional experts to discuss items of interest. It’s an exciting program and I am looking forward to being part of the team for the next year. If any of you have advice regarding possible directions for STEM programming, please share here in the comments or over at twitter where I am found @mrdardy


How to Succeed

Feedback from my students at the end of the year touched, in part, on the idea that many of my students take some time to adjust to my expectations in our course. Years ago, I wrote a document called How to Succeed in Calculus. This was adapted from a document I found online by a teacher I never met named Dave Slomer. I have modified that document for my Geometry class and I want to share my first draft here. I shared it with my Geometry team and we have a nice conversation started about how to introduce and integrate this document. The first reaction from one of my colleagues is that the document might be a tad too long and students might easily put it aside. I agree that it is a bit wordy but I also feel that there is not much that I want to cut out. I would love any constructive feedback either here or through my Twitter account over @mrdardy

Here is my first draft –

How to succeed in Geometry
Over the years, I have found that the best indicator of a student’s success is whether they keep up with their assignments. Students who keep up will likely do well – students who don’t likely won’t. We will be together for a good amount of time this year and we will routinely refer back to ideas and skills that we have discussed together. If you do not keep up with your assignments then it will become increasingly difficult for you to master new skills.

You understand the material best when you can do the problems – and get them right – BY YOURSELF. There is absolutely nothing wrong with asking questions or seeking help from me, from other teachers, or from your fellow students. Everyone will need help sooner or later in this course. However, you must have the integrity to realize that the goal of the assignment is NOT just to get the assigned problems done. When we write our problem sets we are aiming to make sure that there is sufficient practice for all of our students. However, there will be times when you will need more practice than this, and you must have the courage and integrity to realize it. When you ask for extra practice, we can provide you with assignments that will help you to master new skills.

If you take your homework problem sets seriously, if you spend time thinking and working through the problems we present to you, you will feel more prepared for tests and quizzes than if you do not. Hard work spent on daily practice pays off on test days. Athletes who take practice seriously are better prepared for game days. Musicians and actors who take rehearsals seriously are better prepared for performances. Students who take daily practice seriously are better prepared for assessments. We know this to be true.

Your problem sets have narrow spaces available. Do not try to squeeze all of your work in these spaces. It is unlikely that you will be able to read your own work when you look back at your work and it is very unlikely that I’ll be able to clearly see your work and understand your reasoning. Do your work on notebook or blank paper and give yourself space to draw and to think.

If you hit a “dead end” and want to start over, cross out the work you don’t want with a big “X” – do NOT erase it. It might turn out later to be correct. Also, if you come to me for help, the first thing that I will say is “Let me see what you have done so far.” If you tell me that you erased it, it will be much harder for me to help you. Erasing can be a big time-waster on tests (where time is very valuable).

This is important in every class, but in this class the text serves as a valuable supplement to what happens in class. Often your homework will be to read the book in addition to any of the problem sets that we have written. Read the book carefully with a pencil and paper nearby. Pay particular attention to the illustrations and examples. Study the examples carefully. All of you have access to a PDF of the text and some of you will also have opted to have a physical copy of the text as well. Use your physical copy, if you have one, for margin notes. Use your PDF regularly to follow hyperlinks to explanations and activities that have been built in to your text. These are valuable resources and we expect that you will attend to them when you are asked to read.

It is vitally important that we can communicate in the language of mathematics. As you read or participate in class, pay particular attention to the meaning of each new term and symbol. This is a course that is heavy on vocabulary, you need to spend time and energy on this aspect of your study of Geometry.

Luckily for you, tests are cumulative, and we will review in class; therefore review is somewhat automatic. Don’t hesitate to go back to review or seek help on algebra skills or on earlier ideas from this course that you may not have mastered as well as you wanted to.

Good notes are essential for success in any technical field. They are essential for review – not only for tests, but also for the problems you will work that evening. It is far too tempting to sit and listen and watch during class. You may feel comfortable at times following our conversations this way. However, when you sit down at night to do your homework, you will be without a valuable resource and you may not remember well what the conversation was hours ago when we were together in class. Every study of learning that has ever been done suggests that the act of writing something down helps in strengthening our memory. It is my expectation that each of you will come prepared each day to take notes on our class conversations.
You need to use the time at the beginning of class to get ready for geometry. Get out your books, assignments, notebooks, pencils, etc. I will usually have a question on the board or the TV monitor when you arrive in class. Get to work on that and get your mind in its math mode. Socializing may be more pleasant than math, but the goal is to make math more pleasant, and socializing often gets in the way. At the end of the discussion period, begin (or continue) the current assignment right away – what better time to get help if you get stuck? We only spend valuable class time on important topics, so take good notes constantly during class.

Your success depends on your ability to recall (or find, relearn, and then remember) concepts and techniques that were introduced earlier. If your notes and assignments are scattered about, folded inside the covers of your book, papering the bottom of your locker or the floor of your bedroom, you’re sunk.

There are many students, and just one teacher, and time is too valuable for you to just wait – stuck in neutral – for help. Look in your text and your notes for sample problems that might shed some light on your difficulty. Learn tenacity – don’t just “fold” at the first sign of difficulty. Is there another way to approach the problem? You can do it.

Everyone, no matter how smart or proficient in math, will get stuck sometime this year. Perhaps there is a new concept or technique that just won’t fit into place in your brain. Tenacity and self-sufficiency are great attributes, but sometimes there is going to be a quiz on this stuff tomorrow. Sometimes there just isn’t time to be tenacious. Attend conference bells, ask questions in class, just be sure to get the help you need to succeed.

If you have a worry, complaint, suggestion, or concern of any kind let me know. I can’t fix it if I don’t know about it. Remember that just because a problem – or a solution – seems obvious to you, it may not be obvious to everyone. Speak up.


There are some things I do in class that you may find unorthodox. If we understand each other early in the year, we’ll avoid a lot of stress later in the year. There are mathematical facts that I expect you to know and I will remind you that you should know them. There are times when you will ask a question and I may reply with a question. Or, I may redirect the question to someone else in class. This is not done to avoid answering a question, it is done to encourage a thoughtful discussion and to help you to develop important problem solving skills. I believe strongly that we understand ideas more deeply if we can explain our own thoughts to others. For this reason, we sit in groups facing each other, rather than having everyone face me or face the board. I expect that you will explain ideas to each other and that you will ask each other questions. Questions in this class will ALWAYS be answered; you may just have to be patient before the answer arrives.

A quote by Galileo Galilei

“Philosophy [nature] is written in that great book which ever is before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”