Inspired by this post, I wanted to share a little bit about how I introduce circles. When I pose the questions that follow, I usually use PollEverywhere to survey the entire class at the same time. I find this encourages table discussion. Keep in mind, when I show the students these equations, students HAVE seen the Pythagorean theorem, but other than that, this is the first time they have seen anything resembling the equation for a circle. The answer is not at all immediately clear and many students take a "guess and check" approach to finding the solution
When I started my teaching career, I taught the constructions that were required on the state exams by providing my students with an overview of the conventional steps. I soon learned my approach was completely ineffective. No matter how I varied my instructions, many students perceived constructions as little more than "pictures" that needed to be memorized.
In my fourth year of teaching, I completely abandoned my traditional method. On the first day of the constructions unit, I have students take out their compasses and given them one goal and a few rules:
I would say my most developed unit in geometry was my logic unit. I took it as an opportunity to introduce geometry in a refreshing way for student who may have been turned off to math prior to taking my class. For the first several weeks, we focused on logic puzzles that we not "mathematical" in the traditional sense. This encouraged thinking and problem solving, but it also engaged all of my students, as all of the puzzles were approachable and had an accessible solution. The aim of the unit is to get students to write up the solutions to the puzzles in a two-column, "statement-justification" format.
For this activity, students must first be familiar with exam free response scoring rubrics. (I teach AP Computer Science A, which has plenty of resources available online for free response rubrics and scored samples.) When students have seen the rubrics enough to know how to earn partial credit on questions that would otherwise seem to difficult to approach, I turn it up the rigor: students work in groups to write their own rubrics and canonical solutions. The extra tasks turns familiarity into mastery.
I have a review activity that I love. I just started doing it a few weeks ago and I'm pretty sure I'll be doing it a lot more. Simple concept, great effect. After having students complete a multiple choice exam, (as a review, not for a grade) I put them in groups and have them take it again. When they are finished for the second time, I use answer sheets that I can scan with my phone (ZipGrade specifically) to give them instant feedback, telling them only the problems they got wrong but not the answers. They continue to work on the questions until a perfect score is achieved. Lastly, I return their original answer sheets (which I have already scanned) and they use their "answer key" to grade their own papers.
The decision to allow students to retake exams and every conversation surrounding it should be based on the best path for learning. Always remember that.
Lately, I was grappling with the question: "Is a full exam retake necessary and effective for each student whose score is almost perfect?" The question came up because, invariably, every class has those students who earn a 94% but still want to retake the exam and shoot for 100%. I will always allow this, but recently I was wondering if a retake is the best way to earn that extra 6%. I asked myself, "What would help this person increase his or her understanding from nearly perfect to perfect?" For such a student, I think retaking the exam is too mechanical, an trivial item on a checklist to achieve perfection. By contrast, I've heard it said you've never truly mastered something until you can teach it.
This game is astonishing. The base game (no cards) is already unlike anything I've ever played and deeply strategic. Furthermore, the components are gorgeous. If the entire game was just the base game, I would already highly recommend it, but the designer went a step further by adding the cards and including a three- and four-player mode. Some of the cards even allow alternate victory conditions. Though the game is designed for two players, four-player with cards is my favorite. As you can probably imagine, the cards provide too much information to keep track of and it can be a riot trying to plan moves with your partner while considering the abilities of your opponents. We've had some good laughs over the four player games. For people who like more strategy, removing the cards and playing the base game is a serious battle of cunning. I'm floored by all the game offers and its replayability.
If you are visiting this site for the first time, let me introduce myself. My name is Ben and I am a teacher. In 2014, I started advising an after school club. Because students who attended club regularly could earn a credit at the end of the year, I needed to take attendance. Unlike an official class, there was no official attendance sheet so, as was the custom at my school, students signed in by writing their name on a clipboard.
Whether you work in a classroom or an office, if you collect meeting attendance on paper, you understand how tedious paper attendance is. It's messy, difficult to read and especially difficult to enter into a computer. Like me, you may have already attempted to find an app or some sort of small-scale solution to your problem, only to find yourself sorely disappointed. I was disappointed but sometimes if you want something done right, you have to do it yourself..
When I was new to teaching, a mentor challenged me to consider an strategy about the career that lay before me. He said that once a year, I should select the most boring or challenging unit of my curriculum and carefully craft it into something more interesting and engaging. He said even if I had to spend all of my creative efforts on revitalizing that one unit, if I could manage to do that once a year, with some time I would have a some pretty exciting curricula!
Whether or not you teach computer science, you can take my word: teaching sorting algorithms is not very exciting.
About me and my school
When I started teaching AP Computer Science A in 2015, it was easy to approach a subject that was new to me in a way unlike how I had been teaching mathematics. Initially, I allowed students to retake their exams simply because I knew I lacked the experience to write fair exams on my own first try. I kept the policy because it seemed almost natural, the course itself seemed conducive to a policy that allowed students to resubmit code until it worked. At that time, I could not see how the same policy could carry over to my math classroom and a discipline that is notorious as a harsh exam environment. Finally, in 2017, having grown frustrated with feeling that I was perpetuating a culture that rewarded exam performance over learning, (mind the distinction: it’s one thing to take an exam for the sake of one’s learning, I take issue when students perceive they are learning for the sake of their exams) I decided I could try what I was doing in C.S.
A project that is successful in that regard must embody at least three principles:
- It must require student choice. More is better.
- It must resemble a real life application.
- It must be an end in itself. To superimpose exam questions on the project content is to dilute the meaning of the project itself and redirect the students' attention back to the very falsehood we meant to avoid in the first place: an exam is the ultimate end and indicator of success.
This year, I've come up with the "Geometric Dwelling" project.
Over the years I've made dozens upon dozens of geometry diagrams. Most were made for one-time-use. Eventually, I got the bright idea to simply post them online to optimize the utility of each one. All of these diagrams are free to use or revise without restriction.
After years of having my resources bookmarked, saved and otherwise scattered all over the place, I finally decided to draw them together into one location.
Today, football teams all over the country responded to the President's remarks concerning behavior during the National Anthem and I've been unusually upset by the situation. I'm typically quite reserved about expressing my political beliefs. Throughout the day, as I continued to allow my thoughts to dwell on this controversy, I found it remarkable that this would be the one thing that would get me so riled up. But as my emotions formed into words, I found it even more remarkable what exactly I was really riled up about.
I've said this before, but I'll say it again: I hate tests. It's not just that traditional exams fail to simulate a real life, collaborative working environment in which one can consult outside resources, it's so much more than that. Traditional exams actually discourage students from developing necessary life skills. With traditional exams, memorization is prioritized over resourcefulness and individual performance is prioritized over accountability and collaboration.
Despite my strong opinions, over the course of my teaching career and out of pressure to have my students perform well on the State or College Board standardized exams, I have implemented the whole gamut of test preparation strategies and intensities. That my students are accountable to an essentially arbitrary end-of-year examination is something I have just had to accept as a fact of life. My supervisors understand this and more importantly, my students and their parents understand this. Without a massive shift in education, in one academic year I cannot choose to ignore the exam track and change the thinking of my students. I am forced to work with it.
1. Save Time
In my fourth year of teaching, I had become fed up with the lesson planning requirement imposed on me and my colleagues. The documents my administrators expected of us seemed beyond reasonable. At my school, we were asked for a lesson plan consisting of sixteen fields, a unit plan, and curriculum map. I was using a word processor to write up these documents, a tool that I found was utterly inadequate but I could find no better alternative. In 2012, I began to build my own solution.
There are five ways by which a word processor fails to fulfill the needs of a teacher. I designed Spiced to fulfill each of these needs.
Lately, there's been a lot of talk in the math educator community about ditching worksheets. Personally, I'm not a "fan" of worksheets but I'm also not about to abandon them either. In fact, I actually spent hundreds of hours over the course of many years developing a piece of open source software that automatically generates math worksheets. I felt compelled to write about my use of worksheets not just for the sake of voicing my opinion, but I also feel it's important to state the purpose of my software.
This article is about an assessment called "group quizzes." I titled this article "The Assessment That Changed How I Teach" because the advent of group quizzes is the most definitive and material change that has taken place in my classroom since I've noticed a substantial shift in my teaching. That shift is one in the direction of student-centered discussion, engagement in learning and self-reflection. I know that correlation does not imply causation and I've also been teaching for nearly a decade, so I'm sure this "change" can't solely be attributed to the success of an assessment strategy, no matter how fantastic it may be. Perhaps the strategy is really a catalyst for what was already set in motion by both years of experience and other events outside of my control. But I will offer this: if you are a teacher and you are even interested in shifting the focus of your classroom to center on your students and especially if you are willing or have already tried some new techniques to that end, I would say you are in precisely the position I was in when I discovered an assessment that was everything I was looking for.
In my post on "How What I Learned in Theatre Influences How I Teach Computer Science," I ended with the question, "is there a way to instruct students in what is really important that deemphasizes any required exam without being a detriment to it?" At the heart of this question is a confession that, while I hate standardized exams, I recognize they exist and I am still accountable to them. If you are a teacher, this is most likely your reality as well. The rest of "How What I Learned..." post described what I think is truly motivating and most important to glean from a good education. In my post, "How Github Makes Everything About Teaching CS Better", I explained what Github is, how I introduce it to students, and how my students use it on a day-to-day basis to collaborate. With this introduction of the theory and the tools aside, I'd like to finally write about what I do in my classroom to actualize my teaching philosophy. This post assumes a basic understanding of Github.