Making My Mark In The World

I have taught Geometry for many years, and a big part of the curriculum has been proving congruent triangles. If you teach this, you know about what I refer to as the "Fab Five": Angle-Side-Angle (ASA) Side-Angle-Side (SAS) Side-Side-Side (SSS) Angle-Angle-Side (AAS) Hypotenuse-Leg of a Right Triangle (HL Rt. △) I introduce this list with accompanying diagrams illustrating each method. Here is a sample: After generating the list of the "Fab Five", I emphasize to the students that each method requires three parts from each triangle. This, in turn, always results with students asking: "Hey Mr. K. What about AAA and ASS?", the latter of which usually produces a number of giggles. So I ask them: "If you know that three angles in one triangle are congruent to the three corresponding angles in another triangle, why are the triangles not necessarily congruent?" After a little guidance, students will recall our work from earlier in

This year, a colleague announced that he needed to take a short leave from school. This is the second teacher in our department who has needed to take time from work this year. Due to an unfortunate shortage of qualified substitutes, teachers in our department have been asked to take on another teaching section. Some teachers are eager to do it, thanks to the bump in pay (after all, who couldn't use a few extra bucks in the bank?). However, some teachers are reluctant to teach an additional period, citing an already busy personal and/or professional schedule. So when I was asked to teach one of my colleague's classes, I was hesitant. But wanting to help out (and with a son looking at tuition payments next year), I agreed. I knew the leave would only be a few weeks and most of it was during the month of November, a month with days off for Election Day, Veterans' Day, and the Thanksgiving break. So when I was asked to cover his Honors Pre-Calculus class, that combination

I have taught high school geometry for many years now. But as a result of my MTBoS explorations and work with my colleagues in the NYS Master Teacher Program, I have become more aware and fascinated by shapes and their structures. I have also tried to increase student awareness of the beauty and powerful properties of the myriad of shapes that we study and don't study. It is still early in the school year, and my students' understanding and sense of shapes is still developing. So at the end of a recent quiz, I asked the students: "What is your favorite shape? Why?" Here are their unedited responses. Enjoy!  I will try to remember to ask them the same question at the end of the year, after working with a variety of shapes and their properties. Thanks for reading!

I know... sounds exciting right? Please bear with me... I was inspired today! As a geometry teacher, I am always looking for ways to visualize and demonstrate geometric concepts. Often times, I utilize tools like GeoGebra or Desmos. But frequently, geometry can utilize simple resources. This morning, I came across a tweet from Halcyon Foster: I really like how this utilizes simple materials that most geometry teachers have - paper, ruler, scissors, and dice. It looks like the idea is to roll the dice, then take a strip of paper and measure and divide it into lengths (in this case 2cm, 5cm & 6cm). Then fold the strip to try to make a triangle. It's simple and effective, and serves as a great way to investigate the triangle inequality theorem. It inspired me to think of a way to "kick it up a notch". So I turned to one of my favorite geometry tools - bendy drinking straws! Here is what I put together: Supplies: Bendy straws Scissors Ruler Sharpie

After making the change to CC Geometry a few years ago, and after much #MTBoS influence, I took a chance and made a big change in the way I start my school year. Last year, I didn't give out a course outline and require the Ss to have it signed and returned. I didn't lay out the rules and requirements of my course and classroom. Instead, I started with "One Cut Shapes". The inspiration for this came from a PRESENTATION that I took part in last year with Dan Anderson and some other NYS Master Teacher colleagues: It was an interesting investigation that I got into last summer: So last year, I started the first day of class with: "Hi, I'm your geometry teacher, Mr. Kaercher. Let's play with one-cut shapes." It was a freeing experience and probably different than the first-class-of-the-year-experiences that the Ss had that day. I'm starting this year the same way, but I have also revamped my first Geometry unit on "Es

As I am planning my preparations for the new school year, I came across a recent tweet from Meg Craig: She included very simple instructions for using a Google Sheet as "The Easiest, Most Customizable Seating Chart and VRG Generator Ever™". The acronym VRG refers to "visible random grouping", a method for setting seating charts and student groups. Her very detailed directions can be found HERE . After setting mine up to fit my classroom layout, I got the idea of adding a button to activate the randomizing. I had limited experience with buttons and scripts from my days of working with Excel. So I started Googling. First, I found the directions to add a BUTTON .  Once the button was added to my Google Sheet, I needed to develop a script to make the button do it's job. Unfortunately, I am not a computer programmer. Fortunately, with some Googling, I was able to find the SCRIPT that would randomize the name cells with a click of the button.  I m

As I begin the final days of summer vacation, I find myself in a reflective mood. I think it started as we made our way home from our week-long family vacation in Rhode Island. The picture you see above is a photo of Blue Shutters Beach in Charlestown, RI. While my family read, I was content to sit and watch the ocean and think about the summer-behind and the school-year ahead. The long car ride home was also a good time to look back and look ahead. So here is a list of random thoughts from the Summer of 2017: I'm glad that I spent a lot of time playing with GeoGebra, especially the 3-D calculator. With the help of some #MTBoS friends, I was able to construct some pretty cool files. The whole #MTBoS vs. #iteachmath debate was interesting. I do a lot more with math than teach it, so I'm sticking with #MTBoS. College visits with my son were really fun. It so exciting to imagine where he will end up one year from now. As I drove with my son to a concert in the Finger

Last week, I posted this tweet: Before I get into the responses, allow me to provide some context... This coming week, I will be joined by many of my NYS Master Teacher colleagues from the Central NY, Capital Region, Mohawk Valley, and North Country Regions for our annual conference. In addition to many great Master Teacher-led breakout sessions, there will also be "Open Space" discussions taking place around the central theme of "Fostering Interdisciplinary Collaboration". I was asked to facilitate a topic of my choice that relates to the central theme. So after some brainstorming, I came up with the quote in the tweet. I've been teaching for many years and as an experienced teacher, my instructional style has evolved. During my early years, I, like most beginning teachers, stuck to the script. Carefully developed lesson plans became something akin to cue cards and worksheets and packets became the props.  But once I got my teaching legs