I don’t know who to talk to or what to say or where to stand or when to get involved or oh my gosh what do I do with my hands when I’m standing here shouldn’t talking to people be easier but it just seems so forced and am I thinking too long or not long enough and am I staring did I nod enough or too much am I agreeing too much do I need to jump in here what is this person’s name again do they even know I’m here why am I here anyway but maybe I’m doing okay or maybe not you can make it through this I know you can I know you can I know you can just be yourself but not too much yourself don’t seem crazy or strange or weird or insane or maybe just don’t worry about what anybody else is saying or doing but are they judging me and do I even care wait have I said anything lately what’s the right thing to say did someone just say that make sure to nod again smile not too much that looks creepy keep going you’re doing okay you can do this you can do this you can do this it will all be over eventually just hang in there it’s not that bad you will be stronger because of this it’s about the learning am I thinking too much again quick smile and nod and agree and make eye contact okay that’s too much eye contact don’t scare people but you don’t need to stare at their shoes either and make sure to smile and nod and don’t look uncomfortable but don’t look like you’re trying not to look uncomfortable and make sure to say something but not something obvious and don’t make jokes unless they’re good jokes how do I know if that’s funny anyway and do I laugh at my own joke and if someone else makes a joke laugh but not too much because nobody likes someone who laughs too much I don’t think I’ve blinked lately do people usually have to remember to blink or is that just me now I’m blinking too much okay maybe there’s something in my eye play it off okay smile again and nod yes I agree okay good it was nice meeting you okay have a good afternoon see you later I’ll try to be more normal I promise I promise I can do better trust me I’m just like all of you and I really want to be here I really do I really do I really do deep breaths deep breaths deep breaths deep breaths
Many students have trouble with fractions. When I taught at a high school, my 10th and 11th grade students regularly had difficulty performing operations with fractions. As an 8th grade teacher, I’ve tried to help my students develop, refine, and maintain strong fraction skills. Don’t get me wrong: I don’t consider fluency in performing operations with fractions to be the most important skill for my students to have, but it’s certainly one that will contribute to their success at the high school level. With that in mind, here’s an approach I used this year to work on fractions.
After the warmup and overview of the day’s class some time in October, I pulled up a slide with four fraction multiplication problems. These first ones were relatively simple like . Students had little trouble performing the multiplication (yay!), and thankfully, students presented a number of different methods. The most common early responses were and . As I continued to present problems over the next few weeks, I added complications. Students noticed that simplifying often made the multiplication easier (e.g. ). The big breakthrough came when I presented a particularly annoying pair of fractions to multiply like . To this point, I had not pushed students to use a particular method; any simplifying they did came from them not me. Whoever offered the response of did not respond kindly to the question of whether that fraction could be simplified. By this point, students had been doing so much simplifying that it was no surprise to anyone that their lives would be easier if they found a way to simplify before multiplying. A brief discussion of the commutative property allowed a student to rewrite the multiplication as , which everyone in the classroom felt comfortable multiplying. It was a great moment of mathematical discovery.
As the weeks progressed, I continued to throw more and more challenging multiplication problems at them, and I also started to incorporate some addition, subtraction, and division. Students began feeling much more comfortable with fractions than they ever had before, even if they still weren’t the biggest fraction fans around. This fraction work paid off when we wrote equations of lines, and in general, I think it gave students some confidence in an area where they had so little before.
I definitely plan to continue using “Get On My Fraction Level” in my classes this coming school year. I’d like to find a way to incorporate more active participation. I might give students a weekly template to use each day when we do our fractions. I did that two years ago with scientific notation, and it worked pretty well. One big concern is time: with so many topics to cover, it’s difficult to carve out time to work on something that isn’t really an 8th grade standard. Having seen how working with fractions helped so many of my students grow, however, I will definitely find a way to incorporate regular fraction work into my lessons.
I’ve been following the Math Twitter Blog-o-sphere for years, but until now, I haven’t felt strongly about blogging myself. I’m heading to Twitter Math Camp this summer, so I figured there’s no time like the present to start blogging. Here’s a little about me.
I went to a public high school. I earned a bachelor’s degree in mathematics as an undergraduate. For the next few years, I spent most of my time just spinning my wheels. Four years on my local district’s Board of Education reignited a passion for education that I had before college, so I completed a one-year master’s in education. I did my student teaching at an all-boys Catholic high school. Despite never thinking I’d have anything to do with a private school – let alone a religious one – I found the experience to be extremely powerful. After graduation, I found a job at an all-boys private high school. Again, I never thought I’d teach anywhere other than a public school, but I couldn’t pass up this opportunity. I spent three years at that school, taught geometry, algebra 2, and pre-calculus, and coached both cross country and track and field. During my third year, I decided I wanted to try something new, so I looked for a job at a public school. My timing turned out to be excellent, and I interviewed for and was offered a position teaching 8th grade math at my alma mater. Going from an all-boys private high school to a co-ed public middle school challenged me more than anything else I’ve ever done in my life. Now I’m two years in, and I can say that changing jobs was the best decision I’ve ever made. I look forward to every day, and I’m excited to use blogging as a way to become a better teacher!