Last week, my content seminar professor asked us to explore some different blogs of fellow math educators on the Five Practices for Orchestrating Productive Mathematics Discussions – which is a fancy way of saying, “Let’s talk!” A blog I found to be extremely interesting and helpful with understanding this process was Christopher Danielson’s, which you can check out on the following link: http://christopherdanielson.wordpress.com/2011/08/30/five-practices-in-practice/
The five practices are:
1.Anticipate 2.Monitor 3.Select 4.Sequence 5.Connect
So basically, you first anticipate the strategies you think your students will use to solve a given problem. Doing this allows you to be a step ahead in the classroom so you will hopefully know what to prompt and say next. Next, you monitor your students’ work. This allows you to see if what you anticipated was correct. It can also help you to start making mental (or physical) notes of who you will call on when it’s time for the actual discussion. Next, you select. This is where you make your final decision on who you want to have share their findings to the rest of the class. This is extremely important, because the rest of the students are (hopefully) listening and will be learning from their fellow classmates. Also extremely important, is sequence, or order. The order in which you have students present their findings is crucial in that you want student learning to be optimized. And finally, connections. It is extremely crucial that students make connections between strategies of what has just been learned, especially if that means explicitly pointing them out as teachers.
This really inspired me to want to have a great discussion in the classroom. I tried my hand (slightly) at this on Tuesday. It wasn’t planned, but I had read the blog recently and it popped into my head as something that might work with this particular lesson. We were doing an exploration activity that was aimed at getting the students to discover the direct relationship between angle measures and opposite side measures of a triangle. I went around from group to group and wrote down on a note card which groups had different findings, and I had the order that I wanted them to share. What I hadn’t accounted for was that I already had the students set up in groups and discussing it amongst themselves, so when it came time to discuss as a class – they were about all talked-out. This was a classic case of beating a dead horse. However, I definitely won’t let this stop me from using this strategy many, many times in the future. I am really excited to see what kind of discussions can come from this.
“Spoon feeding, in the long run, teaches us nothing but the shape of the spoon.”
I’ve been reading a book called The Teaching Gap by James W. Stigler and James Hiebert, and I must say I was pleasantly surprised. I’ve actually been pleasantly surprised with a few of my required texts this semester, and I’ve found I truly am learning a lot from them and actually enjoying the readings. This book in particular has been comparing and contrasting U.S., German, and Japanese math lessons. The findings are extremely…interesting. Granted, this book was written over a decade ago,but it is really giving me great insight into what types of lessons allow students to actually learn. Or as we math educators like to say, do math.
One thing I have learned this semester, and that this book encourages as well, is the importance of making connections between lessons. I think so often this is where unneeded confusion in the classroom comes from, and almost always this could be easily avoided by the teacher. When students aren’t able to understand how each lesson fits together, all they have is scattered information from multiple different days that they’re trying to keep straight rather than being able to see the bigger picture and how it all fits together. As educators, it is our job to not only allow the students to make these connections but to explicitly point them out to them. I tried to focus on that this week while I was teaching, and I think it went pretty well. At first, I think the students were a little annoyed with how many questions I kept asking them, but they’re getting used to it now. Today, we were learning about regular and irregular polygons and we had just finished a lesson last week on triangles. I asked the students if they could tell me what type of triangle would be a regular polygon. Right away a few hands shot up and I got the answer I wanted; an equilateral. Knowing the students could still recall the classifications of triangles and connect it to the idea of a regular polygon was reassuring, and it felt really good to use a question I had thought about before my lesson and have it go over well. This will continue to be something I work on, as I feel it is one of the most important aspects of teaching mathematics.
Oh yeah, and I received this lovely green apple at the GVSU Green Apple Ceremony welcoming me to the College of Education. Much to our dismay, it was not edible.
“Tell me and I forget. Teach me and I remember. Involve me and I learn.”
We’ve been talking a lot about engagement in one of my seminars, and I couldn’t help but notice the lack-there-of from my students during certain parts of the day. It actually kind of surprised me the first time I noticed it. I was absolutely appalled that there was a possibility that every single student didn’t find me completely entertaining at all times. However, I think it was the multiple looks that resembled (more or less) this adorable picture of a baby that gave away their lack of amusement.
I first noticed this lack of amusement when I was going over specific homework problems with the class. It seemed that only a few students needed help with these questions and the rest of the class was either bored because they knew the content or didn’t care to follow along. Now that I have taken over and started teaching, I wonder if I want to stop going over specific homework problems as a class all together. It seems that this class time might be better utilized doing something else based on the engagement level I have noticed during this time. There have been other times I have noticed a lower engagement level, and I am still working on figuring out how to keep the students engaged as well as what classroom management techniques I want to utilize in my future classroom. For now, I am going to try to use faces such as the ones above as a sign that maybe I should be analyzing my lessons and figuring out how I can make the activities more engaging.
“The object of teaching a child is to enable him to get along without his teacher.”
After only two successful full weeks of Teacher Assisting and two weeks cluttered with five snow days, I officially start teaching my very own unit tomorrow. I. Am. Terrified. Or, at least I should be. I’m not really sure why, but I today I have had a strange sense of calmness about tomorrow, and I’m actually really excited. Maybe it’s because my partner and I get to debut what we have been working on for the past couple of weeks. Are you ready? FOLD-CABULARY! Okay, so maybe I came up with the cheesy name, (which, by the way, has yet to be claimed by any source on Google.) but it is a way for the students to keep track of their Geometry vocab for the unit and I am really excited about it. To get a feel for why the “Fold” part of Foldcabulary makes sense, here’s a picture:
So basically, we will have the students write each vocab word on a tab of paper all with a picture explaining the word, and on the reverse side of the paper will be the definition. And then you FOLD it all together! Genius, we know. Unfortunately, we cannot take credit for all of the genius behind this credit. You can find the basis for this awesome idea at this link:
Dominic and I are extremely lucky to have such an awesome CT that is willing to give us such independence and allow us to teach this early in the semester. By doing this, we will each get to teach at least 2 units this semester. Right now, Dominic will be teaching first block and I will have second. I am so excited and a little nervous, but I’m really excited to get this first lesson out of the way. I’m really going to focus on classroom management, because I’m pretty sure these bundles of joy are going to try to push the limits once the “new teachers” are in charge. I hope they are ready to learn about the wondrous world of Geometry! Because everyone loves Geometry, right?
“Much of education today is monumentally ineffective. All too often we are giving young people cut flowers when we should be teaching them to grow their own plants.”
John W. Gardner