I talked about my version of flipped or preheating in an earlier blog post (yes this is my fourth today but I've been needing to update for weeks). Now, I want to talk about how discovery has and has not worked in my classroom.
Last week, I tried stations with my Trigonometry class. At each station, I had a description about the tests for symmetry (origin, y-axis, x-axis) and even/odd/neither along with an example and a picture of the graph. The goal was for the kids to take their list of functions and determine (based upon the information) what happened to each of the graphs.
Insert exploding bomb now. The kids did not have it. They didn't understand the difference between
-f(x) and f(-x) as well as what it meant to plug in -x or -y.... Basically, it was a big no. Some kids (very few) started to see the patterns like with even functions and the even powers but for the most part, they were shutting down and wanted to just do some examples. Needless to say, unsuccessful lesson Miss Rudolph. However, I did have a kid exclaim to me today that he now understood what those signs meant..... just needed to sit there for about a week and simmer and stew... sigh
After this disastrous discovery lesson, I learned that my kids were not completely ready for this much freedom. Unit 3 started out with piecewise functions, step functions, absolute value functions, and greatest integer function. Along with those guys, I also felt that the Vertical Line test was important. These 5 "sections" were broken into parts on a set of class notes that I provided with the kids. On these notes, I created a couple of questions such as "what is this in your own words?" "draw the graph" "what happens if...". I had slides showing on my projector (which is extremely cool as it's hooked up with Apple TV) for each section. I told the kids, I would slowly go through the slides for that section (each one had 2 or 3) and I would have them silently read the slides, process the information, think about what is being said and try to answer the questions. After they gave this a shot, they were to pair up with their "arcs." (My room is set up such that there are automatic groups of 3) In their pairs, they would compare their answers and explain the concepts to one another. After this, we shared as a group and they put the concepts into their own words for the group. Again, some groups extremely excelled and were able to grasp the concepts and as usual, many groups struggled (not everyone likes group work). Initially, I had a couple of kids pull me aside and tell me, "Miss Rudolph, I am not getting this" and I would respond with "Give it a shot, think about what's being said, give it some time" and by the end of the lesson, smiles had returned and they admitted, "Okay, now I get it". For the most part, the classes did a great job and were able to obtain the initial information on their own by reading and analyzing the words. Discovery? Slightly, baby steps people, baby steps. Just wait til I have them discover trigonometric functions, minds blown.
I'm wondering if this unit is going so much better because of the major presence of teaching themselves throughout. I started the unit out with students obtaining information on their own and processing it solo and then together. Continued the unit with a teach yourself / preheat over the weekend. And of course, we had group examples where we do problems together. Very rarely will I do or tell the class how to do a problem, I refuse and I don't believe in it. I always ask for ideas and will slowly reveal the steps based upon their responses.
Confidence is building amongst the class and I'm pleased to say that I've gone 2 school days in a row with no headache. Happy Miss Rudolph :) Happy kids, it really does make my day when they grasp the concepts and expand their knowledge by digging a little deeper