Tuesday, September 25, 2012

Think Pair Share

Discovery/Inquiry learning is absolutely wonderful. It's something that I truly believe in and am working to bring to my classroom. Unfortunately, it's very difficult to have students just start learning this way after they've been taught for so long with the traditional lecture method. Now, I do believe that there is a time and a place for a standard lecture, I also agree that other methods need to be used.

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

Children's Book - Inverse Functions

At my school, we believe in a mastery systems. Basically, if a student has not "mastered" the content, then they do not receive the credit to move on. I think this is wonderful for math because as we all know, our content builds upon one another.

Unit 3 in Trigonometry deals with piecewise and inverse functions. For the ending half of the unit, inverses, I decided to have the kids create a mastery project rather than assess their ability solely in the form of a test. I just provided the project guidelines yesterday, so I have no status regarding how they look or how they are going but I will on Friday! I've uploaded the project description to scribd (see below) and as you can see, we will be doing a rough draft / peer editing day in class on Friday. The kids also got a handout detailing what I would expect in their rough draft (not uploaded).

The project is due next Wednesday (the day after the unit test) and I have crossed fingers! The kids are feeling pretty confident on this unit and as we all know, happy kids, happy teacher, happy classroom :)

Trig Unit 3 LT4 LT5 LT6 LT7 Mastery Project

Factoring Polynomials Foldable/Project

So, in Trigonometry, we were working with factoring polynomials (differences/sums of cubes, grouping, synthetic division, and long division), which I must say are rather yuck for kids. Anyways, after introducing synthetic substitution and linking it to division, I told the kids that they would be doing a little project over the weekend: researching the other methods (with provided links) and creating a four corner foldable with steps/examples/hints etc.
This was the description of the project that I gave to the kids. The logic behind the project was to begin creating study material for their unit test (this did not prove to be a wonderfully successful one but we're doing better in unit 3) while also having the kids describe steps in the factoring methods and thinking about what was happening.

Some of the projects looked awesome and the kids had some fun with it and others, well they weren't as pretty. It's okay, it wasn't a huge project (they're doing another one right now.... I'll describe it later).



downside: the kids didn't do real difficult examples so when we talked about them, they weren't as pretty (ie: diff/sum of cubes), I should have done a prerequisite day focusing on the factoring done in Algebra 2 (GCF/diff of squares/Trinomials) to better prepare us, I'm also not sure how much they are using them
upside: they did create a reference for themselves on what was occurring in each method (they could have continued to add to their notes), they were very pretty visuals, we got to do a gallery walk where the kids looked at what others had to say

After the gallery walk, I had the kids explain their steps and how to do examples to me and the class. This is where we noticed the struggle with more complex examples. Next time, definitely doing a prerequisite assignment as well as providing specific examples to include on their sheets next to the resource ones.

Welp, we live and we learn! When I did factoring with the Algebra 2 kids, we did stations (much to their dismay, they're not big fans of walking around the classrooms). In the stations, the kids did this exact process with a premade 4 square foldable (I created a word doc with a 2x2 table prelabeled with the different methods and spots for steps/examples/notes). I almost prefer this as I was able to monitor but again, I like the flipped classroom idea. The flipped classroom is something that I've really been trying to start to use in my class or at least the idea of "preheating" the oven.

For example, last week, I had my kids do an Assistment Assignment (this is an online tool that my school uses where I can upload questions or anything, I put Kahn videos and what not into mine where they can leave comments or questions about the topics) where they were to read/watch about finding the inverse of a function. Well this week, 42/62 kids did their homework and Monday, well, it went much better as we had all been exposed to the topics over the weekend so they weren't as scary :) Now, three weeks ago when we tried this an 17/62 kids did their homework, well Monday was simply scary and unit 2 had an ugly test day. I think we've learned alot.

Well, I hope :)

Match the Graph - Graphing Inequalities


Sorry it's been so long! It's been 6 weeks since I've first started teaching and it has been a very busy 6 weeks!! I'm already almost half way through the semester and half way through all the content. Each of my classes has 6 unites and in both classes, we're finishing up the third unit this week/next week.

Algebra 2 had a unit where they were to graph inequalities and eventually systems of inequalities. After doing a few on their own, I then had the class break up into 4 groups and race to place Match the Graph!

It was so incredibly easy to make! All you need to do is take index cards, inequalities (or whatever equation you want), the solutions, tape/glue and bam! You have yourself a quick and easy race!

Everyone loves KutaSoftware and that's what I used for my graphs, since they already provide solutions. I had two different sets (a blue set and a pink set) made from the Algebra 1 inequalities and the Algebra 2 inequalities.


Downside: some kids obviously did most of the work, some kids tried to work it out by hand and then slowed down their group, some kids were able to visualize the solutions easily and didn't explain it to others.

Upside: it was a great lesson for kinesthetic and visual learners, it's great for visualizing what is happening or what is being said by the graph, and it's also great as an additional form of excitement in the class (kids love a good race)

Next time, I do believe that I would make an additional set of cards with systems of inequalities as the main point of the learning target was for SYSTEMS not just single inequalities. Also, I wouldn't put the blank graphs on the cards because they all wanted to draw on them (Miss Rudolph said no) but this wouldn't have been an issue if I had gotten them laminated because then kids could have taken dry erase markers to them....... But of course, I didn't have immediate access to a laminator.

Well! I have several other posts that I need to make but I did want to share this activity!

Stay tuned!

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