I'm attending an amazing Common Core State Standards workshop this week for high school math teachers. It's called the Oklahoma Geometry and Algebra Project (OGAP.) I'm two days into it, and I've already learned so much. For once, I'm actually able to visualize my students doing Common Core level work. Before I learn anything more, I decided that I need to try to write down what I've learned so far and attempt to process it. My list of things I want to do before school starts is growing rapidly.
Before starting this workshop, I was terrified of Common Core. I'd printed off the standards, but I really had no idea where to start. The only help my district provided was a poster to hang on the wall that contained all of the standards. We've been studying the Standards for Mathematical Practice, and I think I'm finally starting to understand what they might look like in the classroom. As we complete activities, we have been finding exactly which standards they align with. The more time I spend with Common Core, the less I dread it. Yes, I'd rather not have to learn a new set of standards. But, these standards will make me into a better teacher. They will help make my students into better thinkers and problem solvers. It's going to be a rough transition. But, I'm excited now to challenge my students so I can watch them rise to the occasion.
I don't know if any of this information will be of use to anyone else. But, I'm putting it out here in the hopes that it might be. And, if it's on my blog, I'll be more likely to find the information again than if I have to go searching for the many post-it notes that this information is currently written on.
One of the first activities we did was a True Colors Personality Test. I had never done this test before. After choosing which words best describe you, the test will tell you whether you are primarily Blue, Gold, Orange, or Green. Blue people value relationships. Gold people value duty and responsibility. Orange people value freedom. And, green people value information and knowledge. I was not surprised to find out that I was almost pure Gold. My perfectionism, my obsession with to-do lists, and my need for order attest to this.
I'll be honest. At first, I thought this activity was kind of silly. Okay, I'm gold. Now what? But, as the week progresses, the other teachers and I are constantly realizing how knowing someone's color sheds a lot of light on why they do what they do. I think this would be beneficial to do with my students at the very beginning of the school year. I'd also love to do this as an activity with my fellow teachers. I'm going to be part of the professional development team at my school next year, but I'm not sure we will have time for this on our only in-service day before school starts.
If you're interested in learning more about this personality test, I found some great copies of the test and explanations of the meanings of the colors online. Let's just say there is a whole lot more to the colors than the one-word descriptors I wrote above!
As part of the workshop, each teacher received a new TI-84 Plus C Silver Edition Graphing Calculator. This is my first time to use a calculator that graphs in color. I like that you can choose what color to graph each line or set of data in. And, the adapter that allows you to plug it in to charge is also a nice feature. The menus and features are similar but not exactly the same as the TI-84s I already have in my classroom. However, it was suggested today that we update the operating system on all of our TI-84s. I definitely need to look into that this summer and get it done before school starts back up! I think the color and other added features may have slowed down the calculator a bit. I find myself sometimes getting impatient with the calculator because it doesn't graph things as quickly as I think it should.
One thing that was mentioned this week was that we need to force our students to choose their own window when graphing with the graphing calculator. Our students need to think. And, teaching them shortcuts such as Zoom Fit doesn't require them to think. Thinking should be our goal. I'm definitely guilty of this.
We've done several activities that involved collecting real-world data, creating a scatter plot on our graphing calculators, and using the linear regression feature to find a line of best fit. As a way to start learning everyone's names, we timed the teachers at the first table as they said their name and their color from the personality test. Then, we timed the teachers at the first and second table saying their name and color. This continued until we had made it all the way around the room. This gave us a set of data to enter in our graphing calculator. We used linear regression to find the line of best fit for our data. I think this would be a great way to review the concepts of slope and y-intercept with my Algebra 2 and Statistics students.
Participating in this activity makes me hope that the grant I wrote for a classroom set of various measurement tools gets funded. I really need stopwatches for my students to use! I'm going to have my Algebra 2 students start getting used to the graphing calculator from Day 1 next year. And, I will expose my Algebra 1 students to the graphing calculator next year to help them prepare for Common Core even though the graphing calculator will still not be allowed on next year's Algebra 1 EOI exam. If I don't start my Algebra 1 students now with the graphing calculator, I will be putting them at a disadvantage when they get to Algebra 2.
We also used stopwatches and our graphing calculators to complete the Bouncing Tennis Balls activity from NCTM Illuminations.
"Collaborative learning [group work] involves more than students sitting around a table and working on the same task."
If I'm going to use collaborative learning in my classroom, I need to establish norms. And, I need to hold my students accountable for maintaining those norms.
If a student is off-task, approach them with a question instead of a command. It's much more powerful to ask, "What do you need to get started today?" than to tell them to get to work.
Teachers must make thinking intentional.
As teachers, we are not the only people with knowledge in our classroom.
Our students need to experience constructive struggling. We read this article about constructive struggling, and it was eye-opening.
We typically give students easy problems that later build to harder problems. What if we started giving our students the hard problems first?
In a collaborative learning classroom, students should not ask the teacher for help unless they have already asked every single group member for help.
Don't ever take the pencil out of the hand of the student you are helping!
Students (and teachers) need to know that helping is not the same as telling.
If you want your students to be accountable, here are some rules you can implement: You can write only on your own paper. You can let people see your paper, but you cannot hand it over to somebody else.
Provide students with sentence starters to help students discuss their thinking together. (I need to make a poster of these to hang in my classroom!)
My Algebra 1 students really struggled with understanding function notation last year. Today, we did a great activity that links the concept of function notation to a family tree. This activity is taken from the October 1987 issue of the Mathematics Teacher. I found a link to a pdf copy of the activity online. Before I use this with my classes, I will definitely be retyping it and making sure that every single person in the family tree has a name that starts with a different letter of the alphabet. I love how this activity quickly moves students from reading function notation to finding the composition of two functions.
I'm hoping that my students will start to understand exactly what function notation is. f(x) does not mean f times x. And, I'm hoping this will help keep them from deciding that they must divide both sides by f in order to get x by itself.