For the first time this year, I employed my idea of an Overview Day. We are about to begin our first unit on Derivatives, so I wrote the words “Derivative” and “Differentiation” on the board with a circle around it. It was their job to research these terms, and add any important words, phrases, formulas, or pictures to the board. When they finished, we had a very nice summary of the entire chapter that THEY created! I went through and explained how each part was relevant to derivatives, and how they would be used. This way, when they see these words, phrases, etc., again, it will reinforce today’s discussion. Here are the results of their research:

A lot of good and accurate work is shown here, even if the students don’t quite understand the meaning of it all. I really like one student’s cross-curricular humor in including a “cellular differentiation” diagram as well as the “derivatives” of Proto-Indo-European languages. And in case you’re wondering, yes, “snap, crackle and pop” are actually terms, albeit facetious ones, used by physicists in their discussions of derivatives.

This is another group’s results. Lots of good research on this one as well. The discussion with this group was more interactive, which you can’t really see, but it’s worth mentioning. I really like the creature that looks like an earless horse.

This class is my smallest class, which explains why there are fewer contributions. They still get the main idea though, and one student even added a joke, which I’ve seen before, but now it makes sense to him.

All in all, I would count today a success, and I will definitely be doing this again. Getting students to seek answers themselves instead of waiting for a lecture should be a life skill that we teach them anyway. I can’t wait to see how this impacts the level of understanding as we progress through the chapter!

It’s Sunday morning, and my younger son is awake and wants to watch his favorite cartoon. I’ve already recorded all of the episodes and can ask him which one he wants. I can then start playing it, and even skip through the first thirty seconds of commercials so that it starts at the beginning of that catchy theme song.

This method of watching TV is not unfamiliar to many of us, but we can all remember a time when we could only watch a TV show when it was on, during a designated time slot, on a specific channel, and hopefully with a functional “rabbit-ears” antenna. (Some of you can go back to an even earlier time, but I don’t want to extend this part of the analogy too far before I make my point.)

Before we were teachers, we were all students, and I’m sure we can all instantly create a “back when I was in school” story. Oh, the menial tasks we were required to do. And my mind naturally drifts to math class. We had to calculate square roots, copy notes from an overhead, solve systems of equations, find inverses of three-by-three matrices – all by hand. (Our calculators only had four functions and one memory slot.)

We can certainly tell our students these stories, but only to the point where they understand what we are saying, like a narrative from a historical figure. But we can’t expect these same students to fully appreciate the experience of carrying out these tasks. And why should we? We have calculators, websites, and tablet apps that take care of all of this for us.

So should we stop teaching these skills altogether? No. Should we only direct students to the appropriate sites and apps to carry out these tasks? No. The key is balance. While it’s important to be able to solve certain problems quickly, using a calculator or other device, it is also important to understand what that device is doing, and what the end result actually means in terms of the original problem.

Let’s start with simplifying radicals, only because that concept was brought up to me this week. I propose that the concept should be taught by hand at first, so that students understand why the original radical and its simplified form are actually equal. After some practice, we can show how to perform the same task with a calculator. The question many teachers ask is, when would they ever need to do this by hand after they know how to use a calculator? The answer – variables. You can always create an “unsimplified” radical with variables, in which case the calculator is practically useless, and the old skills must be used.

Variables appear in the real world more often than we think. Sometimes we don’t have all of the information, and we need to find a temporary solution that we hold onto until the required information becomes available. Sometimes we want to create a rule, or formula, that we can use over and over, with different sets of given information. They can appear in almost every type of problem, including the radicals, systems, and matrices I mentioned earlier.

So let’s balance the old and the new. Do things by hand for appreciation, and in preparation for situations where the calculator can’t help. But don’t abandon the calculator because it “does the work for us.”

Times and technology are changing, and we need to embrace those changes. And on the other side, we also need to help students understand how technology works so they can decide when it is or isn’t helpful. There are times when we can choose technology to get us to the answer faster, but sometimes we just have to go “old school.”

To get back to my original story: While I’ve been writing this, I’ve had to help my son by skipping through commercials, and getting him to different episodes of the same show, all by clicking a few buttons. But I can’t help but think of the day when I will take him to the movie theater for the first time, simply to appreciate the experience. None of the technology we have will allow us to simplify that situation. The movie will start at a certain time in a certain room. It will only play once, and we will not be able to pause or rewind or start over. The lines will be long, the popcorn will be chewy, and the soda will be flat. And we’ll have to sit through all of the previews before the movie actually begins – just like it was back in my day.

This will be my third year using the Flipped Classroom model, and I finally feel like I’m getting into a groove. If new videos need to be made, it’s easily done – recording, editing, posting – all in a short amount of time. The in-class discussions are more natural, and the relationships are getting stronger quicker.

And the proof is in the proverbial pudding. The scores on the IB math tests were higher than ever! Almost a 90% pass rate overall! And throughout the year, I read incredible essays and explorations, and had many impromptu deep mathematical discussions with several students.

All of this makes me excited for this year. Just like last year, there are things I am going to keep, and things I am going to remove from my day-to-day activities.

THINGS I WON’T CHANGE

• Room Layout – This has been so successful, even moreso this year – the groupings, the seemingly absent teacher desk, the empty walls at the beginning. To make things better, my class sizes have gone down to a maximum of 21, so I can move some of my tables and chairs into the hall as workstations for those who need to get caught up on videos or other work.

• Raw Hundo Club – The kids still love this! Sure, it leads to a competitive environment, somewhat, and sure it goes against my philosophy that “perfection is not a reasonable goal,” but there’s just something about seeing their faces mounted on a wall that gives kids a sense of confidence.

• Overview Day – This was very successful, and I think it fits very well with our campus’s Understanding by Design pedagogy. It gives me a chance to talk about each unit in a very general sense so that students can see why we are studying it, and how it fits into the concepts they studied before and the ones they will study after. They can ask very broad questions and I can teach the concept by itself without getting into the mechanics at all.

• Recap at the Start of Class – This is a great opportunity to address questions that students had after watching the video from the night before, especially if a lot of them had the same questions. It creates immediate focus because everyone who watched the video now knows what everyone is talking about.

• iTunes U – There are so many websites on which to post videos, and many of them are more customizable than iTunes U, and more versatile. But then there are district and campus restrictions. Our campus decided that all content would be posted to a Blackboard site or an iTunes U, and those were the only two options. I have tried voicing my opinion, especially after spending three years creating a fantastic Google Site, but to no avail. And my stuff was copied to iTunes U last year, so at least I don’t have to start from scratch. Don’t get me wrong, I love iTunes U, especially after their most recent update. I was just hoping to give the students more options as far as watching the videos in a format that they liked. So I do have my videos posted on YouTube and CrazyForEducation, and I will continue to do so, but only as a secondary resource for students who can’t access iTunes U.

THINGS I WILL ADD

• Worksheets as Practice – I know last year I said no worksheets. But then later I posted that I had changed my mind, and worksheets as an end goal was meaningless, but if it led up to something, then it would be valuable. The point is that while everyone needs a minimum amount of practice in order for a concept or process to be internalized, some people need more than that. So worksheet will be viewed as ungraded practice that I will monitor, and when students feel they have had enough practice, I will offer them two or three questions at a higher level. If they master them, then they have finished for the day. If not, they can keep practicing until they want to try again.

• Flexible Assessment – I will have two test days. If students are ready on the first day, they can take the test as normal. If they are not ready, they can take the test on the retest day and receive a maximum of 90%, just like the retesters would get. Alternatively, as I know that some students are not good test takers, I will give them the opportunity to come up with an alternate assessment – a report, a project, etc. – and the rubric with which it will be graded, both of which will have to meet with my approval. I don’t foresee a lot of students exercising this option, since it is a lot more work, but I’d be curious to see the ideas they have.

My theme this year is not just “learner-centered,” but “learner-driven.” The students will lead and contribute to discussions, and they will take responsibility for their own learning. Even though I am there as a support when they need me, I will encourage them to use me less and less, so that their success is truly their own.