Mission Accomplished

As I publish this reflection, I fear that this moment may turn into something along the lines of another famous moment….


I am very honored to have met #IRL (in real life) the person that inspired this learning goal for me this school year: Having students produce a weekly learnings podcast for public consumption. Joe Young is an incredible TOSA for math and education and he shared this idea a long time ago, and when I had the pleasure of teaching two courses this year, I wanted to challenge myself and use this as one way students would show what they know.

Finally, this week, I found the magic recipe to making this happen, I assigned two students, one in each class to get the job done. Friday marked the turning point for me in doing some of the things I wanted to get done and continue to build on. Friday was also our first Mystery Skype with another group of students. While the connections prevented less opportunities for conversation, it was an entertaining and fun sort of thing.

While doing the Mystery Skype, we also produced our weekly podcasts for both classes. I loved the idea of having students interact with other students around mathematics and this public display showed a proof of concept.

All in all, I was very excited to have been able to edit, publish, upload, host, and publish to iTunes. I am currently waiting on a review of my two podcasts to be approved, and if that works they’ll be in iTunes. The Mystery Skype provided the opportunities for students to strategize their thinking and be able to try to problem solve.

The podcasts are linked:  Math 8    &/or     IM3

Well looking forward to another great week. Hope your week is as magical and moving you forward to meet your new goals.

Technology Enhanced in Math Lesson

What an exciting time to be a teacher, a student, and a learner!

I have a tentative understanding, at best, of human nature, but I do believe that most people find change uncomfortable and difficult to deal with both emotionally and intellectually. I am not immune to these feelings, but I like change. I like to embrace the unknown, I thrive off of dreaming about the possibilities that could be.

One of the most exciting things about the change of standards to the Common Core State Standards in Mathematics is the depth to which students are expecting to dive in their understanding. With this in mind, the fun of being a teacher is to create learning opportunities that facilitate students’ thinking and facilitate opportunities to dive deeper in their thinking.

The original idea for this lesson is hard to nail down, but I do know a large part of it came from the wonderful book Fostering Algebraic Thinking. The results are shown below:

I tried the lesson with sixth and seventh graders, and the biggest thing I realized is that there is a bunch of background knowledge with respect to the technology that students need to be familiar with to take advantage of the lesson. On the other hand, this seems like a natural way to introduce the use of technology in a lesson which has its own advantages.

What would you do differently? What would make this lesson better?

Not ODEs – The Variation of Parameters Method

VersatilityWhen one attempts to define versatile, something like “able to be adapted to many functions or activities” may come to mind. As a classroom teacher (and now working K12) this idea comes even more naturally as I know have the opportunity to see how successful and adaptable an idea or lesson may be with learners of various levels and ages.

Recently, I had such an opportunity to try marry a couple of ideas I have brewing in the back of my mind with four classes, two 6th grade classes and two 8th grade classes. The original idea stems from two separate sources a random search and from Mark Driscoll’s amazing book Fostering Algebraic Thinking in which the heart of the lesson follows. The other idea is my love of working a 3 Act lesson into anything that I can teach. So I will discuss both lessons and what I learned in what follows, but I’ll first set the stage for the lessons.

This year, I have had the pleasure of working a lot in the sixth grade, a grade I felt comfortable with my background (as I have described before) doesn’t lend itself naturally to the younger learners. I am working on getting some practice with many folks favorite age group, the infamous eighth graders. So I had this opportunity lineup, within a day of each other, I had the time to teach the 6th graders on an introduction on Equations and Expressions, and an introduction for the 8th graders on slope.

Enter my normal teacher brain, whose thoughts in no particular order went something like this: 1. I don’t have much time to prepare two very different lessons, and make them meaningful, 2. Students need hands on connection, an anchor, that we will be able to refer to throughout the unit,Teacher Brain

3. Students like to build things and I like to facilitate through questions and setup versus talking to myself in a lecture format, 4. Using 3 Act format gets a lot of buy in early, prompts students’ thinking in the direction I need, and makes for a natural direction to move forward, 5. What do I have around me that would allow me to use the same format, but change the questions (or purpose) of the lesson with the same manipulatives?….

Enter the work setup by Driscoll, he posed a Matchstick problem that extends, this would work perfectly, and the dollar store has popsicles by the hundreds for, well….

My manipulatives clearly in hand, my thinking went to the idea that I wanted the sixth graders to build the triangles, as shown in the video, counting the number of triangles formed and relating that to the number of sticks required to make the triangles. There is a natural differentiation here too, advanced learners may recognize that there are more triangles depending on how they build their triangles together. The relationships that start to form here, are well beyond the scope of this lesson, but what a great learning experience for those kids ready to go beyond. As the students build the triangles, they record the data, and then the extension question(s) go like: 1. How many sticks would we need if we were building 100, 1000, or 1,000,000 triangles? 2. How many triangles could we build if we have 100, 1000, or 1,000,000 sticks?

Good ThingsThe math nerd in me love these questions because it extends to the idea and in light of actually building it, this is a natural way for me to introduce the idea of generalizing, enter expressions and equations. In addition, this also shows the doing and undoing process of the relationship between the number of triangles and the number of sticks, an important piece that we sometime overlook.

Using a similar idea in eighth grade, the idea there was to tackle the misconception that these learners had in regards to scaling, the idea that the ratio of two similar triangles is the same though the lengths of the respective sides may be much different. The learning that I wanted the students to see was that as they build the right triangles, make measurements (by counting sticks) and comparing the ratios of “rise” to “run” they would discover that the ratio was the same. I was expecting some errors, like how the students build and counted the right triangles, which I was hoping would be a great “teachable moment.” Students would get a lot of collaboration and would work with a small data set of 9 other ratios calculated from other student groups, reinforcing their understanding.

What was used is shared is here.

What I learned through this experience is the importance of modeling and being very clear with what was required of the learners. After reflecting on these lessons for a while, and thanks to invaluable input from #MTBoS and #mathchat folks, the lessons need some tweaks here and there. Specifically, the amount of scaffolding and teacher direction are not calibrated for optimum performance. Having giving them a test run, I like the core ideas and I think the experience was very valid, but I know some major revamping I will be doing for next year.

What did go well was the conversation and engagement when students were actually building and working with the manipulatives. I am forever amazed that something as simple as small, wooden sticks could get even the most ardent stalwart working through the lesson. The classroom was buzzing, that’s the moment I love to hear, kids actively involved with their learning. I will update this and other thoughts as I move forward, getting back to blogging and catching up has been a hard road to toll.

Happy Mathing!