2017-09-25 Visual Multiplication of Fractions with Reducing

Recently, I was on a Sunday run when I received a compelling question I couldn’t wait to dive into. The question asked how would I teach the multiplication of fractions with reducing.

The teacher provided some background information to frame the situation. The students had been instructed on how multiply fractions and reduce. When the lessons were over, the students all showed they were competent in both skills on their formative assessments; however, when this teacher gave them a summative assessment, the shock of students’ performances afforded me this opportunity.

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To get started, I didn’t quite know if I understood what the teacher had tried to explain. Luckily the teacher shared images of the student work to shed some light on the situation. Being curious about the student work, without making any inferences was my first order of business.

Next, I thought if this was my student, what would I try with them, given where they are at?

The student’s work made me think a visual model might illuminate the concept, inferring from the student work might be one of the missing concepts.

If I’m going to a visual model, how might I represent this such as the student will tell me their #NoticeWonder statements?

The #NoticeWonder strategy is my go to when trying any learning experience with students. My mentor once said, “Never tell a student something they can tell you….” and creating opportunities for your students to tell you something about their learning is very powerful. I also created a video explanation of the visual strategy and an animation of the visual strategy that the students #NoticeWonder about.

Using the progressions for mathematics and comparing to the California frameworks, I wanted a visual representation that is both flexible and powerful that goes across multiple grade levels. Although, the use of the area model is a strategy students should be familiar with by the time they are done with second grade, the full power of this model may not be fully understood until much later. Utilizing it for how to decompose and multiply fractions seems a natural fit to build upon.

I am always curious when creating a lesson how it will go over with actual students, not just the idealized math lovers we all have hidden inside us. Presenting this lesson with some enthusiasm and, as Dave Burgess says, some sort of hook. I have a steak here that can be prepared so well, but when it’s cooked it gets ruined, so I’m thinking about how to hit that sweet spot of a juicy medium rare in terms of proper delivery. 

What are your thoughts? Would you try it with your students and let me know what changes you made to make it better?

Thanks for helping us all get better together.

2017-09-18 Published 1st Article

Near the end of July, I received a random email message from someone associated with Edutopia….I thought to myself that either this is one of my friends playing a practical joke on me or this email was sent to me by accident. The email asked if I would be willing to write an article on Visible Mathematics for the educational resource, and it wasn’t a hoax.

My reaction was skeptical at first, I had a hard time believing that the amazing resource of Edutopia would want something from me. You have to understand three major problems with this: 1) I am a physics, math, and technology nerd….writing is a huge challenge for me and I don’t think I write very well; 2) Like Dave Burgess says, being creative is hard work (it’s like being good at anything, it requires a lot of hard work); and 3) The article is going to be very public!

The challenge to overcome these huge obstacles was almost enough for me to choose not to pursue writing an article about mathematics. I have a fixed mindset regarding my writing, but I am working on it, so I tried to write the article.

In my first attempt, I wrote a narrative, with myself removed from center stage. Recreating a time when visuals in mathematics made an impact on students learning. I spent a week of writing, revising, and seeking feedback, before, I sent it to the kind folks at Edutopia. Their response was gentle, kind, but let me know that was not what quite the idea they wanted to capture. Although this type of feedback normally shuts me down, I am working on a growth mindset in my writing and I wanted to persevere.

In my second attempt, I focused on a personal story. In my story, I learned something so powerful I will never forget it and use it instructionally whenever I can. I won’t spoil your read of the article, but the learning was powerful and changed me as an educator. The second story flowed out and I was happy with it, so I tried one more time sending it back to the great folks at Edutopia.

Eureka! They were almost there, the tough job for them was on. The editors had to figure out how to display it, clean up my horrible grammar, and get it ready for publication. With ease the process seemed seamless as the folks at Edutopia put it all together.

The night before it was to be published, I felt like a kid on Christmas Eve, the anticipation was killing me.

When I woke up the next morning, I saw it was published, and I let out a squeal. I awoke my wife by jumping on the bed, singing, “Do you know what today is…” Well she didn’t appreciate that at all! After the morning fog wore off, she was very happy for me, and I learned my excitement could at least wait until the sun had risen.

I also find it amazing that writing is a process that shows us how unorganized our thinking is, and it always feels so good when a well written piece is produced. I am so so grateful for the experience and for the great folks at Edutopia for working with me, despite the number of revisions. As I continue my growth journey in my writing, this was a story that I am excited to tell. Happy Monday and have a week worth writing about!

2017-09-11 Coding a Newsletter Template

A journey from last year that I really enjoyed doing was creating a monthly newsletter that indicated the successes we were having as a district mathematically speaking. While I enjoyed creating the newsletter, I was never happy with the design, and always thinking about how I could make it better. Well I went from using pages to Google slide decks (because I love, love, love slides) and still ran into a similar issue…actually I think the Pages version was way better which makes it worse….well new journey this week, I am excited to be working with a teacher and their coding and design clubs, as I am going to pose as a customer to order a new newsletter and they are going to design it for me. I am going to “hire” them and they will design it for me.

I will give them a list of specs and a “budget” to work from, they are posing as a small startup company and this is one of their first jobs. I am super excited to see how this will go and I hope I get a sweet newsletter out of it too!

2017-09-04 Numberless Word Problems

There are two things that I learned about toward the end of last school year that got me so excited I couldn’t wait to try them, Numberless Word Problems was one of them. One of my #eduheroes, Brian Bushart (@bstockus on Twitter), created this idea some time ago, and I was just learning about them. So, I wanted to get a couple reps in ASAP, and I was able to get a couple of reps in before the end of the year, and it confirmed my initial excitement.

With this school underway, I want to jump in early and often to get everyone on board with this idea, exposing all students to this opportunity and making it an ever growing area of powerful learning. On this journey last year, I was able to modify this into a sequence of learning events, where we start with a #NoticeWonder activity that builds the Numberless Word Problem the students create. Since students create the word problem, whether or not there are numbers is there choice, and it is so interesting what they come up with. The students smash their questions together to make a new question, and then they answer their question (or switch with another group and answer theirs) four ways.

Once the students have shared their answers and we’re all on board with the questions and answers, we compare our information to the state standards example(s). Students are always surprised that their questions are much harder than the state examples and think the state question is easy. Compared to previous times when given the state question, they typically shut down because it’s “too hard,” I’d say this is an amazing outcome.

Anyway, it’s still a work in progress and I’m super excited about it. Thanks Brian for sharing and making us all a little better.