Backwards Learning?

Four years ago when I was beginning my first classroom teaching position, I was introduced to Understanding by Design by Grant Wiggins and Jay McTighe. The concept was completely new to me, and not something covered in my teaching courses (completed 8 years before this job), but pretty quickly began to make a lot of sense to me. Planning starting with standards, creating assessments, creating learning activities focused on those assessments, and always providing clear, specific learning targets has been one of the pillars of our instruction at this startup school, so I've been doing my best to keep this practice in the forefront while planning learning in my classroom.

Recently, I've been playing around with the idea of applying this format to the way students learn in my classroom. Getting students to manage and direct their own learning has been something I've always wanted to do, but I've been struggling with getting it to work in practice, especially with how to manage and assess student progress in a more open-ended environment. When I introduce this kind of activity to my students, they often joke that "Mr. Jon never teaches us anything". I would (and do) argue that it's much more difficult to plan activities where students have to form their own understanding than it is to just tell them how to do it. I also think (oh hell - I know) that classes where students explore are more engaging for them and for me, both in planning and delivery.

At the end of every year since I've started, I say to myself, "Ok Jon, you made some good progress this year. You've got some great resources put together; you designed some great activities, and some that need some work, but you know what that work is. All you've got to do so you're not working an extra 12 hours every weekend is stick with what you've done before! FOR THE LOVE OF GOD, don't change everything you do AGAIN! PLEASE!!!" But I haven't been able to make myself listen to myself yet.

So, here's what I'm thinking:

Start with the "test"

Start the unit with maybe a little intro about the standards, and some overall learning targets. Then provide the students with the "test" - a series of assessment questions that are basically the unit test I would normally give at the end of the unit. A student's job over the course of the unit is to 

• Figure out how to do the problems - What skills and understandings will they need to solve these problems? What resources will they use to learn those skills and gain those understandings?
• Explain (written, oral, presentation) the concepts they learned - What academic language do they need to put what they're doing into words?
• Produce their own (hopefully better) problems

Learning Activities (optional?)

For the "meat" of the unit, I'm thinking I just stick with what has gone before. Provide some structured learning activities that will help students build the skills and knowledge necessary to address the "test" problems. The idea is that knowing the kind of problems they're working towards, students will be able to make connections between the things they're doing in the activities and the overall objectives of the unit.

I'm playing around with the idea of making these activities optional. If a student wants to follow her own path (and has a good idea of how to do this), or wants to work on his final product (more about that later) after showing me he already knows how to do the problems, I think I'm fine with that. I need to think about how to manage this part a little bit more. I also don't want students to miss out on activities that work on collaboration and communication skills, so there will probably be a mix of optional activities and required activities.

The Product

Here, I'd like to start with a rubric. Our school uses a 1-4 standards-based grading scale.

1. Students showing an emerging level of understanding have difficulty approaching the task productively. They struggle to find and use effective strategies and resources.
2. Students showing an approaching level of understanding can usually answer the assessment problems, and similar problems, correctly with some guidance. They are in the process of finding effective strategies and resources to build their skills and knowledge. They are in the process of expressing their understanding using appropriate academic language and mathematical terminology.
3. Students showing a proficient level of understanding can consistently answer the assessment problems, and similar problems, correctly with occasional, limited guidance. They have found some effective strategies and resources and used them to build their skills and knowledge. They can consistently express their understanding using appropriate academic language and mathematical terminology, and use appropriate mathematical and technology tools to communicate their understanding. They are working on producing their own problems to address the targeted skills and knowledge.
4. Students showing an exemplary level of understanding can consistently answer the assessment problems, and similar problems, correctly and independently. They have found effective strategies and resources and used them efficiently to build their skills and knowledge. They can consistently express their understanding using appropriate academic language and mathematical terminology, and use appropriate mathematical and technology tools in creative, innovative ways to communicate their understanding. They can produce their own problems that address the targeted skills and knowledge.

So, what I'd like to see from students, at the very basic level, is the assessment problems solved correctly showing work. Further, students should be able to explain in appropriate language the reasoning shown in their work; this is especially important for my mostly ELL students. Top level students should be able to find some creative way to present their understanding to me, and perhaps to the rest of the class. A bonus would be for students to produce their own problems that would address the targeted standards; I've found that when students can pull this off, it gives them a really deep understanding of how math problems work, and helps them respond to them in the future.

Prove it!

There's no way around it: students, especially students on their way to the IB diploma program, have to be able to show their understanding in a formal testing environment. I'll wrap up the unit with a formal test, potentially including student-produced problems. Here, I'm playing around with the idea of letting students take the test when they're ready (or at least early if they're ready). After they've shown an ability to respond to unfamiliar questions, they can either move on or work on enrichment activities. This part really worries me: having a class (or five) full of students working on different things sounds like too much for me to manage right now.

Feedback please!

If anyone's reading this, I'd really appreciate some feedback. I have the feeling that someone out there has tried this kind of thing before; there might even be a name for it that I don't know. Anyone working on this kind of idea now? Is it stupid, unlikely to work, pedagogically inappropriate or wrong? Challenge me, question me, give me advice, point me at resources, etc. 

Thanks for reading.

Calgeomabra 2.0: This time it's personal

So I started this blog back in 2011 as an assignment for some courses I was taking in educational technology at MSU, and this is the first time I've touched it since my last post in 2012. All posts previous to this one were assignments.

I was a math tutor and technology director for a small tutoring company in the states, trying unsuccessfully to get into international teaching, and considering different career paths. Out of the blue, I stumbled into a last-minute position teaching math in a start-up school in China, and I've been here ever since.

The last 3+ years have been incredibly challenging, engaging, frustrating, eye-opening. I was teaching in a classroom for the first time since my student teaching 8 years before; I was the only math teacher for grades 6 and up; I was teaching in a brand new school with no defined curriculum; I was teaching mostly English language learners; I was learning about standards-based assessment, grading, and reporting (which I'd never even heard about before); I was learning about the IB program for the first time.

Needless to say, the last few years have been pretty busy, but here's a little bit about where I am now:

• I'm teaching math to students in grades 7-11: Math 7, Integrated Math 1-3, IB HL/SL year 1. This year, I'm back to teaching in sequence; in the previous two years, one of the classes has been covered by the other math teacher. I like this, because I've been building our curriculum since we started, and it finally feels like it's coming together. 
• I'm kind of steeped in the CCSSM from the experience of putting together this curriculum. I use resources from Engage New York, the Mathematics Vision Project, Illustrative Mathematics, New Jersey Center for Teaching and Learning, Dan Meyer and crew, etc.
• The vast majority of my professional development time and energy over the last few years has been in the area of EAL instruction, and this summer I completed coursework for a certificate in EAL instruction in the mainstream classroom. For math instruction, this means I spend a great deal of effort teaching math as a language and the language of math.
• I've also been spending a great deal of time preparing to teach IB mathematics. I'm currently teaching my first cohort in their first year; my class is standard and higher level math combined.
• Technology is extremely important to my instruction. Our school has a 1-1 laptop program, and I've been working on utilizing this resource effectively since the beginning. 

It's actually the last point that inspired me to start this blog up again. A couple of months ago I learned about Desmos classroom at a weekend workshop. This led me to start playing around with the idea of a paperless classroom, which I just hadn't been able to pull off yet. In the course of this exploration, I stumbled across GeoGebra groups, and felt like I'd found the answer.

For the past month, I've been teaching a majority of my classes through GGB groups, with consistent use of Desmos classroom activities, and it's really changed how I feel about designing learning activities and teaching in general. I'll get into more of that later; for now, I just wanted to get this post out to separate what comes after it from what comes before, and to give anyone who reads future posts a little context. I'm expecting future posts to focus on this journey into paperless instruction, but who knows? Something in me just feels like recording and sharing right now.

Thanks for reading, and stay tuned!