classroom structure discourse

Math Class Starters

I am very distractible. Students know this; I know this. For this and multiple other reasons (including insipid tardiness on the part of my students) the first few minutes of class is often filled with retrieving forgotten textbooks, quieting down the pockets of flirtation, and acknowledging the students who show up two minutes late with a coffee. 

Numerous factors have led me to the institution of class starters for grade 9s. I will do my best to summarize them here and introduce my framework, theory, and pedagogy behind them. 

Why Starters? (The multiple influences)

classroom structure reflection

“__BL” : Education’s Obsession With Labels


Last week there was an interesting twitter discussion on the nature of projects versus the nature of problems.

@dandersod@samjshah@k8nowak@leslie_su76 How is Mega M&M a project rather than a problem?
— Dan Meyer (@ddmeyer) July 17, 2014
It occurred with specific reference between the differences of PBL (project-based learning) and PrBL (problem-based learning). If you follow this blog or scan the provided tags you will find PBL does occupy some space here. There is also a large amount of posts detailing “tasks”. This is a rather artificial term I use to refer to a piece of mathematical work to be done or undertaken.
classroom structure investigation pattern problem posing

Problem Posing with Pills

My class always welcomes conjectures. This is made explicit on the very first day of the semester. This goes for everything from grade nine to grade twelve. As the grades advance, the topics have us venturing into increasingly abstract concepts, but conjectures are always honoured. 

Certain class structures promote conjecturing more than others. Students offer questions during lectures, but they are often of a surface variety. They notice a pattern that has occurred in three straight examples, or think they have discovered a short-cut. I don’t like using tricks, but if they are “discovered” or “re-invented” (to borrow a term from Piaget and genetic epistemology), then we use them. 

classroom structure discourse tasks whiteboards

Creating Communities of Discourse: Large Whiteboards

I have talked about individual whiteboards on this blog before. My school bought me supplies and I was loving the various classroom activities. While the grouping questions facilitated good mathematical talk between peers, I was still searching for a method to encourage more collegiality where my role could diminish to interested onlooker or curious participant. 

So I had this brilliant idea. 
Why don’t we get group-sized whiteboards created where students could work collaboratively on tasks?
area classroom structure estimation probability stations volume

Stations in High School Math

One of the coolest experiences in my university training was the opportunity to invite a kindergarten class into our mathematics methods class for a mathematical field trip. Our class was divided into groups of three or four and were given the task of designing a mathematical activity that the students would try. The afternoon was a hit. Each group set up shop around the room and the kids freely moved from station to station as they mastered each activity. 

Somewhere along the way, mathematics becomes formalized and stationary. I imagine it is around the time of fractions. I assume this for no better reason than teachers and students alike seem to blame most of their problems on fractions. That is until Grade 10, when polynomial factoring squeezes out fractions as the most hated mathematical procedure.

classroom structure flipped classroom Khan Academy numeracy

Becoming “Unflippable”

This post contains no real lesson or task ideas. That is a rarity for me, but every so often a philosophical battle ignites in my brain. More often than not, the question does not come from an established professional development vessel. Our division provides numerous officially sanctioned “PD” events throughout the year. They serve their purpose, but rarely motivate like those questions that come from within–or, in this case, from a student.

Every teacher is familiar with the following conversation:

Teacher: Can you please pay attention?
Student: I was paying attention.
Teacher: No you weren’t. Please put your _____ away.
Student: I was so–I have all the notes.
assessment classroom structure formative assessment whiteboards

My Whiteboarding Framework

This year my department decided to make using whiteboards as formative assessment tools our department focus. This was nice because I had already began to experiment with the process. It just meant that:

  1. I wasn’t obligated to try yet another “thing” in my room.
  2. I would be given better materials and funding to work with.
  3. Other math teachers in my building would see the enormous benefits of the technique.
classroom structure PBL surface area tasks volume

Project Work Scaffold

There are two schools of thought when it comes to PBL:

  1. Start with a large-scale project and fit the specific outcomes within it, or
  2. Build toward a larger project with smaller tasks.
I love the idea of large projects, but also aim to make my work as accessible as possible for those who want to take it and improve on it. I just don’t see option one working within my traditional classroom of 35 students for one hour a day. The existence of an overarching curriculum only further decreases its accessibility.
classroom structure scale tasks unit analysis whiteboards

Gummy Bear Revisited

The giant gummy bear problem has been floating around the blogosphere for a while. When I first saw it, I knew I wanted to use it. I finally have the perfect opportunity in Foundations of Mathematics 20 this year. (Saskatchewan Curriculum).
History of the Problem (As far as I know)
  • Originally presented by Dan Anderson here. Included original Vat19 video and driving question about scale.
  • Adapted by John Scammell here. Edited video and new driving question.
  • Dan Meyer provided a 3Act framework for the problem here.
  • Blair Miller adapted his own 3Act structure here.
My apologies go out to anyone else who played with or re-posted an original interpretation on the problem.
classroom structure PBL projects reflection

Creating PBL 3.0

I have been on my project-based learning journey for a while now. This blog has served as the main receptacle for my inspirations, ideas, successes, failures, and reflections. It is now time to document my next step: wide scale revision.

This post will be divided into two main sections:

  1. A look back at the posts that brought me to this point. (Reading them may provide some context, but not reading them will provide you with more free time…your call)
  2. A look ahead into my revisions and their rationale. I will describe the new administrative and assessment framework around the projects and provide links to the first completed framework online.