In my role, I have the advantage of seeing many great teachers honing and refining their craft, all to provide the best possible experiences for their students. The dedication and professionalism that the teachers I work with continue to demonstrate is what keeps me going in my role!
One particularly interesting benefit I have is when I can be part of the same lesson multiple times with different teachers. When I am part of the same lesson several times I have come to notice the differences in the small decisions we make. It is here in these small decisions that have the biggest impact on the learning in our classrooms. For instance, in any given lesson:
- Who gets the most talk time? You, all students, same few students…?
- How much think time do you give? When?
- Do you show first, or allow time for students to make sense on their own first?
- Do you start with contexts or visuals or questions or explanations?
- Do you allow your students to use technology or no technology (computers, calculators…?)
- Do you build the problem together, or provide pre-determined questions?
- Do you expect manipulatives to be used by all, encourage anyone who wants to use them, or offered only for those who you think need it?
- Do you discuss the learning goal at the onset, during the close, or never?
- How/ when is feedback given? (if at all)
- When a student is struggling, do you ask them questions that get them to think, or ask questions that lead them to the answer?
There are so many little decisions we make (linked above are posts discussing several of the decisions). However, I want to discuss a topic today that isn’t often thought about: Scaffolding.
For the past few months, the teachers / instructional coaches taking my Primary/Junior Mathematics additional qualifications course have been leading lessons. Each of the lessons follow the 3-part lesson format, are designed to help us “spatialize” the curriculum (allow all of us to experience the content in our curriculum via visuals / representations / manipulatives), and have a specific focus on the consolidation phase of the lesson (closing). After each lesson is completed I often lead the group in a discussion either about the content that we experienced together, or the decisions that the leader choose. Below is a brief description of the discussion we had after one particular lesson.
First of all, however, let me share with you a brief overview of how the lesson progressed:
- As a warm up we were asked to figure out how many unique ways you can arrange 4 cubes.
- We did a quick gallery walk around the room to see others’ constructed figures.
- We shared and discussed the possible unique ways and debated objects that might be rotations of other figures, and those that are reflections (take a look at the 8 figures below).
- The 3 pages of problems were given to all (see below). Everyone had time to work independently, but sharing happened naturally at our tables.
- The lesson close included discussions about how we tackled the problems. Strategies, frustrations, what we noticed about the images… were shared.
Here are the worksheets we were using so you can follow along with the learning (also available online Guide to Effective Instruction: Geometry 4-6, pages 191-212):
While the teacher leader made the decision to hand out all 9 problems (3 per sheet) at the same time, I think some teachers might make a different decision. Some might decide to take a more scaffolded approach. Think about it, which would you likely do:
- Hand out all 9 problems, move around the room and observe, offer focusing questions as needed, end in a lesson close; or
- Ask students to do problem 1, help those that need it, take up problem 1, ask students to do problem 2, help those that need it, take up problem 2…
This decision, while seemingly simple, tells our students a lot about your beliefs about how learning happens, and what you value.
So as a group of teachers we discussed the benefits and drawbacks of both approaches. Here are our thoughts:
The more scaffolded approach (option 2) is likely easier for us. We can control the class easier and make sure that all students are following along. Some felt like it might be easier for us to make sure that we didn’t miss any of our struggling students. However, many worried that this approach might inhibit those ready to move on, and frustrate those that can’t solve it quickly. Some felt like having everyone work at the same pace wasn’t respectful of the differences we have in our rooms.
On the other hand, some felt that handing out all 9 puzzles might be intimidating for a few students at first. However, others believed that observing and questioning students might be easier because there would be no time pressure. They felt like we could spend more time with students watching how they tackle the problems.
Personally, I think our discussion deals with some key pieces of our beliefs:
- Do we value struggle? Are we comfortable letting students productively keep trying?
- Are we considering what is best for us to manage things, or best for our students to learn (teacher-centered vs student-centered)?
- What is most helpful for those that struggle with a task? Lots of scaffolding, telling and showing? Or lots of time to think, then offer assistance if needed?
In reality, neither of these ways will likely actually happen though. Those who start off doing one problem at a time, will likely see disengagement and more behaviour problems because so many will be waiting. When this happens, the teacher will likely let everyone go at their own pace anyway.
Similarly, if the teacher starts off letting everyone go ahead at their own pace, they might come across several of the same issues and feel like they need to stop the class to discuss something.
While both groups will likely converge, the initial decision still matters a lot. Assuming the amount and types of scaffolding seems like the wrong move because there is no way to know how much scaffolding might be needed. So many teachers default by making sure they provide as much scaffolding as possible however, when we over-scaffold, we purposely attempt to remove any sense of struggle from our students, and when we do this, we remove our students’ need to think! When we start by allowing our students to think and explore, we are telling our students that their thoughts matter, that we believe they can think, that mathematics is about making sense of things, not following along!
So I leave you with a few thoughts:
- Do your students expect you to scaffold everything? Do they give up easily? How can we change this?
- When given an assignment do you quickly see a number of hands raise looking for help? Why is this? How can we change this?
- At what point do you offer any help? What does this “help” look like? Does it still allow your students opportunities to think and make sense of things?
When we scaffold everything, we might be helping them with today’s work, but we are robbing them of the opportunity of thinking. When we do this, we rob them of the enjoyment and beauty of mathematics itself!
Thinking Mathematically 