Day 3 - Big Ideas - How big is "too big"??

I facilitated my group discussion today, the article was the big idea article, by Randall Charles, it was a long article, 16 pages, and we only had to read the first four pages, because the rest of the article was examples of big ideas, and our instructor didn't like that, because when we are given big ideas on a silver platter, we have a tendency to make our thinking fit into it, whereas if we develop the big ideas on our own, it is more meaningful and we internalize it.

The article itself, I found it very dry and boring and very heavy in the theory. I told my group this at the very beginning. And it was nice to have my hunches confirmed when our instructor said today was the most "challenging" day, it terms of content, which to me is a euphemism for "dry and boring", however, dry and boring doesn't mean unimportant.

I started off the discussion by communicating my background knowledge of the topic, I first heard the concept of the big idea, when I was in teacher's college, about 8 years ago. It was in a science class (which was my teachable), and I remember the instructor talking about the new science curriculum and "big ideas". I mentioned how the science and social studies have the big ideas right in the curriculum documents much like they were laid out in Mr. Charles' document, but nothing like that exists for math, as the curriculum is due for a revamp. So the challenge is for teachers to come up with the big ideas on their own, and as the article states, there is no consensus on the big ideas.

I also brought up the question to my group, how big is too big for a big idea, because the article mentions that if an idea is too big, its usefulness diminishes. Our instructor said an idea is too big if it covers all the content strands. However, a big idea can be too small if it is restricted within a strand, as the article says that articulating big ideas by content strands is not necessary, and the ideas are "big" because they connect several strands.

The main thing to understand is the big ideas are all about connections. The article even references Hibert & Carpenter saying "the degree of understanding is determined by the number and strength of the connections". In our group discussion, it was mentioned that it's hard to make these connections and model them for your students, when your content knowledge isn't deep. This would apply to teachers teaching the course for the first time. However, it becomes easier to do this once you teach the course several times.

The topic of split/classes came up during our discussion, I never planned for this to happen, it just came up which is pretty cool, and that was my big "aha" moment which I shared with the class (as a facilitator I was obligated to report our groups "findings"). I mentioned how in split classes, or even spec ed classes which have split levels within the class, language is pretty straightforward for teachers to program for, whereas math requires them to go to the different curriculums and teach them separately, or at least that was the direction I was given by the MART (methods and resource teacher, or head spec ed teacher) at the school I recently taught at (and she is really experienced).

However, if you were to teach spec ed and split classes math from the lens of the "big ideas", it would be more palatable to teachers from a programming perspective similar to how language is. The challenge is coming up with those big ideas- we did that as a class today, and it took some time, and was great to do it in a group. In a school, that might prove to be a challenge, as it would require all teachers in a grade team to meet on their own time, unless their school provides specific release time (which requires an economic cost in terms of supply teachers).

I did mention to my group that at my school, the grade teams were released during assemblies to give them opportunities to meet and plan (and no release time/supply teachers required!). But not every school does things that way. If it's not realistic to expect teachers to meet each other on their own time after school, when many of them have family obligations, which begs the question, "how can we facilitate opportunities for teachers to meet together and collaborate on big ideas??" Even in this mathematics course, we have allotted time to work on group assignments, because even our instructor does not expect us to meet each other on our own time after class is done to work on assignments.

Finally, the topic of assessment came up, just like it did yesterday, and even though we have a separate day coming up just for assessment, I would like to reflect on my big aha moments here, because that's what help me learn effectively

During our discussion, one of my group members mentioned that her principal told her not to sweat over covering all the specific expectations, and just assess/teach based on the overall expectations. This idea was confirmed by our instructor who said we look at the curriculum through the lens of a big idea, our job is not to go down the specific expectations like a checklist, which is what your traditional test do, as they focus on specific expectations. Our job is to make connections between expectations and assess overall expectations. And the article mentions big ideas, which are all about connections, so there is a text to world connection for you! (text = article, world = something our instructor said).

A couple of other "nuggets" I would like to share:

Instead of telling students "show me your work so I can give you partial marks" ask them to "show your thinking so I know what question to ask to get back your thinking"

To answer the question "Why do I need to know this?", math doesn't have many real-life applications, so purpose of learning mathematics is to grow your brain, expand your thinking, I'm going to make a text-world connection here, that idea is from our instructor and it reminds of an idea I read in a book many years ago (I forgot the name of book and author, but I remember the idea) which is "mathematics is like weightlifting for your brain".

Research shows learning is done through osmosis, so if you can get 20% of the students to understand something the rest will understand by osmosis, so in the classroom, you can have chart paper all over the walls and have students write their thinking on the chart paper, so other students seated at the tables can see the thinking.