The Big Picture
You can’t really get a picture of where you are going in a new city looking only at the zoomed in 30 feet of street that is shown on your phone’s navigation app. That’s handy and helpful, but almost everyone I know starts by zooming out and looking at the big picture. Where am I now and how does that relate to where I am going?
So time to zoom out a bit. Let understand a little about how the course is put together. I promise I’ll try to keep it brief, but I’ll give you places to look for more detail.
From Lecture to Problem Based Learning
For 20+ years a typical day in my classroom begin with going over homework questions, me “giving notes”, and then students working together in pairs or groups to practice the concepts and procedures I had just attempted to deposit in their heads. In my “giving notes” I made it a priority to make connections and help students really understand the mathematics. I tried hard to keep students engaged, asked them to discuss their thinking with their partners, and invited them to ask clarifying questions for the good of all. “No such thing as a stupid question” and “If you are wondering, so is someone else” were repeated again and again.
This was how school had looked when I was a student, and I did my best to replicate and improve on the experiences I had as a learner.
Attempts to venture into changing the way class was organized were difficult. Books were written to break things down into tiny separate procedures, and if I was going to make it through the curriculum, I needed to get through one of those procedures pretty much every day. My classroom structure was the most efficient way to get that done.
If you have been teaching very long, you know that not every student can gain complete understanding and fluency in a day. And so, every year, some kids would get left behind. Not because I didn’t believe “All Means All”. Not because I didn’t give every lunch and after school to support them. Just because the ideas were flying by so fast that it was hard to keep up.
Add to that those students that at 13 just can’t stay focused consistently on a math lecture for 20 to 30 minutes. The in and out of the natural attention span of an adolescent created gaps in understanding, missing connections, and fuzziness regarding procedures even if my explanations were flawless.
It felt like a trap. The only way we could “get through” the material was inadequate to actually have all students learn the material.
Until now.
This new curriculum from IM gives me hope that we can keep all of our students engaged. We can let our students’ understanding of the content deepen over time. We don’t have to leave any students behind. This curriculum is built differently, to allow it to be taught differently.
From this point on, I will be referencing the curriculum course guide. I strongly recommend you take the time to read it. I have only pulled out a small portion of the many parts that I think will really help you get a better view of the big picture
How IM is Built
Unlike the many text book series that I taught from, which were designed for lecture based classrooms, Illustrative Mathematics 6-8 curriculum is designed to support Problem Based Learning (PBL). The overarching idea of PBL is that students learn math by doing math. This curriculum was written to set teachers up to make that happen.
“In a problem-based curriculum, students work on carefully crafted and sequenced mathematics problems during most of the instructional time. Teachers help students understand the problems and guide discussions to be sure that the mathematical takeaways are clear to all.”
From the course guide
One of the pieces of the IM 6-8 curriculum that I am continually impressed with is how carefully crafted it actually is. Here are a few posts from the Illustrative Mathematics Blog that brought this idea home for me:
Warm Up Routines with a Purpose
Vocabulary Decisions
Respecting the Intellectual Work of the Grade
All together, the pieces of each unit tell a story, with each individual lesson bringing new dimensions of that story to the table. “The goal is to give students just enough background and tools to solve initial problems successfully, and then set them to increasingly sophisticated problems as their expertise increases.”**
From the course guide again
How IM is Taught
As a teacher new to problem based learning, the most common error is to focus on what students are doing (fold, cut, pass to the left) instead of what math students are learning. Each activity and lesson has a purpose, and students are supposed to land somewhere. As a teacher your job as you prepare is to understand the mathematical idea behind each part of the lesson, and make sure at the close that you bring those thoughts to the forefront.
“Not all mathematical knowledge can be discovered, so direct instruction is sometimes appropriate. On the other hand, some concepts and procedures follow from definitions and prior knowledge and students can, with appropriately constructed problems, see this for themselves.”
Once more from the course guide (might be worth a peek)
You are the essential piece to the puzzle, the one that makes sure the intended math is clear to all. If you are running out of time, it can never be this lesson close that you skip. However in that close, you don’t have to do all the talking.* Since the kids are working for much of the lesson, you have time to be listening. Be listening for those key learnings that you might draw out from students.**
If you are now hankering to get a peak at what a lesson might look like, guess what? The course guide is a good place to find that information. Time for you to break down and follow a link to the section of the course guide titled How To Use These Materials.
Patience
Because ideas deepen over time, one lesson does not start and end the teaching on a subject.
“The initial lesson in a unit is designed to activate prior knowledge and provide an easy entry to point to new concepts, so that students at different levels of both mathematical and English language proficiency can engage productively in the work. As the unit progresses, students are systematically introduced to representations, contexts, concepts, language and notation. As their learning progresses, they make connections between different representations and strategies, consolidating their conceptual understanding, and see and understand more efficient methods of solving problems, supporting the shift towards procedural fluency. The distributed practice problems give students ongoing practice, which also supports developing procedural proficiency.”
-From guess where? ( spoiler: the course guide!)
I am going to make a prediction here. You are going to worry at the end of a lesson that your students don’t seem as fluent in procedure as they did with your previous curriculum. Be patient. Remember how carefully crafted this work is and trust a little bit. Notice in the quote above the learning progression:
Activate prior knowledge – invites all students in
Introduce representations and contexts – essential for developing an understanding of the mathematics
Concepts – where I used to start if I did a great lesson
Language and notation – where I started if I was pressed for time
Connections and consolidation – the place where students can move to the most efficient method of solving problems
Procedural fluency – what we tend to focus on as the goal.
Being patient enough to let your students have all those stops along the way is the best way to help them learn in a way that lasts past a unit test.
This video by Dr Jo Boaler from Stanford University explains that further:
Concerns
According to one IM trainer, the two biggest concerns that teachers seem to have with the IM curriculum are
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The pacing seems really tight
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There is not enough skill practice built in
I am not going to say to you that pacing will be a breeze or that you won’t want to add extra practice activities from time to time. But I am going to say that both these problems are exacerbated by a lack of patience.
The pacing will definitely be tight if we over-teach. If we think the first time something is mentioned you have to teach everything there is about that subject, you will consistently run out of time. One way to help yourself trust the curriculum is to stay ahead in your planning. First look at the big ideas of each week in a unit, so you can see when things will come up again.***
The pacing will definitely be tight if we try to keep everything else we always have done and add Illustrative Math. This is a complete curriculum. You do not need to be scrambling to make warm-ups and find performance tasks. It’s all in there. Each and every lesson starts with a thoughtfully chosen warm up ready to use. Each and every unit ends with a culminating task that applies the mathematics. And because topics continue on throughout the chapter, going over homework time isn’t the only chance you have to revisit the previous lesson’s ideas. As an example, look at the development of major work of 6th grade:
And what about that “not enough skill practice” worry? Students do need to practice and apply skills. But if you look at the lesson progression above, where do you think it is appropriate to have the bulk of the skill practice? It won’t be on that first day. By spiraling the homework we allow students to get practice over time, as they move through consolidation and toward procedural fluency.****
Trust
We all have a lot of learning to do, but based on the experiences of the teachers who used the curriculum this year, we have a lot to be excited about. We are part of an amazing shift in math education. Finally all really can mean ALL.
Extra Resources:
- *One of my favorite ignite talks about learning to cede the role of sage on the stage:
The less I talk, the more they listen by Graham Fletcher
- ** A fabulous book for helping us learn to lead discussions for math learning is The Five Practices for Orchestrating Mathematical Discussions. Much of the learning from that book is baked into the IM 6-8 curriculum. A couple Illustrative Math blog posts on the topic are linked here:
How the 5 practices changed my teaching
The 5 practices framework- explicit planning vs explicit teaching
- *** Speaking of over-teaching, see this IM blog post on why teaching students to cross multiply is delayed in grades 6 and 7:
- ****A non-IM aside – if you do decide on a certain section that your students need more practice, there are a million wonderful resources for creative skill practice out there that can be just as effective as a 1-31 odd worksheet. Truth -sometimes they are just an old worksheet, just delivered in a more interactive way. Here is a post that lists some popular practice strategies and games.
- Much of what I am going to share in this post can be found in the Course Guide provided by IM for each grade level. If you are looking online, you can find it here:
If you purchased the print Teacher’s Edition that same Course Guide is the small darker green book that came in the package.
More Fertile Ground 