“Students talk about being rushed through content…And I know this isn’t the fault of their teachers. Teachers often feel that they have to rush through content, either because they have a pacing guide telling them to…or because there’s so much content in the curriculum…I wish I could reduce the content in the curriculum or reduce the content in books, look at these US textbooks compared to textbooks from Japan. In the US, we teach everything every year. For example, students learn fractions in grades 3, 4, 5, 6, 7, 8, and 9. We repeat content every year. In successful countries they don’t do that. They teach a few things in depth. And they take students through a lot less content in the school year.
One thing I’ve seen in many successful schools in the US is teachers who don’t try and teach all the content in the common core or other curriculum. Instead, they work out, what are the big ideas in the year and teach those with more open and rich problems. Usually, the smaller ideas and methods get covered. And if they don’t, they’re probably not that important. Schools that do this, even if they don’t teach all the content, end up with higher test scores…
The problem I have with any set of curriculum standards is this: mathematics as a subject is made up of relatively few ideas, but a rich set of connections between them. And that’s part of its beauty, the connections that thread through all of the ideas. What standards do is they take that lovely connected subject and they cut it into tiny pieces. So teachers and students no longer see the connections. It’s very hard for teachers to help students see maths as a connected subject, when they’re given 200 small pieces to teach…It’s a lot of work at first to take time to work out the big ideas and the rich problems it teaches them, but it really pays off in the long run.” (Jo Boaler, Education: XEDUC215N Mathematical Mindsets)
When creating a concept checklist for the course we’re teaching, the quote above represents one of the most important ideas to keep in mind. We have to be careful with the standards we choose and seek to mainly include the most important, big ideas from the course. With that said, it’s important to make a distinction here. A checklist represents all the standards that will be formally assessed/tested. It does not represent every concept or skill that will be taught. It’s perfectly fine to teach many more concepts than what’s on the checklist. However, we should only test the big idea concepts and make sure to dive deep into those concepts. The other standards can be focused on with less depth and sometimes be left out if there isn’t enough time.
We’re about to get a look at parameters I used to create a Geometry checklist this school year. However, here are some general notes before getting started.
- Again, only pick the most important concepts from the course to assess. 20-22 concepts may be a good range to shoot for.
- The first draft will change (probably many times). After teaching the course for a year or more (or teaching other courses as well), you’ll be able to better recognize what concepts are most important. For example, I’d go back and tweak my Algebra 1 checklist now that I’ve taught Geometry and know where the kids need to go.
- “This skill shouldn’t be so small (e.g. “Adding Numbers”) that you’ll be tracking ten such concepts on a week but not so big (e.g. “Factoring”) that you can’t tell how to remediate a low grade.” (Dan Meyer)
- An example from Geometry…Instead of putting “Transformations” as one of the listed concepts, I put “translations, reflections, rotations, dilations, and compositions of transformations” as individual concepts. Transformations is such a big concept that it’s hard to know exactly what a student needs to work on if they have a low transformations grade. In my opinion, this is an appropriate time to breakdown the concept into smaller pieces.
- An example from Algebra 1…instead of putting “Linear Equations” as one of the concepts, I assess calculating slope (this includes all representations i.e. from a line, table, two points), writing equations in slope-intercept form, graphing slope-intercept form, and point-slope form. However, I don’t list a standard for writing an equation of each representation because that begins to create too many skills on the list.
- Overall, it’s a challenging process that takes many attempts to find the balance line. It’s worth it in the end though.
How It Went This Year
Look at State Standards
The checklist creation process began by looking at the TEKS (Texas Standards) for Geometry. In our state, the standards are broken down into 2 categories, “Readiness” and “Supporting” standards. The readiness standards are considered the most important, and if there is a state test for a content area, the readiness standards will be the most heavily tested. So, when beginning to create a checklist, I tried to analyze all the readiness standards first. After that, I only added a supporting standard to the checklist if it really seemed important at some point during the year (more on that in the sections below). Here’s a screen shot of some of our Geometry TEKS (taken from lead4ward).
However, looking at the standards alone wasn’t enough to complete a final checklist. I needed extra help because I didn’t have enough familiarity with Geometry yet (this was my first year teaching the course). Therefore, other sources needed to be pulled from…
Work Through A Textbook
The next step in the process was actually working through the textbook our district uses. Textbooks probably aren’t something to design a whole curriculum through, but they can provide a nice safety blanket to check to make sure we’ve dotted all our i’s and t’s. So, I worked through every chapter of the book to see how it outlined the course and also to get a feel for what the students would be experiencing. I wanted to see just how much was being recommended to be taught and how connected or disconnected it felt. In addition, I tried to determine what concepts seemed to be most heavily emphasized, and I added or subtracted concepts to the checklist based on this.
Compare State Standards to Common Core (or Other Standards)
After working through the textbook, I was confident in many parts of the checklist, but other listed concepts were toss ups. Therefore, those concepts were highlighted so that they could be re-investigated as the school year progressed. What does this have to do with comparing to Common Core or other state standards? For some of the toss up concepts, they were listed in the TEKS but not in the Common Core. So, this was an indicator that there may be disagreement as to the importance of the topic. This was helpful to eliminate some concepts from the list because they already felt a little shaky.
Talk to Other Teachers From Different Content Areas
This was a very important part of the process because my vision needed to be expanded past Geometry. I don’t have experience with teaching subjects beyond Geometry, so I needed help and wisdom from teachers who do. In particular, I wanted to know what concepts in Geometry are foundational for understanding concepts in the higher grades. This actually led to the inclusion of “equations of circles” on the concept list even though it was only a supporting standard in the TEKS. A Pre-Cal teacher helped me to see that, in Texas, Geometry is the only place they’ll see the concept before getting to Pre-Cal. She believed it was really important for her students as well.
Here’s another example from the year…Our book focused a lot on a topic called, “Points of Concurrency,” and there seemed to be a lot of minor skills that didn’t feel relevant for the rest of the course. So, I highlighted it on the checklist as something to investigate when the school year approached that topic. When the time to teach the concept approached, my colleagues determined that Points of Concurrency wasn’t explicitly in our standards, and the topic would not be seen in higher levels of math. Therefore, the concept could be taken off the checklist.
Analyze Amount of Standards Within Grading Periods
Another helpful strategy for determining the final cuts to the list was analyzing how many concepts on the list landed in each grading period. We have 4 nine week grading periods in our district, and there were times where it felt like there were too many or too little standards within certain grading periods. If that was the case, then a cut or addition could be made.
If you’re torn about whether or not to include a concept, check to see what grading period it’ll fall into and analyze the quantity of standards in that period. 4-6 standards per nine week grading period seemed ideal (depending on how related the concepts were to each other).
Closing Notes & “Finished” Product
The entire checklist creation process is about feel and tinkering. My checklist changed as the year went on, and I became more familiar with the course. Also, now that the year is over, I’m starting to think about changes that may need to be made to the list. For now, here’s the Geometry Checklist I ended up with.