We often get the question from teachers, parents, administrators, and just about any other type of adult…what do we do about kids who are “behind”? Everybody wants a nice clean answer, but it's incredibly rare to hear one.
In the past few months, Kristian Quiocho, Shannon Andrews, Chris Perez and I have paired in different combinations to plan and facilitate several full-day task-based workshops on different progressions of some of the content domains. For example, we spent a day with teachers on the OA domain, another day on the K-5 Geometry domain, another on Mathematical Modeling, and another on the Ratios and Proportional Relationships domain – all focused on how the content progresses over time. All of the slides for each of those sessions are in the Workshop Resources page of this website.
In each of those sessions we started with a task that draws out some of the big ideas that we identified in the Progressions Document for that domain. Teachers struggled through the task at varying levels, independently then collaboratively. As always, we used a 5 Practices model to capture some of the teachers' representations, sequenced them, and displayed them 1 or 2 at a time, asking teachers to interpret the representations, to make connections amongst those representations (alike/different), and of course asked questions to connect those representations to the big mathematical ideas that are occurring in them.
Critical distinction… when using the 5 Practices model, we can’t emphasize enough the value in having the creator of the representation to NOT present or talk about their own representation in the “connect” phase, unless absolutely necessary. It’s critical to give teachers (and kids) time to do an informal notice/wonder about each representation that’s displayed, and have an opportunity to engage in discourse with a peer about what they believe the representation is showing, and what the author of that representation was thinking (SMP 1, 2, 6, and 7). Below are 3 of the representations that we asked teachers to connect from the Penguin task in the Operations and Algebraic Thinking session. What's similar? What's different? What big mathematical ideas exist in all of them?
After teachers grappled with the first task, we asked them to generalize the different ways of thinking that they just engaged in and massage the language while keeping it informal. Below is a sample from the Ratios and Proportional Reasoning session that the teachers identified as big ideas that emerged in the first task.
Here’s where it gets intense…we had an almost equal distribution of teachers from elementary, middle and high school in the Ratios and Proportional Relationships session, even though this was technically middle school content. Do you have, or know teachers that have, a class of students with wide variety of “content knowledge” in the classroom…varying levels of proficiencies? Kids that are all over the place, almost all of the time?
Teachers then went into their grade level standards chapter of the CA Math Framework (the Progressions Documents would work if you’re not in CA, or if using another state’s document is unappealing to you) and looked for the same way of thinking from the chart in the content of their grade level. Amazing conversations ensued in the whole group discussion afterwards. Then Jamie Duncan drops a bomb noticing that the “for every __, there is __” way of thinking shows up in her 1st Grade Measurement standards…think about it! Wait...think more about it. Heads spinning in the room, a Trigonometry teacher who the bow on noticing the same way of thinking shows up in developing Trig Ratios...heads spinning faster.
Are you tired of going to committee meetings that are not focused on anything helpful? Ever been to a “Vertical Articulation Meeting” that’s a complete waste of time? What would happen if these meetings were focused on making explicit connections to a domain, where the mathematics was the agenda and context for all of the conversation, and the big mathematical ideas got exposed across grade levels and grade spans?
The rest of the day we spent doing more tasks and refining our language of the Big Ideas that underlie the domain, becoming more formally aligned to the language of the Progressions Documents, and an understanding of what those words mean in the context of a classroom. (As an example, what does the OA Progressions Document mean when it presses on “extending arithmetic beyond whole numbers”?)
The collaboration and deepened content knowledge in these sessions have been just plain awesome…but not the point for this post.
So what is the point?
What’s the connection between giving teachers in-depth experiences into mathematical content, learning about how the mathematics progresses across grades and grade span and the question “what do we do about the kids who are behind?”
I have my own ideas, but if you made it this far into the post, you probably have better ones than me. So let’s hear it…