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…
30 Comments
6/2/2016 03:09:10 pm
It is the most powerful way to change a culture. Teachers need to experience it differently than when they 'were taught' it. Once they see multiple representations & approaches to a problem; learn through solving problems in collaboration, then are going to start changing the beliefs that power their teaching paradigms. I have also been powerfully moved when teachers from different aged classes contribute together and a fuller concept analysis is possible. I didn't think of subitizing as a missing piece in my secondary students. Doing math talks and problem-based learning exposed these pieces as did proportional reasoning (over just fractions fragmented from the bigger idea.)
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Ryan
6/3/2016 07:01:46 am
Thank you Fred! Task-based professional learning across grade spans can be the highlight of a teacher's year (and, hence, mine).
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Graham
6/2/2016 04:31:50 pm
Great stuff here Ryan. I'm really appreciating the emphasis on the vertical progression. More please!
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Ryan
6/3/2016 07:02:21 am
Thanks Graham! Encouragement from a guy like you is powerful.
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So often our students who are behind have 1 of 2 problems (or both, I guess). One, they have a misconception or a non-conception somewhere in their development of the concept at hand. The other issue may be that the student is delayed - for whatever reason - in the development of their thinking. This may be due to a developmental delay, a lack of access to requisite skills/concepts, etc. But, whatever the reason, the student is "behind" and may just need more time and exposure.
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Ryan
6/9/2016 06:46:37 am
Really begs the question how often do we mis-diagnose because of less than optimal understanding of the way the mathematical learning progresses.
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Shelley Carlisle
6/4/2016 08:23:51 am
Ryan, you speak truth. Even though I'm more active in the Ed tech department because it was my Master's focus, I have learned SO much from you. Here are my thoughts. The best practices you've brought into the lives of teachers in LEUSD are priceless. And, It all begins with elementary teachers, who, unlike middle and hs levels are pulled in numerous directions. Math is just a tiny portion of our responsibilities. We've got to ultimately understand and be good at writing, reading, social studies, science, physical education, art, tech integration, ELD, and I know I am missing a lot more. Yes, I have grown as a teacher inspite of all of these demands but it has taken hours of PD on my own time and hard work building my PLN (thanks for being part of it) but until elementary teachers are supported in all areas, math is just going to be one more thing. I'm not a critic, just saying it how I see it. And, elementary teachers are setting the foundation! Yikes! We don't have vertical collaboration imbedded into our professional day nor do we in LEUSD have more than a 50 minute once a week PLC to meet with only our grade level to discuss EVERYTHING we are responsible for. I see a need for change in the way we teach math, but, the system at my level, doesn't support this happening. And, now that you are moving on (I'm really happy for you) I'm scared that all your hard work won't keep moving us forward. THE BOTTOM LINE: It's time to change the system and create a way to support the teachers who lay that foundation or the construction is always going to be defective.
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Ryan
6/9/2016 06:49:20 am
Thanks Shelley! Prioritizing the time for professional learning is important. So is developing a mindset in all adults (teachers, but not just teachers) that we will never learn it all. So what is that, if understood well on our part, would make the greatest impact on student understanding? Hmm...
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6/4/2016 09:29:31 am
This is everything! Understanding the progressions are the only way we are going to get teachers to step out of the silo of their grade level and into a collaborative conversation about coherence. Knowing the content that comes before and after (and is directly related to) their grade level content makes teachers better, period. I love the idea of supporting students who have unfinished learning (sounds so much nicer than "behind") with the content they need through the lens of their grade level learning. Teachers too often spend time going back when they need to be moving forward. Progressions can help us do this!
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Ryan
6/9/2016 06:51:47 am
Now we're cooking...dumping the word "behind" is part of the equation. Understanding deeply the progressions just might minimize the number of kids that we think have unfinished learning, and the amount of unfinished learning that they carry with them. Next post I'm hoping to explore the "how".
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Denise Rawding
6/5/2016 02:27:17 pm
I agree that allowing teachers to experience math as we want our students to experience it is important. I'm a K - 2 academic interventionist, so my focus tends to be with primary level teachers. At these levels, most teachers do not understand the complexity of the math they teach. Counting is so much more than just saying the numbers, and adding and subtracting are so much more than adding to and taking from. The progressions documents make these ideas clear for teachers, but, in my experience, most are reluctant to read them. Without this background knowledge, teachers aren't able to identify misconceptions or even track understanding of concepts effectively.
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Ryan
6/9/2016 06:54:33 am
Oh yeah! I felt it was important to keep the phrase "Teach at the Speed of Learning" at the top of every page on this site. And yes, the teachers and administrators are reluctant to read the Progressions Documents. So the question becomes, if we value teachers and administrators wanting to understand the progressions, and actually understanding them, and the reading the Progressions documents are helpful but not enough, than what else can we do?
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Stephanie Holloway
6/8/2016 04:25:35 pm
If teachers are engaged in these experiences, it exposes where they are at in in their mathematical thought processes. It gives teachers a way to self-reflect where they are at personally within the progression of a given domain. Most teachers know the basics but lack the depth- myself included (I’m a work in progress) How does this connect to students who are behind? As teachers, perhaps we shouldn’t view these students as “behind.” Much like the way we have reflected on our own learning by analyzing the work of other teachers using 5 practices, we find that our foundation is shaky but we are not “behind.” Then, we reflect on our students’ thinking. Where are they at in the progression? Can we meet them there? Can we help stabilize that foundation by providing open ended tasks with multiple entry points? Of course we can. I think the connection is the self-reflection of where we are at and then transferring that same idea to our students. Meet them there and take them forward. Listen to them…give them time to show you what they know. Observe, listen, listen, listen.
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6/8/2016 07:10:51 pm
Or as Prof. Agassiz says, "Look, look, look" to which you can add, "and listen, listen, listen" and I'll add "and care, care, care". There will be a discipline in our noticing with this increasing sensitivity to our learners. (Mason, 2002)
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Ryan
6/9/2016 06:56:23 am
Sha-bam...let's remember that we are in a progression of learning as well. Oh yeah, and if you click the link on the videos page of this site that's labeled "We all need to learn more math", you'll get to hear CCSSM author Phil Daro on the same idea.
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6/16/2016 07:56:18 am
I loved this professional development session! Aside from the initial sessions on SMP's, I can't think of ONE session where I think I learned more. I totally think we should continue to have more sessions like this, working on our vertical alignment through progressions - actually doing the math and digging into the framework. As a primary teacher who hasn't worked on middle and high school level problems in a long time, it is really helpful for me to relearn the content in a meaningful way. Having teachers like you three also gives me hope that I CAN actually do the math, and it's not so scary. I wish I had teachers like you growing up! For me in primary, coming to sessions put together like this help me know how to question students and how to open up ideas that will be developed later. I would imagine working on the progression benefited the high school teachers as well. If it were me, I would be thinking, "Great! Now when I see my kids struggling, I know what experiences they might need to be able to do/have access to the grade level math!"
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6/29/2016 07:05:27 am
Hello! This post was recommended for The Best of the Math Teacher Blogs 2016: a collection of people's favorite blog posts of the year. We would like to publish an edited volume of the posts at the end of the year and use the money raised toward a scholarship for TMC. Please let us know by responding via http://goo.gl/forms/LLURZ4GOsQ whether or not you grant us permission to include your post. Thank you, Tina and Lani.
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7/4/2016 02:13:39 pm
after looking at the array of creative ideas, i'd like to invite you to look at my blog - matholdiesbutgoodies.wordpress.com - because i believe i offer some ideas that would address some of the issues that have been discussed ... and as the title suggests, there are some really effective procedures from the 1800s ... for example check out "allegation" ... thanks ... mark
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