Is it coincidental or by design that our school’s reading initiative is taking me one step closer to a math workshop model? If you’re a regular reader you already know I’m introducing a “reading strategy of the month” using think-alouds. October was monitoring. November is determining importance. Next month the math department will present to our staff how we implemented determining importance during the month of November.
I’m realizing that my determining importance think-aloud closely resembles a targeted mini-lesson–the centerpiece of math workshop. What solidified it for me was reading this graphic from Minds on Mathematics.
I have to admit I didn’t have the math practices in mind when I created the think aloud but they came through anyway.
On a separate note I want to thank bloggers Diana Fesmire and Mr. Dardy, as well as commenter Alisa Carter for stretching me.
Yesterday, I returned an ungraded pre-algebra assessment to the students. Their job was to analyze and discuss each problem at their table. After ten minutes I handed out the key and discussion continued.
I feel so small. I should have begun that practice long ago. Their discussions were incredibly valuable. The students were talking math and I wasn’t the center of attention or the knowledge keeper. Most of class loved the idea of discussing their work with each other. Plus they were able to control the pace. One student thought holding back the key for a period of time added a bit of suspense. On the other hand one student felt self-conscious–concerned that she would be wrong and her classmates would know.
On Friday I became a much better teacher, inching closer to a math workshop approach.
Our December staff meeting will be devoted to the reading (thinking) strategy determining importance. The math department has been asked to present examples of student work and ways this strategy was implemented in the classroom.
I created this think aloud and worksheet for my pre-algebra students. My thoughts are to present and walk through the steps to solve the problem.
I’ll continue modeling how I solve the problem, then the students will have a turn solving this problem:
The sum of the ages of Elmira, Geoff and Rae is 82. If Elmira adds 6 to Geoff’s age, subtracts 8 from Rae’s age, or doubles her own age, it will equal Doug’s age. How old is Doug?
I’ll be curious to see how well they determine what’s important in the problem. Also, the age problem doesn’t prompt the students to create an equation.
We are almost at the point of introducing two step and multi-step equations so this problem will be good timing.
Technically the image isn’t trick photography but the gap in positioning makes you think the size of the missing wrench must be between and of an inch. It may be a form of trickery but could a student argue the missing wrench size is ? How would they justify the break in the pattern?
One of the wrenches is indeed missing. Would students think to mentally close the gap and consider the possibility that the first or last wrench in the sequence is missing? What would be those sizes?
The idea is to let students explore common denominators and the patterns they discover in this task.
I’ll let you know how it goes.
If you were asked to examine your practice, what would you keep, what would you toss, and what would you invent or re-imagine? In so many words our math department has been asked to do just that.
Adaptive challenges are difficult because their solutions require people to change their ways. Unlike known or routine problem solving for which past ways of thinking, relating, and operating are sufficient for achieving good outcomes, adaptive work demands three very tough human tasks: figuring out what to conserve from past practices, figuring out what to discard from past practices, and inventing new ways that build from the best of the past.–Adaptive Leadership
We’re deep in the muck trying to figure out how to raise student achievement and move students forward. We’re an upper middle class suburban district and our kids should be doing better. MAP is our yardstick. Like it or not that is the tool we use to measure growth.
Regardless of the yardstick, how do we move students forward? How committed are we to ensuring that student learning is maximized? We’re not super heroes, but what does it take (without killing the love of learning via excessive testing) to make sure students learn?
I’d like to limit the conversation to instructional decisions that are within our control. Besides a viable curriculum and the art of reteaching and reassessing, what else do you do? How do you differentiate for the capable student, but who is not ready to be placed in a higher track? Do you enrich or accelerate, and how?
I wrestle with these ideas as well as how to incorporate spaced vs. massed practice so the concept has a better chance of getting into long term memory.
What are the high leverage moves you’d recommend? I’m all ears.
I began class today showing this pattern on the screen:
The students had been previously exposed to some pattern problems but a partially completed input-output table was taking focus away from the pattern itself. Frankly, it didn’t occur to me that using a table makes the visual irrelevant until I read Fawn’s post on how she conducts her math talks. Another thing I realized was that Fawn is asking her students to read and interpret a pattern. If they are reading a visual, what’s important information for them to solve the problem?
Our math department is scheduled to present the reading strategy determining importance at next month’s staff meeting. Instead of a typical word problem I thought it would be interesting to apply that strategy to a visual pattern.
I asked, “What’s important in this pattern that will help you predict how many dots are in the 100th figure?”
Students stared at the screen for a good ten minutes. Several had no idea where to start, a few had random guesses with no math to support their claim, but one got it.
Student: I saw that the bottom row in the first figure increases by 1.The middle row is always two more than the bottom row. The top row is always one more than the bottom row. So the 100th pattern will have 306 dots.
I didn’t ask for the equation; I probably should have to see how they would have come up with
t = 3n +6.
In any event, at least one student reasoned and persevered through the problem.
Here are my two cents, Kate.
I started reading blogs about four years ago because I wanted to grow as a teacher, become more informed about the common core, as well as issues surrounding education reform. For teaching and learning I started with the big gun, Dan Meyer. I can’t remember when, but at some point I discovered the comments his followers wrote were so interesting it led me to follow other bloggers.
I don’t limit my blog reading to math. I also read Diane Ravitch to stay current with what’s happening on the education reform front.
Returning to the blog; a repeat customer
I do it for professional development. I love learning and discovering how much more there is to learn. A recent case in point is Fawn Nguyen’s post regarding how she uses her visual patterns site. She wrote, “I don’t teach kids — nor discourage them — to set up an input/output table to find the common differences to figure out the equations. I just don’t because doing so seems to render the visual patterns themselves insignificant.”
I didn’t realize until now, but she’s actually teaching her students how to read and interpret a visual. It’s math and reading combined.
She and others also share their classroom experiences–what lessons went well, what flopped. The challenges they face and the strategies they have tried. Plus the comments offer words of wisdom.
Why do you write?
I’m selfish. I write for me. It’s a journal of my thoughts and ideas and an opportunity to receive feedback.
What would you hope to be hearing from me?
Most teachers attend workshops/presentations to gain knowledge and acquire resources. Aside from a list of blogs and their target audiences, I think your attendees would benefit from learning about the professional development the blogging community offers, why the bloggers blog, and why your attendees should start blogging too.
The only difference between “us and them” is a blog account. It doesn’t cost a dime; the only cost is time; and the time is well spent.
My SMART goal to raise self efficacy was to implement four tasks in the first quarter. I only had two. My standard students experienced the Money Munchers and Variety Show tasks. My pre-algebra class had Molly’s Locker Combo task and the Boomerang task. While I didn’t reach my goal, I am making a wee bit of progress with one student’s self efficacy. I have to admit, it’s not me. Her teacher last year had her in math lab nearly every day.
On Wednesday, she was elated that she was part of a group that was allowed to work in the hall on an extension activity while I retaught a concept. It was the first time she ever experienced such a thing. “I’ve never been out in the hall before! I feel so smart!” Since the start of the year she’s only had to reassess one time. Attending math lab has paid off.
The extra time we devote to our students may or may not pay off this year, but it will in the future.