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https://solveme.edc.org/ looks like fun as well

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https://solveme.edc.org/ looks like fun as well

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Desmos looks like so much fun as a warm up.  

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Desmos looks like so much fun as a warm up.  

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Polygraphs

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Give students the answers.  This also ties into Growth Mindset.

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Giving students the answer to a problem and then they have to show me why that's the answer! So many students don't see the importance of the WHY!

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Which one doesn't belong

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Using the student Desmos was great. Loved everything vocab

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I love the desmos and the Solve me Mobiles! :) 

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I love the desmos and the Solve me Mobiles! :) 

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How do you motivate students who do not want to read or engage in the classroom, even with low risk problems?

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How do you motivate students who do not want to read or engage in the classroom, even with low risk problems?

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Meaningful Practices to Meet the Needs of Every Learner It's about the Process Bridget Dunbar Supervisor of Secondary Mathematics St. Mary’s County Public Schools https://elsdunbar.wordpress.com/ elsdunbar@gmail.com @BridgetDunbar (WiFi) NCTM (Password) NCTM2018

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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Have you ever wanted your math students to get better at using math language?
Have you ever wanted your math students to be able to compare attributes of visual mathematics?
Desmos Polygraph activities supported through word banks is your jam!

Over the past three years as a Digital Learning Coach in my district, I've been able to see Polygraph used in a variety of ways. This post will share a few of the many things I've learned.

My first year, I supported a high school Algebra teacher. We debriefed after she ran the Parabolas Polygraph activity with students. She was a little bummed that students weren't using more of the academic language they had been learning. For example, minimum, maximum, x-intercepts, roots, vertex, etc. I offered the suggestion of providing students with a word bank, possibly carved out on a section of the whiteboard, with the words she wanted her students to use. She one-upped me and put them on a half sheet of paper and printed them out to give to her students next time she played polygraph. I'll revisit this technique in a few paragraphs.

My second year, I supported a Math 8 teacher. She was running the Lines Polygraph activity with her students. I looked at the dashboard while students were playing and many of the students were asking questions about the slope using either "uphill" or "downhill" as their descriptor. I asked the teacher about this. She said this is the way she taught it. I asked her about the mathematical association with uphill and downhill and she replied, positive and negative, respectively. I paused the class (before the pause feature existed, ha!) and drew two lines to represent the "uphill" and "downhill" slopes on the whiteboard. I told the class I noticed they have been using the terms uphill and downhill to describe these slopes. I went on to tell them, this is a great place to start, and now we're going to make your language even stronger by referring to uphill slopes as positive and downhill slopes as negative. For the remaining time, we're inviting you to use positive and negative.

I love this experience, because it validated the work the teacher did while raising the bar for the students to strengthen their mathematical vocabulary. I believe if you set the bar low for students, they'll often meet it with a high success rate. If you set the bar high for students, they'll work toward that high bar, often with a comparatively high success rate.

Back to the word bank.
My third year, I supported an Algebra teacher at our continuation high school. She ran the Parabolas Polygraph with her students and had a word bank up on the whiteboard. We debriefed and talked about making a half sheet of the words she would like students to use. Furthermore, let's make a Taboo list of words we want students to avoid using. She tried the Polygraph again, using the word bank handouts and noticed students were using the academic language a lot more than when the words were up on the whiteboard.

It's not enabling the students by providing them with a half-sheet of math terms you want them to practice and use. It's enabling if you're the one telling them what questions to ask their partner, or worse; you're typing in the questions for them. Providing students with the half-sheet, a physical token, places an emphasis on your invitation to students to practice and use specific math language associated with the concepts at hand.

I've learned a lot over the past 3 years, implementing both Desmos Activities and Polygraphs. I would say the use of a word bank handout is one of the most effective ways to get students practicing and using the math language you want them to use. Here are my current word banks (and Taboo lists) for Parabolas and Lines. You'll notice I intentionally left some blank spaces in the tables so students (and teachers) can add their own. I can't think of everything.

Consider the Low-Tech versions of Desmos Polygraph so students can practice using academic language more frequently without devices.

What words would you add to my word bank (and taboo) lists?

BONUS feature:
You've heard of a swear jar, right?
When someone is trying to curtail their swearing and/or use of bad words, they'll set out a swear jar, placing an amount of money in the jar every time they use a bad word.
*Consider the idea of a VOCAB jar in your math class. ( future blog post coming soon)

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Have you ever wanted your math students to get better at using math language? Have you ever wanted your math students to be able to compare attributes of visual mathematics? Desmos Polygraph activities supported through word banks is your jam!

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I was inspired to coordinate the Intentional Talk book study this summer by a conversation between Tracy Zager and Dylan Kane.

The Intentional Talk book study began in June with various people taking the lead-including the authors of the book Elham Kazemi and Allison Hintz.

This week, Allison Hintz posted a question that lead to a conversation about effective vs efficient strategies. I tried to capture my current wonderings in this 140 character tweet:

@mary_dooms thinking of moving Ss along a continuum of more sophisticated algebraic representations...does that = more efficient #intenttalk

- Bridget Dunbar (@BridgetDunbar) July 14, 2015

At the end of this past school year I came across this task.

I worked with on-level 8th grade students this year, but as the school Instructional Resource Teacher, I spoke with our 7th Accelerated teachers and Algebra 1 teacher to see if they would be on board with giving this task to each of these cohorts. All of the students had been taught systems of equations this year-but notice how unstructured and simply worded this task is. I wondered what sort of strategies the students (at all of these various levels) would apply towards getting a solution for this task. We used it to gauge the sort of student that would be appropriate for a 45 minute algebra class vs a 90 minute algebra class.
The range of approaches was very interesting to me.
The following examples are from the 8th grade students that I worked with...I organized these student responses in the sort of continuum that occurred. (Interestingly, the 7th accelerated and the Algebra 1 students didn't have too dissimilar a range of solution strategies.)
Students that chose graphing...
Student 1: extended the lines but without precision or using any tools

Student 2: asked for a ruler in order to extend the graph in a more precise fashion

Student 3: asked for graph paper and created a graph using discrete points
Students that chose tables...
Student 4: created two separate tables beginning at x = 0 and found the values that represented the intersection point

Student 5: created a single table beginning at x = 10. This student did not pull the correct information from graph to begin the table.
Students that wrote a one-variable equation...
Student 6: wrote each linear equation and then used the substitution method to find the solution. This student did have difficulty at the end because she struggled with what to do with (1/2)x = 8. She eventually made sense of that part.

Student 7: was able to use the substitution method to write the one-variable equation as well. This student is not your typical top student and she was able to easily handle .5x=8. I asked her if she used the calculator (which I had allowed) because she didn't get stuck like a few other of the "smart" kids. She said that she knew it took two groups of .5 to make 1 so she multiplied 8 by 2 and got 16. It was amazing to me how it was so easy for her to flip to ratio reasoning when that last bit was a challenge for some of the "top" students.

This all leads me back to my original wondering...graphing, tables, equations were all effective methods (for some). But, I am considering an efficient method to be one that utilizes grade level understandings and the goal should be to help students work through this continuum.

There has been a lot of discussion regarding the meaning of efficient. Does this mean fast? I think you are probably only able to use an efficient strategy if you have multiple strategies to choose from. Otherwise, your ONE strategy is the effective/efficient strategy.

It's important to give students these sort of unstructured tasks and let them figure out what they'd do on their own. I would definitely use this task again and then use one of the targeted discussion strategies from Intentional Talk.

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#intenttalk Book Study Leads to Questions about Effective vs Efficient

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I was inspired to coordinate the Intentional Talk book study this summer by a conversation between Tracy Zager and Dylan Kane. The Intentional Talk book study began in June with various people taking the lead--including the authors of the book Elham Kazemi and Allison Hintz.

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I worked with a 6th grade student in our In School Intervention classroom today. I do this every day. A boy had been assigned a set of pages from a workbook and had begun the work on his own. From what he had already completed, I could tell that this student had a strength in math. He was unsure of what he had done, so he was looking for validation from me. We looked at this next problem together:

He said, "so you gotta subtract right?" I said, "yes you do, but that's if you're looking for the answer. This is asking you to write an equation."

I talked to him about variables, and how many unknowns were in this problem and he could tell that there was only one.

I asked him to draw a picture of the situation. Here is what he drew.

HMMMM....(maybe they've recently worked on area and perimeter???)

I then asked him to reread the problem and prompted him to draw the house and the airport.

He drew the line between the house and the airport, and I had to do some questioning to get him to realize it represented the distance of 29 miles. We reread the problem and I asked him about the 14 and how he would represent that on the drawing.

He thought to himself for a moment and then began drawing the tick marks. I could tell that he was counting them. He labeled the 14th tick mark and the 29th, and then circled the 14.

I drew the bracket and asked him what that would represent. He said with a questioning tone, "the remaining distance?" Thinking for a minute, he then said, "oh I know...would it be 14 + x = 29?"

We did one more problem together that we represented with a drawing, and then I left him to be independent in the rest of his work.

He came over to show me one of his drawings and the equation he had written:
(In a previous part of the problem they were told there are 150 seats in coach seating.)
We high-fived!

Teaching students how to create math drawings is a valuable sense-making tool that can be over looked in math class. I know numerous reading language arts teachers that ask students to draw pictures to portray what's going on in a story. We need more of that in math class.

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I worked with a 6th grade student in our In School Intervention classroom today. I do this every day. A boy had been assigned a set of pages from a workbook and had begun the work on his own. Fro...

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Creating Math Drawings for PythagThm Problems (Jigsaw).docx

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Use logic to solve visual, interactive mathematical puzzles. Create your own puzzles to share with your friends or the SolveMe Community.