This and That

As the school year winds down, it seems I’ve had less and less time for the ol’ blog.

So let’s get you updated!

First, I had the opportunity to write a couple of blog posts for the National Council of Teachers of Mathematics blog. Here and here. Please, if you get a chance, head over there and leave a comment so the greater mathematics education community knows we care how students with disabilities experience mathematics in schools!

Also, I continue to write for the Global Math Department newsletter. Here’s the latest issue. You’ll always find good stuff in this newsletter, so I recommend you subscribe to receive it regularly in your inbox!

This summer, I’ll be attending and presenting at Twitter Math Camp, a math conference by teachers, for teachers!

Finally, I’ve been busy working with Illustrative Mathematics to create access for student with disabilities to their K-12 open educational resource (OER) curriculum. While working on this project, it is becoming apparent how great these materials will be when finished since everyone involved is already writing lesson and activities with universal design and accessibility in mind. I’ll definitely keep you updated as the project progresses.

Thanks for reading and for all your support!

Word Problems and the Problems with Words

Yesterday, I posted a new 3-act task on the blog. In the tradition of digital mentors like Graham Fletcher, Andrew Stadel, and Dane Ehlert, I will rarely post an activity on the blog that I don’t intend to use in my own class with students. Today, we did Make It Rain.

Here is what my students noticed during Act 1

  • There’s a lot of money
  • There are 20’s, 10’s, 5’s, and 1’s
  • There are more 20’s than 10’s

And here’s what they wondered…

  • How much money is there?
  • Why did it go from greatest to least?
  • Why was it being spread out?
  • What kind of bills were in the pile?
  • How many of each bill is there?

My students are used to analyzing their questions collaboratively. Some of the students noted that we couldn’t answer the “why?” questions without asking the person in the video, who we did not have access to (even though it was me!)

So, then our wonderings looked more like this…

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3-Act Task: Make It Rain!


Act 1

What do you notice?

What do you wonder?

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One Moment, One Decision

Teaching is hard.

As Magdalene Lampert notes in her book Teaching Problems and the Problems of Teaching, “One reason teaching is a complex practice is that many of the problems a teacher must address to get students to learn happen simultaneously, not one after another (2).”

Teaching is hard.

As Max Ray says in his 2014 NCSM ignite talk, “Teaching isn’t Rocket Science. It’s harder.” Max goes on to say that teachers make a litany of educational decisions on the fly based on deep knowledge of content and their students as learners.

Teaching is hard.

As Ball and Forzani write in The Work of Teaching and the Challenge for Teacher Education, “The work of teaching includes broad cultural competence and relational sensitivity, communication skills, and the combination of rigor and imagination fundamental to effective practice. Skillful teaching requires appropriately using and integrating specific moves and activities in particular cases and contexts, based on knowledge and understanding of one’s pupils and on the application of professional judgment (2009).”

Teaching is hard.

As Jose Vilson relates, “We’ve known for decades that building relationships is a central part of our work, but this has even larger implications when we work with disadvantaged students. The teacher-student relationship has so many subtle nuances across race, gender, and class lines that opening our eyes to these nuances would make us better educators.”

So teaching is hard, because reasons.

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A Snapshot

First, a little background.

The theme of our spring unit is always financial literacy. As teachers of students with varying degrees of need, strength, and interest this means different things for different groups of students. One of my groups is working on selling tickets for our school play, Alice in Wonderland.

We sell tickets at two price points. An adult ticket costs $10 and a child/student ticket costs $8. This is partly my doing, because having two different prices sometimes allows my students to investigate more interesting mathematical questions. Today was one of those days.

Show-goers are also able to purchase play tickets in one of three ways: cash, check, or online with a credit card. My students record the type of ticket and the method of purchase for each order in a table. Students then represent this information visually using graphs. We will use these tables and graphs later on to reflect on the trends and patterns in the ticket sales to make suggestions to our play directors for future ticket sales initiatives. But that’s the bigger picture and I promised you a snapshot. So here it is.

I realized I had been giving my students too much information. As they recorded the total amounts of cash, checks, and credit, I was also telling them the type of ticket. Today we began our routine of using math to figure out the type of tickets using our knowledge of the ticket prices and total amount of money. I gave them this problem as a warm-up:

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Book Review: Mathematical Thinking and Communication

Sometimes having a blog pays off and you get advance copies of upcoming publications. This is one of those times…

The good people at Heinemann sent me a book entitled, Mathematical Thinking and Communication: Access for English Learners by Mark Driscoll, Johannah Nikula, and Jill Neumayer Depiper. If you are regular reader of this blog (and why wouldn’t you be?) you may be thinking, “English learners? I thought this blog was about students with disabilities, why are we talking about English learners?” That is a good question, faithful blog reader, so I’ll address it first.

There is a well documented disproportionate representation of English language learners in special education. Amanda Sullivan notes this may happen because”both underreferral and overdiagnosis occur because of misunderstanding of the educational needs of students identified as ELLs (Case & Taylor, 2005), poorly designed language assessments (MacSwan & Rolstad, 2006), and weak psychoeducational assessment practices (Figueroa & Newsome, 2006).”

ELL special ed disproportionate table

Taking this into consideration, the following review is going to focus on the pedagogical framework highlighted in Mathematical Thinking and Communication: Access for English Learners. Even though most English learners do not share the same cognitive challenges that some students with disabilities do, they do share challenges relating to expressive and receptive language and communication. Thus the strategies to create access for communication of mathematical thinking can be shared by teachers of all learners.

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Productive Struggle vs. Frustration

This past Friday, I gave an introductory presentation on the educational ramifications of new brain and psychological research, specifically, Carol Dweck’s Mindset. What came out of the discussion during the session, was that our school already does a fairly good job of inherently implementing most of the underlying themes in Dweck’s research.

What we realized we still needed to work on as a school, was allowing students to struggle productively. Robert Kaplinsky recently posted his ignite talk from the Northwest Mathematics Conference. Kaplinsky gives a very accessible account of the differences between productive struggle and what he calls, “unproductive struggle.” In our school, “unproductive struggle” is frustration.

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