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Nutting things out and intellectual play

July 2, 2014

This week’s #EduRead is the topic Constructive Struggle from the article Faster Isn’t Smarter. Author Cathy Seeley states students should be challenged with more complex problems. I agree. End of post.

What spin can I offer on this article? For one, I wish James Tanton was Cathy Seeley’s editor. He’d ditch the title and rename it, “Nutting Things Out.” His word choice speaks volumes about his approach to math. While I imagine the two would both vote for more math complexity, the Seeley read is a tad highbrow and offers no concrete suggestions on infusing more complexity. I’m a fan of Tanton. His playfulness and enthusiasm are infectious. Watch one of his videos and you’ll get a google of ideas on nutting your way through things…


as well as engaging in intellectual play.


In addition to the problems posed in Tanton’s videos and books, Dan Meyer and Michael Pershan recently discussed less scaffolding as a means to make problems more complex. Yet another alternative is Marian Small’s book More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction which offers Open Questions and Parallel Tasks.

Suggestion 1: Open Questions

A number pattern includes both -3 and -13  as terms. What might be the general term of the pattern?

Suggestion 2: Parallel Tasks–students are presented a task and can choose one of two options

Can  -3087 be in the pattern described by the given pattern rule? How do you know?

  • Option 1: The pattern rule is: Start at 9. Keep subtracting 3.
  • Option 2: The term value is 4 times the term number +3

So now you have more resources for Constructive Struggle. I mean nutting things out and intellectual play.

Integer choice assessment part 2

June 30, 2014

The other day I posted a work in progress–an assessment menu for adding and subtracting integers. Matt Coaty’s comment inspired me to explore how students would share their understanding, as well as develop assessment criteria.

Today I’m unveiling a new and improved version. I’ve taken the idea of a literary book club meeting where students bring a discussion tool to talk about a novel and have turned it into a “Mathematics Symposium” where students bring activities they’ve created about a concept and share their mathematical understandings with the group.

Here’s a revised 2-5-8 menu with descriptions of the criteria for success, suggested product ideas, and a check on whether students have met the expectations, or if they are not yet there.


Each student will have up to ten minutes to share their activities. When the group is finished they will assess each other using this two sided rubric/checklist. If a student marks any area as superlative (italics) they are to indicate on the reverse side what distinguished it from the other choices.

symposium reflection

symposium notes

To determine a “final” grade, I’ll review the artifacts along with the students’ input. I’ve successfully used this format when I taught literature and it was quite successful. I’m looking forward to seeing how this translates in a math class.


Standards based choice assessment

June 28, 2014

For the past couple of years our math curriculum committee has been focusing on creating performance based assessments with leveled problems. Now that we have a clear vision of the standards and what we want our students to know and be able to do I want to start offering some variety, some choice.

I’m toying with the idea of offering choice once per quarter. Here’s a 2-5-8 menu I created for adding and subtracting integers.

integer menu1

integer menu2integer menu3

In addition to the differentiated content, I like how this format requires the student to do much more thinking and problem solving because they have to come up with their own scenarios and problems. Even the Knowledge and Comprehension levels ask students to think.

One element that is missing is differentiating by product. What options do you suggest? Ideally they shouldn’t take hours to assess. Also if you have other activities to suggest or other input please comment.

Data walls

May 27, 2014

For the last three weeks I’ve been preoccupied with the notion of data walls. What’s your opinion? Do they motivate students, or reinforce status?   Does it promote student ownership of their performance, or is it another form of ranking?

I tweeted an unbiased question to Ilana Horn and Rick Wormeli. As you can see Ilana responded, no holds barred. She followed up with another tweet linking to one of her informative posts on status.


I don’t believe I’m cherry picking, but below are two examples I see as typical. Are any of these classes tracked? If you were Student #9 in Group 5 how would you feel?  Is this the type of motivation we want? Even though #9 is anonymous, I’d bet his/her classmates could identify the student.

data wall 1

Here’s another example. Student identity is less revealing, however don’t be fooled. The students know who owns what sticker.

data wall 2

Equally or perhaps even more important than the idea of motivation or “capturing” learning (I use “capture” loosely)  is how data walls contribute to a social structure where students are ranked and status is assigned to various students.

Please read Ilana Horn.



[Retro games] Before the first person shooter there was the second person thinker

May 5, 2014

I recently read Edutopia’s article 3 Ways Coding and Gaming Can Enhance Learning and it brought back memories, specifically text adventure or interactive fiction from the 1980s. If you’re old enough to remember Zork, or have played it, you know what I’m talking about. Instead of navigating with a mouse, controller, or joystick, you type text to maneuver: open mailbox, take leaflet, go south, etc.

Zork game

Edutopia was promoting Inform 7 for students to write their own code. I couldn’t agree more. I encourage you and The Hour of Code people to add Inform 7 to their coding list.

I don’t have much programming background but my students used Inform 7 to create their own interactive fiction games as an interdisciplinary unit when I taught 6th grade math, literature and language arts. One of the best was Stealing the Stolen, written by Rachel and Sabrina.

Stealing Inform

View within Inform 7


stealing the stolen

View when playing online.

The engagement and problem solving were incredible. The project did take a few weeks to complete and some days were filled with trouble shooting, but it was one of the best learning experiences my students ever had.

If you forward this post to an LA teacher, they would be interested in knowing student writing was modeled using Grammar for Middle School, A Sentence Composing Approach.

Everything you need to have students create their own text adventure can be found here.





Introducing systems of equations: graphing

May 3, 2014

Many of my pre-algebra kids continually seek context, so I thought I’d head them off at the pass by introducing graphing systems of equations as an exploratory activity using a couple of word problems. Here’s one of them:

systems problem


We’ve been graphing linear equations for a while so I purposefully added the “How could graphing each equation help you?” question to guide their thinking.

I came to learn that some students would rather not have the context and just be given the systems to graph–it’s a lot easier. “I hate word problems,” said several students.

That’s my fault. I need to do a better job of applying these skills in context. After we talked about context it was time for some graphing practice. As I checked their work I was reminded that a few haven’t improved their “number sense” when it comes to graphing. I wish I had snapped a photo of one student’s work, but I’ve recreated it below.


My questions to her were: 1) While your table is accurate, why did you choose values that fall outside the graph?  2) How could the slope and graphing the y intercept help you?

This particular student doesn’t recognize how less accurate her lines will be if she picks points beyond the coordinate plane that’s provided. If students are graphing using a table, it’s a great opportunity to discuss when it’s appropriate to choose negative values in order to stay within the graph.

In previous conversations with this student I also know she doesn’t have a strong grasp of the meaning of rate of change. I need to get her into math lab.





Students learn to give feedback with a growth mindset

April 22, 2014

Yesterday Algebra’s Friend introduced me to a new professional development blog Read…Chat…Reflect…Learn! While I enjoy reading blogs for lesson ideas, I also love reading journal and magazine articles, books, research studies, etc. as another way to stay current. I’m glad I found this blog and I’m thrilled to see that it’s in its infancy, only because it makes me feel that I haven’t missed out on too much!

The current topic is feedback. The article for discussion was How Am I Doing? It offered a good overview, but what was missing was how to provide feedback using a growth mindset. This excerpt, Types of Feedback and Their Purposes,  gives clear examples. One type of feedback I tend to focus on is descriptive as opposed to judgmental feedback.

When examining student work for feedback I’ve collected their work in progress, and provided descriptive feedback. I won’t kid you. It’s time consuming. But an idea was floating in my head. What if I taught students to give each other feedback with a growth mindset?  I don’t want you to think I am shirking my responsibilities, but could math students offer feedback similar to students who participate in peer editing compositions?

After reading Algebra’s Friend post I thought I would give it a try. Yesterday and today I showed my students this Would You Rather problem. They were to work in groups of four to solve.

After the groups worked for about 10-15 minutes, I collected their work, redistributed them to different groups and asked the new group to provide feedback. Here’s an example:


Kids being kids, their feedback was somewhat judgmental and not of a growth mindset. Had they rephrased their wording to questions such as, “How could labeling help explain your thinking?” or a statement such as “The final answer is not clear,” would definitely put them on the track towards feedback with a growth mindset.

Doing this activity in groups made it quite manageable as only six responses were being critiqued. While I monitored each group I asked them what questions they had about the other group’s work. I also asked them to be positive with their feedback. Each problem was circulated twice. Doing so also gave groups the opportunity to see how others approached the problem and perhaps revamp their thinking.

Here’s how the above group implemented the feedback:



The next time I see them we’ll continue the conversation of how to offer feedback with a growth mindset. With more practice they’ll get better at it.

I should have thought of this at the start of the year.





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