The corner deli sells roses in bunches of 6. If Dylan buys 3 bunches of roses, how many roses does he have?

A. 3

B. 9

C. 18

D. 24

Almost half the third graders (46%) in a group of schools I was supporting chose B. The correct answer, C, was chosen by 31% of the students. I don’t recall being all that surprised, but as I have thought about it over the years, I’ve come to see it as one more piece of evidence that many students do not do “sense-making” when they’re doing math. They look for numbers and guess what operation they’re supposed to do (addition is very popular). I have a theory that if you had asked those same third graders to draw a picture of the story, many more of them would get the problem correct. So the problem above becomes this task:

The corner deli sells roses in bunches of 6. Dylan buys 3 bunches. Draw a picture of the story.

To informally test this theory, I invite anyone with access to students in grades 2-5 (or older kids if you think they might be good subjects) to run a small experiment for me. I’ve written two sets of questions, one math and one drawing. Each has three questions. The math questions are taken directly from some Grade 3 benchmark tests, but I can see them being used in grades 2-5 for the purposes of this experiment (though you are welcome to use them with whomever you want – it’s an experiment, after all, not hard scientific research).

Since I am interested in how students solve problems when they think they’re supposed to “do math” versus when they might not realize they’re engaging in mathematical thinking, I’d ask that the math questions be given during math instructional time and the drawing questions be given during literacy instructional time, or, barring that, any time that isn’t math, and that the two sets of questions be given a couple of weeks apart.

The attached PDF contains 26 copies of each set of tasks (labled Student A through Student Z), instructions, and a roster sheet so that you can keep track of which student corresponds to which letter. (If you have more than 26 students, be creative.) You can report results through an online survey or send me copies of the completed task sheets (as a scanned PDF, or toss them in an envelope) or both.

Download the files: Fetter Sense-Making Experiment v1 [PDF]

So, wanna play? I hope so!

]]>We all know that Harry can be a clever guy! What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts! ]]>

I want to bake blackberry cobbler. The recipe calls for a 9″ pie pan. All I have are rectangular ones.

]]>One year, on December 31, Curtis, who doesn’t trust banks, put $1000 in a can and buried it in his back yard. He plans to continue adding $1000 to the can on the last day of each year until he’s ready to retire.

On the same day, Bill invested $1000 in a bank account that will pay 10% interest annually on the last day of the year. Unlike Curtis, he does not plan to continue investing more money each year.

One fourth of the vehicles at Danielle’s Cycle Shop are tricycles. The rest are bicycles. Danielle counted a total of 45 wheels in her shop.

We have considered a number of possibilities, including an option (chosen by the teacher) to show just the scenario for a problem and then have fields in which students can submit their Noticings and Wonderings. That sort of thing would require some significant programming time, so while we are working on putting it in place (I’ll blog about it more before we get too far), we are first going to support the PoW process through some wording changes in the submission process. We’ve come up with some possibilities and wonder if anyone has alternative ideas.

On a problem page, it says, “Compose Answer”, which of course implies you have “an answer”. We’re thinking of changing that to “Submit Ideas”, which seems a bit more welcoming to submissions that might not actually contain an answer yet (or ever).

Once you get to the “submission” page, there are four spots we’re suggesting alternative wording:

**Original:**Credit for this problem will be given to ….**New:**Credit for these ideas will be given to ….

**Original:**Summarize your answer in a sentence or two**New:**Summarize your ideas in a sentence or two.

**Original:**Explain how you solved the problem. Include your math.**New:**Explain your ideas and how you figured them out.

**Original:**If you’ve created an image as part of your solution, you may upload it here.**New:**If you’ve created an image that illustrates some of your ideas, you may upload it here.

What do you think? Would these sorts of changes convey “process” to your students? Do you have any other suggestions?

]]>*[reflect]***read**a blog post inspired by activities/thoughts from that week*[respond]***comment**on one of the blog posts*[inspire reflection and responses]***write**a new blog post

Here are some I’ve found in case it helps to have them in one spot:

August 7: Dandelions

August 7: Starting Anew and Regrets

August 9: Feedback for 140+

August 10: Listening to Yourself

August 23: What is EnCoMPASS?

August 8: Grateful for EnCoMPASS 2014

August 9: More Metaphors for my Teaching Journey

August 6: The choice to blog

August 27: The Professor in Me

August 24: First Two Days of School

August 1: Ignoring The Meaning of “Feedback”

August 8: How does feedback help?

August 6: People Circles

August 5: Exhaustion

August 26: Formative Assessment Responses

Here are blogs that I’ll be watching. I’ll add to the list I’ve assembled above if/when I notice any EnCoMPASS-related posts:

- Peg Cagle: Peg Cagle’s Math Education News & Views You Can Use
- Justin Lanier: I Choose Math
- Chris Robinson: Constructing Math Instruction
- Lisa Bejarano: Crazy Math Teacher Lady
- Ashli Black: Learning to Fold
- Dave Coffey: Delta Scape
- Bridget Dunbar: Reflections in the Plane
- Sadie Estrella: Who’s a Math Nerd? *raising hand*
- Wendy Menard: Her Mathness
- Jami Packer: Undefined
- Megan Schmidt: Number Loving Beagle
- Sebastian Speer: Making Sense of Numbers
- Annie Fetter: Annie at the Math Forum
- Daniel Lewis: Daniel at the Math Forum
- Tracey Perzan: PoWerful Ideas
- Max Ray: The Max Ray Blog
- Casey Sneider: Casey at the Math Forum
- Steve Weimar: Steve at the Math Forum

If you notice any posts to add, feel free to comment and/or email me directly! Thanks. ~Suzanne

]]>Specialist Lee Alejandre, who is 6 feet tall, had leave time from the Army, some of which he spent basking in the sun at Swarthmore College in a couple of different chairs:

dimension |
larger chair |
smaller chair |

width of seat | 57 3/4″ | 21″ |

length of arm | 80″ | 29 1/2″ |

front leg | 26 1/8″ | 9 1/2″ |

**Annie’s “Phone in the Pocket” Idea**

Some time ago I overheard **Annie **suggest to a teacher that she use her SmartPhone to record herself. (Can’t you just hear Annie’s voice as she explains this!) Annie said that you should just turn on voice recording on your phone, stick the phone in your pocket and after about 10 minutes take the phone out of your pocket and turn it off. Casual. No fuss. Then later in the day when you have 10 minutes, listen to the recording and ask yourself

What do you notice? What do you wonder? … and what do you want to try next time?

**Suzanne’s Addendum to Annie’s Great Idea**

During the week, change the time in the class period that you try this. So, for example, start by recording the first 10 minutes of class. The next day, try to record the second 10 minutes and then make it later into the class until you also record the last 10 minutes. Resist taping the entire class because it’s unlikely you’ll sit later and listen to the entire recording. You want it to be manageable so that you can make use of the recording.

I can’t help but point to what **Max** wrote in **Chapter 3** of * Powerful Problem Solving* and, in particular, the section titled

*The first step in creating a classroom in which students actively listen to one another is to convince students that what their classmates are saying is worth listening to.*

On **page 27** Max lists some suggestions for “*making whole-group conversations in math class more like conversations at a dinner party*.” Fun would be to pick a few of those, make your 10 minute recordings and then listen to see how you are doing.