Tracy Zager’s New Book

[Posted earlier today on FB.]

Two plus years ago Tracy Zager contacted me for an interview about a post I’d written; she said she’d like to include parts of it in a book she was writing. Of course I was stupid with joy and honored. Then I got to meet Tracy in person at a math conference in 2014. Her warmth radiates wildly and affectionately. Then I got to be her designated live-tweeter for her ShadowCon talk the following year. But between our two face-to-face meetings, Tracy had been diagnosed with breast cancer. Cancer fucked with the wrong woman. Tracy is grace and heart and badass. How blessed and honored I am to call her my friend.

Here is her beautiful book.


Expected publication in December 2016

I’ll be sure to remind you when it comes out. :)

Posted in Teaching | Tagged , , | 2 Responses

A Few Thoughts

A few questions and thoughts are bouncing around in my head this week.

What is computational thinking? How much of what my students are doing can be considered computational thinking? I like this related post from today. Hoping to talk a lot more about this after I’ve gathered more background and practice.

Many of our students needed a lot more time for the CAASPP than we’d allotted. Then their laptops keep booting them off the system, how does this affect their concentration and their will to finish the test?

[This problem is on my desk, so I cannot not see it. I got this problem from Michael Shaughnessy when I took his problem-solving course back in Portland, OR.] In medieval times, the inhabitants of a remote village decided to lock the village valuables in a giant chest to protect them from marauding thieves. They placed a number of locks on the chest, with each lock needing its own distinct key. For additional security, the villagers made sure that any three people from the village would always have among them the keys needed to open the locks, but no two people would have the keys to do it. How many locks are required, and how many keys?

What is the difference between cilantro and coriander? I’m having a quasi-argument with a friend about this. I think I should win this debate just because I’m Vietnamese and our dishes incorporate more herbs than any other culinary cultures I know of. (Btw, this is how you pronounce herbs — 0:51 to 0:57.)

I’d appreciate it if God could turn down the stress dial for me a bit. It’s set between MED and MED HIGH right now. But if I were a big pot of water, then I could take all the heat and then blow off steam. But I’m not. So I remember a joke Annie told me on Saturday and feel a bit better: “What did the blanket say when it fell off the bed? Oh sheet.”

Sometimes I wonder how I make it through the week. Then scrolling through my phone to see my son’s texts to me, I know how.


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Teacher Appreciation

Today I remember my 7th grade home economics teacher Mrs. Quiggle. Marge Quiggle. She was already old when she was my teacher. I didn’t speak a whole lot of English then, but I suppose one does not need to be well versed in the language to sew a sundress or make a baked Alaska. A couple of months ago I started sewing again, and I thought about Mrs. Quiggle a lot, how she made me press open every seam before continuing on.


Then there was Mr. Anderson. He was my 8th grade social studies teacher. I had a crush on him. I don’t know why because he was not particularly handsome. I worked extra hard to submit an extra awesome book report on Nigeria. Before I moved away (leaving Minnesota for Oregon), he gave me a picture of him standing next to his wife. Nobody cared about his wife of course, but he was my favorite.

Today I’m also reading my 6th graders’ responses to this warm-up. The answer is there are 30 days left of school.



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Joint Investment

Would you have known immediately that the number 1729 is the sum of two cubes?

You think you’re so smart, but you’re no Ramanujan. He told Hardy that 1729 is the sum of two cubes in two ways: 13+12and 93+103.

I read The Man Who Knew Infinity a few years ago. I might check out the movie when it hits a theatre near me. Like Netflix.


Also, I subjected my students to this 14-minute podcast about Hardy and Ramanujan.

One more “fair share” task for my 8th graders from Peter Liljedahl’s site because I like it and don’t want to work in the textbook as our students are taking the Smarter Balanced Tests this week.

Joint Investment

Six years ago you made an investment with a friend – you bought a house together. It wasn’t only an investment, it was also a favor. Your friend didn’t have a place to live and didn’t have enough money to buy a house. So, you pooled your money and bought a $300,000 house for your friend to live in. You provided $50,000 for the down payment and your friend provided $25,000. Because of the size of the down payment it meant that the mortgage was relatively low – only $1000 a month – which your friend paid. During the six years all property tax payment were split evenly between you as were all major renovations and upgrades. Well, it is now six years later and your friend is getting transferred to Ontario. So, you have sold the house for $500,000 (the market has been good to you). There is still $200,000 outstanding on the mortgage. How will you split the $300,000 equity between you? Justify your decision.

A couple of solutions thus far:



Posted in Math 8, Problem Solving | Tagged , , , , | 1 Response

The Shoe Sale

(On a side note, I’m not sure what I love more, my left foot or Google Classroom.)

This problem is from Peter Liljedahl’s site.

The Shoe Sale

You decide to take advantage of a buy 2 pair get 1 pair of equal or lesser value for free sale at the local shoe store. The problem is that you only want to get two pairs of shoes. So, you bring your best friend with you to the store. After much deliberation you settle on two pairs of shoes – a sporty red pair for $20 and a dressy black pair for $55. You friend finds a practical cross trainer for $35. When you proceed to the check out desk the cashier tells you that your bill is $90 plus tax (the $20 pair are for free). How much should each of you pay? Justify your decision.

Peter lists this problem under “Senior High School (10-12).” I give it to both my 6th and 8th graders. I like this problem because I like hearing how kids think about “fair sharing.” A few 6th graders think each person should pay $45. I don’t think these kids have too many friends. (That was mean.)


One of my 6th graders says one person should pay 2/3 of the $90 and the friend pays 1/3. But her answers are $59.40 and $29.60, respectively. My math says 2/3 of 90 is 60, so I call her up to explain. She has her calculator in hand, and I see her punch in .66 while mouthing “two thirds.”

It was an opportunity for me to yell and scream at the children for turning a perfectly good number of 2/3 into mush.

Posted in Course 1 (6th Grade Math), Math 8 | Tagged , , , , , | 2 Responses

Hashtag MTBoS30

I’ve written two posts in the last 8 months. Naturally that means I’ll [try to] write 30 posts in the next 30 days. Anne Schwartz @sophgermain is entirely behind this. Hashtag MTBoS30.

We, Anne and I, each drive 70+ miles toward each other to catch up on life over a late lunch.

Unknowingly we both order the steak and arugula sandwich. I ask for mine to be toasted though. (I’m not sure what I think about people who eat non-toasted bread. What is wrong with you?) The mustard horseradish sauce drips out with every bite I take. I don’t want Annie to judge me, so I resist the urge to lick the sauce off my plate.

We talk about lots of things. She’s wise and bubbly and always unapologetic. Meaning she’s really lovely. I’m old enough to be her mother, but I’m listening and learning. I tell her a story that makes her nod out loud something like, “Fawn, you are the world’s biggest idiot.”

We both agree at one point that Tina Cardone @crstn85 is perfect.

I ask Annie about what it’s like to be white.

On the drive home I think about all the times I try to act white. I crank up Purple Rain and sing along.

Posted in General, Teaching | Tagged , , , | 6 Responses

An Update of Sorts

It’s been a while. Thought I should post an update.

I moved out to an apartment back in October, four days after breaking my foot. I planned the former, and the gods of stairs planned the latter. The foot is much better, but I’m walking with a discernibly cautious gait. I have two colleagues who broke the same [fifth metatarsal] bone; they healed completely after four weeks, and I’m still limping after four months.

My son — who just turned 21 — moved in with me. He has a part-time job and is my biggest cheerleader. Even when I’m attempting pull-ups, he cheers me on, You’re a champion, Ma! One more for Jesus!

I’m really happy. No, not 24/7 happy — these folks, if they exist, need to be punched in the face. I’m happy to still be in the classroom teaching mostly adorable middle school students. I’m happy that I’m healthy, eating and sleeping well.

I continue to present at workshops, always grateful for the opportunities to engage with and learn from other math educators. My schedule looks a bit crazy, starting with NCTM in April, but I’m excited to contribute a little bit and gain a lot at these conferences.

Around Christmas time I entertained leaving the classroom for a math coach position, but then I thought better of it. Maybe the same opportunity will come up again in the fall, I’ll worry about it then. As I write this, I’m thinking there ought to be at least 112 damn good reasons for me to leave the classroom because that’s how many students I have. God knows how much I love these kids.

Last weekend I got to play host to Megan Schmidt and her husband Scott. What a gorgeous couple, even if one of them is a Nebraskan.


with megan and scott with Scott

Here’s hoping I’ll catch y’all soon at a nearby conference.

Posted in Teaching | 6 Responses

Giving Feedback with a Highlighter

I attended John Scammell’s excellent 3-morning sessions on Formative Assessment at #TMC15. We were asked to share strategies that we may already be doing to give students feedback . I shared about how I used highlighters for this. I promised my group that I would write a short post about it, but I waited until now since I needed the school year to begin to have student samples to share.

I used highlighting to give my 6th graders feedback on their first PoW (Problem of the Week from The Math Forum).


It’s challenging, as I hope all PoWs are, and even more so when it’s the first one they get. I give no specific instructions on how they should write up their solution — nothing more than the usual “show all your work in order to receive credit.” I want to see what raw stuff I get on this first submission. We’ll worry about quality control soon enough.

I’m familiar with what I can expect with the first harvest of solution write-ups. One-fourth of the papers are pleasantly stellar, one-third show candid efforts (especially the ones with parents’ writings on them), another third make me get up and stick my head in the fridge to find a cold-and-alcoholic beverage, and the rest of the papers remind me that some of my 6th graders are still working on finessing the opening of their combination locks. The other right, sweetheart. There you go.

Years ago I taught a writing elective. I was at the beach — at the Oregon coast — because that’s where you should read and grade all writing papers. I forgot my red pen. I only had a yellow highlighter. The highlighter transformed my grading. I no longer cared so much about the writing mechanics — fuck spelling and punctuation and syntax. You got voice in your writing, kid. Your heart was wide open in this third paragraph. How did you know the rain smelled differently depending on what part of Portland you were in?

I highlighted sentences and words that spoke to me. I highlighted a brave sentence. I highlighted the weak ones too. The highlighter allowed me to interact with the kids’ writings differently. I didn’t add to or cross out anything they’d written. The highlighter didn’t judge the same way my red pen was judging.

And that’s the history of using the highlighter for me. But back to math. I have over 100 students and to write feedback for their bi-weekly PoW write-ups is all too time consuming. The different colored highlighters come to my rescue.

I’m going to continue using my binary scoring system because it worked well last year. I look through all the papers, separating them into two piles: papers that got it (full 1o points) and papers that fell short (1 point). These kids will get another week to revise their work and re-submit.

I use my yellow highlighter — just swipe it somewhere on their paper — to show that I’m having trouble understanding their work or that their work is lacking.




I use the pink highlighter to show that the answer is not clear, not specified, is partially or entirely missing.




I use another color (like green or blue) if the papers warrant another something-something that I need to address. I didn’t need to with this week’s PoW submissions.

If necessary, I will write on their papers directly. But I don’t have to do too many of these because kids’ mistakes, more often than not, are similar to one another.


When I pass the papers back, I tell students what each colored highlight means and what they need to do to revise their work, including coming in to get help from me. It’s a helluvalot faster than what I used to do.

Guess that’s it. Feels good to write in this space again.

Posted in Problem Solving, Teaching | Tagged , , , , , , | 24 Responses

A Love Letter to MTBoS (a.k.a. my #TMC15 keynote)

Thank you to Lisa Henry for asking me to talk at TMC and for believing that I could pull it off. Thank you to Baylor for the letter below that kicked me in the gut and said, “Stop whining and finish the slides.”


I looked out to the audience and began with this ad lib.

And off I went. Here are the slides for my keynote.

Thank you for being the kindest and most gracious audience.

Much love,

Posted in Teaching | Tagged , , , , , , , , | 6 Responses

A Book: Thinking Mathematically

I’m re-reading Thinking Mathematically, an assigned book from a math course I took years ago in Portland. I was teaching science at the time but signed up anyway because I’ve always loved math.

Thinking is still so good and resonates much more now that I’ve been teaching mathematics.

In the Introduction, under “How to use this book effectively!”:

Recalcitrant questions which resist resolution should not be permitted to produce disappointment. A great deal more can be learned from an unsuccessful attempt than from a question which is quickly resolved, provided you think about it earnestly, make use of techniques suggested in the book, and reflect on what you have done. Answers are irrelevant to the main purpose of this book. The important thing is to experience the process being discussed.

… our approach rests on five important assumptions:

  1. You can think mathematically
  2. Mathematical thinking can be improved by practice and reflection
  3. Mathematical thinking is provoked by contradiction, tension and surprise
  4. Mathematical thinking is supported by an atmosphere of questioning, challenging and reflecting
  5. Mathematical thinking helps in understanding yourself and the world

These assumptions need to live in our classrooms.

The problems in Thinking are mostly brief and simply stated — yet each one has the potential to make you linger a bit longer because you want to savor your own thinking. Not even productive struggle, this is sweet struggle.

How many rectangles are there on a chessboard? [Page 43]

I have just run out of envelopes. How should I make myself one? [Page 35]

A certain village in Jacobean times had all the valuables locked in a chest in the church. The chest had a number of locks on it, each with its own individual and distinct key. The aim of the village was to ensure that any three people in the village would amongst them have enough keys to open the chest, but no two people would be able to. How many locks are required, and how many keys? [Page 176]

I’m finding out that the 2nd Edition came out in 2010. Amazon does not have it in stock currently, but when it does become available, we can rent it for $54.77 or buy it new for $91.29. What??

Posted in Problem Solving, Teaching | Tagged , , , , | 8 Responses