Come and Observe

I don’t know what else to do except to suggest to an anti-Common Core parent to come and visit my classroom. Visit for a period or stay for the day. Come back again the next day. Stay for a week. Come back again next month. Become a parent volunteer in my room. Help me help a child because God knows we all have children in our room who could use some one-on-one support.

Parents should be our allies. A few are crazy. But there are a few teachers, doctors, plumbers, postal workers who are crazy too. Parents love their kids and want what’s best for them. They are concerned that their kids won’t be developmentally ready for Common Core (CC). They fear that it’s one-size-fits-all, that CC controls kids’ minds and stifle their creativity, that national testing and national curriculum will soon follow. The list of concerns just keeps piling up.

Both sides are quite passionate and create a lot of noise. I engage very little in this noise because I feel my energy in doing so does not get converted into anything useful. It dissipates too quickly, leaving me hollow and out of breath. But I’m talking now by writing. It’s midnight and really quiet here.

I want parents to observe their children do Taco Cart and Always, Sometimes, and Never. I want them to listen in on the kids’ math talks. I want them to walk in on a day when I’m doing direct instruction — and observe how much the kids direct their own learning, how much they try to make sense of something new.

I want parents to observe you — my local and online colleagues whose lessons I steal from and whose support only makes me work harder.

So, that’s my plan. I will invite my parents to visit my classroom whenever they want (I actually prefer unannounced) and see how a CC lesson plays out. The worst that can happen is I fail miserably. But I guarantee their kid will not.

Speaking of curriculum. (Wasn’t I?) I found some very old arithmetic textbooks, dating back to the 1800′s at Open Library.

page 13

Bonnycastle, John. Arithmetic… 17th ed. London: Longman, 1843. Print.

These prefaces are quite remarkable. I’ll just share from two textbooks.

Adams, D. (1848). Arithmetic: in which the principles of operating by numbers are analytically explained and synthetically applied : illustrated by copious examples : designed for the use of schools and academies (Rev. ed.). Keene, N.H.: J.H. Spalter & Co..

Exertion, then, to bring teachers to a higher standard, will be more effective in improving school education, than any efforts at improving school books can possibly be. It is here where the great improvement in must be sought. Without the cooperation of competent teachers, the greatest excellences in any book will remain unnoticed, and unimproved. Pupils will frequently complain that they have never found one that could explain some particular thing, of which a full explanation is given in the book which they have ever used, and their attention only needed to have been called to the explanation.

Colburn, D. P. (1862). Arithmetic and its applications: designed as a text book for common schools, high schools, and academies. Phililadelphia: H. Cowperthwait & Co..

In the first place, such tests are unpractical, for they can never be resorted to in the problems of real life. What merchant ever thinks of looking in a text book or a key, or of relying on his neighbor, …?

When a pupil, having left the school room, performs a problem of real life, how anxious is he to know whether his result is correct! Neither text book nor key can aid him now, and he is forced to rely on himself and his own investigations to determine the truth or the falsity of his work. If he must always do this in real life, and if his school course is to be a preparation for the duties of real life, ought he not to do it as a learner in school? Is it right to lead him to rely on such false tests?

Besides, the labor of proving an operation is usually as valuable arithmetical work as was the labor of performing it, and it will oftentimes make a process or solution appear perfectly simple and clear, when it would otherwise have seemed obscure and complicated.

But some of the exercise problems are just insane. I intentionally looked only for exercises in division of whole numbers. And all these textbooks were for school-aged children, grades 4 through 8.

1909, Walton & Holmes:

  • 408903 ÷ 3508
  • 147500 ÷ 6190

1921, Thorndike:

  • 748275 ÷ 825
  • 42974 ÷ 8523

1862, Colburn:

  • 55673 ÷ 6349
  • 2700684 ÷ 19743

1848, Adams:

  • 46720367 ÷ 4200000
  • reduce to lowest terms: 468/1184

1843, Bonnycastle:

  • 4637064283 ÷ 57606

Common Core looks better than this.

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MathEd Out

Adrian Pumphrey was very kind and patient when he interviewed me for this month’s MathEd Out podcast.

Other folks whom Adrian had interviewed thus far:

  1. Julie Reulbach — blogs at I Speak Math
  2. Dan Meyer — blogs at dy/dan
  3. Lynne McClure – Director of NRich
  4. Daniel Schneider — blogs at Mathy McMatherson
  5. Sue VanHattum — blogs at Math Mama Writes

Upcoming interviews:

  1. Bill McCallum — Lead author of CCSS
  2. James Grime – Numberphile
  3. Malcolm Swan – MARS

Thank you, Adrian, for the honor and pleasure to do this. I’m really bummed that I won’t be at #TMC14 to meet you in person.

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Rates and Proportional Reasoning

I’ve been hyper focused on “rates” and “proportional reasoning” for a project I’m working on. Not that one has to look far and wide either, unit rates and proportions are all around us. We intentionally and inadvertently compare things.

(HA! I didn’t even realize what this product was until I’m cropping and re-sizing them for this post. Really, I was in the same aisle getting lactase pills for my daughter!)

Take a look at this one product and its label. We can cover up just ONE piece of information — price, weight, “14-day” duration, purpose :), etc.  – and go to town on the [estimation] questions. Or, if we’re doing unit conversions, ask “How many grams are in 8.3 ounces?”

photo 1

When we have more than one size of the same product, it makes for a great real-world rate/unit rate problem. Prior to showing the image below, we may ask , “How much should a 30-day supply weigh? How much should it cost?”

photo 2

And I’m sure we can come up with lots of questions — or have the kids generate them – when we have more images of the same type of product.

Of course we know this already, so the main point of this post is to remind ourselves to capture images of stuff we already interact with daily and bring them into our lessons. Encourage our students to do the same. The stuff that kids see on a cold textbook page (even if they were images of real things) somehow appears removed and foreign to them. Heck, we hook the kids into caring immediately when we introduce these pics [or actual products if we got them] with, “Look, I was up all last night planning for this lesson while enduring a major constipation. So, pay attention.”

photo 3

photo 5

photo 4

And then there’s this set of images.

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

Math Talks and 180 Days Restored

It often takes just one teacher* to ask me to do something — like putting the sites back up — that motivates me like no other. Because I know that if I could do this for this one teacher, then I’m doing this for his students. I have heard a few teachers say, “I’m not sharing my stuff with the new teacher! I spent ____ working on this unit.” (This is not unlike divorced parents behaving like assholes when we’ve lost focus of the kids.)

So, 180 Days is back up again because Karlene’s comment and generous offer to help rebuild the site prompted both of us — she did more than half of the posts — to work nonstop in one day. (I still need to go back in to tag and check links on half of them, so please be patient.)

Kara, thank you for offering to help with Math Talks. Then Joe’s sense of urgency “Is the website going to be back up before the start of school? I hope so!” was all I needed to put aside sleep to get the site restored. For having only 15 weeks/posts on the site, the task to reformat each kid’s comment and insert images was hellish.

I’ve started a spreadsheet “Math Talks Prompts” that includes questions I’d used last year. I’m hoping you can add to and share it widely so we can build up this great bank of questions that we all have access to. It’s important that we don’t just throw out two random numbers connected by a random operation for students to do a number talk on.

Speaking of math talks, Jo Boaler’s How To Learn Math: For Students is up and ends mid December 2014. (You may start and end the course any time during this time period.) Spread the word! Our school will put it in the first week’s newsletter, we’ll mention it at Back-to-School Night, my colleague Erin will show some clips from the course in her Exploratory class. I think Jo’s course is one of the first key steps in bridging the gap between Common Core and parents who have lots of questions about CC.


* Andrew Stadel, don’t even try. Even though your tweet is pretty funny.

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The Right Question Institute


Isidore Rabi, winner of a Nobel Prize for physics, was once asked why he became a scientist. He replied: “My mother made me a scientist without ever knowing it. Every other child would come back from school and be asked, ‘What did you learn today?’ But my mother used to say, ‘Izzy, did you ask a good question today?’ That made the difference. Asking good questions made me into a scientist.”

A week ago my superintendent, principal, and 7 of us teachers attended a full day workshop The Right Question Institute in LA. Luz Santana and Dan Rothstein, authors of Make Just One Change, facilitated a worthwhile and engaging session, so I just want to share some highlights and my takeaways from it.


(Some of these might be direct quotes. I’m just writing from my notes.)

  • Not knowing what to ask is the fundamental obstacle to participating and therefore to learning.
  • The skill of question formulation is the single most powerful renewable source of intellectual energy.
  • How can we easily develop students’ question formulation skills? It’s simple. But simple does not mean simplistic — it means doing it so everyone can access it.
  • Six components of the Question Formulation Technique (QFT):
    1. A question focus — the teacher gives a prompt related to topic currently being covered in class, prompt can be visual. It should be a statement or phrase and not as a question. The simpler, the better.
    2. Producing questions — in small groups, students share questions that they have related to the question focus (prompt), one person records on large poster paper or whiteboard. But before starting, everyone is reminded of these rules:
      • Ask as many questions as you can.
      • Do not stop to discuss, judge, or answer any question.
      • Write down every question exactly as it is stated.
      • Change any statements into questions.
    3. Categorizing questions as “open” or “closed.”
    4. Prioritizing questions — choose 3 most important questions from list, pay attention to the question focus.
    5. Next steps — what’s one way you could use your priority questions?
    6. Reflecting — what did you learn and how did you learn it?


  • Luz and Dan are really lovely people. Warm, hard-working, fun. Their book — and this Institute — mark the arrival of a twenty-year journey for them! (Arrived, yes. Settled, no.)
  • This task of having kids ask their own questions is not unlike Act 1 of a 3-Act math task that many of us are familiar with.
  • But the QFT process can be used — and is used — in a variety of academic disciplines and in communities outside of school. (Their journey actually began when they worked on a dropout prevention project and heard from the parents who were not coming to the school meetings because they “don’t even know what to ask.”)
  • This is another powerful structure that empowers students when asking questions becomes a natural tool for them. They think more critically because the QFT process helps them hone in on their questions. Dan and Luz categorize the learning of asking questions as going from divergent thinking to convergent thinking, then that last component of reflecting is metacognitive thinking.
  • Teachers and students will get better at implementing the QFT. It’s building classroom culture, so it takes time.
  • We’re doing this already with our students to some degree with varying expertise. Maybe we just need to be more intentional about it. Give it a name.
  • If not, perhaps Make Just One Change.
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Finding Ways at WordPress

I have a new site because of the little note below. I thought about taking up boxing on roller skates because that just seemed much more doable than rebuilding the blog.

When we retire all QuickBlogcast® accounts on June 25, 2014, you will no longer have access to  your account, including its content, and your blog will no longer be available on the Internet.

Darling Nik Doran figured out a way to save all 192 posts, including the images. The work to rebuild 84 of the 192 posts that you see here had been daunting and desperate. Text-heavy posts were essentially just copy-paste-reformat. However, most of my lesson posts included images that were part of the story telling, and these just took a lot more time to reconstruct. The remaining 108 posts shall remain dormant as I doubt anyone will miss them.

With the exception of 2 posts, I kept all the post titles exactly the same as before, and with a much more receptive search button in WordPress, you should be able to find that post you are looking for or may have linked to.

I’m most appreciative of any and all comments you’d left for me in the old space. They too are saved.

The posts for 180 Days of Math at Mesa and MathTalks are also salvaged, but they’ll have to stay offline for now, or forever.

Thankfully Visual Patterns remains intact.

I hope you’re finding lots of ways to relax and replenish this summer. I have have few commitments to keep me out of trouble, but I’m much more rested and finding excuses to try a new IPA every now and then.


[Updated 07/16/2014]

Karlene Steelman helped me get 180 Days back up, and I finished restoring MathTalks.

Posted in Misc | Tagged , | 5 Responses

What Our Students Thought of Ability Grouping

A month ago I wrote about Ability Grouping and within that week asked my students for their thoughts, but I’ve been swamped with work to share any sooner. My teaching assignment was:

Geometry: 32 students. All were 8th graders, largest group we’d ever had, 45% more than the year before. A handful of them were not ready for the rigors of this high-school equivalent course; it was more due to scheduling that they ended up here. (We have about 200 kids in the junior high, 2 sections of each level, so it’s not easy to be flexible with our schedule.)

Algebra 1: 38 students. Ten were 7th graders, the rest were 8th graders, and 3 of the 8th graders worked independently out of the Algebra Readiness textbook at midyear as they struggled to continue on, but they joined the rest of the class for all problem-solving group tasks which happened about twice a week.

Math 6: 69 students in two classes, but 2 of them were in RSP for math, so I only saw them on Fridays.

My colleague Erin helped me give her students the same survey questions. I don’t know her exact roster counts, but she taught two classes of Pre-Algebra (all were 7th graders) and one class of Algebra Readiness to 8th graders.

I began by telling the kids a little bit about ability grouping at our school, that it existed in grade 7 and grade 8, that we tried to place them based on several measures (grades, work habits, CST scores, benchmark tests). I did not tell them how I felt previously or presently about ability grouping, but I wanted to learn what they’d thought.

I gave each student this strip of paper and asked them to check one box.


I then added these three questions:


I’m going to summarize what boxes the kids checked for both parts above like this:


From the Geometry kids (there was some city-level academic competition going on that day, so more absences than usual):


From the Algebra 1 kids:


From the Algebra Readiness kids:


From the Pre-Algebra kids:


From the 6th Graders:


So, about 83% (151/183) of the kids said YES to ability grouping. Sure, there were a few kids who seemed to have conflicting responses by checking NO to the first question but had more YES responses with the 3 questions that followed, and vice versa.

I don’t know.

I do know this: Erin and I really love our students and love what we do. She has a math degree, I do not, but we both love problem solving and are proud math enthusiasts. She let me talk her into going for a week-long training in Palo Alto to jump start — actually it was more of a revival of — a Math Teachers’ Circle in our area.

I want to believe that Erin and I made a difference in how our students felt about their learning of mathematics. Doug left a comment on my Ability Grouping post. His last paragraph strikes the perfect note of what I want to say right now:

I wonder if the bigger problem is teaching students to not be so concerned with who is “ahead” of whom. Maybe the problem has less to do with what class you put the students in, and more to do with how you treat them once they get there. We need to foster the growth mindset. Maybe our fixed-ability mindset (ala Carol Dweck etc.) primes us to be unnaturally sensitive about placement. Most of us will live and die always knowing there is someone, lots of people, more competent/talented/accomplished than we are at everything we do. But we have to live for ourselves, and pursue what we care about, regardless. The bigger issue is making sure every classroom has a good teacher presenting quality material. Then it doesn’t matter who is in what room with whom.

Thank you, Doug.

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Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers

Sue VanHattum’s blog Math Mama Writes was one of the earliest math blogs I frequented. Sue and ShireenDanKate, and Sam were among the first people who showed me - through their passionate writing - that there was an online community where we may share the teaching and learning of mathematics in the classroom.

When I started this blog, Sue dropped in to leave a comment or two. Or five. We even talked on the phone, and she shared with me how her son got his name. I remember reading someone’s post and wanting to leave a comment because I connected with the piece and its author in some small way, and inevitably I would find that Sue had already left a comment. This happened over and over again. I felt we were reading the same stuff; and the same stuff touched us in similar ways.

Then, within a year Sue asked if I would like one of my posts to appear in a book she was putting together.

So, it’s with much love and honor that I get to help launch Sue’s new book:

Playing with Math book

[cover art by Ever Salazar, @eversalazar]

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers brings together the stories of over thirty authors who share their math enthusiasm with their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math too.

To know Sue is to know that she loves teaching and learning mathematics, and she loves writing, therefore this book - this work of consummate love - has to happen.

Playing With Math is really a collection of love stories because the authors, including yours truly, want to share something we’re pretty crazy about. It’s the stuff we do beyond the regular school day - we play with math after hours, at the dinner table, on a napkin at the coffee shop, with our own child or with a neighbor’s child, at a family picnic, with our in-laws whom we don’t even like.

So, today is the first day of our crowd-funding campaign to cover production costs. We’re hoping to find support in our community of teachers and parents and math connoisseurs - a community of people whom I adore and respect. You can contribute anything from $1 to $1 billion. But for a contribution of $25, this wonderful book will be sent to you as soon as it’s printed. Please see more details here.

Thank you so very much.

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Ability Grouping

- Elementary school (Saigon)

My father is a well respected and loved math teacher at the local Catholic high school (grades 6-12) where my older siblings attend. The “grade” we get is simply where we are ranked in the class. Kim, 3 years older, is always ranked #1 in all her classes. My teachers, upon learning that I am my father’s daughter and Kim’s sister, openly express their disappointment that I don’t measure up. Kim must have taken all the smart genes and none was left for you, haha.

I think I know my times table, but when my teacher asks me for a multiplication fact and I don’t answer fast enough, my palm gets a big whack with the stick. If I — by sheer reflex of not wanting to be hit — pulled my hand back and made the teacher miss, then I would get double the whacks. So I have to use my left hand to hold the wrist of my right hand to keep it extended in place. I never cry even though it stings a lot.

- Middle school (Minnesota)

I’m learning English, so I have no clue what’s happening in any of my classes. I remember just copying word for word everything I see in the textbook onto my notebook. The longest word I remember copying is be-cau-se — because. I don’t know what it means, but it sure looks funny.

I remember seeing the words “thank you” in print for the first time. I already know the meaning because I even hear people say it back in Vietnam. I’m really confused though because if I had to guess its spelling, it’d look more like thang-kew. I mean I don’t hear the “you” part at all. People already talk so fast in this country, and now I learn they don’t even pronounce words correctly.

But math suddenly becomes my favorite period of the day because it’s the only thing I understand; and I’m even ahead of the class. I know this stuff already.

- High school (Oregon)

Freshman year I’m on my own in algebra class – meaning I work through the book by myself. I don’t know why, maybe because I’d passed some pre-assessment with a high score. Sophomore year, same thing happens in geometry. I don’t remember anything except my teacher’s jokes. When someone asks him an obvious question, he asks back, “Is the Pope Catholic?”

A month into sophomore year my English teacher transfers me out of his class and into the TAG (talented and gifted) class. He tells me my writing is really good. I don’t get it, but I’m not supposed to argue with the teacher. How can it be good when I just write three short paragraphs for homework each night about some dry prompt like: What do you know about the Three Mile Island accident?

So I get into this TAG class and quickly learn that it’s a big fat mistake. Kids in here actually havetalent, for God’s sake. They can play a musical instrument – you can hear them play. They are on the debate team – you can watch and listen to them argue with fancy rhetoric and big arm gestures. They can draw – you can stand back and admire their amazing handiwork. They can play a sport – everyone shows up to their games and screams out their names. In other words, they can all perform!

Who wants to read a 3-paragraph account of a nuclear meltdown? I’m such a loser.

But Joe is in TAG, and he makes the class bearable. He calls me beautiful. It does not matter that he’s the fattest boy in the school. Joe is an orator extraordinaire, and he’s sweet. I want to marry him some day because when someone calls you beautiful while no one else in the room sees you, then you just have to marry that person.

The above memories kept flashing through since our UCSB Math Project workshop last Thursday. My friend and co-presenter Jeff led us in a discussion about ability grouping. In dyads, we shared our thoughts on the what-when-where of leveling children in school. But first he wanted us to share about our own experiences when we were in school.

I held these beliefs about ability grouping:

We group kids all the time in sports, and no one thinks twice about this. You’re not playing on the varsity team if your skills are not of varsity quality. Why shouldn’t we group by math abilities too.

It’s easier to teach a class of students who have a common base of content knowledge. We should demand excellence at every level anyway. I don’t care what level you’re at, but wherever you are — and when you’re all at about the same level — I can focus better on your needs.

Students will fall even farther behind if we don’t help them shore up their skills and fill in the gaps. Now that would be even more criminal — pushing kids through when they’re not ready.

The 7th grade math curriculum is a waste of time. Just take a look at how well my 7th graders do in algebra without a lick of 7th grade math, and they continue to do well in geometry as 8th graders.

It’s easier to keep up with the curriculum pacing guide.

I no longer hold these beliefs. I’ve read enough about the detriments of ability grouping and tracking, especially for students of ethnic minorities.

I’m ashamed and surprised that I was part of the problem by supporting tracking because I’ve faithfully implemented problem solving into every math curriculum that I teach. But I don’t want to beat myself up too much about this because I’ve always tried to do right by my students. I know math ability doesn’t define them. It doesn’t define anyone. What defines any human being is our level of kindness.

I need to learn more, read more, pay attention more. I need to define my beliefs more clearly for me — so I may serve my students better.

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I’m very grateful to be here at the 3-day MAP Conference in South San Francisco — finally got to meet Malcolm Swan whose lessons I’ve used with my students for many years. I was delighted to see this slide because we did this lesson and it was one of my favorites.

Malcolm Swan

At the end of today’s session, we were asked to share questions that we may have for tomorrow’s panel of speakers. A teacher asked this question, and it stayed with me. He said something like this:

The students in the video [during Malcolm's talk] are awesome. But my students are not there. They are at zero. Not even zero, they are at negative something…

Negative?? Zero??

It made me sad to hear this. No matter how “low” his students are, no matter how out-of-control they appear, no matter how unmotivated they seem, they cannot be at level zero. That’s impossible.

We talk a lot about students’ mindsets. I worry more about the teacher’s mindset. Maybe this teacher didn’t mean it the way I’d heard it; but I’ve heard teachers say directly to me, “My kids can’t do that.”

How do we know that unless we give them a chance.

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