First Two Days of School

Tomorrow is the day. I’m excited to meet my new Math 6 students – all 71 of them, two classes of 36 and 35. I should know about half of the 33 Math 8 kids because I taught half of them in 6th grade. Then I get a big break in class size with just 9 students in Geometry. (We’re phasing out tracking, so we do right be these kids and we’re done.)

I have the first two days planned. My mind thinks in terms of conversations, so it’s just easier for me to write in this format.

Day 1

Math 6 (periods 3 and 5)

Hello everyone! Welcome to 6th grade math! I’m Mrs. Win — spelled N-G-U-Y-E-N — I’d be thrilled if you could spell my name correctly because I’ll do the same with your name.

Whatever seat you’re in right now is fine. We’ll have a seating chart by the end of the week; it’s mainly so I can quickly learn your name. Okay, fire drill. It’s the most important procedure I have for first day because you never know, so listen up.

I tell them about the escape route and something about not panicking. Right.

Now I need to take attendance. If I mispronounce your name, I apologize in advance and please correct me. Also, if you go by an entirely different name, please let me know. I once had a student named Anne Marie — her real name — but she went by Bob. Yup, Bob. Reply with a yes or hereNo grunting.

Oh, how many of you have older siblings who had me as their teacher? Yeah? Did they say that I’m really mean? Well, your sister is a liar.

Enough chit chat. Let’s do some math. Please take out a piece of notebook paper. Name and date in upper right hand corner, same as what you’ve been doing for the last 25 years. Write Pattern #2 at the top of your paper.

I show them pattern #2.

You’re seeing the first 4 steps of this pattern. Please draw what you think the next step, step 5, might look like. It doesn’t have to be pretty — just something to show that you know how the pattern is growing.

This might very well be the first time these kids work with a pattern like this. I don’t know. But I’ll guide them through.

Well, what we just did is a warm-up. As we do more, and you get a hang of it, it’ll go faster. By the end of this week, we’ll skip drawing the next step and go right into trying to find the equation. We do a different type of warm-up each day, so on Mondays we do a visual pattern. I’ll tell you what we do on Tuesdays when Tuesday gets here. You’ll need to do tomorrow’s warm-up on that same paper, so let me see you put it away in your binder where you can quickly retrieve it tomorrow. Do it now.

How’s your first day so far?… Good to know. Okay, that’s enough sharing.

I’m passing out a puzzle called Noah’s Ark. I’m willing to bet that in five minutes, it’ll become your favorite puzzle ever. Please follow along as I read it aloud.

Please quietly read it again on your own…

I then ask a few questions to make sure they understand the problem and what it is they are trying to solve.

Okay. I’m going to give you some time to work on this problem quietly by yourself, I think 10 minutes. I’ll set the timer. When the timer goes off, I’ll put you in random small groups of 3 to continue working on the problem. My sincere hope is that I’ve picked the right problem, meaning one that you understand what is given and what is being asked of you, but that it makes you struggle. Oh my God, you have no idea how much I love for you to struggle in this class! You’ll hear me say that word a lot — struggle. It’s all good. You know how after a good workout, your body feels kinda sore? Well, I want your mind to be sore like that.

AND OH!!! This is really really important. Rule #1 for you in my class: DO NOT TELL AN ANSWER. Meaning when you think you have an answer to a problem, please don’t just blurt it out. I know I completely shut down and don’t care to work on the problem any more when somebody does that. So, please, keep your wrong answer to yourself.

I suspect our 55-minute period would end before they even get into small groups. Depends on how long our warm-up takes. (I don’t care if the warm-up takes up the whole period. Initial tasks that are part of the curriculum and norm-building cannot be rushed.)

About 2 minutes before the bell rings…

What’s on this quarter sheet of paper is instruction on how you and your parents can subscribe to the texts that I send out. It’s mostly to remind you of homework. You can only receive texts from me, you cannot reply. You can also receive my “text” message as an email instead. Show it to your parents.

Sadly, there is no homework tonight for math. But you’ll get about 3 hours of math homework tomorrow night, so clear your calendar.  Of course, you’re welcome to continue to work on the Ark problem, but you don’t have to. Remember not to share the answer!

When the bell rings, I need you to be seated and quiet. Please pick up any trash around you and toss it into the trashcan by the door on your way out. Thank you. Have a great day and I’ll see you tomorrow.

Math 8 (period 2)

Having taught half of these kids already in 6th grade will make it easier for me to call them by their name. Same as Math 6, we’ll start immediately with a visual pattern, but pattern #1 for these guys.

Then our math problem is the classic The Proof is in the Pudding.

Geometry (period 1)

I just taught all 9 of these kids last year in Algebra 1. Also, pattern #1. So sure we did this pattern already last year, let’s see what they remember.

They get Using Fibonacci Numbers. I wrote a short blurb here.


Day 2

Math Talks will be our warm-up for Tuesdays. I still need to figure out which of these to ask first — and create a thoughtful sequence. Since I’m only doing one a week, all I need are 40 really good ones.

Then we’ll continue with the problems from wherever we’d left off. I imagine we’ll be in small groups and then on to whole-class sharing and reflecting.

If we have time, I’ll go over everything they need to know about the class — all on one page or I slit my wrist because these are really dry.

image of geometry class

Geometry

Math 6 and Math 8

Math 6 and Math 8

So, I think after two days we’ll get these 3 procedures/routines sorta established:

  1. fire drill
  2. warm-up routine
  3. dismissal bell

And I got 1 rule out of the way, even though I’ll remind them of it each and every time we do problem solving:

  1. never tell an answer

Kids forget things you tell them anyway, so I figure it’s better to tell them in context when they need to be doing the stuff.

I stopped having parents sign my rules/procedures handout. It’s not that sacred.

I’ll probably assign textbooks by the end of the week and give them their individual access codes to the online textbook and resources.

I’ve already assigned a Math Forum PoW to each class and will need to give each kid a log in ID and password (it’s rather generic — no one is getting a handout for anything — it’s just “your first initial plus your… plus… “) to allow students access for online submission of their solution.

I’ll update should we end up doing something entirely different like assembling Estes rockets and dissecting fetal pigs. (These were highlights from my science teaching days.)

Don’t forget to tell kids how amazing you are.

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The Number Sense by Stanislas Dehaene

I heavily skimmed the middle parts of this book when I bought it in May 2012. [Thanks to Christopher Danielson for recommending it.]

photo (9)

I’m re-reading some parts now, and the sub-section Teaching Number Sense [pages 124 - 128] resonates with me, not just in elementary school mathematics, but in K-12 mathematics.

If my hypothesis is correct, innumeracy is with us for a long time, because it reflects one of the fundamental properties of our brain: its modularity, the compartmentalization of mathematical knowledge within multiple partially autonomous circuits… The numerical illiterate performs calculations by reflex, haphazardly and without any deep understanding.

… A good teacher is an alchemist who gives a fundamentally modular human brain the semblance of an interactive network. Unfortunately our schools often do not quite meet this challenge. All too often, far from smoothing out the difficulties raised by mental calculation, our educational system increases them… But our schools are often content with inculcating meaningless and mechanical arithmetical recipes into children.

This state of affairs is all the more regrettable because… most children enter preschool with a well-developed understanding of approximation and counting. In most math courses, this informal baggage is treated as a handicap rather than as an asset. Finger counting is considered a childish activity that a good education will quickly do away with. How many children try to hide when they count on their fingers because “the teacher said not to”?

Despising children’s precocious abilities can have a disastrous effect on their subsequent opinion of mathematics.

… It seems more likely that many of these “mathematically disabled” children are normally abled pupils who got off to a false start in mathematics. Their initial experience unfortunately convinces them that arithmetic is a purely scholastic affair, with no practical goal and no obvious meaning. They rapidly decide that they will never be able to understand a word about it. The already considerable difficulties posed by arithmetic to any normally constituted brain are thus compounded by an emotional component, a growing anxiety or phobia about mathematics.

… We need to help children realize that mathematical operations have an intuitive meaning, which they can represent using their innate sense of numerical quantities. In brief, we must help them build a rich repertoire of “mental models” of arithmetic… The day the teacher introduces negative numbers and asks pupils to compute 3 – 9, a child who only masters the set scheme judges this operation impossible. Taking 9 apples from 3 apples? That’s absurd! Another child who relies exclusively on the distance scheme concludes that 3 – 9 = 6, because indeed the distance from 3 to 9 is 6. If the teacher merely maintains that 3 – 9 equals “minus six,” the two children run the risk of failing to understand the statement. The temperature scheme, however, can provide them with an intuitive picture of negative numbers. Minus six degrees is a concept that even first-graders can grasp.

But let us leave this chapter with a note of optimism… In the United States, the national council of teachers of mathematics is now de-emphasizing the rote learning of facts and procedures and is focusing instead on teaching an intuitive familiarity with numbers… Number sense — indeed, common sense — is making a comeback.

In fact, most children are only too pleased to learn mathematics if only one shows them the playful aspects before the abstract symbolism. Playing snakes and ladders may be all children need to get a head start in arithmetic.

By the way, I don’t read this and put the blame entirely on myself and my colleagues. As long as we place more emphasis on test scores than we do on learning, we are at best hypocrites.

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Privilege

The word privilege is being spoken and written many times over. Within the past couple of years I’m seeing and hearing privilege used in an undeniably distinct context. (Or it could be that I was unknowingly and partially deaf and blind to this context.) The word is written on cardboard signs, on people’s faces — and no matter what surface it’s on, the impact it has seems unbearable to the canvas that holds it.

I was organizing my classroom yesterday, putting away new supplies, tossing out items that I’d kept for too long. I have enough paperclips to last me two more lifetimes. Elmer’s glue bottles and glue sticks fill up an entire shelf. Same with staples and pattern blocks. And why would I get mad at a kid for not having his pencil — I have a shitload of pencils. I remember feeling a vague sense of shame of not having certain school supplies when I was in grade school. I remember mashing up rice to use as glue.

Kevin was a black teacher-turned administrator at my former school. When his second daughter was born (maybe 15 years ago), he said, “I thank God I have daughters. It’s hard for a black boy to grow up in this country.”

My husband is white. It never occurred to me how white he is until we were walking the streets of southern Vietnam. People looked at us (much more at him than at me) with foreign expressions. I felt safe with him by my side. Although I had no reason to not feel safe. I was back in my homeland — unknown to everyone around me — yet I was thankful to have a personal bodyguard because Hey, I’m with the big white dude.

Graham Smith, age 11. Me, age 11. He said to me, “Go back to your country.” I actually didn’t understand what he said, my Vietnamese girlfriend provided the translation. His expression matched what she said. I’m terrible with remembering even just first names. But I remember Graham Smith.

Michael missed the bus and had no other ride home. I went to the office to see if I may have permission to take Michael home. My vice-principal, Mr. M, reminded me, “Fawn, he just threatened you last week! And no, you may not transport a student.” (Right, when I sent Michael out of my classroom, he said he wished he had a gun.) I said something like, “I don’t think he has a gun on him though. C’mon, I’ll sign whatever papers. The kid needs a ride home.” Realizing that I was ignorant of the teacher handbook, Mr. M got up from behind his desk and approached me, close enough so he could whisper, “A young Asian teacher should not take a black kid home.” I never thought that statement appeared in the teacher handbook, but what struck me was Mr. M, himself a black man, was saying this.

One year the housing committee at my college decided to move our entire floor of student residents to a different building on the other side of campus because it needed our floor for the football players to move in. Upset, I went to the school’s newspaper in hoping they’d give us a louder voice of protest. Near the end of our conversation, the interviewer said to me, “You are very beautiful. For a Vietnamese.”

Poor. Refugee. Gook. Boat people. Foreigner. Young. Asian. Vietnamese.

It’s been a quiet storm for me.

It’s been a violent storm for others.

It was a fatal storm for Michael Brown.

I close my eyes and take your hand. We ride this storm together, and this shall be my privilege.

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Pacing Guide

For someone who has openly admitted to not following curriculum pacing guides, I sure spent a ridiculous amount of time churning one out. Our middle school is adopting CPM Core Connections 1, 2, and 3. Aside from our own reviews, the decision to go with CPM were also based on:

  1. Desmos is embedded in many lessons
  2. Other teachers’ reviews, including Riley Lark’s

I don’t know if this would be of any use to you, but I might as well share the doc math 8 pacing 2014-2015. It’s kinda pretty.

pages 1 and 2

pages 3 and 4

I replicate our school calendar and put in all the holidays and half-days. I go to each chapter in CPM and write down the guiding questions. Matching up the standards to each chapter was a pain in the ass. (CPM does it the other way around: they have the standards in one column and the different lessons that cover those standards in another.) The suggested number of days for each chapter does not include assessments, so I add about 6 days on top of whatever CPM recommended. I’m going to post the pacing guide near my desk — probably the only document I will print in full color this school year.

(Oh, I took out Chapter 1 because it’s on problem solving. C’mon, I got this.)

Then I’m going supplement it like crazy. I can’t teach straight from the textbook. Just can’t. So the 6 days that I add to each chapter will hopefully allow us some wiggle room to do other stuff.

Other stuff includes, but not limited to, what you see on the right sidebar of my blog.

We also need time to begin each class period with math talks because it was one of the most powerful things we did last year. (Grrrrr. Just realized that most of the images on the math talks site are not there. Why now.)

I was brainstorming with a couple of 6th grade math teachers at another district, and we were listing out a possible warm-up/math talk schedule, something like:

My assignment this year looks almost like last year’s: 2 sections of Math 6, 1 section of Math 8, and 1 section of Geometry [1].

I wish you a healthy school year. Teach what you love and love the kids. Follow the rules, but break a few if doing so makes it better for the kids.

 

[1] I’m happy to say that we will no longer be tracking kids in math. However, we need to finish out what we’d started with these 8th graders who took Algebra last year as 7th graders. So this group will do some geometry, some stats, and a whole lot of problem solving.

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Teaching is hard work.

Teaching is hard work.

We struggle to make the lesson move forward the way we imagined it would. We fail to sustain the mathematical conversation outlined in the teacher’s guide. We gain weight. We lose humor. We allow inertia to overstay.

We feel less whole because we keep a mental scorecard — our failures are ahead by five. And it’s only December. Or, it’s already December.

But if we know that teaching is hard work.

Then we are supposed to feel how hard it is.

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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.

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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

From www.aish.com:

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.

Highlights

(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?

Takeaways

  • 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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