Jelly Beans or No Jelly Beans

What’s not to love about Would You Rather; I use it with my students and always recommend it as one of the great warm-up routines. This one caught my attention last week.

Each entry always includes this statement:

Whichever option you choose, justify your reasoning with mathematics.

This statement is important, especially the word “mathematics,” because you might have a student who says [truthfully] that she doesn’t like jelly beans or is allergic to them and will prefer to give them all away. Then, you might have another student in the same class who [untruthfully] makes the same claim to avoid having to do any maths. There’s also that thoughtful student who wants to give more to his friends and keep fewer for himself. Or a student might consider giving more away to make friends. If I were to pose this question to my students, I’d mention the above possible reasonings, but then I’d add, “This question assumes that you love jelly beans and want to keep more of it for yourself. For now, it’s the mathematics we’re after.”

I didn’t ask my students this question though, I asked them to choose between this question and the one on the right.

As a student, would you rather be given the problem on the LEFT (jelly beans) or the one on the RIGHT?

Using the same image above, I asked on Twitter and of my colleagues.

As a teacher, would you give your students the problem on the LEFT (jelly beans) or the one on the RIGHT?

*****

Out of my 68 sixth graders, 71% of them chose the left problem. The words they used for their reasoning:

colorful, vivid imagination, visual, more pleasant to the eyes

interesting, engaging, not boring, not basic

better reason because you like jelly beans

My fellow educators, meanwhile, overwhelmingly chose the left problem — of the 781 people [at this moment] who took the survey, a whopping 90% chose the left problem.

Well, I prefer the one on the right [that I’d typed up]. How did I get it so wrong? I’m normally not this lame. But, truth be told, I don’t love the jelly beans question. At all. Maybe the one on the right is the wrong “fix” for the left one. If I could retype the problem on the right, I’d remove the equal signs since the question is just asking which one yields a larger difference, not caring exactly what each difference is.

I want to believe that anyone who spends 5 minutes with me learns that I love mathematics. I love numbers, I love math problems and don’t give two shits if they are real-world either. I’m the one who loves the problem about carrying 3,000 bananas across the desert and the one about the emperor pouring oats on every other guest’s head. One of my 247 all-time favorite problems is Noah’s Ark, even if I grew up in a house with a Bible in every corner and found it hard to wrap my head around this story. (However, Eddie Izzard’s take on the Ark — language caution — makes me laugh.) I love problems that are simply stated, yet they beg you to savor your perseverance as you think deeply and creatively. There’s great joy in solving a good problem, especially the ones that at first blush, you weren’t even sure how to begin.

The jelly beans problem above is not one of these problem-solving tasks. It asks for a mathematical justification, so I’m going to assume that the mathematics is finding the difference or another arithmetic operation. I see it as a number talks problem. Students get to share their strategies. Mine might include:

364 minus 188… I’d need 12 more to go from 188 to 200, then 164 more to get to 364, so the difference is 176. Similarly, to do 281 minus 137, I’d need 63 more and 81 more, or 144. Problem A has a bigger difference of 176.

Comparing the two totals, 364 and 281, the difference is 19 plus 64, or 83. While the difference between the give-away quantities 188 and 137 is 51. I start out with 83 more in problem A, but I only have to give away 51 more, so problem A leaves me with more to keep.

That’s why I prefer the one on the right. Numbers are beautiful. I want students to focus on the numbers and play with them, learn to regroup, try massaging them and making them flexible, be comfortable with numbers. Math is badass, so let’s do maths for maths’ sake. I feel protective of numbers and don’t see why they need to be dressed up in colors or dunked in forced contexts. (I suddenly think of little dogs in ridiculous outfits that I doubt if anyone asked for the dogs’ permission.)

Nine out of ten of you disagreed with me. That’s okay because I can make phở better anybody. But guess what though? My own 23 and 25-year-old kids chose the one on the right. This fact was comforting! Sabrina (23):

If you were one of the survey respondents, I thank you thank you thank you.

Posted in Course 1 (6th Grade Math), Course 2 (7th Grade Math), Teaching | Tagged , , , | 3 Responses

2019 Is an Odd Number

The arrival of 2019 means I have to scroll down even farther to find my age year when I fill out an online form. Ugh… 1985… 1975… 1970… 1967… Here it is… 1965!

I just came back from a short trip — via long-ass flights — to Melbourne for my niece’s wedding. I did a lot of walking and eating (not unlike what I do elsewhere), but the highlight was seeing my all-time favorite, koalas.

             

Around this time, two years ago, I wrote These Twenty Things — the nerve I had to suggest we should do this and that. But, I do wish I had more time to write because recording in this space helps me reflect on what I enjoy most about teaching, which is mainly about what my students take away from a lesson, and perhaps more importantly, what they put into it.

There are a variety of things in education that I still don’t have a good grasp on, like differentiation and Problem-Based Learning (PBL). I get what they are, I just don’t think they play out in the classroom [of 35 students] nearly as efficiently and effectively as intended. They are hard to do, most teachers have not had the training, or the training they get is from people who have never consistently implemented them.

But here are a few things I trust I have a good handle on.

Begin with a challenging task so everyone has access to it. Fully invite students to work on the problem, individually at first, then in small groups, then with the whole class. When sufficient time has been devoted to this (this can mean 30 minutes or two days, depending on the task and your students), then go do your regular routine, but invite students who finish the regular stuff to continue with the challenging task. I normally see this gets flipped around a lot, that teachers ask students to do the challenging task after they finish their regular work. The problem with this is 1) at least half of the students don’t get to it, and 2) those who get to it don’t care about it simply because the teacher didn’t care enough about it to fully introduce it. It’s not lip service when I introduce each PS with, This is definitely my favorite one!

Wait time and asking for a classmate’s help. Y’all know about the wait time. I usually wait, then I say to the student, “Would you like to call on a classmate to help you?” If the called-on student is not able to help, then I ask the same of this student. This should keep more students paying attention, and it’s one more way for me to stay out of it.

Deal with “bad” behaviors in a different (unexpected?) way. I have two recent examples. I was on detention duty, and instead of copying down a selected passage we gave, the student had written a very angry note to another teacher. He had hoped to hide it from me. When I finally got him to produce the note and read it, he started to tear up. I said, “Do you feel better now that you’d written all this down?” He said he was mad and didn’t mean anything by it. I said, “You wrote it, and I read it, and now it’ll go into this garbage can. Done. Sometimes it helps to get it on paper.” Another one was when a student brought a pencil to me and said, “It has bad writing on it.” Along its skinny spine was the inscription: fuck you bitch. I thought of one particular child who may have written it. The next day, at the start of each class, I projected the pencil under my doc camera. I said, “The spelling is all correct, that’s always good, but punctuation needs work. Anyway, if this is your writing, I hope it was a good stress release. Next time though, please write it on a piece of paper instead, this was our classroom pencil, and now I have to throw it out. Waste not!”

Go ahead and give your students lots of advice because you can’t do this with adults without risking getting punched in the face. My usuals:

  • That soda is not good for you. Eat a doughnut instead. (Hey, the sugar ratio of soda to a doughnut is 3.5 to 1.)
  • If you want to cheat off of your friend’s paper, I offer a free how-to clinic at lunch. I mean you do a horrible job at this, I can TELL for chrissake.
  • It’s not all about you. Learn that early and learn that fast. Your parents may love you unconditionally, but have you ever tried to wake them up early for no good reason?
  • Always brush your tongue too.
  • Don’t trust places that claim “We’re like family,” and yet they don’t let you eat for free.
  • Your real friends are not the ones who attend your party. They are the ones who show up when no one else does.

Oh, and there’s a book that you or your school should get. It’s Necessary Conditions by Geoff Krall. I know it says “secondary math,” but that’s some marketing talk, it’s really for any teacher, you!

And finally, I’m incredibly honored and grateful to be at the following meetings this year:

  • February 20: Washington ESD, Vancouver, WA, full-day workshop
  • April 5: NCTM Annual, San Diego, IGNITE
  • April 25: Ross Taylor Symposium, Duluth, MN, full-day workshop
  • April 26: MCTM Spring Conference, Duluth, MN, keynote + session
  • May 3: Wisconsin Math Conference, keynote
  • June 19: HIVE, Open Up, Atlanta, talk + panel
  • July 11: CAMT, San Antonio, keynote + sessions
  • August 7: Ohio Annual Meeting, keynote + session
  • August 15: NYS Master Teacher Program, full-day workshop
  • May 8, [2020]: OAME, Ontario, featured speaker

I sincerely hope I get to connect with you at one of these places!

Posted in Teaching | Tagged , , , | 2 Responses

Mrs. Quiggle

I didn’t know they made teachers so old, but Mrs. Quiggle was that old when she was my 8th grade Home Economics teacher. She perched on a high stool in the corner of the classroom, leaning over a wooden podium that she used as her desk. Home Ec was my favorite class, along with math — two classes that didn’t require a whole lot of talking in front of your peers, you just gotta follow the instructions. There was one instruction that I tried my best not to follow, and that was pressing the seam open after sewing a set of stitches. Oh good Lord, ain’t nobody got time for this laborious step, and I hated ironing more than sin.

Mrs. Quiggle could always tell though when I skipped the ironing nonsense, “Now, here, young lady, you didn’t press the seams open again! See how it’s puckered here and not lying flat as it should here? I’m going to need you to remove these stitches and start over again.” All I wanted to say in reply was, And I’m going to need you to retire, Mrs. Quiggle, before your body gets cold.

I sewed pretty sundresses with gathered ruffles and biased trimmed shorts. I made baked Alaska and chocolate fondue. I appreciated Mrs. Quiggle’s teaching and all, but I wished she’d stop bothering me about the pressing-of-the-seams. Why couldn’t she be like other normal old people who took breaks often and drank tea and ate Honey Maid graham crackers?

It was now springtime. I went to check the mail and found a letter addressed to my parents from Mrs. Quiggle. Well, hell, Mrs. Quiggle, you know my parents are still back in Vietnam, and it’d be a hundred years before they could come over! By the way, they don’t know English anyway. What is the point of writing this, Mrs. Quiggle, what could you possibly want to tell them — how I failed to press the seams between stitchings?!

I opened the letter, read the full-page of Mrs. Quiggle’s perfectly slanted handwriting to my parents, beginning with, Dear Parents of Phuong Nguyen.

I sobbed. I read it again and sobbed. Mrs. Quiggle wanted my parents to know that in all her years of teaching, I had surpassed the number of points earned by any student by a wide margin. I got well over 200 points, beating the last highest score of 70 something. (I should have this letter saved in a box somewhere — the same box where I keep my three children’s ultrasound images.)

She never had to remind me to press the seam again. I continued to sew through high school, through college, through mommyhood. The secret to a beautifully sewn article is in the pressing of the seams. This sets the stitches and removes tiny wrinkles. It’s like origami where each fold needs to be creased precisely and sharply before the next fold. It’s like doing the right thing the first time when we already knew what the right thing was. It’s like telling the truth the first time when we already knew what the truth was.

Posted in General, Shallow Thoughts | Tagged , , | 2 Responses

St. Cloud, Minnesota

I don’t remember the landing. It’s been a very long flight. Nor do I remember walking through the airport. We have no luggage anyway, like none.

My first memory of America is sitting in the back seat of TuAnh’s uncle’s car — an Oldsmobile wagon with wood panel trim. I’m almost eleven and a half years old, and this is the second time I’m in an automobile, a car car, which is much smoother than a bus or a van, and you’re not squished between strangers. The Oldsmobile is taking us straight home, not having to make a million stops along the way like my last bus ride from Saigon to Mũi Né.

Home is in St. Cloud. I’m not yet aware of how far it is from Minneapolis. It’s dark outside, around midnight dark, but my eyes are fixed on the passing landscape. I’m tired but I want the ride to last; I feel like I belong to a rich family that can afford a car.

TuAnh is my oldest brother’s wife. She’s the prettiest lady. The uncle’s family will share their home with us, and us being six people. The uncle and aunt have six kids of their own for a total of 14. (This is the first time I pause to realize this number. When you live in Vietnam, and there’s still floor space in the house to sleep on, then another kid will be born. My mother comes over to America and thinks it’s an utter shame to use garage space for cars. My goodness, a family of eight can live comfortably in this spacious 2-car garage.)

The aunt has chicken phở already made. It’s the first time I have the chicken version. She says the mint is from her garden. You’re supposed to eat phở with basil, but nobody cares, there’s mint in St. Cloud!

I will sit and watch the news with the uncle. I have no idea what they are saying, but I just like seeing white people’s faces and listening to how fast they talk. The best part is there’s always something on TV, there’s no curfew. I have two favorite shows, The Price is Right and Happy Days. You don’t have to understand very much English to watch The Price because prices are numerical, and English numbers look the same as Vietnamese numbers, except Americans are weird to write $50 instead of 50$. They claim to read from left to right too. I like Happy Days because it’s a show with cute boys, Chachi and Fonzie. (My family calls me Fawnzie. My name morphed from Phương to Fawn to Fawnzie. More recently, my son Gabriel probably sensed that I was stressed in our conversation and said, “Mom, I need you to be Fawnzie right now.” And I knew what he meant.)

English class is the hardest. Each word has way too many letters. While sitting in the school office waiting for the uncle to enroll me, I learn the spelling of the word(s) you say when you want to thank someone: THANK YOU. I don’t get it. I don’t hear the YOU part at all when people say it; until then, I thought it was one word, you know, THENGKEW. I believe Vietnamese is a monosyllabic language. Vietnam is actually Việt Nam. Saigon is actually Sài Gòn. While Nguyen might be the longest Vietnamese word (I don’t know, is it?), it’s just one syllable, so it’s Nguyễn, not Noo-yen. I spend hours breaking up each word into parts, I can only remember the word BECAUSE by seeing it as BE-CAU-SE to write it down. I am a mute in all my classes. I only talk when I’m with my ESL teacher, Mrs. Schnettler. Then eventually — a long long time really — I wake up one morning and realize my thoughts are in English. Someone has flipped the switch in my brain. Except it’s one direction, I can’t flip it back.

I spend the first eleven years of my life seeing only brown eyes, so it’s pretty cool to see other colors, shades of green and blue. Weirder is when kids from the same parents have a mix of colors. Weirdest is when a blue-eyed person sees the same red color on an apple as a brown-eyed person. Speaking of eyes, or just eye, Graham Smith has only one good brown eye, and he’s the one who yells at me to go back to Vietnam. The uncle’s daughter translates his words for me. I want to punch him in the face, knocking his eyeball out of his head, but then he’d be blind.

My sister Kimzie is three years older, so we’re now 12 and 15. (Her name went from Nga to Kim to Kimzie, which is dumb, at least Phương and Fawn start with the same sound, she says she wants to go from three letters to three letters and no more.) We know two lines from a Peter McCann’s song, “Do You Wanna Make Love,” and we belt them out at all hours of the day. Just two lines over and over again: Do you want to make love… Or do you just want to fool around… Then one day, my brother’s friend asks him if we girls knew what the words “make love” meant. We shake our heads and continue singing.

The six of us have now moved out to our own house. It’s a big white house with a big yard, there’s a porch too. In the winter, the snow would pile up as high as the single detached garage in the backyard. I make Jell-O by just leaving it outside for 30 minutes. I remember the few days in the dead of winter when we run out of oil to heat the house. I learn to ride my bike around the block, in the summer that is. A friend was surprised to learn that I didn’t know how to ride a bike until I was 13. I told her it was kinda tough to learn to ride when I didn’t own a bike growing up. Obviously, I didn’t know how to swim either. What sad kid doesn’t know how to swim in the “land of 10,000 lakes.”

I get to visit St. Cloud this August; it’ll be my first time back since I left in 1979. I’ll be facilitating a full-day workshop, and St. Cloud will just be 70 miles away. I’m flushed with nostalgia and gratitude — going back to my first home in America.

Posted in Shallow Thoughts | Tagged | 44 Responses

Another Round

Exhausted and hungry, I walk to the restaurant a hundred feet from the hotel’s lobby. The hostess greets me and asks how my day has been. I tell her it’s been a long day, that I just came in from LA on a 5-hour-plus flight. She asks about my reason for being in Philadelphia. I tell her I’m here for a math conference, and she volunteers, “Oh… I’m not a big math person.”

I follow her to my table and want to say:

What the fuck does that even mean that you’re not a big math person??? Are you a small or minuscule math person then?!? I don’t care if you say that you’re not big on eating raw octopus or fried worms, but math??!!

Her nonchalant proclamation is the last thing I want to hear this evening. She doesn’t know that her words form the straw that breaks my mathematical patience’s back. I am hungry, how dare she! She doesn’t know that I hear the likes of that statement each and every time people learn I’m a math teacher.

I think about my keynote at 8 AM tomorrow and how I open with a story about running into a former Navy SEAL parent at the gym only to hear him confess he’s afraid to see me because I might ask him a math question.

So many people don’t like math — they are just not big math people.

My annoyance at her words quickly turns into sadness and guilt. I know I have students who may utter the same words leaving my class. While I believe I have made great strides in improving math learning and math teaching in my classroom, I haven’t done enough, there’s still a lot of work to do.

I can do better and I will, I get another round of teaching mathematics starting on August 22.

Have a restful summer, everyone.

Posted in Teaching | 15 Responses

House Cleaning and Lesson Planning

I posted this on Facebook:

There is something else that I do way better than teaching mathematics, even though teaching has been a 25-year plus career. That something is house cleaning.

Then, a friend asked for advice on this, adding, “Will desperately be awaiting your response.” I responded with:

Thought no one would ever ask. :) Here comes the list, the order is important.

  1. Throw everything out.
  2. When done with step 1, repeat step 1 again bc we both know you really didn’t throw everything out.
  3. With remaining [ideally just 3] items, ask, “Is it really really pretty?” If so, it should be displayed in your home in a pretty spot. Ask, “Is it useful, like a wine-bottle-opener type of necessity?” If so, keep it in a drawer.
  4. Unless it’s a piece of furniture, a houseplant, or a 4-legged friend, forbid it from touching your floor.
  5. Counter space is only for items that do not fit inside a drawer/cupboard and are used almost daily — e.g., toaster, Nutribullet, knife block.
  6. Swiffer products should be regarded as essentials like toothpaste and TP.
  7. The person who did not put the TV remote control away in a designated spot shall be banished from the home (or get punched in the face).
  8. Make your bed every morning.
  9. Never go to bed unless the kitchen is clean. (If you dread this, then don’t cook.)
  10. If you find the above 9 steps difficult to implement, then try step 1 again.

Friends and family have seen me in action and tossed out this comment, “You like to clean, don’t you.” I always want to respond with, “Hell, no. I’d like to be on the beach drinking a margarita right about now.” I have to clean because I want to live in a clean place. Pretty sure it’s not an OCD thing, my classroom and my home have harbored enough episodes of disarray and germful cultivation.

It turns out that the above ten steps mirror — in a stretchy kinda way — how I do lesson planning. Something very cathartic about removing stuff.

  1. Throw everything out.
  2. When done with step 1, repeat step 1 again bc we both know you really didn’t throw everything out.

If you’re at all familiar with my teaching practice, it’s what I try to do all the time, like here, here, here, and for the last two months now, I’ve been removing the visual pattern steps and leave kids with just one step to build on.We remove the question when we do notice-and-wonder. We remove the correct answer when we do Which One Doesn’t Belong, we remove anxiety when we do Estimation 180. We invite great discussions when we do #smudgedmath.

  1. With remaining [ideally just 3] items, ask, “Is it really really pretty?” If so, it should be displayed in your home in a pretty spot. Ask, “Is it useful, like a wine-bottle-opener type of necessity?” If so, keep it in a drawer.

I have a hard time letting students use class time to make things pretty.

What’s beautiful to me is a paper full of mathematical thinking — a big mess of it — with scratch-outs and start-overs and AHAs! And I get what pretty is, like anything and everything created in Desmos is pretty. (My students use GeoGebra and Geometer’s Sketchpad too.)

  1. Unless it’s a piece of furniture, a houseplant, or a 4-legged friend, forbid it from touching your floor.
  2. Counter space is only for items that do not fit inside a drawer/cupboard and are used almost daily — e.g., toaster, Nutribullet, knife block.

Steps 4 and 5 make me think of the furniture in my classroom. I’m seriously connecting with some folks to get my walls covered with whiteboards. (Earlier this month, I finally got to hear Peter Liljedahl talk about Building Thinking Classrooms at #OAME2018. Alex Overwijk walks the talk.) I’ve already asked my superintendent/principal if I may get tables next year instead of the same clunky student desks that I’ve had for the last 15 years.

  1. Swiffer products should be regarded as essentials like toothpaste and TP.

Essentials, like equity and access. I’ve become weary of the true deployment of these two words. There are broad guidelines, but looking at my own practice and those around me, I’d be lying if I thought for a moment that we have access and equity all squared away and project nothing-to-see-here-move-along. I’m convinced that every teacher move speaks to how much we care about equity and access. So, the more intentional we can be in our lesson planning — from the questions that we ask, to the groups that we form, to the wait time that we give, to our body language — the more we can make strides in this endeavor.

  1. The person who did not put the TV remote control away in a designated spot shall be banished from the home (or get punched in the face).

All kidding aside (maybe), this one is about respect. Literally, it’s about putting things back where they belong. It reminds me to always give credit to the source, to share the lesson, to pay it forward. The teacher species Herohomo supersapien has been known to beg, borrow, and steal, and now, put it back.

  1. Make your bed every morning.
  2. Never go to bed unless the kitchen is clean. (If you dread this, then don’t cook.)

Fresh starts. Do-overs. We all have bad-no-good-horrible-vomit lessons. We tell our students to pick themselves up and try again, and again. We need to practice forgiving our bad lessons with grace and gratitude. The #MTBoS community gets this. Jonathan’s tweet was part of this thread.

I don’t know about 10 crap ones, I mean I am Fawn Win, so maybe just 8 for me.

  1. If you find the above 9 steps difficult to implement, then try step 1 again.

Like house cleaning, lesson planning can also be an asshole, especially on the weekends. On that note, I’m gonna hit the beach in an hour, the laundry and the lesson planning will just have to wait.

Posted in Teaching | Tagged , | 6 Responses

Broken Straps

Robert Kaplinsky drops me off at the front of the district building. I make my way to the room where I’d be presenting. I set up. I go out to the hallway, walk around, long enough to get lost. I’m looking for something. I don’t know where my backpack is. Where did I leave my phone? I don’t have my wallet either. Maybe I left everything in Robert’s car. I’d call him if I had my phone.

I take a few more steps and look down because I feel something is coming off. I’m wearing flip-flops. It’s broken. No, both straps are broken.

I can’t walk in these. I stare down at the broken straps. No, the straps didn’t just get pulled through their intended holes, they are torn! I note the crude and cruel fate that my shoeless feet are in right now. More importantly, why am I wearing flip-flops to a presentation?

Only three or four people are walking about in the building. No one sees me. No one notices me standing idly in the middle of the hallway with non-functional sandals. I yell out to the woman. She comes over. I point to my feet, hoping she’d notice what had happened to the straps without my having to explain. My voice is full of deep self-pity, “I’m trying to get back to my room. Where I’ll be presenting today. I don’t know the room number, but it exists, I was there earlier. I don’t have my stuff. Like nothing. I have no shoes.”

I jolt awake.

As if the nightmares before the start of school are not enough. I have #PDNightmares now. I’m about to board my flight, excited to facilitate another full-day PD. I’m wearing my favorite Italian leather boots, thanks.

Posted in General | Tagged , | 3 Responses

Maybe Less Tech in Math and School?

I’m sipping hot sake while waiting for my food. I scan the restaurant, about half full already for an early Friday evening. Two kids are on their smartphones at the table with their parents. They don’t even look up as the waiter arrives to take their orders; I guess the parents already know what to order for them. At the next table, I see a young child sitting in his high chair and watching a video on a propped up smartphone. Nearly every kid in the restaurant is doing something on his/her phone. Never mind the adults.

This scene is all too familiar, too common — so common that it would be “odd” if we didn’t see this. And we’ve been seeing it for some time now.

I embrace technology like it’s the softest fluffiest stuffed animal. I need my laptop and cell phone — every goddamn thing is on them. (I still need a real book to read from, however, like this one that just came in the mail because the Internet said I should read it.)

But the restaurant scene is particularly jarring to me because I’ve always valued meal times as sacred, a time to say grace and connect, a time for storytelling, a time for pause and reflection. Dinner time is a time to be social. Ironically, our children are silent at the dinner table because they are on social media with 600 of their best friends. I’ve seen kids with earbuds on too while dining out with the family.

If children are plugged in at dinner time, then I’m going to assume that they are plugged in most of the time at home. This makes me wonder if schools should embrace less technology. I witness that we have over-digitalized everything, not because there was a critical consumer-ish need for it, but because we felt the weird need to do so. Recently, I tweeted this and meant every character.

 

 

We have an incredible privilege to reach our students in the space and time that we have them. I want them talking and interacting more than anything! Learning mathematics is a social endeavor. Here’s my perennial classroom routine, “Turn and talk with your neighbor.” I want to bring back the arts of speaking and listening, reading and writing, debating and presenting. Last week, Jennifer Wilson (you’re missing out if you haven’t heard Jennifer speak in person) wrote about how time is needed to develop MP3 in our students, “It takes time to determine the conditions for truth.”

I’m happy and grateful that technology is here to stay. But I hope we seek opportunities to connect more humanly.

Posted in Teaching | Tagged , , , | 15 Responses

Scoring an Ordered List

My 7th graders have a question on their exam that asks them to put eight numbers (integers and fractions) in order of their distance from 0 on the number line, starting with the smallest distance.

These types of questions are tricky for me to grade, and because there are eight numbers in this sequence, the task of grading it fairly suddenly becomes thorny and irksome.

Let’s change the question to this:

Put these numbers in order from least to greatest: 5, 7, 2, 3, 1, 4, 6, 8

The correct order is 1, 2, 3, 4, 5, 6, 7, 8 (you’re welcome) — for a possible score of 8 points. How many points would this response earn?

1,  2,  4,  5,  3,  7,  8,  6

So, only the first two numbers — 1 and 2 — are placed correctly. Is the score just 2 out of 8 then? But I want to give some credit to 4 and 5 being next to each other, likewise with 7 and 8.

I’ve tried to come up with some metrics to score this, and then I would want to apply the same metrics to different sequences to see if any would break my invisible “fairness” barometer. For example, whatever score I came up with for the above sequence, I think the below sequence should get a lower score because the 7 and 8 are farther upstream than they should be.

Anyway, I have some ideas. The above two sets are Sets A and B below.

I wonder if there’s a way to score an ordered list that half of us math teachers can agree upon. I’d like for my students to think about this too. Meanwhile, here is a spreadsheet with my scores if you’d like to take a look and play along. Just enter your name in row 1 (and link your name to your Twitter, if you want) and the scores you’d assign to these sets.

[02/01/18: @MrHonner had a similar question over 4 years ago: Order These Things From Least to Greatest.)

Posted in Teaching | Tagged , , , | 24 Responses

How I Use “Between Two Numbers”

I’m overwhelmed by the number of teachers who have asked how I use Between 2 Numbers (B2N) in my class. So this post is for all three of them and for anyone else who might be interested.

It has become one of our regular warm-up routines. (We do visual patterns and math talks, too. Duh.) Before I launched the site, I was just referring to this routine with my kiddos as a “tidbit.”

Take tidbit #5, for example. I ask three questions on Google Form, the first two are identical.

Question 1 is asking for a guess, an estimate, a gut check, a what-do-you-think.

Question 2 is the exact same question, except now, students are allowed to search the internet and use their calculator to figure out the answer. However, on a few of these entries — like #2 and #6 — I let kids know ahead of time that they may NOT search the internet but may still use their calculator. The reason is the internet readily provides the answer with a simple search.

Question 3 is always the same.

When about two-thirds of the responses have come in, I then make an announcement that I’m setting a timer for two (or so) more minutes. When the timer goes off, I ask for all students to please submit their form.

I show the class their guesses for Question 1.

In their math journals, we go over the calculations to get to the answer. Then, I reveal their responses to Question 2. (Thank goodness this class had done well on this question. On others, not so great and some downright dismal results, yup, my kids need more practice working with ratios and using the calculator.)

The site has allowed us to:

  1. Learn some fun facts
  2. Explore large numbers, imagine the magnitude of these numbers relative to other large numbers
  3. Work with scientific notation and use the [EE] key on the calculator
  4. Work with equivalent ratios

We have a friendly competition among the four classes (two 7th-grade classes and two 8th-grade classes). One of the students suggested this scoring scheme, and it’s what we use: 3 points for the class with the highest percentage, 2 points for second place, 1 point for third, and the 0 for the lowest.

Of course, Jules Bonin-Ducharme (@jboninducharme) is responsible for translating all the entries into French! (You just need to hover your mouse over the section links near the top to see the entries in French.)

I hope you can find some time to try this with your kiddos, and I’d love to hear how it goes.

Posted in General | Tagged , , , , , | 3 Responses