Finding Ways to Nguyen Students Over

Powdered Beignets

Due to a sequence of shitty events, I find myself at the airport three hours early for my flight.

I'm carving into my first of three overly powdered beignets.

A mother sits an arm length to my left along the wall booth. Her teenage daughter across from her. They talk about colleges. Mother attended Cornell and reflected that she was a moron for not taking a course from Carl Sagan. Daughter is here to check out Tulane; she's a junior now. They talk about her classmates and where they're considering. Nothing out west, they say, even though Stanford would be awfully nice. 

Mother: We're going to drive you there.

Daughter: I can fly. 

M: I know. But we want to drive you. Time for us to talk. I like that they want the freshman and sophomores to live on campus. 

D: We'll see.

A father-daughter pair sits next to them. The four start chatting as if they know each other from back home. One girl congratulates the other who has already spent over three hundred dollars at her future school's bookstore. This one replies, "Oh, I have to decide first! Then I'll buy all the stuff!"

They finish their entrees and the mother orders some beignets for them to share. Mother points to my plate to tell her daughter what beignets are. 

Their easy conversations. They talk about the college choices they have. It doesn't matter whether they will fly or drive. The opportunities are there. They barely touch the beignets. I'm eating my last one.

The girls and their parents are white. I think about half of my students who are not. I think about my Felix, my Andres, my Jaylene, my Israel. Kids whose parents don't always speak English. I don't imagine them having these easy conversations about colleges. Why is that. The privilege afforded to some. I get stupid teary.

Time for me to board.



Prices, Proportions, Percents

I was in Garden Grove with my son on Sunday, and he insisted that I try this smoothie place called Tastea. With Jamba Juice and Blenders and all the other juice bars around town, I was skeptical that this joint's concoctions would be anything different. He ordered a taro milk tea and I got a Thai tea, both with boba. Just one sip and I said to him, "Let's order another round! It's a long drive home!" Soooo delicious.

 

While there I saw a math lesson brewing, so I picked up their menu with prices. This is the lesson with my two classes of 6th graders.

Me: (I tell them about Tastea and how I wish it were closer.) Okay, let's start with something you might be more familiar with, Starbucks. I love that now I live within walking distance from one! Do you know the different sizes that they have there?

Class: (When I refer to "class," I don't mean the whole class, of course, but somebody in the class joins in on the conversation.) Tall, grande, venti.

M: Do you know exactly how much liquid each size holds? (They make various guesses. I bring out the 3 sizes that I got from Starbucks so they have a visual.) I normally order a tall mocha frappuccino, let's say the price is $3.50. Do you think the venti, which is twice the volume of the tall, would cost twice as much, or $7.00?

C: No.
 
M: Why not?

C: You normally get a better deal with a bigger size.

M: What do you mean by a "better deal"?

C: (All their answers show me that they understand the idea of more bang for your buck. Then finally someone says...) Lowest unit price!

M: Right! That's why so many families go to Costco. Buying in bulk normally saves us money because the item has the best unit price. Well, we're talking about Starbucks now, so buying more is a better deal, but drinking more is not so good for our body. Let's fill in this sheet. (I pass out this 2-page worksheet.) How do we calculate unit price? What place value should we round it to? How do you write thirty-one-cents-per-ounce?




M: Tastea has three sizes: mini, gigantic, and even more. Their teas can also be purchased by the "partea jug," which holds a gallon. I've given you the prices of the 10-ounce minis for the three different types of drinks, your job is to figure out the prices of the other sizes. You'll work in small groups to figure out these out. So, do you think the gigantic will cost twice as much as the mini because it holds twice as much?

C: No. It'll cost less.

M: How much less? Well, that's your group's job to come up with the best estimate. We have Starbucks' prices for their three sizes, you could look at how they price their drinks. But here's the sweet deal for you. You and your group mates do the math that you need to, then write down your first estimation right here in this column. Bring your paper up to me (only the "captain's" paper), give me a few seconds to figure out the percentage that your estimation is off by, and I'll write it in this column and give you back your paper. What percent do you want to see, large or small? What if your estimation were the actual price — what percent would I write there?



I tell them that they could figure out the actual price of the drink if they knew how I calculated the percentage of error. So, work work work. Think think think. What makes sense? Oh, I remind them that the percentage does not indicate if their estimation is too high or too low. So, again, what makes sense?

We also note that prices generally end in a 0, 5, or 9. So, even if the calculation tells them the price should be $4.23, they might want to change that to $4.25 or $4.20.

When they bring up their paper again with the second estimation, all I do is write their estimation again in pen and circle it — this is so they can't change their answer and I know that I've seen it. I do NOT fill in the "Actual Price" column at this time because the groups are working at different rates, and in a crowded room, it's easy for kids to see each other's papers, even inadvertently, and the game of estimation is over if they saw the actual price beforehand.



They simply move on to the next size to make a first estimation again. We repeat the process. 

When all groups are done with estimations for the first type of juice — smoothies — I tell them what the actual prices are. 

Now, it's their turn to figure out the percentage of error. I give the groups about 10 minutes to do so without help from me. At the end of the 10 minutes, either there's at least one group that knows how to do so and can show it to the class, or no group knows how, then I'll walk them through the calculation by asking them questions to figure this out.



They continue in the same manner for the Slushy Freeze and Specialteas on page 2. This time hopefully they'll be able to work backward from the error percentage that I give them after their first estimation.



Reasons I'm proud of this lesson:
  1. It's about proportions, but many priced items in real life are not directly proportional. The kids knew this coming in because they've been consumers.
  2. We get to talk about business strategies that entice people to buy the larger sizes while still make a profit. (Starbucks calls it "tall" because it rhymes with "small," but clearly the word tall naturally elongates the imagination.)
  3. Students get to make estimations throughout, but they know these aren't "wild-ass guesses." They start with the calculation of proportions and adjust the prices accordingly. They get to critique and argue with their group mates to come up with the best estimations.
  4. I get kids to think about percentage in a context that they can wrap their heads around. And they want to know how because their second estimation could be dead on if they knew.
  5. It's fun that the error percentage does not indicate if their estimation is too high or too low. A few groups do go farther in the wrong direction. Oh, well — good to learn that now.
  6. It'd be fun for me to get Starbucks or Jamba Juice for the group with the lowest total in percentage errors.







April 05, 2014: I got some thoughtful reflections on this lesson, I'll just share two:

I learned how to work backwards with percentages and try to get the number spot on. I also learned how business would price things by dropping the price by the perfect amount. My number sense got a lot better from all the multiplying, dividing, and reasoning. It was very difficult, which I'm very happy about. 

The teamwork was probably the hardest part of the project. M and I are very competitive, and we got different answers a lot. I learned how to work together with others a lot better, and it doesn't move your team along to place blame and argue. I'm really grateful we did this project because it was very hard and worthwhile. It was a great use of three days!

***

I learned how to use different data to get answers. Also, we have to see a pattern. This Tastea assignment was really fun. I enjoyed it and look forward to another. Teamwork is really important even though people can't agree, you got to support it. If your group gets it wrong, but your answer was right, you can't blame someone or put them down because probably they will get some right for you. So always stay positive to your teammates and encourage them.




What the Kids Thought

Recently Dan Meyer asks Mathalicious which of these three questions is "real world"?



Karim Anifounder of Mathalicious, and others have opined without consensus on this particular question and on the general notion of real-world vs. fake-world problems.

I wonder what my 8th grade geometry kids think of this question.

I give them Version A on a strip of paper and ask them to work on it alone for 5 minutes. I tell them that I'm interested in learning if they understand the question as is, therefore I'm not answering any clarifying questions about it. After the 5 minutes, I put them into random groups, and they work on the problem for another 10 minutes.

Then I show them Versions B and C and ask for their preference and reason for each version.

Version A: 18 likes, 14 dislikes

Highlighted reasons for LIKING:
    • It gives every detail you need to know. It tells you directly all of the information. It also seems easiest to solve.
    • It isn't as confusing as looking at fast-motion pictures of a circle and a square. Doing math is more exact than visual guessing. [Did he translate the animation to mean guessing?]
    • I am able to make my own diagram and I can try to solve an equation to find out the answer.
    • It is simple and not confusing. It allows me to think the way I want to and not be misled by a moving picture.
    • With the given information, you could construct the two shapes by working backwards.
    • There's enough given information to make the problem interesting and hard.
    • I like this one the most because you can actually read the problem and refer back to it.
    • I think it can be solved using an equation, and be solved more easily than B and C.
    • It's a more accurate way to find their areas and make them equal.
    • I like this version because I understand the problem.
    • Instead of a picture of it on paper, you have to visualize it in your head first.
    • You can get an exact answer. It is challenging.
Version B: 18 likes, 14 dislikes

Highlighted reasons for LIKING:
    • It would be cool to build the animation in GSP and solve it that way.
    • It's a lot more simple. It provides an image and idea of what it looks like.
    • I can visually see when they are equal. It will be easier to see when they are equal instead of having to do a load of math.
    • It is visual.
    • I feel I have a higher chance of answering the question with a right answer.
    • You can easily see when the shapes have the same area.
Version C: 15 likes, 17 dislikes

Highlighted reasons for LIKING:
    • It seems easier because you can just count the candies and see if they're equal.
    • Anyone can count how many candies there are, then subtract the extra space to get the correct area.
Some students like and dislike more than one version. My takeaway on their responses:

Version A
LIKES: (see above)
DISLIKES: Not understanding the question, or "I'm a visual learner, so I like Version B better."

Version B
LIKES: It's visual. It's easy.
DISLIKES: Too fast and hard to follow. One student, "The movement is distracting and confusing. I feel like it's too abrasive and violent. Math should be more elegant than this." 

Version C
LIKES: You just count the number of candies. It's visual.
DISLIKES: Too fast to follow. It seems too easy. There's space between the candies. One student, "You can't get the exact answer... And the leftover space in one shape may be more than the leftover space in the other."

I collect all their papers before telling them which version I like. I like Version A for its simplicity. I'm curious if the stated question is enough information for them to understand. This student's reason nails it for me: "It allows me to think the way I want to and not be misled by a moving picture." 

We all have students who struggle with word problems. I don't think this means we should give them fewer word problems. I think it means we should give them better word problems — ones that are written with just enough information and not embedded in contrived contexts that either confuse or insult the students. And for students who need help with the question, they get to hear an explanation from a classmate. 

Version B is okay, but I don't want to start with it because I feel I'd be wasting a perfectly good question in Version A! I'd reach for a piece of string to explain this question, if needed. Version C gives me a headache.

At least one person in each group understands the question, and they do their best to make sense of it in just the short 10 minutes that we have. They're trying. And making mistakes.

  


Our whole-class discussion at this 8th grade level:
  1. That "arbitrary" point P is pretty darn close to the middle of A and B. You can roughly tell from using a piece of string. Or you can tell from arriving at y2/(4pi) = x2/16 (where x is distance AP forming the square's perimeter, and y is distance PB forming the circle's circumference) — the denominators are almost the same.
  2. Likewise, P cannot be at the center because pi doesn't reconcile nicely in the equation. 
  3. We can solve for x and y using some arbitrary distance AB, and we find y to be slightly shorter. 
  4. We can ask a related question: A circle's circumference and a square's perimeter are equal, what is the area enclosed by each? Kids can certainly think about optimization and do a little bit of calculation outside of a formal calculus class.
In addition to asking the students which versions they like, I also pose Dan's exact question to them: Which of these is a "real world" math problem? Or is none of them a real-world math problem?

Their answers vary as widely as those of math educators'. However, I find this correlation that doesn't surprise me: kids who like math more do not care if the problem is real-world or not. 

This [Version C] is the most "real-world" solely because of the fact that it involves a material object which in this case is the candy. However, the thing you're solving for in this question is not very "real-world" at all. Personally, I don't care at all if a problem is "real-world" or not; I just like to solve problems.

If a problem didn't have to do with "real-world" I will still do it if I like it. It doesn't really matter.

I don't think any of these problems are "real world" math problems. I like how they make me think. But I don't think I need them in the "real world."

I wouldn't care if it is a real-world problem because I was there to learn. I think all versions can be a real-world problem because it can be needed in some situations.

I feel like all of these problems are real world... But honestly it doesn't matter at all to me. It doesn't matter if it's real world or not, it doesn't affect me wanting to solve the problem.

So, one from the kids.



Teaching Absolute Value

I know Common Core does not have absolute value in grade 8, but I'm teaching it anyway because we're still doing "algebra 1" this year. (A year ago Raymond Johnson looked into the inclusion of this topic in the different grade levels.)

My 8th graders know that the absolute value of 5 is 5, and the absolute value of -5 is also 5. Some recall that it's the distance from 0 on the number line. 

We begin by solving a few of these: abs(x) = 4, abs(a) = 0, abs(w) = -3. A few trip up on the last one but recover quickly and move along.

Me: What is the distance between these two points?


Class: Eight.

M: How did you get eight? 

C: Subtract. 

M: What about this one? The points are at -3 and 9.


C: The distance is twelve.

M: This one?


C: Thirty-two.

M: Good. Distance is always positive... How did you find the distance between the points again? What operation did you use?

C: Subtraction!

M: Then I'm going to add an equation below each number line showing subtraction. Is that okay?


M: So, the distance between 5 and 13 is 8. Then, what is the distance between 13 and 5? 

C: Eight

M: Woah! It's the same? Meaning I can write the equation either way?


Kids agree that subtraction can be commutative when it's inside the absolute value bars because we’re just measuring distance. The distance from Johnny to Julie is the same distance as from Julie to Johnny. I'm not going to argue.

Me: Given two points, you can tell me the distance between them. So now I’m going to give you just one of the two points but tell you the distance between them, and you find the missing point x.

C: x is ten.

M: Yea, ten works. Let's try to read this open sentence. How would you say it?

C: x minus six... The absolute value of x minus six is four.

M: Hmmm. Oh, you say the words 'absolute value' because they're there. Let's try again without saying those words. Use the word 'distance' instead.

C: The distance of x minus six equals four.

M: Let me show you again the first one that I'd asked you. I remember just asking you, 'What is the distance between 5 and 13?' What did I not say even though it's there?


C: Minus.

M: Right. Let's not add stuff we don't need. You know naturally that finding distance implies subtraction. So, say the equation again.

C: The distance between x and six is four.

M: Or you could say...? Can we switch the points around?

C: The distance between six and some point x is four.

M: Alright. Is 10 the only answer for x? We are trying to find a point on the line that makes the equation true. So, let's use the number line to solve this. Because we know 6 is one of the points, let's locate it. We need to find the other point that would be a distance of 4 away from 6. So, it could be to the right of 6, or to the left of 6. Where does this put us at?


M: Oh, why isn't the point -6? I see a 'minus six' in the equation.

C: Remember, that minus is for subtracting. We need it there to find distance.

M: I remember. We need it.

We do a few more of these. Enough to bore us, need something new. 

M: Let's try this.


C: No subtraction sign. 

M: And you said we needed it. Then create it. Make it happen without changing the problem of course.

C: Change it to minus minus...


M: What does this problem say now?

C: The distance between x and negative eight equals five.


We do a few more of these. Enough to bore us, need something new again. 

M: What about this?


M: Nothing terribly exciting. The other point(s) that we find is now worth 2x, so we just need to solve for x.


Then we do a batch of these: 


Hey, what about these, where there's more stuff stuck around the absolute value quantity. Oh, we just need to first isolate the absolute value, then it's business as usual.


We spend the next whole class using Desmos to explore the shifts/changes to the parent absolute value function. Students need to write down their predictions first before graphing. One student was very excited when she got the V-shape to turn upside down.


We discuss some real-life scenarios that may involve absolute values: margins of error, ranges of measurements: distances, scores, speed, temperatures, pH levels, elevations, etc. 

Not proud to admit that I spent a lot of hours in college playing pool instead of studying, but never once did I associate the path of the ball as an absolute value function. Consider me odd if I always thought of angles instead.



Solving absolute value inequalities start similarly enough. 



Kids know from graphing inequalities that there's "shading" involved. They also know the difference between open and closed points. So I just have the kids use their thumb and forefinger to indicate the distance between the two points, then if the inequality says less than [or equal to], then it's natural to pinch their fingers closer together, indicating that the region inside the points need to be shaded.

 



The textbook will tell kids to set up the "two cases" to solve these inequalities (same thing with equations). Then, kids are asked to graph the solution.



But if kids learned to solve using the number line itself, then there would be nothing to memorize because they learned distance way back when they started learning to crawl. And since the graph shows the solution, then writing what that solution is is easy because it matches the graph. Like below, x lives on the green line between -8 and -2, being ≥ -8 and ≤ -2.



For greater than inequalities, the student would naturally spread his fingers apart to indicate shading outside of the points. 


 



I don't know why there seems to be a lot of rules when learning to solve absolute value equations — which inequality sign for when it's and or when it's or. Oy.






Moon Badges

When you watch too much Khan Academy you earn moon badges
When you earn moon badges you can tweet that you earn moon badges
When you tweet that you earn moon badges your followers say what the hell
When your followers say what the hell you feel you need to explain
When you feel you need to explain you make no sense in 140 characters
And when you make no sense in 140 characters you lose all your followers
So don't lose all your followers, get rid of videos and upgrade to direct instruction

All kidding aside, I'm having kids spend no more than 5 minutes of class time to write one of these for a math trick or math something. They may illustrate it outside of class if they want. Here's the first one from a student who was in the room when I was thinking of this idea aloud.

When you cross multiply to solve a proportion you waste a lot of time
When you waste a lot of time you don't finish your test
When you don't finish your test you get a bad grade
When you get a bad grade you can't get into college
When you can't get into college you can't get a job
And when you can't get a job you become homeless
So don't become homeless, get rid of cross multiplication and upgrade to algebra





[Added 03/13/14 and later...]


When you don't struggle in math you get bored
When you get bored you fall asleep in class
When you fall asleep in class you get sent to the principal's office
When you get sent to the principal's office your parents start yelling at you
When your parents start yelling at you you get sent to military school
And when you get sent to military school you get stuck in a bunk with someone who never showers
So don't get stuck in a bunk with someone who never showers, get rid of not struggling and upgrade to Mrs. Nguyen's math class! :)


When you don't label your units people don't understand you
When people don't understand you they think you're illiterate
When people think you're illiterate they don't talk to you
When people don't talk to you you go insane
When you go insane you start eating things off the street
And when you start eating things off the street you get rabies
So don't get rabies, stop not labeling units and upgrade to labeling units


When you guess you don't get an exact answer
When you don't get an exact answer you have to do twice the math
When you do twice the math you get tired
When you get tired you start sleeping in on school days
When you start sleeping in on school days your mom is late for work
And when your mom is late for work she loses her job
So don't make your mom lose her job, get rid of guessing and upgrade to exact answers


When you FOIL you can only multiply two numbers in each expression
When you can only multiply two numbers in each expression you can't complete algebra
When you can't complete algebra you can't move onto geometry
When you can't move onto geometry you get held back in freshman year of high school
When you get held back in freshman year of high school, you don't have friends
And when you don't have friends you stab yourself with a fork
So don't stab yourself with a fork, get rid of FOILING and upgrade to double distribute

When you don't memorize theorems you don't know what to write in your proofs
When you don't know what to write in your proofs you fail your geometry class
When you fail your geometry class you lose all your confidence
When you lose all your confidence you decide to work at a dead-end job
When you decide to work at a dead-end job you get hired to become a low-budget amusement park mascot
And when you get hired to become a low-budget amusement park mascot you get tackled by an immature middle aged man
So don't get tackled by an immature middle aged man, get your theorems memorized and upgrade to a math tutor

When you get straight A's people call you a genius
When you get called a genius you work to make yourself a genius
When you work to make yourself a genius you become the next Albert Einstein
When you become the next Albert Einstein you make theories
When you make theories you want to test Einstein's theories
And when you want to test Einstein's theories you get sucked into a black hole
So don't get sucked into a black hole, ignore people who call you a genius and upgrade to a critic


When you don't do your math homework you don't understand the subject
When you don't understand the subject you fail the class
When you fail the class you flunk the grade
When you flunk the grade you feel depressed
When you feel depressed you continue to flunk
And when you continue to flunk you become a twenty-five year old man in a fourth-grade class
So don't become a twenty-five year old man in a fourth-grade class, do your homework and upgrade to the next grade level


When you say math isn't  your forte Mrs Nguyen gets mad
When Mrs Nguyen gets mad she yells at you
When she yells at you you feel like a loser
When you feel like a loser you don't succeed in life
When you don't succeed in life you can't get a job
And when you can't get a job you work on a smelly old fishing boat
So don't work on a smelly old fishing boat, get rid of saying math isn't your forte and upgrade to loving math

I Can't Afford Not To

When I share with teachers what my students do outside of the textbook/curriculum, I get the familiar and reasonable concern from them that there's not enough time to cover the content as is, how is it possible to do "other stuff," such as:
  1. Math Munch
  2. Problem Solving (weekly, in-class, group)
  3. Math Talks (including Visual Patterns)
My reasons for doing the above, respectively, are: 
  1. I want my kids to take pleasure in seeing how beautiful math is, to appreciate the elegant proofs, to imagine the possibilities.
  2. I want my kids to think deeply, to struggle, to persevere, to honor the process of problem solving instead of just answer getting. These skills directly help students with content material.
  3. I want my kids to share their thinking out loud because a quiet math classroom is a scary place. 
It's very simple in my mind why I do what I do. If my administrators told me tomorrow that I could no longer do any of these, then I know it would be time for me to leave the classroom. I don't follow fads and reforms and jargon. I don't enter into those conversations in real life or online because I don't know how or have anything to say.

I want to follow these reflections that my kids (6th graders) write:

First of all, the equations are coming so much easier to me! I think what helped me is opening up my mind to other methods, and trying out methods that I've seen other people use. I feel that the reason I have trouble with some problems is that in my mind, I make the problem seem so much harder than it actually is. After doing them week after week, everything is coming to me a lot easier than they used to.

This week I have learned a lot. I've learned new methods of solving problems and reviewed old ones too. Math Talks have helped me a lot in homework and class work too. God I'm brilliant.



So I have a lot to reflect on because there were a lot of Math Talks. I really liked the shopping problem because, you know, I'm a girl, and I like shopping. Sometimes I don't get anything about a problem or pattern at all, then someone explains it really well and I get it. And I think, "Why didn't I see that?" That happens to me a lot.

The next time I think I could think a bit more because this time, now I thought I should have thought about it a little more, seeing all the other people's answers got me to think that I should have done better. Yesterday I wish I raised my hand before some other people because I had it up and other people were saying the same thing as me.

To improve I could get more time and after talking to Mrs Nguyen I understand more when she explains it better. The thing I found most difficult is problem solving & solve the patterns because it is hard to finish up mentally.

After talking to others it always makes more sense and they help. To improve I could get here earlier.

I think I'm getting stronger each day doing mental math and patterns. My favorite math talk this week was the pattern on 2-26-14, I thought it was clever because towards the end it wasn't the rule, it was your rule.

I really loved the math talk on last week's Friday. It was the buy one get one free or get 45% off. Because after you told us the answer and it could go either way, I thought to myself like how didn't I figure that out. So there's no right or wrong to the question.

I thought the guess-and-check that Cristian did was very helpful and it really helped me learned the strategy.

This week of math talks was very fun. I like the problem solving puzzles and equations. After talking to Skylar, she helped me understand the problems more.

This week I had better understanding with math talks. The one that really helped me was Janae's; it was different and extravagant.

My favorite day this week was "would you rather get 45% off everything or buy one get one free." Although it was simple, it was fun to share our different opinions.

One of this week's math talks equation that really helped me understand was Seth's equation from Thursday. It was when you divide money but you ignore the decimal and add it in later. This one helped me a lot.

On 2/21/14 math talk I did not get it at all, then when Diego explained how you were supposed to do it, I got it and that was good.

I am going to use different kinds of math strategies that everyone was using because some of the strategies help me solve a problem faster.

...

What I'm reading is that they value their classmates' different ways of doing mathematics; they benefit from them.

A month ago Sam Shah started Explore Mathematics! with his Advanced Precalculus class, then last week Sam shared with me what one student had written:




I choose to dedicate some of our math time to explore out-of-content mathematics because I can't afford not to.



Blessed

Some people make six-figure salaries, but I bet they don't get to feel as rich and as blessed as I do tonight when I read these two Friday reflections.



I feel like geometry is more of a puzzle rather than a chore. Having to find ways of proving something seems more like fun than a class. Learning about shapes and things I thought to be impossible are really cool. I can't wait for what amazing discoveries I'll learn next. [Grade 8]



You've really inspired me and now (more than ever) I want to be a teacher. [Grade 6]


I'm crying and thinking I should quit teaching because it can't get any better than this — like quit while I'm ahead. 

But you know what though. You, you, and you, and you over there, yes, you too — have helped me do this really hard job better than I ever could on my own. This is the best time to be a math teacher, and I thank you.



Classroom Management

Give or take, scenes from my classroom last week:
  • A walks into class, talking at full volume until someone shushes her and points to the obvious math talk on the board.
  • B slouches in his desk, head barely above seat-back.
  • C decides to dump out contents of his binder to find the math paper from 24 hours ago.
  • D talks while I'm talking. 
  • E and F are talking while someone else is sharing.
  • G and H are playing footsie; H is better at this.
  • Someone lets out a shockingly loud fart — we all look at row 7, seat 5 because the occupant is giggling and beaming proudly.
  • I continually scans the room like she's seeing it for the first time.
  • J asks to use the restroom when there are fewer than ten minutes left of class.
  • K and L try to talk to each other half way across the room.
  • M makes squishy noises with his water bottle.
  • N taps his pencil.
  • O clicks his pen.
  • P and Q... well, they're just minding themselves.
  • R blurts out, "I already got the answer!"
  • S needs to borrow a pencil from classmate for the 95th day of school.
  • T volunteers, "Yes, I'm very bright. I'm a genius. But I need help with section nine four."
  • U returns my look with a look of what-Mrs.Win-?-I'm-doing-my-work-see-?-hehe-okay-I'll-do-my-work-now.
  • V yells at person sitting in front of her, "Stop pushing your desk into me!!"
  • W walks across room to get a drink of water. Five sets of eyes follow W and then at me to see my reaction.
  • X asks out of the blue, "Have you eaten at that Korean place, Mrs. Win? It's so good."
  • Y sticks out his foot to trip Z as he walks by.
  • A through N immediately engage in lively conversations just as I say, "I need you to take out a piece of graph paper." So, I have to say, "Guys! You don't have to talk just to get out a piece of paper!"
  • O through Z immediately engage in lively conversations just as I say, "Make sure your name is on the paper."
I may only talk about classroom management with your understanding that my own classroom is sometimes chaotic, sometimes louder than it should be, sometimes messy — but somewhere in this soup of chaos, noise, and mess, I have to believe that there is learning of mathematics. More so on some days.

I can't help but draw parallels between teaching and parenting because both roles have defined me. Their enormous responsibilities have brought out the best and worst in me. It's easy to love children. It's much harder to discipline them. A wise colleague once reminded our staff that discipline is not a dirty word — to discipline means to teach. And I think teaching is the purest form of love because teaching is sharing.

Classroom management is used interchangeably as classroom discipline, and that's okay. It's all part of classroom teaching. I've been around long enough to see teachers leave the profession because they lacked "classroom control." Nothing in teacher school adequately prepares you for this. No manual outlines what to do when a kid cusses you out. Step 1: remain calm. Step 2: breathe deeply and count to 10. Step 3: fuck this shit and find another job.

I bought this hardcover book long ago. 


I'm sure it's full of good intentions and sound advice. (Serendipitous that 20 years later the author Randall S. Sprick enters my life again when our school currently adopts his CHAMPS program.) But it's really hard to see classroom management in action from reading a book or a blog post. It's ideal to directly observe a teacher and her students, and not just for a day or two, but over a period of time. The classroom culture is undeniably real and one has to be in it to fully appreciate and honor this culture. I know there's a thing called student teaching where one is immersed in a real classroom for a semester. But I swear to God, the kids we get during student teaching are sent down from Heaven. And the real kids, the ones we get after we're hired and on our own, are sent up from the Other Place. 

What I'm saying is it might be very helpful to observe these same kids whom you currently have in another teacher's classroom.

It was around the end of the first quarter of my third year in the classroom when a colleague – a new hire – told me the vice-principal had suggested for her to observe me for a couple of periods. Afterward, she said, “Fawn, Joey is like a different kid in your room. I never knew he could sit still for 5 minutes! He’s out of control in my room. In your room, he just… blends in.” 

Apparently Joey behaved differently for different teachers or at least in different settings. The teacher didn't come back the next year — and this made me sad because she worked hard and wanted to be a teacher. There were other teachers who left the school after putting in just one year. It was a “tough” school – plagued with the usual inner city inadequacies and brokenness.

Having said that, I find kids are kids. I've taught in the poorest neighborhood and in the most affluent. Kids who live in fancy homes have better rides to school and wear designer labels, but at their core, they are kids who mostly want to learn and not be shunned at the lunch table.

We can't say we possess great classroom management skills if we could pick and choose where and whom to teach. There's a quote out there that I like: Parents are sending us their best; they're not keeping the good ones at home. So, if we took the students out of the classroom-management-success equation, we are left with two variables: the teacher and the classroom.

The Teacher:

  1. LOVE the kids. Fine, we don't have to love all of them because inevitably each year there's always one (or two or three) who pushes all our buttons and makes us throw wild tantrums at home. But aren't we supposed to be tougher than the toughest kids? How is this child's home life? And is this child behaving like this in all her classes? There's something to be said about killing 'em with kindness. Why are we in teaching if we didn't love children and love helping them learn? 
  2. Show students respect. It should be the other way around — that kids must automatically respect us for our age and our college degree. But whom are we kidding. We all know of a few adults with advanced degrees who need to stay the hell away from us because they're mean and psychotic. Kids tend to misbehave more for teachers whom they don't respect. Do we honor their struggles and offer to help? Do we show up at their games and show genuine interest in something they do outside of school? Do we say please, thank you, and sorry each and every time that warrants it? Do we spend time outside of class to help a kid like we said we would?
  3. Command respect. Respect has to be mutual. Like trust. We have a great opportunity to be a role model for many kids. We can't command respect by being "pals" with the students. We all know of parents who try to be buddies with their kids. We should never ignore a disrespectful comment/tone/gesture from a student. Because if we do ignore it, it won't be the last time it happens. How do we speak of our colleagues and administrators to students? How do we speak of our family to students? Are we consistent and honest with them? Do we follow through with consequences? 
  4. Have a sense of humor. When was the last time we laughed with the kids? The lighter moments make us more approachable and compassionate. When was the last time we shared a bonehead mistake we made? Who makes us laugh? Humor allows us more room to breathe when we need to get tough with a kid. 

The Classroom:
  1. Have good lessons. I can almost tie every misbehavior or off-task behavior to the lesson itself. A good lesson is no good until it's delivered well. Logistics. A content-rich lesson that doesn't take into account student movement and/or material management is asking for all sorts of mayhem. Please don't envision a "good" lesson only as a hands-on task that involves group work. A good "lecture" — aka direct instruction (maybe) — should capture students' attention too if we drew them in with questions and invited them to make conjectures along the way. Good story telling [that relates to the math topic] will have their eyes wide open and ears perked up. Good lectures are awesome.
  2. Establish routines:
    • One of the best things we have established school-wide (K-8) from the CHAMPS program is a hand signal for silence. What's your signal? And we need to wait for that complete silence before we speak. 
    • Kids will forget some of the routines and look at us like we're crazy when we remind them. So, remind them and don't look so crazy, like don't make a big deal out of it.
    • We need to remember that kids [and adults] crave structure. We are creatures of habit. A good structure does not mean it has to be fixed; it means it's flexible. Like a building that's earthquake hearty. (Ooh, I like my just now invented analogy for classroom structure. I'm brilliant.) 
  3. Noise level. What is our tolerance level? Dead quiet has to mean dead quiet. Whispering is not dead quiet. What's the appropriate noise level for small-group work? How often do we find ourselves yelling? There's no rule that says we can't stop the activity — especially when it comes to safety — if kids aren't following protocol. 
  4. The ONE thing. Do our kids know the one thing that upsets us? My one thing is I hate mean people. So I get really, really upset when I see a kid doing something mean to another. The lesson stops. Everything stops because this is a big deal. Most of them will say that they were just playing around. We talk about that — playing and inadvertently hurting someone. Our classroom needs to be a safe place. And I want this to be a money-back guarantee with kids; it's my one thing.
—————

I'd taught at my first school for 8 years before I interviewed with another school. Near the end of that interview:

Vice-Principal: Fawn, there was one thing in particular that your former vice-principal had shared about you that stuck with me.

Me: Yeah?

VP: He said, She was the only teacher who could get our eighth graders to walk perfectly in a straight line and quietly from her room to the gym. How did you do that?

M: I just asked them to.

VP: You just asked them?

M: I mean they know what quiet means and what a straight line is. I told them that we needed to show respect to the other teachers and their students when we pass by their classrooms. We show this respect by walking quietly and orderly so we don't disrupt them.

VP: How long did it take to get them to do that?

M: First time. Well, we simply didn't move unless they were all quiet and in straight line! I saw pride in them as they walked. At least one teacher would happen to watch them go by and complimented them. When we got back to our room, I always thanked them and told them they made me proud.



Crab Walks and Real Life

Algebra class, first few days into second quarter, 2004. I remember this because it was the last time that a student had asked me this question in class. His question: When are we going to use this in real life?

At his parents' urgent request, he was transferred from Algebra Readiness to Algebra at the beginning of second quarter. He struggled mightily with basic arithmetic, thus his initial placement. I knew he asked the question because he was lost in what we were doing, especially having missed the first quarter of Algebra. But his question was his way of throwing it back at me — I heard it more as, "I don't know how to do this, but what's the point of learning this stupid thing anyway?" 

He transferred back to Algebra Readiness by the end of second quarter.

I presented a session on Problem Solving this past weekend at the South Dakota Annual Math and Science Conference, and a teacher asked me how I would respond to a student with the same question. I gave my best brief answer that I knew, realizing that not one student has asked me since that time ten years ago.

Yesterday Mike Lawler shared a post on how he and his two sons had worked on a problem that I'd tweeted. Mike also mentioned sharing this problem with a principal on their dog walking, and the principal commented, albeit jokingly, that the problem had no real-life connection.

Then the first thing that popped up on my Twitter feed this morning was Chris Robinson's tweet of his post When Will I Ever Need This? Chris writes, "students resort to this proclamation when they're lost conceptually and don't understand how to connect their present situation (learning) with prior knowledge and level of understanding." I agree. I also agree with Chris that boredom is another reason.

So I'm carving out a small space here to answer this question because I'm wondering why the hell are we — math teachers — the only ones to get this question from students. I don't know of any English or Social Studies teacher who gets asked this question. 

I spent many seasons watching my two boys at football practice. Aside from practicing their specific positional drills, they had to do sit-ups and push-ups, high-knees and karaokes, bear crawls and crab walks. None of the kids ever asked their coaches when real-life crab walking might come in handy.

I remember having to do sentence diagrams in school and thinking this might save my life one day. Such scenario:

Cranky person (comes up from behind me): You! Drop and give me a diagram of this sentence or I'll blow your head off!

Me (arms raised in the air to show my English teacher had prepared me for this): Ummm... What's the sentence?

Cranky: Try this one, The bored students were considering shooting spit wads.

M: May I borrow a pen?

C: Will a pencil do?

M: That's even better. I might make a mistake.

I did my best, praying Cranky would approve.



C: Very nice.

M: Oh, thank you very much! My handwriting is normally much better though... Arms are still sore from yesterday's bear crawls that I had to show another assailant.

Our high school History teacher taught by telling "war stories" all the time. He was funny and made me look forward to an hour of learning mostly about dead white men. I enjoyed writing poems too in English and made no qualms that neither war stories nor haiku poems would likely add to my real-life toolbox.

Writing a haiku

Does not need to explain why

Same with equation

—————

When are we going to use this in real life?

You're using it NOW, dear. Doing mathematics is like exercising. It's mental conditioning. Sometimes it gets boring, sometimes it's difficult. If it gets boring, you either have mastered it and need something more challenging, or you don't have a clue of what it's asking for and just need a more level appropriate challenge. Or it's boring because someone has made you watch and take notes on the third video of the same topic and you'd rather poke needles in your eyes. And about it being difficult — I hope it is. Not the level of difficulty of having to do 50 burpees followed by 50 box jumps followed by 50 death squats. But it should be difficult in the sense that you aren't quite sure initially how to do it but you know it's worth trying because you're interested in solving it. The math task is making you think, inviting you to try a different strategy, daring you to be flexible — this is the NOW work you're doing to know you're alive. 

You love mathematics more than you know. In Chapter 1 — Why Do Math? — of his book Letters to a Young MathematicianIan Stewart writes:

I sometimes think that the best way to change the public attitude to math would be to stick a red label on everything that uses mathematics. "Math inside." There would be a label on every computer... on every airline ticket, every telephone, every car, every airplane, every traffic light, every vegetable...

You go to the movies? Do you like the special effects? Star Wars, Lord of the Rings? Mathematics. The first full-length computer-animated movie, Toy Story, led to the publication of about twenty research papers on math...

If anything makes use of math, it's the Internet. The main search engine at the moment, Google, was founded on a mathematical method... It's based on matrix algebra, probability theory, and the combinatorics of networks.

Modern communications systems simply would not work without a huge quantity of math. Coding theory, Fourier analysis, signal processing...

You don't hate math. You can't. Everything that you love requires math. You must mean you hate school math. And that I believe; and I'm working hard to change your mind. In Edward Frenkel's Love and Math: The Heart of Hidden Reality, he writes:

I want to tell you about all this to expose the sides of mathematics we rarely get to see: inspiration, profound ideas, startling revelations. Mathematics is a way to break the barriers of the conventional, an expression of unbounded imagination in search for truth.

Mathematics is as much a part of our cultural heritage as art, literature, and music. As humans, we have a hunger to discover something new, reach new meaning, understand better the universe and our place in it. 

There is a common fallacy that one has to study mathematics for years to appreciate it. Some people think that most people have an innate learning disability when it comes to math.

One of my teachers, the great Israel Gelfand, used to say, "People think they don't understand math, but it's all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he won't be able to tell you. But if you rephrase the question: what is better, 2 bottles of vodka for 3 people or 3 bottles of vodka for 5 people, he will tell you right away: 2 bottles for 3 people, of course."

—————

There are many Music Appreciation and Art Appreciation course offerings. We should institute one in Mathematics Appreciation. 

Dan Meyer's recent post Culture Beats Curriculum makes my heart sing because if you know me in person or via this blog, hopefully you also know that any set curriculum and its cousin, the pacing guide, take a back seat to my students' learning through problem solving and to their opportunities to appreciate and marvel at the inherit splendors of mathematics. It's a culture we've created together. It's sacred.

Instead of waiting for When Will I Ever Need This? to come up in the middle of our favorite lesson, let's address it on Day 1 of school. Let's show (not tell) our students how beautiful and useful math is. How fun and challenging learning math can be and should be. Show them a math video and read them a passage from a math book that make us cry.

And when our kids need to do something they might consider boring — like a worksheet of skills practice on dividing mixed numbers, solving systems of equations, factoring polynomials, integrating by substitution — let's beat them to it and be the first to call it boring. Kids sometimes like to prove their teachers wrong, so they might disagree with us and say, "It's kinda fun actually." 



Barbie Bungee Revisited and Better Than Yours Class Lists

This year I've taken away a lot of my step-by-step instructions for the Barbie Bungee activity that I'd posted 1.5 years ago.

They get no handouts, only some verbal instructions:
  • See that gob of tape up there? That's leftover tape from previous years where Barbie had taken her jump. It should be at 3 meters up. Well, a small ruler will come out perpendicular (somehow) to that pole where the tape is, and that's Barbie's jumping platform. The ruler is like her diving board.

  • The goal is to give her the most thrilling jump — her head dips as close to the ground as possible without actually touching it. Yes, her hair hitting the ground is fine. Her jump line is made of rubber bands tied together with slip knots. (Why must we use brand new rubber bands?)


  • So, aside from the Barbie doll, what do you think your supplies will be? Rubber bands! How many? Lots! A hundred! Try six. Actually seven, but one must be completely wrapped around her ankle, like this.

  • With only 6 rubber bands, your job is to figure out how many more rubber bands she'll need for the most thrilling jump from 3 meters. Can we weigh her? This is like the Vroom car! So we have to graph, then do the extension thingy. Extrapolate. Oh, the equation is in slope-intercept form! (We've been looking at word problems and writing linear equations that would be more appropriate in standard form or in slope-intercept form.)
  • Your team will have until the end of tomorrow's class time to submit your number of additional rubber bands you'd want. 
For easier management of the rubber bands, I get them ready in (L): bundles of 7, one to each group for testing and data gathering, and (R): bundles of 10 and extras to give out as requested on jump day.

  


I liked the messiness of their initial work(I didn't give a handout or many instructions for Vroom! either, and they did fine.) Kids doing whatever they think they should do, measuring incorrectly, plotting ill-looking graphs, talking and criticizing one another. I was debating when I should intervene, but it was good for me to just observe and listen in. 

I waited until the next day to point out stuff. Actually I never told them what they should do, I tried instead to ask them how something should be done. I don't think one single idea came from me — someone always had the answer I was hoping for, so all the "correct" ways to do things came from them. 



My phone apparently didn't have enough memory after this one clip. It was fun. (One kid also brought up that this was like the Stacking Cups lesson that we did.)


**********

This might seem to you a DUH! share, but I only thought of it earlier this year, and I feel like I invented the paper clip. 

We all have class lists, of course. But is each of your class lists on a strip of paper like this? And in different colors? I didn't think so. 


I have semi-thick stacks of these to use for just about everything. What a pain to write down kids' names for this and that. Instead I just pull out a strip and highlight so-and-so's name and note the reason. 
  • I staple one set of strips together, put a date on it, and kids pass it around to each other to sign in for after-school help — they just need to put their initials next to their names.
  • Those who need to come in at lunch recess get their names highlighted on the strip.
  • I use it as a hall pass when I need to send 2 to 3 students at a time to the library.
  • I highlight a kid's name whose parent I need to contact, then use the back of the strip to make notes from our conversation.
  • It's a great tally sheet for whatever during class.
  • Endless uses. 



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