Mathalicious

Lately, I've been trolling homeschooling sites looking for ways to supplement what AJ's learning (or not learning, as the case may be) in school. This morning the site Homeschool Recess posted a link to a site called Mathalicious. Mathalicious is aimed at middle schoolers. What attracted me was this statement on their splash page:

Here, we’re guided by a simple philosophy: Math isn’t something you learn, but a tool you use to learn about other things. Our mission is to help transform the way math is taught and learned by focusing not only on skills but on the real-world applications of math, from sports to politics to video games to exercise.

If you’re a teacher, parent or student, we invite you to use our content in your homes and classrooms. So poke around. Have some fun. Get some smart.

Content is organized by subject area (e.g. "fractions and decimals" or "probability and statistics") and can also be sorted into one of three levels: "middle school math," "algebra I," and algebra II." This is not curriculum, but individual lesson plans that could be an after school project or a supplemental exploration in class or in a gifted program. All of them use math to explore some real world question. For example, in the most recent project posted, mathalicious looks at calculating the area of a TV screen and other screens, explains aspect ratios and theories of Pythagoras, etc. It includes detailed worksheets and files to use with geometer, a geometry software program.

Check it out!

Math series at The Opinionator

Steven Strogatz, a professor of applied mathematics at Cornell, is blogging at the New York Times' Opinionator about math for the next several weeks. In today's post, he talks about his plans for the series:

I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.

His first post starts with preschool and includes a video from Sesame Street that addresses the question, "Why do we need numbers?" You can read his post here

Math methods

When I was in school, I was pretty consistently a math underachiever, always scoring in the top percentiles on standardized tests, but rarely succeeding in class. My mother blames this tendency on my second grade teacher, who liked to announce to the whole class when I made a mistake. Some of it may also be due to gender bias -- girls weren't supposed to be good at math. But whatever the reason, it was my own lack of confidence in math that kept me from achieving well. I second guessed myself all the time. Frequently I would look at a problem and know the answer, but without knowing exactly why I knew it. Then, in trying to prove it to myself, I'd make a mistake. It wasn't until I was in sixth grade, while at the American School in London, where my math issues were identified appropriately. I didn't need remedial math. I needed more challenge and confidence. So along with 3 or 4 other kids in my grade and the grade above, we were pulled out of our regular math class and put with Mrs. Heumann.

Mrs. Heumann was one of the very best teachers I ever had. She was tiny and wildly energetic, one of those people who seemed to inhabit her whole body and also several inches of the space beyond. I had thought I'd been thrown into remedial math, but Mrs. Heumann didn't seem to know that. She worked us hard. On the very first day, she took away our pencils and paper. "We're doing math in our heads. Because you need to know that you can." And I could. We all could. And we were good at it. I moved away before the end of that school year and I was very sad to say goodbye to Mrs. Heumann. But amazingly, some of her lessons stuck, especially the one about "you can do it." I still battered my head against the wall sometimes with math, but I kept at it. I was even on my junior high math team for a year. I couldn't believe it.

But after high school calculus, I never took math again. I went to a college without distribution requirements outside the major. The closest I ever came to math again was a microeconomics class that was so bad, I stopped going to class after the first month. The teacher was canned after a single semester and I got the only D on my college transcript. Pretty good, considering I only ever showed up on test day and rarely cracked a book.

But as I see AJ struggling in similar ways, I've been thinking about all this again. AJ has a brain that absorbs higher math concepts readily. He's had a good understanding of complicated issues since preschool. But those things that require memorization or tedious practice often give him enough time to talk himself out of the simple solution and into something more complex and erroneous.

One of the things that can, I think, help students like AJ and like me back then (and maybe me now) are some alternative ways of thinking about the problem. One of the great strengths of the Everyday Mathematics curriculum that AJ's school uses is its support of multiple solving methods. But as the curriculum is actually taught, there are not that many methods endorsed. I've been digging around for other possibilities to help. AJ is very visual and physical, so here are two that have interested us in particular.

1. Finger Math. At one point in my own math struggles, my mother came home from the library with this book, or one very much like it.

I was fascinated. Based on a system used in Korea, Finger Math takes counting on your fingers to a new level by assigning different values to your fingers. The fingers of the right hand are worth 1; the thumb is 5. The fingers of the left hand are worth 10; the thumb is worth 50. This allows you to count to 99 on your fingers. The book also explains how to use fingers for adding, subtracting, multiplying and dividing, although I no longer remember the methods. I need to reacquaint myself with it. Here is a website that explains the same system.

2. Chinese method. Earlier this week, Dedicated Elementary Teacher Overseas posted a video of a Chinese method of addition that fascinated AJ and I. It involves drawing lines to represent the columns of numbers and adding the points of intersection. AJ and I were both fascinated and need to play around with this a little. Here's a video explanation:



Do you have any alternative math methods or tricks you like to use? Fill us in!

More on Math

AJ and his teacher are continuing to struggle with math. They really just don't understand one another. But now when his teacher doesn't get why he is making mistakes, she has started sending things home to me to go over with him, which allows me to figure out what the problem is and explain it to her, so hopefully communication will continue to improve.

This week, Mrs. F. sent AJ home with a worksheet on a estimating addition, something they've been working on in class. AJ has been struggling with estimation, because he doesn't see the point of the technique, where they round to the nearest 10 and then sort out the ones to get the total. He doesn't like the imprecision of estimation and it takes him longer to do it than it does to add the "normal" way, so he's been assuming he's doing it wrong and keeps coming up with these crazy algorithms that aren't really functional but which explain whichever problem he's working on. Once I explained to AJ that his class was learning a bunch of different ways to add and this was one way, then he was fine. He is a kid who needs to know why he's doing something before he can understand it. I know, because I was a kid like that too.

This morning I was tutoring his reading group. They were looking at an interview between a modern Wampanoag and a pilgrim interpreter from Plymouth talking about the way their respective people did things in the 1620s and creating a Venn diagram based on what they learned (the second grade is very bigg on Venn diagrams). One of the questions asked how many were in their respective settlements and the pilgrim replied "9 score." So we talked about what a score was and I asked if anyone could figure out how much 9 score was. "9x20!" AJ barked out without hesitation. But he was crushed when another kid got the answer before he did. If he can't be first, he doesn't want to participate. While I'm sympathetic to that point of view, I also know how paralyzing such self-expectations can be (talk to me about my decade-old dissertation some time). Still, when such pressure is internal, what's the best way to help ease it?

Parent-teacher conferences

At our first parent-teacher conference of the year last week, AJ’s teacher Mrs. F handed us a packet of grade 3 and 4 math worksheets that AJ has been assigned to work on when everyone else is doing the regular curriculum. “I’m not sure why he’s having trouble with this,” Mrs. F. said. “It shouldn’t be hard for him. But I find him just sitting there staring at it and not doing it. I even asked him to put a star on the pages he thought were hard and a smiley face on the pages that were easy. But he starred some of the easiest pages.” I told her we’d go over it with him over break and I’d try to get to the bottom of it.

AJ is starting to struggle with the format of school. His teacher this year is much more structured than any he’s had before. I get the impression that he feels like he’s always doing the wrong thing, but I haven’t yet figured out why. His teacher, who is trying to do everything she can to help him, is truly frustrated and perplexed. His test scores are off the charts, but he is having trouble with a number of class activities.

We had trouble working on math over break, a subject that AJ has always dearly loved. But every time we’d sit down to try to look at it, AJ would burst into tears. I have been trying so hard not to let it come to this point. My own love of math was squashed by a clueless (and downright mean) teacher in the second grade. This is what I’ve been afraid of. But eventually, we were able to get past the tears and into the problems. And AJ started to have fun again.


This morning, I sat down and wrote a long email to Mrs. F.:

AJ and I went over the math packet over break and I tried to get a sense of what had made him star some pages. He also worked on a few pages on his own and we talked them through afterwards. After looking more carefully at the packets, AJ decided that it was all pretty easy for him but mostly not so incredibly easy as to be boring (except for the time pages, at which he rolled his eyes).

I think his stars say more about his difficulty understanding instructions, both those you gave him on starring things, and also the ones on the starred worksheets. He said they are easy now that he knows what they are, but that he didn't know what things like "expanded notation" meant at first. [AJ’s class curriculum is the somewhat controversial Everyday Math program; the packet is drawn from the much more standard Spectrum series; the presentation and some terminology is markedly different.]

He also isn't clear on what the "show your work boxes" are for [each problem has a space on the right margin marked “show your work” -- are they required or are they just there when he needs them? Because he does a lot of the work in his head, if he needs to show his work, someone might need to show him what that means. I did talk to him about how he will at least at some point, need to demonstrate how he figured things out (we talk about this a lot at home, so that shouldn't be a total surprise to him, but he's not used to writing it, and he may balk at it because it slows him down). You'll see how he tried to fill in the "show your work" columns on some of the pages and I think it will give you a good window into how his math brain works. For example, On Lesson 2.3 of the Spectrum Math grade 3 (page 22), the first question gives digits for the various places and he has to figure out what number it spells. The number is 600,903, which he got correctly. In the "show your work" section, he wrote out the number, and then wrote the numbers for each place squished in underneath each digit(100,000, 10,000, etc.). Below that, he wrote "3x3=9" with arrows connecting the 3 and 9 with their twins in 600,903. Then he wrote "3x2=6" and drew arrows between the 3s and 6s. He told me that he thought it was cool that you could make all the digits out of 3, so he decided to show that. Further down the page, where he had to write biggest and smallest numbers made with the digits, he ended up writing the (correct) answers in the "show your work" column and leaving the answer blanks blank. He was so worried about showing his work, that he forgot to write the answers where they were supposed to go.

But AJ also wasn't sure what "hard" meant -- from his perspective, it was too vague. He doesn't always deal well with grey areas. I explained it to him as "hard is something you don't know how to do by yourself and you need someone to show you how to do it." By that definition, the only stars that remained were on the "expanded notation" pages. And once he figured out what that meant, then those stars disappeared as well.

Based on this, I'd like to see him gaining more independence on worksheets like this, being able to carefully read and figure out the instructions for himself. But I also think he may need some spoken words about what to do before each one. It's not so much that he gets it wrong all the time, but that he doesn't trust himself to be getting it right. He seems to expect that he's going to do it incorrectly and wants reassurance.

The other thing it seems like he needs work on, is interpreting word problems. There weren't actually too many examples of that in the packet, but he doesn't trust himself to turn the word problems into equations a lot of the time. He wants constant reassurance. And when the word problems involve subtraction or division, he doesn't always get the order right.

And, perhaps most important, overall, defining things with almost comic precision helps him out a lot. If there is an exception of any kind, he will find it and be confused by it. He hasn't yet learned the psychology of figuring out what the question is asking by what makes sense, not just what is literally stated.

I think, although I’m not certain, that his teacher is turning him loose with extra work and is not willing or able to spend much time explaining things to him. And I know that AJ is not always willing or able to get up in the middle of class and go ask his teacher what he needs to know. His class is very large and, as generally happens, those who are struggling to work at grade level get more attention than those who are working too far above grade level. But all second graders need help and personal attention, no matter what level they’re at. None of them is independent yet. I didn’t want to come right out and say, “pay more attention to my kid,” because I know she’s doing what she can. But at the same time, she needs and wants to know how to help him. I hope I was diplomatic enough while also being clear.

It's Starting to Add Up

The other day I figured out exactly how many mpg my car gets: 31.6. Which is not bad. I'd originally estimated it at 32 based on the average miles I drove on a tank of gas and the fact that I have a 14 gallon tank. But on Wednesday, when I coasted into town on fumes, I completely filled the tank. The machine stopped at exactly 14 gallons. I looked at the odometer afterwards, before resetting it and noticed I'd gone 440 miles on one tank of gas. So, I did the math - long division, on paper, all by myself. I double-checked it on a calculator later and got 31.4 but, hey, I'm not a math whiz and there's the proof.

I've always loved numbers but because of a piss poor education, I've always done horribly in math. And its one of the reasons I want Dusty to do well in it. She doesn't have a super math whiz gene (few in our family do) but I want her set on the right track now. I don't want to her derail like I did.

Which is why I'm happy she's where she is. The school system instituted full-time gifted and talented teachers in EVERY school over the summer. We met Dusty's new G&T teacher this week and I am very pleased.

The teacher, Mrs. G, has been teaching at the school for a number of years so the environment, and many of the students, are familiar to her. She outlined how the G&T thing will work this year. Last year, Dusty worked with two part-time G&T teachers - both of them brilliant and capable but doing an impossible task. The two of them taught at four or five different schools on different days. I don't know how they pulled it off, but they did.

This year should be even better. Mrs. G explained that they have clustered the G&T students into certain classrooms. Which explains why Dusty is still with her BFF and her partner of the last two years, Nathan. All G&T kids. This cuts down on Mrs. G's workload because she doesn't have to be in every single classroom every week. But she does do that on occasion, especially when a teacher in a non-G&T cluster room discovers a possible G&T candidate.

Mrs. G and the classroom teacher co-plan their lessons and co-teach them. There are no pull-outs at this level. They co-teach and then break the classroom into groups for small group work. Mrs. G gets the G&T group, Mrs. J gets the other students.

Best of all, Mrs. G teaches an accelerated math class for 5th graders. It's a pull-out class and she's a math person so I feel really good that Dusty's in good hands. In all aspects.

Not only that, but Dusty will soon get Spanish lessons. Students at the closest high school have started a Spanish Club that will meet at Dusty's school on Monday afternoons. While the county continues to "consider" foreign language classes in the elementary schools, Dusty will get a change to learn a second language. She'll get a tiny step up.

At this point, I have zero complaints. Dusty's in very good hands.

I also learned - through Mrs. G - about the Johns Hopkins Center for Talented Youth. I'm considering signing Dusty up for the next testing date (which is in Feb or March). If she passes the test, which is given locally, she would qualify for a number of educational opportunities, classes, etc. that she wouldn't have access to otherwise. She won't run quite so far if she's not wearing the right shoes. I want to give her those shoes.

Meanwhile, I'm going to go back and check my long division work. While 31.6 is close, it's not 31.4. Maybe Dusty'll be able to point out my mistakes soon. At least, that's what I'm hoping. I only had kids so they could help me with my homework.

Fun with Math and Science

AJ had a great time at Camp Gifted. We were really impressed by the end-of-session documents that were sent home. AJ's projects and lab notebook were fantastic, of course. So was the DVD that the physics teacher made of the kids' egg drop and Rube Goldberg projects. But we also really appreciated that each teacher sent home a summary of the course and list of websites and books and things to do if we wanted to do more of the kinds of things they did in class. I thought some of these references would be appreciated by readers here. The two science classes were targeted toward gifted children entering 2-3 grades. The math class had a broader age range of 2-6th grades.

PHYSICS

Websites
• http://www.invention-engine.com
• Search youtube for "Rube Goldberg" (this one is AJ's and my favorite)
• http://www.funology.com/laboratory/lab_physics.htm

Books
• Arlene Erlbach, The Kids' Invention Book
• Laura S. Jeffrey, American Inventors of the 20th Century

Places to Visit
• Museum of Science and Industry, Chicago
• American Science and Surplus, 5316 N. Milwaukee Ave., Chicago, IL 60630 (773-763-0313)

MATH

Math just sent home one recommendation, which is for kids' sudoku puzzles:

http://www.printactivities.com/Kid_Sudoku_Puzzles/Free_Printable_Sudoku.htm

I would add to that the essential, websudoku.com.

CHEMISTRY

Experiment books
• Tamara Perchyonok, Chemistry and Fun for Kids of All Ages
• Robert W. Wood, 39 Easy Chemistry Experiments (Science for KIds)
• Judi Hechtman and Karen P. Hall, Explore and Discover Kid Chemistry
• Janice VanCleave, Janice VanCleave's Chemistry for Every Kid: 101 Easy Experiments that Really Work

Websites

• PBS Kids Kitchen Chemistry
• Bill Nye Home Demos
• Build your own Volcano at Discovery Kids
• Experiencing Chemistry at OMSI: How to Make Flubber
• Chem4Kids Website
• ChemShorts for Kids: Links to a variety of experiments

The Shape of Things To Come

An amazing thing happened recently. Dusty, my first grader, read out loud. To the class. This might not seem like such a big deal to you but it is a milestone reached. A year ago, Dusty started kindergarten. We knew she was smart. She’d taught herself to read by age four. She had already begun to read chapter books to herself the summer before kindergarten and had proven herself to be quite a talented artist as well.

At the beginning of that first school year, I approached her teacher and emailed the gifted and talented teacher. I explained that Dusty was smart, that I wanted her monitored and assessed as soon as possible. I know, to them, I probably sounded like a typical parent: convinced MY child was smarter than all the others. MY child was special. Please pay close attention to her! But I am not a hoverer. I just wanted to make sure that her needs are met. I didn’t want her to get lost in the shuffle like I was.

I was told that testing for the gifted and talented program happened in January. We’d have to wait. So we did. But we kept a close eye on things. Dusty’s teacher could tell she was smart but not to what degree. Why? One of the main ways of assessing her reading level was by listening to her read. Out loud. Something Dusty would not do. Not to her teacher, not to the reading specialist, not to the principal or her parents or her classmates. Occasionally she’d read out loud to the trash can but her teacher had to be paying attention at just the right moment. Blink and you’d miss it.

We hit a wall. Dusty started to complain about all the “baby work” they were doing in class, how she was bored. The math was “too easy”, the reading….don’t even go there!

At our parent/teacher conferences, we were assured that Dusty was fine. She seemed happy (and she was and still is) and was a full participant in the classroom. But. They were having a hard time figuring out where she really stood because she wouldn’t play the game by their rules. Not that I blame her but it was frustrating all the same.

Then January rolled around. Dusty was tested. She became more comfortable in the classroom. She opened up more (though still occasionally complaining about boredom and how easy the work was) and was given more challenging work.

Dusty was accepted into the G&T program for first grade. The first assessment of the year showed her to be reading at a fifth-grade level.

When the school year began, we met the G&T teachers and I have to say I was very impressed. I’d gone to a public school that had been full of long-term, burned out teachers with too many students. And, while these women not only job-shared but school-shared, they were full of enthusiasm and great ideas. They seemed really happy. They loved what they did. That in itself goes a long way to engendering a love of learning and an enthusiasm for school in children. Their upbeat attitude is clearly infectious.

And Dusty has really blossomed this year. The G&T teachers (one’s in her classroom on Tuesdays and the other on Wednesdays) co-teach with the classroom teacher and then break the class up into groups. The regular teacher works with one group and the G&T teacher works with the other group. The group that just happens to have Dusty and her intellectual counterpart, Nathan, in it. I get weekly emails from the teachers summarizing the lessons.

They take the regular classroom lesson and go as far as they can with it. The teacher challenges them to think in different ways. Here’s a recent lesson:

Language Arts Collab: Brave Stories ~This lesson provided a literature based creative writing experience in conjunction with on on-line Internet experience. After reading the story Brave Irene, by William Steig, the students discussed how brave Irene must have been to battle the harsh wind, snow, cold and darkness to deliver a gown to the duchess. They also viewed stories on the Internet written by children about times in their own lives when they had to be brave: http://comsewogue.k12.ny.us/~csinger/projects/braveirene/braveirene.htm. Students then brainstormed about times that they thought they displayed brave characteristics and what it meant to show courage. Students have started writing their own brave stories and will also be illustrating them on the computer.

Not only that, but I get periodic notices of classes in which Dusty can enroll. This past Saturday, she attended a Science with Toys class, with her dad, through the city’s Math & Science Center. Dusty came home with a battery powered motor and a bag full of cool stuff.

Last week was also the school’s Read-a-Thon. We documented everything Dusty read and everything we read to her every night on a chart. We pledged five cents per minute read (the proceeds go to pay for a mural in the school’s new library – opening in the spring). We logged 595 minutes!

The first day of the Read-a-Thon was a Read-In. Students were encouraged to bring in two books to share with their class. Dusty brought her two favorite Sock Monkey books. And it was one of those that she read to her class. Dusty! Reading out loud to her classmates! Amazing.

So, Dusty’s experience in school has been a good one. She will never have quite the disconnect that AJ does between intelligence/capability and emotional/chronological age but she will most likely always be a bit beyond her schoolmates. We do not have the dilemma that faces Harriet. She will remain where she is, in a well-funded public school with top-notch teachers (how we got so lucky, I do not know.). She’ll continue to carry the G&T label throughout her school career in the county in which we live. Whether her “gifts” will get sorted out later, I can only guess. She is strong in all subjects right now, but I have a feeling that reading, writing, and drawing will continue to be strengths, while math may get “hard” in a few years if we aren’t paying close attention to things. Not that “hard” is a bad thing. If she’s taught correctly, she may never have the issues I did with the subject.

And I haven’t heard Dusty use the word “bored” much this year. But this week the math unit will cover shapes.

To quote Dusty, “Shapes? I already know shapes.” Yes, and even though this is really shapes as pre-geometry I have to agree with Dusty. We already know this. So, no matter how great things are right now, we will have to stay ever-vigilant.

Devilish

AJ's interest in pi has not waned. After several years of obsession with space, which he still likes reading about, he seems to be transferring his obsession to math. The remainder of this post also appears at Spynotes.


Scene: Harriet's car. AJ and Harriet are driving home from an early morning yoga class (Harriet was taking; AJ was hanging out playing video games). They are listening to Car Talk.

Radio caller: I have four kids ages 10, 9, 8 and 6.

Radio host: Four kids! Holy cow. You need Prozac!

AJ: That's funny. Four kids.

Harriet: That's a lot of kids.

AJ: It's funny because there are 4 of them and the youngest one is 6. And 6+ 4 is 10, which is the age of the oldest one.

Harriet: You're right. That is funny.

This scene is brought to you courtesy of one of AJ's Christmas presents, The Number Devil by Hans Magnus Enzensberger, which has AJ thinking about numbers day and night, backwards and forwards, right side up and upside down. He's figuring out his own number tricks and learning some of the oldest ones there are. This is one exciting book, perfectly pitched for AJ right now. The topics are explained exceptionally clearly without at all talking down to children (except, perhaps for a certain amount of sillification of terminology: for example, roots are called "rutabagas" and factorial is called "vroom" because of how fast it gets a number to grow huge; traditional terms, however, are listed in the back of the book). The novel that frames the mathematical concepts and the pictures are both engaging. AJ is on fire with excitement about math right now, so much so that I'm wondering how he can possibly go back to counting at school on Monday. I may be sending a copy of this book to his teacher.

AJ got a lot of books for Christmas: G is for Googol (which we've had out of the library approximately googol times, so I made sure he got his own copy), Stuart Little, a book about Abraham Lincoln, a book about Global Warming, and the first in the Charlie Bone series. But The Number Devil is the one we've been reading over and over again. I purchased it on a whim when I felt funny about buying him G is for Googol, because he's already read it so many times. The Number Devil came up in the "you might also like" of the order page. I took a chance and I'm glad I did.

The Number Devil has had AJ calculating square roots at bedtime, building pyramids out of breakfast cereal, creating his own magic triangles, experimenting with factorials and exponents, and drawing pictures using the Fibonacci series. This is one exciting book. It's particularly fabulous to see AJ at work with some graph paper and cereal and a calculator while wearing AJ's favorite item of clothing from his Christmas haul -- a pi baseball shirt sent to him by the lovely Lass. This shirt, which he has owned for less than two weeks, has already been washed five times and showed off to all of AJ's friends, along with the medal he won in a basketball tournament.

Apparently, this year math is the new science.

But AJ hasn't left the world of science experiments behind entirely. His school's science fair is coming up in a little over a month and he's currently pondering some kind of gravity-related project. Or maybe we'll throw hot dogs at pi to see what happens.

Leftover Pi

Scene: Harriet's kitchen. It is breakfast time. AJ has just finished playing a game of multiplication baseball on the computer.

AJ: You know what my favorite number is?

Mr. Spy: What?

AJ: Pi. Do you think I could have pi on my basketball jersey? [AJ's first basketball practice of the season is this afternoon.] How do you write pi?

Mr. Spy: [who was probably getting ready to go for a run and not just passing the buck] Go ask Mommy to write it down for you.

Harriet: Pi looks kind of like a table with a little curve in the top on the left. I'll show you. [Harriet draws a picture of the symbol for pi=the word pi, and also a pie chart equalling the word pie.]

AJ: Can I write it?

Harriet: Of course. [She hands AJ the pencil. And he writes it out.] I don't think they'll put it on your jersey, though.

AJ: It would take too long to write it in numbers.

Harriet: Yeah. Your jersey would be WAY too big for you.

* * * * *

AJ and I then proceeded to look for websites to help us with calculating pi, because even after coffee, I am not up to it on my own. We found this page to help us. But even better were the instructions for how to calculate pi by throwing frozen hot dogs. We will definitely be trying this sometime in the future. But first, I need to go to the grocery store.


[Crossposted at Spynotes]

Numbers Game

It is the 21st day of the school year (not counting the half day at the beginning) and here in the Harriet household we are encountering our first signs of resistance. AJ doesn’t want to do his math homework.

The whole idea of homework has taken some getting used to, along with a school day that is four hours longer than last year and eating lunch away from home. AJ averages about 30 minutes of homework a day. 20 minutes of this is his reading assignment, which is a book that he and his teacher and I pick together, currently Chasing Vermeer. This is challenging and he likes the story, so this part of the homework is only a problem when his friends are standing on the front porch wanting to play kickball. The other ten minutes is supposed to be spent reviewing spelling words and doing math homework. The spelling words are so ridiculously easy for him, that we play games with them instead. We write crossword puzzles, put them in alphabetical order, write sentences using as many of them as possible, etc. I suppose we could skip them altogether, but I’m also trying to teach him that he needs to follow his teacher’s instructions and that he needs to figure out how to make his work interesting, because he’s going to have to do stuff that he thinks is boring some of the time. That’s just life. So we do our spelling like everyone else, but a little differently.

The real problem has been math. Our school uses the contraversial Everyday Mathematics series, a revamping of the traditional methods of teaching math to elementary school students that came out of research done at the University of Chicago. The idea is to teach kids how math relates to the world around them in much the same way that English is taught by relating writing to things the child knows and can write about. The curriculum seeks to eliminate rote memorization in favor of explaining the concepts about why things might be useful. Those who think Everyday Math is misguided usually focus on the lack of memorization and ability to handle basic arithmetic problems. But from my first views of the materials, that would appear to be a problem with the teaching and not with the materials itself. As a kid who refused to do my work unless I knew why I had to do it, I think I could have benefited from this approach, and I think it will ultimately be good for AJ too.

However, the early material is extremely basic. The math work in school for the last three weeks has pretty much consisted of counting things. AJ could count to 100 when he was 2. This is kind of a drag. But not as much of a drag as the homework, which has almost entirely consisted of finding numbers somewhere in our house. Yesterday he had to write his phone number, his grandmother’s phone number, and think of three other things in the house that have numbers on it. Last week he had to count the number of calendars in our house. Another day he had to count the number of thermometers. This is getting really old.

AJ has always loved numbers. He anthropomorphized them when he was little. “Let’s play the game where the numbers talk to each other,” he’d demand over and over again. And we’d take his foam rubber numbers and pretend they were going to school or to the playground or to a birthday party. He made puzzles out of them, trying to fit as many numbers into as small a space as possible. Counting was one of his favorite games from his earliest years. But by age 6, he’s looking for something more. “When are we going to get to do math problems?”

I wish I knew. We do them at home, but he wants to do them at school with his teacher and friends.

I feel like it’s still early to be worrying about this, so I’ve decided to wait it out for another couple of weeks to see what happens. I want to communicate to AJ that it’s important for him to do his homework even if he thinks it’s stupid, but that it’s also okay to ask for something more challenging if he finishes what he’s supposed to do. I was reassured in my approach by my job as a classroom volunteer this morning. I spent an hour collating math homework from the last half of the school year, homework that looks a lot more interesting than what they’re doing now. There’s still none of the multiplication or division that he craves, nor even subtraction that uses borrowing. But there are pages of problems that ask for multiple solutions, demanding that the students thing broadly and creatively, not just solve by rote. There are fractions worked both numerically and geometrically. There are complicated charts.

“Everyone is starting from a different place,” I tell AJ. “School is for everybody, so sometimes things will be easier and sometimes they will be harder.” I hope that this is true. Are we doing the right thing? Is it better for AJ to learn in a group of unlike abilities than to have lessons tailor-made for him? I think so. But I’m not sure. I wish I had more support. I wish I knew even one other parent in our district who’s going through the same thing. But from what I can tell, there aren’t any other kids like AJ, at least not in his grade. We are our own discrete subset.

Everyday Mathematics

Scene: Harriet’s car. Harriet and AJ are en route to the local ice rink, as they are at this time every Friday morning.

AJ: You know what I think?

Harriet: What?

AJ: I think that if there’s no end to how big numbers can get, then there’s no end to how small they get either.

Harriet: Interesting theory. Why do you think that?

AJ: Well, because if a number can always have a bigger number, then there should always be a smaller number too. But I can’t figure out zero.

Harriet: (parking in front of the ice rink). There’s another way to think of it. What if you were trying to go somewhere but you could only go halfway at a time?

AJ: Then it would take you two times. You’d go halfway and then you’d go the other half.

Harriet: But what if you could only go half of the distance to the door. Here, I’ll show you what I mean. (They grab their skates and gear and lock the car). We’re going to walk halfway to the door of the skating rink and then stop.

AJ: O.K. (He eyeballs the distance and walks to the halfway point). I’m halfway.

Harriet: Good. Now we’re going to walk halfway between here and the door.

AJ: Oh, I see. And then we’ll go halfway again.

Harriet: That’s right. What’s going to happen?

AJ: We’re never getting to the door. The door is zero!

Harriet: What happens to the distance we walk?

AJ: It gets smaller and smaller to infinity!

[AJ runs into the ice rink and spots his friend D., who is waiting for him inside the glass doors.]

AJ: Hey, D.! I just ran infinity!

* * * * *

Blazingstar recently left me a link to a contentious debate about the teaching of math in elementary school that is being waged on YouTube. One of the subjects of the debate is Everyday Mathematics, the curriculum that has been adopted by AJ’s school. The first of the videos can be seen here. There is also a series of responses, most of which I’ve had a chance to watch yet. The basic problems the first video has with Everyday Mathematics is that 1) it doesn’t teach the traditional algorithms for mathmatics, 2) it teaches math in a way the parents don’t always understand 3) it forces the students to come up with more than one way to do a problem (which apparently prevents “mastery” that is better acquired through rote memorization) and 4) it relies on calculator use.

Everyday Mathematics’ take on the teaching of curriculum as well as the rebuttals to the video, believe that the problem with teaching rote memorization is that we’re not teaching comprehension but the following of instructions. Everyday Math seeks to teach children how to problem solve. They spend a lot of time on the practical uses of math, having children figure out how to find math problems in everyday life.

I find the debate interesting, because I was one of those kids who balked at rote memorization. I’m still like that. If I didn’t know why I was supposed to memorize something, then I just wouldn’t remember it. AJ is the same way. AJ is, however, quite good at traditional algorithmic-based math. He likes practicing counting by 3s or 5s or 10s. He likes doing pages of problems. And he also craves the sense of mastery that the completion of a task, like the memorization of times tables or finding quick and accurate solutions to a page of problems provides. The big question I have is why does asking “why” and showing “how” necessarily mean that no memorization is happening? Can't they be used in tandem?

I feel like AJ’s current way of learning math is ideal for him. It is “Everyday mathemetics” at its fundamental sense. He thinks about something he notices in the world and we try to figure it out together through numbers. Numbers, to AJ, are yet another way of exploring meaning, the same a language or art or music. He plays in the real world with numbers, but he also likes to play with the numbers themselves to see what they will do. It's like the way he plays with Legos, sometimes building buildings -- a house, the Sears Tower-- sometimes just experimenting to see how he can put them together

After the conversation about infinite smallness, I found myself noticing AJ’s mathematical mind at work on the ice rink. Or rather, what I noticed was that other kids run into each other all the time but AJ almost never does, unless someone gets him from behind, out of his line of vision. Why? Because AJ triangulates with amazing accuracy. I’m sure this is more an issue of his attention than his ability – he doesn’t like to get run into. He’s never been the kind of kid who hurls his body around without fear of the consequences. But it struck me what a complicated skill it is to figure out how you, a moving object, might intersect another moving object, where that intersection is likely to take place, and then adjust your own speed and direction to avoid an intersection. That could easily be another math problem from the everyday, although I’m not sure I’m qualified to do the calculations.

But it is still a mathematical skill, and a much more useful application of math than pretty much anything I remember ever doing in an elementary math class. You do the math, you stay on your feet. You fail the problem, you hit the ice. It’s that simple.

[Crossposted at Spynotes]

Numerology

AJ walks into my room every morning at 7 a.m. on the dot. The first thing he asks for is his good morning hug. The second thing he asks for is a glass of juice. The third thing he asks for are math problems. AJ’s brain seems to be at its most mathematically oriented first thing in the morning. Unfortunately, I need truckloads of coffee before I can think about numbers. What’s a mother to do?

While we play a lot of more active math games at other times of day – things like multiplying window panes while I wipe off fingerprints or doubling and halving cookie recipes – in the morning we’ve been turning to the internet to assist us. Here are some of the websites we’ve found particularly helpful. Our criteria for what makes a good math website is somewhat flexible, but generally 1. It has to be fun; 2. There has to be some kind of reward (fake applause, points, cheering) for doing well and 3. The website is set up in such a way that it allows AJ a certain amount of autonomy. This last criterion is key, not so much because we’re not around to help – I’m generally just a few feet away, if that – but because AJ needs to feel like he’s in control of the technology in order to feel like he’s in control of the math.

To give you some idea of the level of the websites we’ve been looking at, AJ’s currently pretty solid on addition and subtraction, including borrowing. He does okay with multiplication, but still has to count it out sometimes. We’re working on fractions and division and also on how to convert word problems into equations. He’s also getting interested in geometry, God help me. Mostly the latter interest seems to lie in a more artistic direction – he likes drawing cubes. Many of these sites offer a variety of math games and quizzes at a variety of levels. My brief reviews, however, are based solely on my experience with AJ’s level.


1. Math is fun!. This website is pretty low-res as sites go and its name always serves to remind me of the Barbie flap from a few years back (“Math is hard!”). But the basics are there. AJ likes “Who wants to be a mathionaire” game especially. There are other, glossier versions of the mathionaire (or mathonaire) game elsewhere, but most are higher level math – more complicated equations, algebra, etc.)

2. Math Arcade at Funbrain. This site is a little confusing to navigate, requiring more intervention from me than is ideal, but AJ likes it because the progress is marked through a board game. What AJ doesn’t like, however, is that you are expected to go through the game in order. He doesn’t like going in order – whether on websites, or in workbooks. He likes to find the most interesting-looking things first. He is coming around to working in sequence in his workbooks as he learns that jumping ahead often means you’ve missed something important. But on websites he still expects free play. Still, the games are good and the graphics are more sophisticated than mathisfun.

3. Cool Math 4 Kids Arithmattack at Cool Math 4 kids offers a range of customization – choose your operation, the largest number, and the level of difficulty. You then solve as many problems as you can in two minutes. There are other games too, but we have yet to explore them. This requires a little adult supervision to get it set up, but once he gets going, AJ can manage this site on his own.

4. Maths Year 2000 This site is relatively new to us and many of the games require a knowledge of more complex math than AJ can handle at the moment, but the Maths Activity Pack and Maths Circus are both entertaining and have more compelling graphics than the typical online math games.

We have discovered some of these sites through other sites with good lists of educational websites for kids.

Internet 4 Classrooms is a well-organized list of sites organized by topic and grade level aimed at teachers looking for ways to supplement classroom learning with computers.

This site is run by the Mifflin County School District in Lewiston Pennsylvania. If you click on the “Curriculum” button at the top of the page, you can access site lists for other subjects as well.

Any of these sites should have enough math activities to keep your child busy through at least one cup of coffee. Maybe even two.