Math & Art: Big Numbers

Check out this site. Really cool images.

"Depicts one million plastic cups, the number used on airline flights in the US every six hours."


"Detail at actual print size:"

What's the percentage of "adders-across" in Numeracy?

In the past, I've given diagnostics before a unit so as to be able to compare pre- and post-instruction scores. Now, in the spirit of differentiation, I'm going to go one step further.

The next unit is about adding and subtracting fractions and mixed numbers. On my diagnostic, I wanted to see what percent of the students are still "adders-across" (#25 down: snakes that are bad at math). That would be 68/80, or 85%. The remaining 12 students could all do the basic algorithms, but most stumbled on the more complicated mixed number subtraction problem.

So here's the plan. In each class, I will assign one of the non-adders-across (NAA) to an adder-across (AA), tasking the NAA to help the AA learn over the coming lessons. If I see that they remain on task during practice time, the NAA will not have to take the quizzes, earning an automatic 100% on them. This seems reasonable, since they have already shown me they know the skill. Additionally, if the AA passes the quizzes (i.e. becomes an NAA!) then the NAA helper will earn some oh-so-coveted extra credit points. This way, the NAA has strong incentive to help, but there is no penalty if the AA doesn't make enough improvement.

Since almost no students showed mastery of the mixed number subtraction problems, every one will need to take that quiz when we get to it.

Now, the only thing that remains is to pair up the NAAs with the AAs effectively. I need to factor in personality, motivation, and so forth. Also, this experiment really highlights the imbalance between classes, even though we try to avoid any tracking (a constant difficulty in a small school). Here are the numbers of NAAs by period... Period 1: 5, Period 2: 4, Period 4: 2, Period 6: 1.

My mini-whiteboard love-hate relationship... Can you help?

I've been using mini-whiteboards daily in my numeracy classes all year. Students use them most of the time, except when I have a worksheet for them to do (and even then, they tend to use them for scratch work).

Positives:

• I can see, from anywhere in the room, what students are doing, and if they are on task.
  
• Students enjoy writing on their whiteboards more than on paper.
  
• Students don't have to waste paper for scratch work (this is especially helpful for those students who have still not mastered the art of bringing school supplies to class).
  
• And I don't have to make worksheets for every single task either.
  
• It makes collaboration easier during pair/group work tasks.
  
• It's great for quick checks of understanding - put a problem up, students do it on their boards, and then immediately lift them up for inspection.
  

Negatives:

• We burn through markers like nobody's business, and the ones that are low-odor cost about a buck a piece. I've tried the cheaper ones, but they run out really fast, or have fumes that cause much complaining of headaches.
  
• Tables and hands tend to get really messy (for some students more than others...) Our beautiful white laptops are getting covered in whiteboard marker smudges.
  
• "Mr. Greene, can I please go wash my hands???"
  
• Some students not able to respect materials, destroying markers by pounding in their tips, or writing with them on paper till they run out.
  
• Some students unable to stop drawing beautiful works of art when I am presenting material. Or maybe this is a positive because I can see that they are off-task, whereas if they were doing plain old paper-and-pencil doodling, I might not notice?
  

I was wondering if anyone had any ideas to help with the logistical issues of mess and expense? Remember the Magna Doodle?

4.58 x 10,000 = 4.580000

Most of my numeracy students remember that helpful rule from middle school: "Multiplying by 10 means adding a zero", and so we get results like the title of this post. This is one of those fundamental place-value problems, the type of thing that betrays just how little some students really get about the number system. It's taken about two weeks of practice to get them comfortable with the idea of shifting the decimal place left and right (and remembering which way to shift it, depending on the operation).

We are also currently struggling with the issue of the missing decimal point... when there is no point shown in a number, where is it really? Some of my students still think that you put the point at the front of the number. Why do they think this? I'm not sure. Before break, we spent a whole lesson on what the decimal point means, and it seemed to go well. Since we've been back in the second semester, the question of where the missing decimal point goes has been asked and answered many times each class period. They are getting better at comparisons: if I ask them to compare 473 and .473, or .4 and .39, or .4 and .04, they are usually getting it right. And yet, when faced with the problem 473 ÷ 100,000, some students seem to forget it all and start with the decimal at the front of the 473 (or sometimes between the 4 and the 7), forgetting that this changes the value of the number.

No wonder scientific notation is such a bear to teach in Algebra... To reinforce both concepts, I've been teaching scientific notation (with positive exponents only) in this unit, and it's finally starting to work. From the start, my students could tell me that 10^6 was the number 1 followed by 6 zeros, but they couldn't see the relationship between the problems 9.02 x 10^6 (which was totally confusing) and 9.02 x 1,000,000 (which is finally becoming easy). Converting a number into scientific notation is starting to make more sense to them now, since I've finally figured out another flaw in some of the students' understanding: they don't really get the significance of the equals sign. I would show over and over why 302,000,000 = 3.02 x 10^8, and some kids just weren't catching on. But then, when I asked them what they would get if they multiplied 3.02 x 10^8, they were surprised to see that it was 302,000,000. I would get lots of "ohhhs" as they realized that the two parts of the equation had to be the same, and that you could multiply to check your answer. The main problem I still have is getting them to remember that the first part must be between 1 and 10. But at least we're making progress! Though we have been learning dividing by powers of 10 at the same time, I don't want to introduce scientific notation with negative exponents now (since they have never seen negative exponents before). I want to give this time to sink in, and maybe come back to it later in the year.

We have the rest of this week off for winter break; when we start next week, I think it's time to move on from this percent and decimal concepts unit and start in on fraction operations. 1/2 + 2/3 = 3/5, here we come! (One of my favorite things to show numeracy students is why this equation doesn't make sense.)

Welcome

Most of our students are English language learners, but most have Spanish as their native language. As of a few weeks ago, we have a new student who is a refugee from Myanmar - she showed up in my SSR period and in my Numeracy class. Not only is language a huge barrier, there is also her difficult past. Working in her favor, however, is a massively strong desire to learn.

An article came out in today's paper which gave us all more insight.

Here is the text of the article (if the link is bad).

Orphans survive wars, find safety in Bay Area
REFUGEE CHILDREN ADOPTED THROUGH UNITED NATIONS
By Rebecca Rosen Lum
Bay Area News Group
Article Launched: 02/18/2008 01:33:04 AM PST

Kate's smooth brow buckles when she thinks about the soldiers who muscled their way into the house where she lived with her grandmother - plundering belongings, forcing their attentions on her and ordering them to prepare meals.

"The soldiers make me too sad," said Kate, discriminated against as an ethnic minority in Myanmar. "I don't like."

One day Kate, now 16, fled to the home of sympathetic friends in a neighboring town. She learned soon afterward that the soldiers killed her grandmother in retaliation.

After a desperate flight through underground channels of Southeast Asia, Kate has found a lasting safety: She now lives with a family in San Jose. "Baba" and "Mama" are the Rev. Ben and Anne Daniel; she has three siblings.

As rain pounds on the roof of Ben Daniel's church, Kate sits comfortably between her new parents, a delicate girl with shiny black hair and a wide open smile. She has been here little more than a month, but she says this is home.

"Everything OK," she said. "Not tired. Not scared. I happy."

Kate is one of a trickle of refugee orphans finding homes with Bay Area families through a special program of Catholic Charities, one of two agencies that contracts with the U.N. High Commissioner on Refugees to place the children.

In such countries as Liberia, Uganda, Sri Lanka, Myanmar and Nepal, children have been driven out by armed conflict or pressed into service by government militias and rebel groups - as combatants, sex slaves and virtual pack mules.

If an adoption always includes risk and reward, these adoptions offer a double dose of both.

Preparing food is now a source of surprise and delight for Kate. She likes oatmeal with hot sauce. At first, she dissolved in giggles at the sight of Baba popping up a skillet of popcorn on family movie night. (Men don't cook in Myanmar). Now they fix dinner together.

Kate dropped out of school after her fourth year to help her grandmother farm corn and beans. She asked to start school the morning after she arrived: "I want right now," she said, laughing. She studies music with Anne and says she hopes to become a minister, like Ben.

Kate's odyssey hardly seems likely for a child, but it is mirrored throughout countries where war and strife have made homelands unlivable. Many have been persecuted for religion, ethnicity, or political affiliation. They have been separated from their parents or seen them killed. The children escape brutality by guts, wit and luck, walking for miles, hiding in jungles, riding on the backs of sympathetic elders to safety - mainly, in refugee camps.

Five million refugees have fled their homelands, according to Refugees International, a non-profit organization. If one includes those who are trapped in their home country, such as in Darfur, that number balloons to 14 million. They can't go home in many cases because home is no more; their villages have been destroyed.

Tracy Weiss read all she could get her hands on about the conflicts that racked the Eastern coast of Africa after she agreed to adopt three siblings from Monrovia, Liberia.

When she picked them up from Mineta San Jose International Airport, Sadiki, the eldest and tallest, stood in front, "scanning everyone, looking for danger in every direction." His sister Maryama tucked in behind him, holding a bag, the U.N. signal for a refugee arrival. Antimana, called "Ansu," crouched behind his two siblings. They wore donated clothes - Ansu, a 1930s-era man's suit.

"I said, 'Hi. I'm your new mom,' " Weiss remembered. "Ansu was the first to break into a grin."

The trio has been living with Weiss in Los Altos for three years and - Maryama counts on her fingers - six months.

Rebels executed the children's Mandingo father, as well as Sadiki and Ansu's mother. The children and Maryama's mother ran from rebels, living in the bush, moving constantly, sometimes getting separated. They settled for a time in Bo, a village in Sierra Leone. Sadiki - he thinks he was 3 or 4 - made many friends there.

"Then things got bad if you are not a citizen," said Sadiki, now 18. "We had to find a way to stay alive."

Sadiki's earliest memory is of a village in chaos, with people running everywhere to escape the approaching rebels. Alone, he held up his arms in hopes someone would carry him to safety. Someone did.

He thinks the family spent five to seven years on the run.

Chatting one afternoon, Sadiki's new mother asked him if he had any photos from his earliest years.

"Mom," he said evenly. "You are running with a whole stack of things on your head. You step and you fall in the river, everything gets ruined."

They eventually made their way to the Bandajuma refugee camp, where his stepmother died from complications of diabetes.

It took them some time to get used to the idea that they could make the four-block walk through their wooded suburban neighborhood to school without getting mugged, that loud pops were not likely to be gunshots. Weiss had to quickly abort a July Fourth trip to see fireworks in San Francisco when the multiple blasts badly shook the children.

While life here brings a sense of safety, negotiating the social minefield of a new culture can prove dicey.

Language is a separator at the outset. Then come the mutual misconceptions of American kids and the newcomers.

The refugee orphans are surprised to see all Americans aren't wealthy and white. Alternatively, few Americans have had to run for their lives.

"One kid said to me, 'Did you ever fight a lion?' " Sadiki recalled, howling with laughter. "I said, 'Yes, two.' "

Many don't even know where Africa is, Maryama said, and they know much less about the violence that devastated her homeland and scarred her family.

"I can't be angry at them," she said. "They don't know. When they know, they care."

Divide by Zero?

This is pretty cool. I've never heard of the animated lego genre before, but I guess it's pretty popular. Most of these films are shorts, but some are feature length! Wow..

Caught Being Good

If you're a Harry Potter fan, you've probably noticed that classroom management at Hogwarts isn't much of an issue. Sure, they get to fly around and do magic all day. And parent involvement seems quite strong. But what else do they have that keeps the young'uns in line and focused on getting to a four-year wizard college? An entirely hassle-free incentive system. I'm talking, of course, of the Hogwarts' House Cup, and the constant cries of "10 points for Gryffindor" and the like.

At DCP, we've only formally developed negative consequence systems (detentions, referrals, contracts, etc.). These work to an extent, but not for all students, and not in all cases. For a while now, I've wanted to get a positive system put into place as well. I thought that this would help increase student buy-in, especially for the freshmen making the transition to DCP and becoming a college-prep student. So, combine this need with our students' love of getting points, use Hogwarts as a model, and presto-hey you've got the "Chalice of Pride"!

I got some other teachers together, and we made a plan for this at the beginning of the year, but we haven't been able to get it off the ground until now (time, time, time...). We originally had a more complicated setup, but the lack of magic wands put a damper on our plans - the system had to be totally easy for the teachers, or it wouldn't fly. So here's how it works: each freshman tutorial class (there are 5) is competing for the Chalice of Pride. Students can earn a Ganas Point (i.e. a "caught being good" ticket) for any behaviors that really demonstrate one of the school values. This is simply handed to the student by the staff member. The student then must put the slip into the clear plastic locking drop-box that is assigned to his or her tutorial (these are attached to the wall in a central location). At the end of each month, we tally up the slips in each box, and the winner gets to display the "Crest of Community" and claim bragging rights. At the end of the year, the tutorial with the most total points earns the "Chalice of Pride" and a field trip (like a day at the beach, or whatever floats their collective boat). We're in day 3 of the system, and I'm starting to see slips in the boxes already. I'm looking at this as a kind of experiment in positive incentive systems - clearly, it can be done more effectively - but we have to start somewhere.

Continuing on with the positivity trend, we've also updated our homework checker system for the new semester. For the past few years, students have had to carry a homework checker with them to each class; it got marked each time they didn't have their homework, and then the checker would be looked at by the tutorial teacher and the parents. Of course, this would cause students to "forget" their checker on days when they did not have their homework. Therefore, we gave detentions to students for not bringing their checkers (to force them to produce them), and this really never led anywhere good. So, we made a simple switch to stamping their checkers when they do have their homework, with some simple rewards attached to getting a certain number of stamps over the 6 weeks. The rewards and reward-levels were created by the student council: 85% = prizes like stickers, candy, etc.; 90% = a free homework pass; 95% = free dress day and double lunch. We also started this on Monday, and so far, it seems to be working well. Students really want the rewards, and they are making sure to get their stamps. Even if they miss a homework, they will still be more likely to produce the checker the following class period so they can get the next stamp (in the past, they knew we would just mark all missing homeworks when they finally brought out the checker, so some students never would).

Who knew how effective stamping and stickering could be in high school?