Writing in math rocks my socks

I handed out and used the reflection journals in my Numeracy class for the first time today. Of course my first class was too fast for me and half the covers were tagged before I could even react; but I learn fast and outlawed tagging script for the rest of the classes. "Aw man, no tagging??" But they listened for the most part..

I know countless other teachers do the reflection journal, but it isn't seen as much in math. And I've never tried it before. The kids were a bit unsure what to write, and I was a bit unsure what to tell them. My prompt today was something like "write about what you learned today in class and what you feel that you still need help in". I also told them they could choose to follow my prompts, or write something else. General ideas: what are you understanding? What are you confused about? How did the class go? Is there anything you want or need to let me know? I did confirm for one girl that the writing should, indeed, be at least tangentially related to what is going on in class. She seemed to find this reasonable.

So far, I am totally into this. The last 5 minutes of class are silent, as kids process what they just learned, and think about what they still don't get. At the end of the day, I read through 3 classes worth (~60 students), in about 20 or 25 minutes, and responded to what they wrote. The immediate feedback was awesome. Most found the Bar Model method long and seemingly difficult, but they almost all conceded that it helped them to understand the problem better and make it easier. The kids who were totally confused let me know. One girl said she was proud of herself for having learned the new skill. Another told me that I talk too fast sometimes but that she thinks I'm going to be a good teacher anyway and is looking forward to the year. One boy told me his stomach hurt from lunch and that he needed to use the bathroom (he's in Numeracy for the second time - but I dig his sense of humor).

I'm going to try to commit to reading their journals every Friday at least.. I think that the more I write, the more they are likely to write to me.

I collected their math autobiographies today (only 3 or 4 kids didn't do them!) and I am looking forward to reading them later on. I'll probably post a few choice excerpts.

Wha?

The first day came and went in a blur. We started the day with a special assembly, in which all the departments came up with a little skit to present themselves to the students. There was a lot of energy, and the kids had a good time. The math department came out as if we were doing an encore to a show - we brought costumes and real instruments, and rocked out to "Cult of Personality" (i.e. Cult of Math Ability). Then we introduced ourselves, including our new stage names. This year, I am "Bass 10". Hah!

I saw 2 Numeracy classes today (80 minute blocks), plus SSR and homeroom classes. Lots and lots of freshmen everywhere. They are always so different in the first week or so of classes: silent and afraid to stand out as their brains are processing all of the new social cues and are trying to make sense out of their new world. Or something. I promised I'd know all of their names by the end of the week, but that may be pushing it.

In Numeracy today, I asked them to start by brainstorming around MATH - what images does this loaded word bring to mind? As this was the first day, discussion was hard to draw out of them. Someone would finally mention fractions, and I'd say, "Is there anyone in here who doesn't really like fractions", and every single hand would suddenly shoot up. See, you guys do have things to say! Then, I handed out a math survey to try to measure their self-perception and self-confidence, among other things. We'll repeat this at the end of the year so I can see what changes have been made.

Then, I handed out the Math Autobiography assignment. It had some questions to get them thinking about their math experiences thus far, and they need to write a full 3/4 sheet autobiography for homework! I'm sure there will be some really interesting ones, and I'll post them once they come in.

We burned through class rules and expectations as fast as possible, and then I began the whole-class unit on integers. (Differentiation will start later on, once I figure out when our laptops will be coming in.) I introduced what integers are (and we talked about applications like money, position, time zones, temperature), and then I showed them how to use unit cubes and an integer mat to model integers. We also learned about zero pairs, and how to simplify integer mats by removing zero pairs. I feel like not rushing things is a good plan. Spending a few lessons really scaffolding integer addition, I think, will pay off in the long run. The kids did a good job with the manipulatives, but reading directions is going to be (as usual) a constant challenge.

I'll try to keep posting about what is happening in Numeracy - though maybe not full lesson plans. If anyone has questions about details, always feel free to leave a comment.

It begins!

Ok, I think I just laminated more things in the last three days than I have previously in my whole life. I've got up the class norms (1. Show respect to yourself, each other, and the class. 2. Always focus on learning math. 3. Try hard and take risks.) I've got up the 8 step process for solving problems with Singapore bar modeling. I've got up the signs for the Readiness Check (Binder and homework out; pencils sharpened; backpack at the back of the room; working on the Do Now) and I made the Readiness Checkers - an idea I stole not 5 hours ago. Each time the student completes all the readiness tasks by the bell, they receive a sticker on their grid of 9 spaces (3 weeks). When the grid is completed, it turns magically into a coveted get-out-of-homework pass. I've got up the giant sign with the answers to "Why should I learn math?" (see previous post) which took the help of two other teachers and 4 boys from the soccer team to color in. Oh yeah, and three kids from the robotics team to laminate it and cut it out. I've got the homework checkers laminated and up on the wall; each day, students receive a check mark or an X depending on whether they completed their homework or not. This system is a good way for them to continually be reminded of the effort they are (or are not) putting in. Plus, parents love to see them when they come visit. On parents' night, the homework checkers are the single biggest draw (as they are easy to understand and give an immediate sense of parental satisfaction or dismay). My blank journals are unpacked and stored on the shelves, labeled by period number. I came up with a new idea today - the "Days since the last referral" wall. Each class period has a sign up, with a referral stapled next to it on the bulletin board. The signs are laminated, so I can put a check mark each day that no one in the class gets a referral (or I can rip it down dramatically when someone does!). If they reach 10 days with no one getting a referral (that quite a lot for a low-skilled freshman class), there will be some sort of group reward. There are famous mathematicians on the walls smiling smugly over the room. I've got up the number line on one wall and the place value chart on another wall and a magic eye calendar on the back wall. I've got up a map of the US and another of the world. These are great to have up in general because students don't know where places are or how big they are relative to others. I always think back to my Algebra 1 student (who is now safely graduated) who, in a scientific notation lesson busted out with "Alaska? What's Alaska?". On the world map, I can show them where Singapore is. The manipulatives are shelved neatly and the copies for tomorrow's lesson are all made and laid out on the desk. I helped the other teachers remaining here at this ridiculous hour move stuff and get stuff prepared. And I just finished making my seating charts now that the class rosters have finally been sent out. You have to be a teacher to really understand how much goes into preparing for a new year...

I'm excited about my classes - both my single Algebra 2 class and all my little freshmen that will be in Numeracy. Going into my 7th year of teaching, I finally don't feel nervous because I know how most things are going to play out and I feel prepared. But last year I had a light schedule because I was working on another project for the school part time; this year, I have the 5 classes plus SSR and Homeroom, so I'm going to have to fight to get my teacher legs back. It's time to go home, get some sleep, wake up, pack lunch, and dive in to the deep end. I think I'll be holding by breath till Thanksgiving.

Leer es poder!

In preparing for Numeracy this year, I've been reading up on the Singapore Math curriculum and philosophy. They really seem to know what they are doing. Everything has a logical, mathematical reason, and it all fits together neatly. I just read through two books which I highly recommend for anyone teaching primary level math to high schoolers. In just under 2 hours of reading, I've gotten some really good and practical ideas - both big and small picture.

Handbook for Primary Mathematics Teachers

8 Step Model Drawing

I read this next one a while ago, and have recommended it on this blog before, but it bears repeating. It is a fascinating comparison study of teachers in the US and China, and what kind of mathematical knowledge and ability is required in order to teach primary math.

Knowing and Teaching Elementary Mathematics

What books do you find useful/enlightening/interesting with regards to teaching math?

Numeracy 07-08: Project DI

If you're a new reader of this blog, it's important to know a bit about my school, which serves students 9th graders whose average grade level in math is 5th grade, and we seek to have all students ready for 4-year college in 4 (or sometimes 5) years. All students take Algebra 1 when they first arrive, even if they have "passed" it in 8th grade - which many have. The majority of the students also take the Numeracy class, which I have written a bit about before, though I mainly wrote about Algebra 2 last year.

I wrote the current Numeracy curriculum 3 years ago, but the students have not gained as much as they could from the class due to the wide range of skills (and deficits) they bring with them from middle school. My plan this year is to take some of the best elements from the old curriculum, but to differentiate instruction. The units in the old curriculum went like so: Place value and addition/subtraction facts; multiplication and factors; division; fraction concepts; fraction addition and subtraction; fraction multiplication; fraction division. The first three units were not that useful for about half of the class, while they went too quickly for the other half. No one really got what they needed. So here is the plan for the new year (revised a bit from what I sketched out in an earlier post):

All students will spend the first half of the 80-minute class working on a mandatory curriculum. This will start with a unit on integer operations, and then will move on to fractions/decimals/percents. There will be heavy use of manipulatives to ground the students in concrete understanding of the concepts (which is what they lack the most), but I will also move them to algorithmic proficiency as quickly as possible. I'm going to try this year to focus more on representational fluency between fractions, decimals, and percents, instead of teaching them sequentially.

The second part of the class will consist of shorter units that target specific skills: multiplication/division facts; multi-digit operations; place value; rounding; multiplying and dividing by powers of 10, and so on. But here, students will take a quick diagnostic before each unit. Those who need the help will work with me during this portion of the lesson. Those who don't will now work with ALEKS; this software is totally individualized, so students can choose to work on whatever skills they need most help with - and are ready to learn. This will allow me to focus on the weaker students, and to provide them with a conceptual foundation for whatever the skill is, as ALEKS is really only good at providing practice with procedural fluency. I am also looking into the possibility of having students work on ALEKS as their homework, instead of doing worksheets. This will depend on the percent of students who have ready access to the internet, and if I can make the computers accessible to them during tutorial. But if this works, and I don't need to assign and check worksheets every day, that will be a huge time saver for us all.

In addition to this differentiation scheme, I plan to add in two other key components. First, I want to incorporate writing and reflecting into the daily activities. Our students even worse at explaining their work than they are at doing it! We decry their inability to explain and justify what they are doing, and to see how what they are learning connects with their other classes, the real world, and their future - and yet, we never really give space in the curriculum for them to improve at this. I read the book Writing to Learn Mathematics by Joan Countryman; it is a slim little volume, but it has a lot of good, practical suggestions. I'm going to start by having a daily 5-minute quick-write, where students respond to a prompt (or can write about something they learned or still have questions on), and then a longer journal entry every couple of weeks, where students are asked to explain mathematical concepts in more detail. I plan on reading these journals every weekend, and responding to as much as I can. I hope that this will help the students make more powerful connections, and help me understand better what they are really getting (and still needing) from the class.

Second, I plan on teaching students the bar-modeling method for solving word problems that is used in Singapore Math. If you look at some of the problems that 6th graders are expected to do in this curriculum, you'll see that many of our high-schoolers would have trouble doing them efficiently (or at all). I think the bar-modeling method is simple and powerful, and that it will be a tool my students can really use. I've purchased the series of primary math workbooks (and their series of challenge problems), and I plan on adapting these to fit my classroom. My plan is to spend a few days at the beginning of the year (before the differentiation kicks in) teaching this method with simple addition, subtraction, multiplication, and division problems. Then, as the year goes by, students will be assigned a "problem set" (in addition to their daily homework) that will be collected and graded every other week. This will give them a chance to practice the foundations of problem solving, as well as multiple chances to meet a longer-term deadline. I expect that many students will wait till the last minute for the first few assignments, and will learn how to better plan as the semester goes by.

So this is the general plan. I am interested in hearing any comments, questions, concerns, and suggestions as I embark on this new stage of my teaching practice. I don't pretend to have it all figured out - I just have a lot of ideas and a lot of hope that this will come together and help my students really, finally learn some good math.

Why should I learn math? (Take 2)

I'm back, and beginning to plan for the new year. There are going to be lots of changes this year as we revise our program. I will be working primarily on Numeracy again, which will be totally overhauled as I plumb the depths of differentiated instruction. I'll also continue to work on Algebra 2; however, we have decided to stop having a separate honors class. I will be collaborating with another teacher to create a rigorous class that our target student can pass (if they put in the work), and that also provides academic opportunities for those who want to dig deeper and prepare for pre-calculus. I'll write about both of these challenges more in the upcoming days. For now, I am starting to think about setting up my Numeracy classroom and what sorts of things I want to get up on the walls. Most of the stuff you can buy is tacky and uninspiring to students. I had the idea to create a giant butcher-paper poster with the title "Because" (in huge letters) "you can..." (in smaller letters), and then a series of hand-lettered-by-sharpie, colored-in answers to the implied question. Here is the list I've come up with so far. Any suggestions for additions or changes?

1. Design video games
2. Defy negative stereotypes
3. Become a doctor or nurse
4. Avoid getting cheated
5. Know when politicians are lying
6. Make stronger arguments
7. Graduate from high school
8. Manage your money better
9. Become a forensic scientist
10. Design and program computers
11. Help your family and community
12. Get rich in the stock market
13. Solve challenging problems
14. Show the world how smart you are
15. Get a college degree
16. Become a better thinker
17. Increase your opportunities
18. Become a teacher
19. Understand statistics
20. Become a lawyer
21. Study criminal justice
22. Design bridges, cars, and buildings
23. Run your own business
24. Discover a cure for cancer
25. Help your children with their homework
26. Fly airplanes
27. Run for Congress
28. Start a new school
29. Study psychology
30. Make your family proud
31. Change the world
32. Believe in yourself

DCP Student in the Mercury News

I am still on vacation and having a great time. I just checked my email and found out that a student of ours, who recently attended the Mosaic Journalism Camp at SJSU, had a piece published in the Merc about the difficulty undocumented students face due to their inability to get financial aid for college.

The readers' comments are predictably negative (i.e. calling for her and her "entire clan's" deportation and so forth). However, the chancellor of UC Berkeley agrees with Dulce :)

Here is her piece if you don't have an account at the Merc:

College door closed for talented undocumented students
By Dulce Martinez

Mayra, a 17-year-old who graduated recently from Downtown College Preparatory in San Jose with top grades, had hopes of going to a four-year university and becoming a lawyer. There is only one problem, which she can't fix.
She entered the United States illegally when she was 4 years old after her parents determined that if they stayed in Mexico they could all starve. As an undocumented immigrant, she's ineligible for government financial aid.
At her high school, Mayra was in Leadership, a program for students who help with campus activities. She was a member of the associated student body and MEChA, a Latino student group. She prepared and distributed sandwiches and water to day laborers in front of Orchard Supply Hardware while they waited for jobs.
Mayra thought that she was as American as anyone. She never thought that being an illegal immigrant was going to be a problem until she applied to a university. Then she found out that she qualified for almost no aid. That limited her college choices.
"I feel that it's not right that I worked so hard to improve my future and now I'm not sure what would become of my plans," said Mayra, a tall, brown-haired and brown-eyed girl from a poor Mexican village.
I know many teens who, like Mayra, had their dreams destroyed when the U.S. Senate turned down the latest immigration reform bill. They shattered the hopes not only of illegal immigrant students in San Jose but also, students living all over the country.

Another deserving undocumented immigrant student who worried about her future is Perla, a thin "jarocha," or native of the Mexican state of Veracruz.
Perla's parents smuggled her into America when she was 9. Also a 2007 Downtown College Prep graduate, she has all the qualities universities look for: She participated in student government, passed Advanced Placement classes and tutored struggling students. And yet when it came to applying to a university, she had all doors slammed in her face. "I feel betrayed by the country I call my home," Perla said.
When the Senate derailed the immigration bill, they punished innocent young people who had no input in their family's decision to enter this country illegally. Undocumented immigrant students in schools are not treated any differently than citizen students. They are always told that they can succeed, become lawyers, psychologists or teachers. But that's a lie if they are not able to attend a college because they don't qualify for government financial aid. I have met many students who have an unclear future waiting for them. Some decide that there is no point to working so hard and they start falling behind and start hanging out with gangs.
These undocumented immigrant students never rest because they are afraid that they might get deported at any second. It is not fair because they have worked really hard educating themselves, learning our country's history, speaking our language, contributing to their community, taking the hardest classes. They don't deserve to be treated so badly.
What happened to the American dream? For these students, the dream became a nightmare and now they have no choice but to remain here, stuck in the lowest ditch in our society because they can't go back to a country they no longer consider their own. All people are created equal, but did Congress think about that when it put the lives of thousands of undocumented students on hold?
Members of Congress should face the problem with their heads up high instead of running away and hiding. Is this what America wants, to destroy the hopes of so many bright and hard working young people who want to become productive citizens?

Vacation

I know it feels a little dead around here lately... I'm leaving the country for most of July and probably won't be posting. I'll be doing my best to not be thinking about math or school. But rest assured, once we hit the middle of August, I'll be back and posting regularly. There will be big changes in my Numeracy class that should be quite interesting to document, and I'm sure lots of other fun things to think about. See you then!

Common Denominator Division

I just finished helping facilitate a week-long workshop for most of the people teaching 5th - 9th grade math in two of our school districts. It was very interesting to be a part of, and to see what kinds of content and pedagogical knowledge teachers do (and don't) have. I'm not going to write much more about it, except I did want to post about common denominator division (CDD).

I brought this technique up to see if any teachers use it, and none had even heard of it. I've been teaching it to my students, as part of the scaffolding toward understanding the "multiply by the reciprocal" algorithm. Though not as efficient (typically), I think the CDD method can really help students see what is going on in fraction division, in terms of "the number of times the divisor fits into the dividend". It also fits nicely with multiplication, as "divide across" works just like "multiply across". The only problem is that "divide across" only comes out nicely when the denominator of the divisor is a factor of the denominator of the dividend, which is why (I assume) it is not the standard algorithm that is taught.

Once students know both methods, I give them a set of fraction division problems, and ask them to solve them with both methods. They then discuss which types of problems are better solved with which method, and why.

Here are some pictures that illustrate what is happening:


In this last one, you can see that the bottom shaded area fits into the top shaded area 1.5 times. This is the type of problem that I think really shows the benefit of CDD.

Here is a short proof that "divide across" works. Note: when the denominators are the same, dividing across yields 1 on the bottom, which I didn't write above.

Last Day

Another year, come and gone. We had an end of the year assembly today that was super long - about 2.5 hours. There were lots of recognitions of student successes, good-byes to leaving teachers, the Numeracy Project played, I presented the winners of the Algebra 2 treasure hunt, and we saw the DCP mini-movie (once it gets published to the web, I'll link to it).

I gave back the finals to my Algebra 2 honors students - all of them passed the final but two, and everyone did end up passing the class. Here's how the course grades were distributed:

10|6
9|0 0 2 2 4
8|0 1 2 2 2 5 5 6 6 7
7|0 4 7 8 9
6|
5|

The student with the 106% is a math monster... She's gotten more than 100% on just about every single assessment I've given (she always gets the bonus question, and usually doesn't miss any regular credit). She is also one of the pair who found the treasure. When I gave out class awards, she won the "I'll know more math than Mr. Greene in a few years" award.

After the assembly, there was a pizza lunch (along with food tasting from our new food company for next year, Revolution Foods), music, dancing, soccer, yearbook signing, and so on. I did photo shoots with different students, informed kids that need to take summer school (I wanted to tell them first before they got a notice in the mail, and encourage them to look at it as a chance to improve their skills), and got a marriage proposal from the student I wrote about in my previous post! I declined, but told her I'd be happy to help her make a study plan next year instead. I got some notes of thanks, and the best student gift ever: some of my A2H boys called me over, clustered around me, and gave me a bird-cage shaped present wrapped in toilet paper and tape. They said it was in appreciation of all that I've done for them this year. It was a Transformer from the new movie coming out this summer (they remembered me talking about my love for Transformers all the way back to the functions unit, when we did transformations and translations). This year, like all years, has had its fair share of challenges and problems. But it was nice to end it like this - out in the sunshine, shaking hands and giving hugs, congratulating students, and wishing them a good summer.

Tomorrow, I'll finish cleaning out my classrooms and packing, and tomorrow evening is graduation. Then, the year will really be over. I can't believe that I've been here for 7 years now, but I don't know how I can ever tear myself away from these kids.

Next week, I'll be helping facilitate a math/pedagogy workshop for all the elementary and middle school teachers in a couple of local school districts. The education department at San Jose State got a large grant to put this together. I don't know how it will go, but it will be very interesting. I'll post what I can about it as it happens.