Thursday, August 30, 2007

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.

Tuesday, August 28, 2007


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.

Monday, August 27, 2007

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.

Thursday, August 23, 2007

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?

Sunday, August 19, 2007

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.

Saturday, August 18, 2007

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