I stole a great activity from my colleague for my Math Lab this week. It involved making collages to represent the things that we need in our lives and the things that we need to learn math. Students were first asked to select things they need in their lives from a list of words containing things such as “security,” “play,” and “be to understood.” Then they cut pictures out of magazines and decorated their collages.

Most students enjoyed the activity, some even asked if we could do more collages. However, there was a group of boys that did not want to do the activity. Perhaps it was peer pressure or the fear of looking appearing “good” or studious in front of their friends that prevented them from working. This group has so far not participated much in class.

There seems to be one girl who is in this circle of friends. She was one of those who enjoyed the task and asked to do more. After class, she happened to linger in the room and I took the chance to chat with her briefly. I asked her to be on the look out for ways to engage the boys in her circle of friends in class. She seemed to be on board. Stay tuned…

One of the arguments against greater school accountability and performance-driven school reform is that the introduction of more tests to measure student performance will lead to more teachers “teaching to the test.”

I’ve been thinking about this a lot lately as our district’s first periodic assessment is coming up this week, and us teachers were given a copy of the exam so that we can prepare our students for it. I’m a bit nervous about my students taking the exam as we are behind where most other students should be in an Algebra class or a Geometry class. After all, we lost almost a month of instructional time at the beginning of this school year due to constantly shifting enrollments.

Do I prepare my students for the test or not, and if I do, how will I prepare them? It’s not just a matter of wanting my class or my school to have higher scores–if students see their low scores they will lose some of the  precious confidence in their math skills we’ve been building so far, and confidence (specifically, belief about self-efficacy) matters a lot.

So I’ve been wondering: what exactly is “teaching to the test” and what is it about “teaching to the test” that carries negative connotations? Standardized tests often ask students to think about mathematics or to decode mathematics presented in peculiar ways. If the content of these questions is something far removed from a teachers’ usual curriculum and the teacher is compelled to help students acquire that content, is that bad? What if that content is potentially helpful or useful for students’ mathematical development?

Consider one of the test questions on this week’s periodic assessment: (I’ve modified it slightly for this blog.)

Which is greater, 5x+1-(1-2x) or 6+2x-1-(2x-4)?
A. 5x+1-(1-2x)
B. 6+2x-1-(2x-4)
C. Not enough information
D. They are equal

This question requires students to be able to combine like terms, to be proficient with positive and negative numbers, and to reason about which of the two expressions is greater. We’re still working on combining like terms and adding and subtracting positive and negative numbers in class so would that be considered “teaching to the test”? (Doesn’t seem like it.)

To help my students answer this question successfully, I would probably have to start them off with questions such as

Which is greater, 7x or 9?
A. 7x
B. 9
C. Not enough information
D. They are equal

If I pose questions like this, am I “teaching to the test”? Seems to me a moot question. If I find the content compelling for students’ mathematical development, then I will help them learn it. If not, I’ll let students struggle with the question and let the test question do its intended job: give me information about my students’ understanding and skills.

I think what I’m trying to say through this post is that “teaching to the test” is a catch phrase that galvanizes people in educational debates, not unlike the phrase “public option” in present U.S. debates about health care reform. It seems to me that the kind of teaching that tests encourage is mostly determined by the content of the those tests. Test writers have a great deal of power as they can shape what is taught in classrooms. A bad test could potentially fill math classrooms everywhere with useless, unimaginative content. A test could even be used to circumvent state and district standards for mathematics as it can establish a de facto curriculum. And let’s not forget that developing a good test can be expensive.

Closing side note:  What I find fascinating is how teaching happens on so many scales at once. The public and academics mostly talk about teaching at macroscopic scales (districts, curricula, schools, classes) but when you think about what actually happens every day in every classroom, it’s what the teacher does and says and how students process it that really matters. How will Teacher X’s beliefs about what mathematical topics are important affect the way she or he prepares students for a standardized test? How does Teacher Y’s beliefs about the way students acquire knowledge affect the way she or he implements a curriculum? Will Teacher Z maintain the high level of cognitive demand in a rich curriculum like CPM? And who is watching/can watch what happens in every class every day?

UPDATE: A friend astutely reminded me that in the “backward” teaching design process, we (1) think about what it is we want students to learn, then (2) determine acceptable evidence for students achieving those goals, then (3) plan learning activities and experiences. (I believe strongly in this design method and try to follow it when I can.) This design process necessarily involves preparing students in step (3) to do well on the assessments determined in step (2) so if that is considered “teaching to the test” I would be guilty as charged.

Monday morning, here I am at school again. Why didn’t I take a “normal” sabbatical like other people do? Am I going to make it to June if I already feel this way in October? Is it wrong to complain seeing as how real teachers don’t even get the chance to have a sabbatical?

Almost all of the teachers and professors I know struggle with balancing their work and personal lives. We work during the day, then go home and work some more. It’s hard to keep this kind of effort going, and I’m not as energetic as I once was.

Today was my first day back in the classroom after being out of the country for a few days. The substitute teacher did an excellent job. I’m glad to be back, and missed seeing my students.

Students didn’t do so well on the first quiz that I left with the sub. I expected as much, however. The school is asking all departments to make common assessments and we put these things together at the last minute. Some of the questions on the test were on topics unfamiliar to my students. I told my students that the quiz will be a “practice quiz” and that we will take another quiz next week.

After talking with one of my colleagues, I’ve decided that the approach to take for my Math Lab class is to help students enjoy mathematics. I’m not going to try to make it my goal to help them learn any particular math content or to even get a good grade in their math class. I hope those things will happen, but I’m not going to make it my primary goal. We will do fun things, and I have decided that I need to enjoy the class too. I can’t be dreading this class for the whole year.

We all stayed late at school tonight for Parent’s Night.

I met about 8 or 9 parents tonight. Many of them couldn’t speak English and relied on their children to translate for them, but I felt that I got to form an important connection with each of them. I told parents about our classroom rules, how they could get in touch with me, and most importantly, how to help their children in mathematics (ask children to explain their work to parents, reinforce positive attitudes towards mathematics by combating the “I’m just not good at math” myth). I also warned parents of Algebra 1 students that the CPM book looks very different from a traditional math text book and assured them that students will learn a lot from this approach. I didn’t tell parents anything about my background or reasons for teaching math; just felt like that wasn’t really important.

I’m also off to a workshop so won’t be updating this blog for a few days. I’m hope my sub has a pleasant, stress-free experience.

Another first today: lock down and shooting

A female ninth grader was shot half a block away from school just as school let out today. The student was not critically injured. Police descended on the campus and we were locked down for about 90 minutes while they searched for the suspects.

In other news, students are still being shuffled around between classes, though my enrollments have been relatively stable. One colleague just had one of her classes changed into a new section of geometry. This is already the sixth week of school. Many colleagues are frustrated and teacher morale is low.

Update: A student in one of my classes claims to be a friend of the girl who was shot, and told me that the bullet was not intended for this girl but for someone else. School seemed to run as normal the next day, students didn’t seem affected. Perhaps it shows that these students just see these kinds of things as part of their daily lives?

Another first for me today: broke up a fight in my classroom.

Just as sixth period was starting (after lunch), a group of Armenian students came into my Algebra 1 class. They started having an altercation with one Latino student who was already in the room. I was scared because so many students came in all at once, but I quickly isolated the Hispanic student from the one student that seemed to be the target/instigator of the fight.

Thankfully, the teacher with whom I share the room was in the room and she also helped separate people and get the group of kids out of the class. She went to get help and together we were able to diffuse the situation without any punches landed, only a little bit of shoving.

It was nice to see some of the other kids in the class trying to help too. They were saying things like, “Hey, calm down” or “There’s no need to get so dramatic.”

I have no idea why the fight started, but it was clearly racially motivated. Most of the insults that were hurled were racial.

It was incredibly hard to get any learning done in that class today, and I don’t blame the rest of the students for finding it hard to concentrate. I also found it really hard to pull it together for the rest of class.

P.S. Another first today: having a student try to access my laptop from his/her cell phone via Bluetooth during class so that the name of the phone (which had some obscenities) would show up on the projector. How creative.

UPDATE: I was told that the fight started in gym class when one student crossed out another group’s graffiti, which was an expression of racial pride. That escalated to the incident in my class. There was a big fight after school. Admin tried to prevent the fight but Latino student somehow sneaked out of where he was being sequestered.

Brief excerpt of what happened in fifth period Math Lab today.

Me: <explaining about the importance of working together and that employers see teamwork as an important skill, which is why I am randomly assigning students into groups of four>

Students: <grumble grumble grumble>

After one or two minutes, students are finally getting to their seats, except for a few.

Me to Student A: Student B is waiting to sit down because you are in her seat. Would you please move to your seat?

Student A: No.

Me to Student A: Your team needs your cooperation, please move to your seat.

Student A: No.

Me to Student A: This isn’t a choice. Everyone has to sit in their assigned seat.

Student A: No.

While this is going on, Student C goes to my computer and messes up the seating chart so now no one knows where they are seated. I am so furious but have to control myself. I send Student C out of the room. More chaos ensues as I now have to make a new seating chart and everyone has to move again. It takes more than 10 minutes for students to get settled in their assigned seats.

Many students are upset at being moved from their friends and refuse to work with each other, a few openly criticize their team mates, saying things like “I don’t want to work with him, he’s boring.”

The thing that upsets me the most is that I can’t seem to win over a critical number of students to make the class run well, as I have been able to in other classes. Instead, the ones that were previously on task are being drawn off task by others. This is my most challenging class by far. Students in this class aren’t taking the tasks that I give them seriously, even though I’ve tried to think very hard about what to give them that would be fun, interesting, and mathematically meaningful. (Today I tried to use the Disc-Ness activity from Balanced Assessment in Mathematics.)

A flurry of short updates today:

1. Algebra 1 class seemed to go well today. By the end of class, I was able to observe almost every student correctly adding and subtracting polynomials, even when there were negative numbers involved. I didn’t see much of 3x²+2x=5x² today, and I think the algebra tiles had much to do with that. Most students were on task a good part of the time, and I’m starting to build more rapport with some of them.

2. I co-teach third period Algebra 1 class with a resource teacher. He has 9 students in the class, I have about 19. We are working together to fully include all of his students with learning disabilities. I absolutely love working with this teacher. It is so incredibly helpful to have another adult in the room.

3. In my geometry class, I asked students to design a parking lot to maximize the number of parking spots given a number of constraints. Students were on task most of the time and did well given the difficulty of the task, but I noticed that some students who had previously been diligent in class before were now goofing off because of the individuals in their group. Peer pressure is such a powerful force, I’m noticing. Also, small details such as how many copies of instructions are handed out, how the copies are distributed, how instructions are conveyed have such a huge impact on students’ products and learning. Complex instruction, indeed.

4. I now have textbooks for nearly all of my Algebra 1 students, but still no textbooks for my geometry students.

5. It seems weird to me that teachers don’t have keys to the office where we make copies. The office is locked during certain parts of the day. I guess we’re not supposed to make copies during those times (for example, during lunch).

6. High school kids are so filthy! It’s hard to imagine how they are able to get so much dirt, markings, pieces of trash everywhere so quickly. The classrooms get cleaned every three days, but we have to sweep the floor ourselves more frequently if we want the room to be presentable.

7. My class enrollments have been pretty stable for the last few days. Hooray!

Wondering today if I made the right choice to teach this year. The monotony of teaching everyday is already setting in and it’s only October. I hope I’m only thinking this because I had a rough day with unruly students today.

Today, I hope that the algebra tiles helped students see that x+x=2x and not x². We’ll see…