Archive for August, 2010
This post was written by a college student who interned (and occasionally student taught) at my school for the summer. I asked her to write about one of the lessons she took with her from the experience.
If you don’t believe me, watch a video of students at her school. Note the pin-drop silence at the end of the chants. Note the folded hands. Most importantly, note the absolute glee. That’s not an act. I watched it happen every day.
If my teacher had ever told me to put down my pencil and pay attention I would have been reduced to tears of shame. So I was way outside of my comfort zone when the task of correcting students fell on me.
On the second day of school, when I held two students after class for my first hallway conversation, my heart had seldom beat so fast. To my delight, no tantrum erupted. We reviewed the rules and discussed strategies for next time. I worried I had just sacrificed my relationship with these students for the sake of maintaining high disciplinary expectations. But on the contrary, one of them gave me a hug the next morning.
It turns out that teacher-nice and real-world-nice are vastly different. In fact, failing to be strict is, in its own way, teacher-mean. It’s not fair if a student is allowed to sit in your classroom and behave in a way that impedes his peers’ or even his own learning. It’s not fair to you, to his peers or to him. There’s a lot riding on the amount of knowledge that wandering eyes and pencil tapping will take from your classroom, and it’s possible a student doesn’t even realize it.
When expectations are maintained to challenge students to be better, and not to harp on weaknesses, teacher-strict is teacher-nice. Students want to succeed. A strict teacher demands that they behave in a way that will allow them to succeed. If done right, students don’t resent this. Most of them actually appreciate it.
I’m infinitely grateful to have learned this so early in my teaching career. I sincerely hope that all teachers have the chance to observe this sort of kind strictness in practice. You’ll know it when you see it. It’s breathtaking. Furthermore, I’m proof that if you watch closely enough, you can bring it to your own classroom.
I’m not someone who really feels okay spending extra money just because a store is locally owned and operated. But then I go to a place like Frager’s Hardware, which is reasonably priced. And well stocked. And locally owned and operated. And THEN I meet an employee named Justin who spends 2 hours helping me build the place value toy that I made up in my head. And I am Frager’s most dedicated customer. Forever.
So, first of all, thank you, Justin, and thank you, Frager’s. You have done your good deed for the year.
And now, for my invention…
My students really struggle with writing numbers from words because they leave out the zeros. We talk about how place indicates value, but when they write a number, they label empty spaces with place values names, and frankly, they don’t believe me if I say that no one will be able to read their mind to find out which blank spaces are supposed to have value.
So, I’ve always wanted to have some kind of tool that physically shows students that it is necessary to put a zero unless they want to change the value of the number, a tool that doesn’t leave room for blank spaces.
This is it. Students can put the little pieces between the wood and plexi glass, and the pieces slide over to the decimal point. If you forget the zero, the pieces still slide over anyway.
I have told Justin that when I get rich on this, I’ll cut him in. So nobody start selling this before I do, okay? You can however make it yourself, and it only costs $30 for four of them!
(1) Buy one 1″ by 6″ by 8′ piece of wood and two 1/2″ by 1″ by 8′ pieces of wood. (Note: If you actually measure these pieces of wood, that is not their true lengths, but that is the lengths they give at hardware stores.)
(2) Cut each piece of wood into four 2′ pieces to make four bases.
(3) Stack them on top of eachother like in the picture, and fasten them with screws or liquid nails (which doesn’t leave any holes). Clamp them together to dry (if you own clamps).
(4) Drill a screw for your decimal point.
(5) Buy four 1/4″ by 5 1/2″ by 2′ pieces of plexi glass. Usually you have to get these cut for you.
(6) Stack the plexi glass on top of wood and fasten with silicon. Silicon is good because it’s clear. You can’t use screw with plexi glass because it tends to break. Clamp these together to dry (if you can).
Now the main piece is done. You can make the little pieces by writing on plexiglass with a permanent marker. I had about fifty 1/2″ by 2 1/2″ by 2″ pieces cut for me.
If you don’t want to make your own place value slider, then the toys below are pretty much the most popular ones for teaching place value. I haven’t seen anything like what I made here, but if you have then please let me know!
The Singapore Math model drawing workshop I took last week went from 11am to 5pm (with few breaks in between). While this schedule was kind of exhausting, I think I prefer it to attending several shorter workshops in a single day. By focusing completing on model drawing, I really got to practice with the approach, and I have already started planning how to incorporate Singapore Math model drawing into my classroom this year. In fact, it inspired a Donors Choose project.
During the workshop, the presenter, Anni Stipek (who was incredibly engaging and informative) shared the way that she did daily problem solving by having each student get a sticker on which she had printed the problem of the day. They would put the stickers in their notebooks, and then use model drawing to solve. She would dedicate 15 minutes every day to work time and follow up discussion.
Model drawing is effective because it uses the relative size of the blocks to indicate the relationship between quantities in the problem. The use of modeling also gives structure to the steps of problem solving. There are many great websites (and resources) that describe Singapore Math model drawing, but I will summarize the steps that I thought were so useful to show how student could solve two different problems:
I think those questions are pretty challenging but Singapore Math model drawing makes them easier to solve.
These are some Singapore Math model drawing resources if you’re interested:
- http://www.thinkingblocks.com/ (This is interactive!)
- http://www.thesingaporemaths.com/ (This has a lot of sample problems!)
There are two different publishers of the Singapore Math curriculum in English:
Last week I attended a workshop on Singapore Math model drawing. I picked the workshop because I am really interested in teaching problem solving to students, and I know that Singapore Math has a great reputation.
Americans have had an Asian math fetish for a while now. We don’t always know exactly what makes Asian math special, but we’ve heard that Asian countries beat us on international tests. The most famous of these tests is called the TIMMS (Trends in International Mathematics and Science Study). I love using questions from the TIMMS because they are very different from state assessment questions and require students to deeply understand the topic. For example, this is a 1995 4th grade question:
This is a 1999 8th grade question:
Primarily, the TIMMS is used to compare different countries. From page 7 of Highlights From TIMSS 2007:
You can imagine that these results spur a lot of debate. It’s important to note that education is not compulsory or even available for every student in every country. Taiwan, Singapore and Hong Kong are also quite small. But, there is always something to learn by studying a different approach, which is why I took the Singapore Math model drawing workshop that I’ll discuss in tomorrow’s post.
As for Asian math instruction, I have often heard it described as “an inch wide and a mile deep” whereas American math instruction is “a mile wide and an inch deep.” Whether or not we can really generalize, it is important for any teacher to struggle with the tradeoff between covering a lot of material and covering it well. I have heard people say that standardized testing encourages teachers to do the former. But that is not a problem with standardized testing, it is a problem with the number of standards.
That is why I encourage every teacher to go through their standards and chunk them together into “power units.” If we think of our many standards as pieces of several large units then students really can delve a mile deep into each topic. We do not need to choose.
Last week I attended a workshop called Brain-based Learning: Brain Power! with Deb Estes. The presenter was both funny and knowledgeable. She used the strategies she wanted us to use as she was presenting. But it was not demeaning the way it can be when adults are taught as if they are children. It was simply fun and informational.
The presenter offered lots of teaching ideas as she described the chemistry and biology of learning in the brain. I could not possibly include everything she discussed here, but I will tell you that costumes, toys and songs are not only entertaining. They are an important way to grab students’ attention and wake up the brain when it starts getting sleepy.
Certain costumes, toys and songs can act as memory anchors after students have explored a concept and made meaning of ideas. If not directly related to a new learning concept, they can be a way to build a positive classroom culture – as in the classroom “celebrations” offered by Dr. Jean at www.drjean.org.
My favorite part of our workshop was when the presenter asked us to stand up and belly laugh silently. You would think this would feel awkward, but the silence made it easier. And after a few seconds of fake laughing, you can’t help but real laughing. And then you start laughing harder because it so hard to laugh silently.
Our presenter said that the brain needs movement at least every 14 minutes in order to receive enough oxygen and glucose. So, go on! Get celebrating!
Test results are coming out across the country, and it is a time of intense reflection. When confronted with lower than expected test results, some people blame the tests. Some people blame the system. Some people blame the kids. For me, it’s just time. When you are doing the same thing long enough, it’s easy to get burnt out. And with burn out comes a slow lowering of expectations. In my case, this came in the disguise of work/life balance. I started doing less so that I could spend more time at home. I wasn’t being selfish, I just thought I knew what it took to teach and could relax a little bit. I didn’t realize that one of things it takes is a feeling like what it takes will never be enough.
That is why I am so grateful there are standardized tests to let me know when I am starting to take the backward slide. I am also wary of standardized tests because I think a few years of good results made me think I had this job down.
More than anything I am grateful that there is the work of other teachers out there to remind me what is possible and exactly how hard it is. That is why I plan to spend a lot of time observing other teachers in rigorous, high-performing classrooms this year.
I suspect that everyone feels like their job is uniquely difficult, but man, isn’t teaching so hard? If it is not hard, it is not being done right. But that is also what makes it so rewarding.