Student tutors

Tutoring yesterday at the Tobin School involved more MCAS preparations and working in pairs. Students from the class next door came over to tutor the kids in my class. Again, this week, I concentrated on my girls and how they were doing. Some of the pairs worked well together but one of my girls made her partner a bit upset. It might've been my extra attention and my student got overexcited. So I backed off and let them work together again. The other pair worked on different topics.

It was really amazing to see students teaching other students. Our teacher then handed out a test they had previously taken and encouraged the tutor students to guide them through the test - "They should be able to take the same test again and do much better!"

I actually learned how to divide a second way yesterday also! One of the tutor-students despises long division and taught me the open array to divide. The open array works best with single digit numbers, but I used the open array to divide 792 by 17.


The strategy is a multi-step process, but I compressed it into one picture. So I'll explain.

1) The array is set up with an open array with the divisor on the side. For 487 divided by 9, you have the 9 on the side.
2) Start building to the answer by making arrays with easy numbers (10s, 20s, etc). I tried to explain using estimation to help speed up the process. If you know 50 x 9 is close but not quite, it's much easier than starting off with lots of 10s.
3) Continue building until you get as close as possible with a remainder (or not).
4) While you're adding more arrays, remind your students to keep a running total at the bottom. If you track it well, you won't go over and waste valuable standardized test time.
5) Finally add up your multiplicands/multipliers at the top to get your final answer. Don't forget your remainders!

The technique works well with single digit divisors, but like I said, it will work with multiple digit division problems as well. A strong sense of estimation and close tracking of sums will greatly help your students. I enjoy this strategy because it's using partial sums to get to a final answer.


Having students teach each other is great reinforcement for what the students have already learned. If you can teach it to someone else, it means you really know what you're doing. I also used this technique at MathSTARS with some of my 9th graders who were working on physics. Not only did tutor-student reinforce her knowledge of the physics concepts, but the student being helped could understand and relate to the extra help.

I also use the student-teaching method when there are too many students who need help and it's harder to help all your students at once. For example, when all four of your students are asking questions about completely different problems. I tend to ask the student who is done already, or finished the particular problem to help his/her classmates.


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My weekend math

Hi math fans! I'm just going to briefly talk about my experience with math over the weekend. I didn't get a chance to do any paper and pencil math, but I did watch a few basketball games and revisited one of my favorite awful-yet-amazing TV shows Xena: Warrior Princess.


I don't get a chance to watch a lot of professional basketball, but one of my roommates is a die-hard Spurs fan. So we watched the Spurs play the Suns on Friday night and again on Sunday night. Some players are much better mathematicians than others. Steve Nash is a genius at basketball math and while Tim Duncan is a good defender and guard, his math for making free throws needs work. Just listening to the sportscasters was interesting, they talked about basketball statistics a lot, how many shots they've taken and how many they've made. The percentages for whole team, how many points the bench has, etc. Lots of math, but no one went to the AT&T stadium to hear or think about math. It's sad that the Spurs lost, but I got to see lots of math in action.

I also found that Netflix has Xena online for members, and I took advantage of that by watching a few episodes of season 1. Keep in mind, Xena the Warrior Princess is a very old-school action show with low budget graphics, exotificiation of cultures, campy humor, and plotholes galore. But I grew up watching the show with my family on Saturday nights, and I'm obsessed with Lucy Lawless (who is more talented than most people give her credit for).


No matter how improbable or completely outrageous the show is, Xena is an excellent mathematician. One of her main weapons is the chakram, or a metal disc with sharp edges that she either 1) chucks at the bad guys or 2) uses to cause avalances. She takes her geometry and trigonometry into consideration before she throws her chakram and always hits her target. She uses angles to ricochet her chakram all over the place. It's some pretty accurate math if you ask me. Sure, the laws of physics make it difficult to tell if she can actually do such chakram acrobatics, but it makes for a good show.

A video of her chakram

And that's what a math nerd thinks about over the weekend. More soon!


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When I grow up...

I want to be older.

It's been a few days since MAM ended, so now we're back to regular tutoring entries with a few extra MAM bonus days thrown in.

For Math Rules! volunteers who are reading my blog, the following are my takeaway points:

• Check in with them and ask how things have been going before you start tutoring. It's a good gauge of how the session will go.
  
• Encourage your students in the following couple of weeks before MCAS, let them know they can do well no matter what happened in previous years.
  
• Remind them to take their time to read the questions carefully, check their answers, and answer in complete questions for word problems.
  
• If you can, take an extra five minutes at the end of your session to chat with them about college and careers. Talk about your college and/or career. For the most part, students are very interested in college but may or may not have someone to ask. Even if they're 3rd graders, if you get them thinking about the future it will help them in the years to come.
  
• Help them realize that you're there for them and want them to succeed in everything, not just math!

Yesterday I worked with my fourth graders. They're preparing for the MCAS in two weeks so I helped two students who needed a bit more practice. It's sad because it seemed like my other two students wanted to work with me too. In the end, I think it was better that I was only working with two because I could focus and give them more attention. Also, my teacher has changed her schedule - to prep for MCAS the students are doing 1.5 - 2 hours of math until the MCAS.

MCAS prep means working off of last year's test and trying to figure out best approaches to problems. We went over the standard algorithm for multiplication and division (long division) computations. We also talked about alternative approaches to multiplication problems such as using the array to help with multipication problems. Finally we focused on word problems, which was a good exercise for them to take their time and carefully read all the instructions.


I tried my best to give them test taking strategies like checking answers, rereading the word problems, not falling for the time-wasting tricks, showing all work on the test, and making sure they knew their multiplication and division algorithms.

I found out that both of my students didn't get very good MCAS scores last year and I think it's because they rushed through and didn't check their answers. When we went through the packet, they seemed dejected when I told them their final answers were wrong. It's interesting because most of the work is right, but the final answer is wrong and then they assume they failed.

One of my students kept repeating that she hadn't gotten anything higher than 2s on practice tests throughout the school year. I tried to encourage her by telling her "that was last year, this year you can do better!" I'll see how her self-confidence levels are next week.


We also got a good chance to chat in between problems. I found out that one of my students wants to be a teacher or singer when she grows up. My other student didn't know, and when they asked me, I said I don't know either. :) She retaliated and said "What do you mean you don't know?" That's one of life's secrets, adults sometimes don't actually know what they want to be when they grow up, it's a self-discovery process. We also discussed college briefly which was a good thing, they brought it up and asked me if I was still in college and if it's hard. I told them that it is tough, but if you work hard, you'll end up learning so so much.


We also got off topic and one of my students asked to interview me for a job, which is ironic because I'm in the process of interviewing right now. I also got a chance to interview her and found out some things I didn't know before. She took on a different persona and told me she was a 21 year old singer living in Florida who was interviewing for a teaching position. It was a great chance to bond and talk about jobs and our personal lives. I told her about my new pet hedgehog (shameless plug) and I found out that we both have four siblings.

In a program meeting, we started talking about how to improve Math Rules! for next year and I'll definitely take into consideration how many students are working in a group and the length of math time. These longer math sessions mean more time with the students, more personal attention, and it gives me some space to chat between math problems.


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