Friday, February 26, 2010

Barf, tears, and crushes

I will apologize in advance for this post and the title, but if you read on, it sums up my tutoring today very nicely.

I had the opportunity to help in another classroom today, a 3rd grade Sheltered English Instruction (SEI) class with roughly 20 squirmy third graders doing multiplication word problems. I got a warm welcome chorus of "Hi Ms. Minh!" from 20 eager and excitable children and a speed round of names to memorize in thirty minutes.

The teacher Ms. Ph had the students on the carpet and was asking word problems like "There are 8 dogs, each dog has 6 puppies. How many puppies are there?" and the students would have to repeat the equation and the answer.

No more than five minutes after I got the classroom, a student with some stomach virus threw up on the carpet and made a trail to the trashcan. I'm not even going to sugarcoat this one, it was naaaasty. Nasty.

I was surprised at how well the kids handled the situation though, most of them kept their focus and we continued on with the math. The students finished up with group work, and went back to their desks to do all class multiplication fact families. Ms. Ph would ask and write on the board:

11 x 12 =

To which the students were to compile the fact family:

11 x 12 = 132
12 x 11 = 132
132 / 12 = 11
132 / 11 = 12

I walked around and helped the students. I was about to say "This isn't how Math Rules! works" but I felt I would be more helpful by circulating the entire class and helping to check fact families, I let it go. The students were enthusiastic about math which was nice to see and experience. By circulating I got a good sense of which students needed help, which students wanted attention, and which students wanted someone to check over their answers.

At one point, another student came to inform my class they would have computer class instead of science (or something like that). This student unfortunately disrespected one of the students in my class, which upset her and she started crying. Which is not very nice at all. Ms. Ph handled the situation well, but the upset student wasn't ok. I stepped in and used a mentoring moment to tell the student that it was just probably because the offending student doesn't like herself very much that she has to put others down. I hope it made her feel better, but you can never really tell. I think I'll follow up next week with her. It's a shame because she seems like a very bright student and enjoyed doing math.

Math homework was given out, the students had to copy equations on a sheet of paper and bring back fact families. Two students who were sitting next to each other were bickering, and I asked them what was up as I was circulating. Each time I came by there were new developments. They were teasing each other:
"She punched me"
"He kicked my shin"
"She threw this piece of paper at my face, look what it did!"

I did not point out the fact that this probably means they liked each other, but it was incredibly adorable and amusing to say the least.

I'm extremely excited to be working in the class now, there's a lot of good math potential, positive energy, and interesting characters in this class. I'm looking forward to it.

Have a great weekend everyone!


Wednesday, February 24, 2010

We like fractions!

Yesterday's tutoring involved an introduction to fractions in my 4th grade class. I think it's cool to see the intrinsic nature of understanding fractions. For students, doing math computations with fractions quickly becomes difficult. Even as adults, we shy away from fractions, decimals, percentages, and ratios, which all express the same ideas. It's hard to conceptually think of a quarter of a third or to add up 1/6 a teaspoon to 3/4 of a teaspoon and even more so to compute complex fraction equations. Personally, I can't verbally explain what happens when you divide a fraction by another. Completely out of my realm.

However, being able to divide something into fractions and the visual understanding of equal parts is something kids pick up quickly. Our class was dividing up 4x6 arrays into fractions, like a quarter, an eighth, thirds, and sixths. The arrays have 24 smaller units inside, but my students did very well with dividing up squares and rectangles into thirds then sixths. I pushed them further and asked what 1/3 or 1/6 of the whole represents in units, which they quickly got as well.

One of my students came up after we had finished and declared, "I like fractions!" which I thought was nice. I just hope she continues to like fractions when you start adding different denominator fractions...

Mr. Steven Strogatz's newest article is also about the existence of fractions and the ensuing chaos of irrational numbers.

More cartoons of fractions.


Thursday, February 18, 2010

Group work pt II

So how does a Math Rules! volunteer manage a small group effectively? I found an article online that is pretty dense in content, and doesn't even address group work in schools. I still thought that many of the main ideas apply to working with a small group of elementary school students. The Personal Functions section is especially nice to note. The Managing conflict, Stopping conflict escalation, and Disruptive Behaviors sections are important for volunteers who have been having a grand ol' time trying to manage their small groups.

This article called Promoting Problem-Solving Skills in Elementary Mathematics is also quite useful for managing and provides best approaches to math group work. I have seen the teachers I work with use the Problem of the Day and Whole Group Learning techniques as the group lesson for the students and also for me to guide the group work afterwards. My teacher would write a problem on a flip chart, ask the students to copy down the problem in their notebooks and then to solve it. Afterwards, she asks for volunteers to explain what they got and how they got there. Directly from the article, the big group lesson for the day allows students to:

o identify the parts in the question
o find the best problem-solving strategy and explain why it is the best
o describe two different ways a problem could have been solved
o share student-generated questions
o ask other students to solve the problem and justify their answers

These skills and approaches to teaching are also useful in small groups. The article outlines that students benefit from being in mixed-ability groups (to encourage less motivated/focused/confident students to work with and learn from the more motivated/focused/confident students) as well as similar ability groups. Hopefully, Math Rules! groups are more similar ability small groups. I've also mentioned before on this blog that even in "similar ability" groups there is a lot of variation in specific abilities.


Group work pt I

Before coming to Boston Partners in Education and becoming a Math Rules! volunteer, I had never worked with and helped tutor a small group of students on math before. My personal experience with math in elementary school and higher was doing individual math homework and discussing problems in class. I rarely worked with another student on class problems except in fifth grade. I was given an "advanced" math book and told to work with my good friend on the advanced math. I somehow got ahead of her on the homework, and ended up working mostly by myself with the occasional group work when helping my friend.

That ends my experiences with math group work. In other subjects, I dreaded group work. Group projects usually meant I would end up doing a significant portion of the work while other groups members slack off and still get credit for the work I did. I would later learn that this is called social loafing and happens in all kinds of group work activities. I think the main problem with group work is that teachers don't manage the small groups well enough. It's one thing to put students in a small group, but another to make sure all groups and individuals are contributing equally.

Math Rules! provides more structure to small groups, with an academic mentor, the group isn't supposed to exhibit social loafing. The way that Math Rules! is set up builds off the Investigations curriculum that Boston Public Schools uses for elementary schools. I honestly didn't know what Investigations was until I went to Math Rules! training. Even then, it wasn't until I started volunteering in an actual classroom to understand how the curriculum works. Investigations is a different approach to math education with more focus on the multiple approaches and perspectives to a math problem. Showing and explaining your process is more important than the final answer itself. The Investigations curriculum also encourages and works best in small group situations, where students work together to come up with possible solutions for a problem.

Many studies have shown that small group work is ideal for students. Although I couldn't get the full article, this study summarizes that "pupils in the fifth grade produced superior answers on questions requiring original contributions" and that group work creates "classroom conditions that foster positive social interaction and productive intellectual activity." The article also notes that small groups allow students to develop "investigation and problem-solving [skills], with pupils cooperating in seeking and interpreting knowledge from a variety of sources." On top of it all, this study was done over 30 years ago. Other studies and many years of research have shown that group work is most beneficial for students in a variety of subjects and across age groups. "Group work also helps students practice essential social, problem solving and communication skills needed for success in the workplace." Students who never get a chance to work with other students face difficulties in the future jobs that more often than not require working in groups and teams.


Tuesday, February 16, 2010

Too much candy?

The kids were a little hopped up on an entire day of sugar last Friday. It took a lot more effort for me to keep them focused on their work. They had a substitute so we had a review worksheet the kids had to get through. Adding and subtracting decimals and then comparing decimals ( < , > , = ) that sort of busy work. I managed to convince them that the comparing decimals side was much easier, and they whipped through it. The other side was a lot more tedious and boring for them. I got a lot of "can I go get a drink?" and "can I go sharpen my pencil/can I go get another pencil?" today. I put up with it and let them go as needed, but compromised with their work.

One of my girls is extremely studious and finished the worksheet by herself before the other kids had a chance to finish just one side. One of my other students is a very sharp student but had a lot of trouble focusing today, so I bargained with her. She could finish the rest of the addition problems if she could make up a fraction of what she had finished. At first she balked and said that was too hard. Fortunately for me, I pushed her a little more and worked through it with her. We talked about numerators and denominators and came up with a reduced fraction representing the addition problems she wanted to do. I also used this trick with the boys on Friday because neither one was very intent on finishing a review worksheet.

In summation, it was tough to keep all four students focused on their work, but I managed to trick them into doing "less work" with a challenge question that actually required more work than simple addition and subtraction.


Steven's third installment of his math column discusses negative numbers.


Sunday, February 14, 2010

Valentines Day

Special Valentines Day Blog Post!

I've been reading xkcd for a while now. It's a funny and nerdy webcomic about math, science, computer science, and silliness. This one is one of my favorites: Serpinski's Valentine

A math inspired poem: MIT Alum David Feinberg's poem: The Square Root of 3

Steven Strogatz's guest column on the differential equation elements of love.


Thursday, February 11, 2010

Tutoring resources pt. I

Hello math tutors and supporters! This blog post contains resources and interesting things to think about when working on math with students:

Short and sweet article on tutoring tips to use with students


TERC's library of free information about the Investigations math curriculum that the Boston Public Schools uses. Includes overviews of what grades cover in the year, sample sessions and even online teacher resources.


I've also been reading through a San Diego tutor's blog with tips and advice on math tutoring, as well as other student related topics. I haven't read through the entire blog, but what I have read is pretty good advice that I will definitely use in the future.

Although many of his posts are about higher math (middle school, high school, and standardized tests), there are a few highlights from Mr. Casteneda's blog that talk about tutoring in general:

The importance of students knowning their multiplication tables.

Leading questions I use often to get students to explain their reasoning.

Comments on ADHD. Personally, I agree with Mr. Casteneda on ADHD. It came out of nowhere as a behavior problem for students and children and everyone started medicating and diagnosing children for it. Back in my day, ADHD didn't exist! Or more accurately, ADHD wasn't a 'condition' that had a list of symptoms. From the previous blog post: "I wish more parents would [take] the time to bust the "ADHD" label into pieces, and figure out what exactly is going on behind appearances in the particular case of their child." Although I don't know very much about ADHD or the medical procedures for diagnosing ADHD, I feel like ADHD is a label adults and children use to avoid figuring out and working to solve the root cause of attention deficits.

A blog post on encouraging postive thinking in students who don't feel like they're good at math.

And finally, a post on the unexpected skills tutors gain.

Monday, February 8, 2010

Fish fish fish fish fish fish

I've been perusing through the blogosphere to try and find content that applies to math tutoring and math topics. Turns out there are lots of math nerds out there. And I thought I was the only one. Though statistically speaking that's impossible...

My supervisor sent me a link to a new blog series on math from Steven Strogatz. Over the next few weeks, he'll be covering math topics starting with elementary number sense to higher order math concepts.

So far, it's been very relevant to understanding how children develop math concepts and build on math proficiency. His first post includes an introduction to numbers as presented by Sesame Street. The second blog post in the series talks about groups and patterns.

This one blew my mind!!

I'll try to keep everyone updated on the blog and the main points of the articles. If you have time, check out Mr. Strogatz's blog for yourself!

Thursday, February 4, 2010

Giving them space

Another great day at the Sportsmens' Tennis Club and MathSTARS. I find there are very few days that I don't enjoy at MathSTARS. The students are such great kids, hard working students, and very dynamic personalities.

I sat in the quiet room yesterday just to mix things up a bit. The quiet room is the designated room for people who don't want loud music or distracting conversation. Students who need the quiet are encouraged to study in the quiet room and enforce the level of quiet they need. For a while, the quiet room had a "no talking at all" rule, but that quickly changed when the students voted otherwise.

It's interesting because the quiet room definitely has a different vibe and flow to it. Most of the students who use it go to socialize more than do their work, but yesterday I found the students who had homework were very productive. O, N, and A stayed in the room most of the time, so I'll talk about my interactions with them in this post.

I was surprised to come into MathSTARS yesterday and O waved to me enthusiastically. We haven't worked that closely on his homework in the past, but being waved to and acknowledged made me feel really good. He's a very social young man with his peers and friends, but definitely enjoys and needs independence in his homework. I've rarely seen him working closely with another tutor, so sitting in the quiet room, he did his work by himself and finished pretty quickly.

N is one of my favorite students. I know we're not supposed to have favorites, but she's definitely up there. She's a very strong leader, mostly positive, and very silly. She didn't have much homework either, so she decided to paint her nails instead, which is all right by me and the afterschool director. She was also helping her friend A with homework on imaginary numbers and the quadratic formula (which I have regretfully forgotten...) so that was very helpful of her.

The last student is A, who is new to MathSTARS this year, and we've bonded over several weeks. I think we connect so well because she reminds me of myself a little bit. She's a very caring girl who is quiet more often than not, but is quick to laugh and joke around. She's also quite hardworking and gets her homework done pretty much every time I've worked with her.

I think the best part of yesterday was that when N stepped out of the room, A come over to ask me for help. She approached me! In the MathSTARS tutoring world, this is huge! She was working on imaginary numbers (which I told the kids is practially useless in the real world) and the quadratic formula, good ol' algebra. I managed to struggle through and asked A to re-explain the quadratic formula to me, which worked out well. She retaught me something then I helped her through the rest of the problem.

At one point she missed a simple computation and I called her out on it. "-7 + 2? Where'd you get that -4 from?" Sometimes I worry that questioning their answers is detrimental to the tutor-tutee relationship, but I think it's better for the students to get the right answer and to remember to check their work.

What was so great about the session yesterday was that I sat at my own table and started a craft project while the three of them were working. I was semi listening in to their conversation and concentrating on my project at the same time. I think middle school students need that space to dictate their own work pace. I've noticed hovering and imposing oneself onto this age group ends negatively. It's tough though because when I was starting out as a tutor at MathSTARS, that's all I wanted to do, was to ask the students what they were working on and if I could help or sit with them and work along with them. Some students need the tutor to initiate while other students will ask for help when they need it, but need their space when they don't need help.

I think the MathSTARS format is unique in that way. Students don't have a matched tutor, they can choose to work with any number of tutors who come, or they don't work with a tutor at all. It allows the tutors and the students lots of flexibility in who everyone is working with from week to week. Sometimes this is great, I get to work with lots of different students. But sometimes it's harder to build a strong one-on-one relationship with "your" student.

Either way, I love my time at MathSTARS. Yesterday I managed to crack some jokes the kids really enjoyed. We were laughing so loud the other room had to run in to check on us, we had a good time.


I want to apologize for the length of my posts. I try to keep it short, but I end up telling a story of what happened at tutoring. Then I add in commentary, and side notes, and the pictures.

Blogs are interesting in that way I guess. Long blog posts usually turn people off and they skip over to the next thing. In a time of technological ADD, diminishing time and financial resources, and ever increasing numbers of interesting blogs in the interwebs, it's understandable.

In some ways, I don't notice the length because I'm documenting what happened, what was so significant about the events, and how to improve my tutoring skills. If anyone has suggestions for shortening my blog posts, please comment or send them my way!

So I'd like to thank anyone who has read through my blog, read through one entire post, or just glanced at the length of a post and came back later to read. Thank you!

Wednesday, February 3, 2010

Money subtraction

Working with money and math has always been a fairly easy thing for me, just because it's so concrete, it makes sense in the real world, and everyone has had to deal with it in one way or another (unfortunately). I wanted to help my students be able to easily compute money math because it matters in the real world (as opposed to abstract uses of Calculus in the real world).

The class was working on word problems involving subtraction and money and I got to help with a worksheet the kids were working on. Somehow, a few extra students wanted to join the table, so I ended up with five youngsters to help.

Though the extra peer support was somewhat necessary, it got a little crowded at the table, and one of my students asked if he could move to a different place with his math buddy. It really showed initiative and independence which was great. They worked together and when I checked up on them, they said they had finished the front of the worksheet and needed some help on the back.

The example questions the class worked on together invovled multi-part questions such as: "David got $37 from his mother for his birthday and had saved up $48 from his allowance. He wants to buy a $100 video game, how much more money does he need to save?"

While the class could articulate that you add what he already has ($37 + $48 = $85) then subtract it from his goal ($100 - $85 = $15), the worksheet problem was more difficult for my students yesterday. I'm not sure if it was the math problem itself that was distracting them or if the extra students were, but two of my students weren't listening as intentently as I had hoped. I even asked my independent student to explain his reasoning to the others, but they weren't paying attention. I felt sorry for him because he explained it really well.

Dividing your attention between several students is sometimes harder than usual and yesterday was one of those times. I think I'll try to only work with my students next week to give them more personal attention and to keep distracting students out of the group.