Saturday Tutoring #5

Today, I tutored a sixth grader named Mizan. I asked her if she brought any homework to do, but she did not have anything with her. No backpack, no folder, no papers, no pencils. For a moment, I was at a bit of a loss of what to do. I asked her what she was learning in school, but all she said was “triangles.” She would not elaborate further on what they were doing with triangles. I had no idea if they were learning about the different types of triangles and angles, finding area and perimeter, the Pythagorean Theorem, etc. 

I decided to start with the basics. I had her draw four different types of triangles--equilateral, isosceles, scalene, right--and then describe the defining characteristics of each. She did fairly well with this. 

“Have you ever found the area of a triangle before?” I asked. 

“No, but I know how to find the area of a rectangle,” she replied.

She knew that the area of a rectangle could be found using the formula A=b*h. I proceeded to show her how a rectangle can be divided diagonally into two right triangles. Therefore, I showed her, the area of a triangle could be found using the formula A=1/2*b*h.

I had given her a problem in which the base of the triangle was 2 and the height was 5, making the area 5.  She quickly memorized this equation and put it to use successfully. However, there was just one problem.

“How do I multiply 10 times 1/2?” she asked me. 

As a student at the end of sixth grade, I had not even anticipated that Mizan would need help with multiplying fractions. 

One thing that I have noticed happens frequently with students from underserved school districts is that they often are missing important pieces. It’s analogous to constructing a building but leaving many important structural components out of the foundation. Especially in calculus this year, I have learned more than ever how important a good foundation in math is, and the middle school years are some of the most critical. 

Mizan and I sidetracked from our triangle lesson for a while to instead focus on fractions. 

“I don’t want to do fractions. I hate fractions.”

I showed her what I consider to be the easiest way to multiply a whole number times a fraction:

10 x 1  ---> multiply the top two numbers             = 10  = 5

 1    2   ---> multiply the bottom two numbers           2

She understood this concept very quickly and correctly answered every problem on multiplying fractions. On occasion, she would forget to simplify the fractions after multiplying; once I would remind her, however, she had absolutely no trouble reducing fractions. 

While we were at it, I decided to show her how to divide fractions. While she had technically learned this in school a few years ago, she could not remember how to do it (and had probably never mastered the topic when first taught). 

I taught her that dividing fractions was just like multiplying by the reciprocal. I think the term “reciprocal” scared her a little at first. Once I showed her that you just had to flip the number in the numerator with the number in the denominator, she no longer struggled with dividing fractions.

Next, I made a bold move and decided to show her the Pythagorean Theorem. Again, the was initially really freaked out by the title of the concept. While she wasn’t particularly jumping for joy over learning some new and harder math material, she didn’t object to it, either. 

I gave her a problem with a right triangle that had a base of three, a height of four, and thus, a hypotenuse of five (which is the most simple of the Pythagorean identities). Mizan understood how to square three, four, and five, but she had absolutely no idea how to square root twenty-five. She didn’t even know what a square root was. Again, I was slightly surprised, just because squaring and square rooting sort of go hand in hand, like addition and subtraction or multiplication and division. I briefly showed her how to square root a number and she subsequently got the right answer for the problem, even though it took some time.

After such a challenge, I decided to review something a bit simpler with Mizan. We reviewed how to find the area and perimeter of a rectangle, along with the basic properties of a rectangle. After just a few practice problems, she became very quick at solving anything that had to do with a rectangle.

It was now halfway through the tutoring session, so I decided to give Mizan a series of problems over all of the topics we had covered today, along with a “challenge problem.” At first, I was only going to give her five problems.

“Do you think five problems is enough?” I asked, anticipating that she would tell me that it was actually more than enough.

“I think you could actually give me six or seven,” she replied with a sly smile. 

I felt victorious. At the beginning of the tutoring session, Mizan could only talk about how much she did not like math, especially fractions. Now, she was asking for more questions! 

So I gave her seven problems, with the last one being a challenge problem. She got nearly every problem right. The few errors she did have were just with forgetting to simplify fractions and the like. 

Mizan even came very close to solving the challenge problem. The problem I gave her was of a shape made up of a right triangle and a rectangle. She was able to see that the shape could be broken down into a triangle and a rectangle. She also found the area of both the triangle and the rectangle independently. After giving her a small hint about adding the two areas together, she did so correctly, successfully conquering the challenge problem.

At this point, Mizan seemed much more open with me, and I could tell how much better she felt about her progress in math. 

A few minutes later, it was juice and donut time. Mizan and I talked for a while, actually more than most kids are willing to talk. She asked me about my school, about the classes I was taking, and how my spring break was. She was also very surprised to learn that I was just a high schooler and not a college student. Only students at the Saturday Tutoring Program think that I am older than I am (5’2” problems). 

After juice and donuts, Mizan received the writing assignment for the day, which was relatively simple since it was the last session. Mizan had to set three academic-related goals for herself and sign a contract that she would follow through on these goals over the summer. 

Mizan made the following goals:

1. Read 40 minutes a day

2. Go to the library at least once a week

3. Practice her math skills

After finishing the contract, I told her that we could play a game for the remainder of the session. She chose BrainQuest, which is a game where you ask trivia questions from various subjects. However, Mizan would only play if she asked me questions as well.

Even though the questions were designed for 6th graders, a few of them even stumped me! The nice thing about these questions was that they prompted further discussion regarding academic topics.

For example, one question read: 

Which is the smallest unit of an element: an atom or a cell?

Mizan said a cell, which is obviously the incorrect answer. However, this prompted our conversation about the difference between living and non-living things, what an element was, etc.

We continued playing BrainQuest until the session was over. Mizan was very polite and helped me put all of the pencils, books, and supplies away. She thanked me for helping her and wished me a good spring break.

“I think I’m gonna save these notes and these problems you gave me,” she said as we started to leave. “I want to keep working on this math until I understand it fully.”

I was very happy with Mizan for all of the progress she made and for being such a cooperative student.

Saturday Tutoring #4

March 21st, 2015

Today, I tutored a little girl named Evelyn who was in fifth grade. I also remember having tutored her last year. She is one of the only white students in the program. 

Since Case Western was still on spring break during this tutoring session, the room for fifth and sixth graders was incredibly crowded. Many people were even on the floor, sitting on bean bag chairs and pillows. Luckily, Evelyn and I found a spot at the end of a table which was much more comfortable.

Evelyn mostly needed to work on math during the session. She was working on dividing decimals in her math class--something I hadn’t done by hand in a long time. At first, Evelyn was really struggling with this topic and had no idea how to do the problem. I am not sure if she learned it in school but still found it difficult or if it was brand new material for her. Either way, I tried to think of a way that would be the easiest for her.

One method that usually makes students more excited or willing to math is by using white boards. It also makes it easier for me, as the tutor, to show her example problems. I went over to the table in the room to grab some white boards and Expo markers, but almost all of the boards were dirty and dented. Additionally, none of the markers worked; in fact, most didn’t have tips at all. Because of this, I am thinking about donating some supplies to the Saturday Tutoring Program or holding a drive for next school year. Even though I will no longer be tutoring there at this time, I think that the program would benefit greatly from new school supplies.

Anyway, I’ll now get back to telling the story of Evelyn. While she could not initially divide with decimals, Evelyn was very good at normal long division. As a result, I showed her that you could move the decimal place over to make divisor a whole number. From there, you could carry out long division normally. At the end when you get the answer, you just had to remember to move the decimal place back to where it’s supposed to go.

This method made a lot of sense to Evelyn and I was glad that I found a way that made the process a lot easier for her. She had a worksheet with twenty-five problems on division with decimals and actually finished it rather quickly. As she went along, I checked her answers and almost all were right. The only mistake she made was forgetting to move the decimal back to where it is supposed to go at the end of the problem. However, after reminding her of this, she was able to complete the worksheet correctly. 

After doing about twenty-five long division problems, I decided that it was probably time for a change of pace. I asked Evelyn what her favorite subject in school was, and she told me that it was science. I went to look for books that were about science and found them in a classroom set. However, these books featured writing that is typically found on a standardized test such as the OGT, so the content was not the most engaging or interesting in the world. Despite this, I ended up finding a book about cells and another about outer space, both of which Evelyn read for a while. 

After completing the reading, Evelyn and I decided to tackle the writing prompt, which didn’t speak to her very much. The prompt was about doctors, nurses, and dentists. She had to write about her experiences at the doctor or the dentist, about whether she’s interested in these careers, times she had been sick or had a broken bone, or what the doctors and dentists did to make her experience as a patient nicer. 

Evelyn said that she did not have an interest in a career in healthcare. She also had never broken a bone or been in the hospital. Despite this, she still managed to write a half a page about what doctors do to make her feel better, about why she isn’t interested in a health-related career, and how she didn’t really have any significant medical stories to tell. 

Compared to many other kids in the Saturday Tutoring Program, Evelyn wrote very well and did not have many spelling or grammar issues. She also did not have trouble writing a substantial number of sentences. Because of this, she was able to finish the writing prompt very quickly.

Between math, reading, and writing, Evelyn accomplished a lot in the session, so we were able to spend the last few minutes enjoying juice and doughnut time and conversing.

Saturday Tutoring #3

Today was an exceptionally challenging day at Saturday Tutoring. For the first time ever, I had to tutor three kids at once. Since Case Western is on spring break, the number of tutors was significantly lower than usual. At first, however, I only had two first-graders. 

One was Salil, the boy I tutored last week as well. He had his familiar sly smile, but this time, I was much more prepared to work with him and keep him on task.

The other was a little girl named Justice. She seemed fairly shy and quiet at first, but she was never afraid to challenge the boys in the group.

Salil brought a few math worksheets with him, and I instructed him to work on them for a bit while I helped Justice, who didn’t have much material to work on independently. While she didn’t have many worksheets, Justice did have a book in her backpack that really fascinated her. It was a book on all of the presidents, but it seemed like it was meant more for a sixth or seventh grade audience than for a first grader. Despite this, the presidents book looked as if it was Justice’s prized possession.

“I can name all of the presidents!” Justice proudly declared. 

“Wow, that’s incredible! Wanna show me?” I responded. 

I’ll admit that I didn’t really believe her, since she was in first grade. Most first graders I had worked with in the Saturday Tutoring Program struggled to read words like “boy,” let alone names such as “Franklin Delano Roosevelt.” However, I always try to keep an open mind since there are always situations where kids surprise me with how much they do know.

This turned out to be one of the situations where I was very surprised, and for the better. With virtually no mistakes, Justice pronounced the names of all of the presidents correctly. She even knew the order of the presidents. For example, while we were still reading the page on Abraham Lincoln, she told me that she knew Johnson came next. I’m pretty sure that some of Justice’s knowledge regarding the presidents surpassed mine, and I even took AP US History last year! This just goes to show how much something as simple as a book can impact a child’s life and inspire in them a genuine love of learning.

Salil, on the other hand, was struggling to stay focused on his math worksheet. At this point, I let Justice read her book for a little while so I could help Salil finish up the double-sided page of homework. While he was somewhat reluctant, Salil cooperated with me better than last time and understood the importance of completing his homework. I also told him that he could play a little with the calculator after doing his worksheet. 

Just like last week, Salil remained just as fascinated with the calculator. Sometimes, he would get a bit out of control and start slamming all of the keys down or banging on it. I explained seriously to him that you could not bang on a calculator because it would break, so he settled down a bit. However, Salil was always on a mission to create the biggest number.

Since Salil’s short game time turned out to be playing with the calculator, I decided to make it into a group lesson of sorts for everyone. I gave each kid an arithmetic calculator and showed them how to add, subtract, multiply, and divide. By using calculators, I helped them learn things, such as the fact that multiplying makes numbers bigger and dividing makes numbers smaller. 

After a few minutes of incorporating the calculator into my lesson, J’Shawn and Salil both tried to get the biggest number on their calculator by multiplying large numbers together. Each time they believed they got a bigger number, they would show me the screen of their calculator, incredibly excited.

However, the minutes with the calculator were short-lived. I decided to take away the calculators and instead make the three kids work on their addition and subtraction facts. Salil was manipulative, though, and acted like he was going to go to the bathroom but instead grabbed another calculator. Soon, J’Shawn picked up on this and followed Salil’s lead to get more calculators. Eventually, I was able to make the boys hand me over their calculators. For the rest of the tutoring session, they did math in their head rather than using a calculator.

For a while, I held up flashcards and called out addition and subtraction facts to be answered by the kids. I decided to make it sort of into a game to see who could answer each problem first. I got really enthusiastic about the game, and even Salil found himself enjoying it with a wide grin on his face. In fact, he answered his addition and subtraction facts without needing to use a calculator at all.

About halfway through the tutoring session, the kids wanted to take a break and play with blocks. Since they did cooperate with the math facts, I thought that they deserved a little break. Soon, however, things got out of control, mainly with the boys, since they were building large structures with the blocks and then proceeding to knock them down, which was distracting other people who were working. As I was putting the blocks away, Ms. Wilson luckily intervened and used her authority to get the boys to behave.

After the fiasco with the blocks, I decided to read a book with the kids in order to keep them all on task. Ms. Wilson picked out the book, which was titled Henry’s Freedom Box. This story chronicled the journey of a slave named Henry who managed to escape to the North by hiding in a shipping box. The four of us took turns, each reading a page. Salil in particular protested when he reached a page with lots of words on it, but he knew that I would not let him back out of reading. Henry’s Freedom Box kept everyone’s attention very well, and we even had a small discussion about the historical context of the story.

Even though tutoring three kids at once was a challenging experience, it opened my eyes to how hard it must be for teachers to deal with a classroom of twenty, thirty, or more students.