Gina at the Math Forum

I can’t believe how fast 6 months went by. I feel like it was just yesterday I was sitting down in the conference room with Suzanne, Casey, AJ, and Brianna discussing our work duties. The math forum was an experience that I’ll never forget. I got to be involved in classrooms and talk to students, which I would not have been able to do with any other co-op. Besides that I gained good friendships through working here. I became good friends with the two other co-ops Casey and Brianna and Casey and I have actually been taking some classes together. Everyone in the mathforum seems like one big family and I think that’s what I’m going to miss about it the most. (Unless I can work part time, which i’m hoping for) Besides doing all of their work, they discuss tv shows together, get lunch together, and most of all throw mini parties for all of their birthdays. The secretary Tracey never misses a birthday and does what she can to make everyone feel special. Suzanne, my boss is always there to talk, listen, and lend a helping hand. I could go on about everyone at the Math Forum and how special they are, but I’d run out of space. Overall I’m very lucky I got to have this opportunity and will definitely miss making packets, helping students, and the staff!

The tangram is a puzzle consisting of seven different pieces that are made to fit into a square. There is 1 square, 1 parallelogram, and 5 triangles. The Tangram puzzle originally came from China, but we do not know much about the history. There are various myths and stories on how this intricate, dissecting puzzle first came about, but we do not know for sure which story is true. The earliest written documentation about these puzzles was written in 1813, however, it is though that the puzzles had been around many years before this. When the puzzle first came about sources say that Western sailors who traded opium often played these puzzles with their Tanka girlfriends, which makes many people believe this is were the name came from, a mixture of Tanka and tramgram, an English word meaning puzzle. Another story often told to children about the history of Tangrams, was that an ancient orient was asked to carry a piece of glass to be placed in the house of a King and Queen and on his journey he dropped the glass and had to put it back together. He had seven pieces and with these pieces he was able to make various shapes, but needed to make a square, which he eventually did. The King was amazed when told this story and became very interested in the concept. Even though this fictional story is told to children, it still gives you some idea of what could have brought these puzzles around. People believe that their isn’t much history about these puzzles because at the time, before they became popular,  tangrams were considered a game for women and children, and would not be taken serious by scholars. However, over time the game became known by the Chinese as the “wisdom puzzle” and would be used to test the intelligence of people. Tangrams eventually made their way over to Europe and America due to the immense amount of trading occurring with China. Sailors would bring home books containing these puzzles to their family and friends.

Even though one may look at a tangram as a fun puzzle, it actually holds a lot of mathematical value. By solving these puzzles you learn a lot about geometry by playing with different shapes. You can also learn about area, by finding the area of each individual piece, which would then result in knowing the area of your whole figure. These puzzles could be used at an elementary level to first introduce students to shapes or at a middle school to high school level to test their understanding with area and with configuring shapes to make a bigger picture.

(picture taken off of google images/wikipedia)

**This blog comes from part of a project I worked on in a History of Mathematics Class

All of my previous post have involved mathematics and education, but I actually only became an education major this year. I came into Drexel as a mathematics major and decided to switch to education as well. I always knew I wanted to teach, but was unsure of what grade level. I decided to do Secondary Education, which is High School Education. Algebra and Calculus are two parts of mathematics that have always interested me. I had my first education class this past term and it was History of Mathematics. Besides learning strictly about the history we also taught the class mini lessons, so I was able to experience some actual teaching and lesson planning.

Since I recently became an education major, I wanted to get more involved in the program. I ran for secretary of the FEDs club which stands for Future Educators of Drexel. I was so happy last Friday when I found out that I had gotten the position! I will be keeping track of all the minutes for the meetings we have. I’m super eager to find out what else I will be doing! I feel as though I will be able to bring forth new ideas to the club and help get more people involved! Being secretary of this club is the first step in advancing my carreer as a teacher!

I was recently enrolled in a history of mathematics class and definitely learned a lot. Many people, besides us math majors, or math educations majors, do not find much interest in the history of mathematics. I feel as though if they knew how different math is today then it was thousands of year ago, they would have a better appreciation for it. Each and everyday people take the numbers 1 through 9 for granted. I do not think this would be the case if they knew at one time babylonians used symbols of fish or men to represent numbers. Drawing this symbol takes a lot longer then simply writing the number. I’m not saying everytime someone writes a number they should praise the creator of the number system we use today, but maybe just think in the back of their head, “Hmmm this is pretty easy, I’m glad it doesn’t take long.” Writing numbers comes as simple as tying your shoes, you learned them once and do not have to think twice about them later, you already know how to do it. Learning about numbers was only one of the historical mathematical events we learned about. In my next blog, I will to talk about place holders.

So, In conclusion, which do you think is easier to draw?

or

Is the normal 3 easier to draw since this is the way we’ve known all along?

(both of these images were taken off of google images)

Now that the summer is coming to an end, I keep reminiscing about all the schoolwork I used to have to complete over the summer to get me ready for the next and upcoming grade. Every summer I would have a summer reading book to read. I hardly ever had math work to complete, which I find interesting. I only remember having a math packet to do over the summer once. I find it puzzling that most schools do not offer a summer math packet. Each year students learn new concepts in math that will help them the following year. If one student does not practice these concepts over the summer, how will they remember them? I feel as though if more schools (speaking of school levels k-12) required summer math packets, this could cut down on a lot of time teachers have to use each year reviewing material from the previous year. Say for instance one year you learn derivatives, and then the next year you are supposed to learn integrals, practicing derivatives over the summer will make it a lot easier to jump into integrals in the fall since they go hand in in. Requiring mandatory summer math packets would help a lot of students as well as teachers in their mathematics career.

When I first started working at the Math Forum, I was given the task to complete packets for Primary students. I had to think of various methods on how to prove that 3  - 2 = 1. After having many years of mathematics, I simply wanted to use subtraction in my head to solve this problem, but I could not. When creating primary packets,  besides creating a numerical equation using counting which would be just setting up 3-2 = 1, I also used other methods such as drawing a picture,  using a number line, and using manipulatives. Using manipulatives is just a fancy way to say using counters.

I then started working on other packets for Pre-alg and Math Fundamental packets. I found coming up with methods for these problem a bit more difficult. When creating these packets, I first solved the problem myself, giving me one method to work with. I then thought very hard and looked through other students solutions while also comparing with my co-workers on methods they could come up. In many of the Pre-alg problems I used Algebra as a method, such as coming up with an equation using a variable, but then I also started using algebraic reasoning. Algebraic reasoning is almost identical to algebra, except instead of using a variable such as x or y, you would put the actual thing you are solving for in the equation. Say for example you have a problem where x represents the number of adults at a carnival and y represents the number of childen and the total is 100. Instead of writing:

x + y = 100

You would write:

adults + children = 100

It’s very simple, but its just an easier way to understand/read the problem.

Besides these methods, you can also use logical reasoning as a method, which is basically just gathering the facts you have and making a conclusion with little to no math involved. It’s almost like a guess, but definitely more educated and supported.

Creating a table or a list became very popular methods that I began using frequently. They are both easy ways to organize all of your information making the problem easier to understand. You may have one method as algebra and then another as creating a table, where the math may be the same, but it is organized in a table making it easier for someone to read.

An example of a table would be:

This week I finished watching all of the videos that we took in the schools. For those of you who don’t know, we went to a school and tried different methods of teaching with the students including our most famour “I Notice, I Wonder” method. While trying out these methods, us co-ops video taped the teacher-student, as well as student-to-student discussions. I Notice, I Wonder is a method invented by one of my fellow staff members at the math forum, that asks the students to list everything they notice and wonder about a picture or story told to them, without actually giving them a question to answer. In one of the classrooms I videotapes, Valerie (a fellow mathforum staff member) had the students keep the paper upside down, then flip it over only for a minute. After the minute passed she made them turn it over and asked them again what they noticed and wondered about. I was suprised how many notice/wonders the students came up with only after a minute of looking at it. Finally she had them turn it back over and keep it face-side-up. A list of more notices and wonders were compiled on the board.  

A few students eagerly wanted to answer what they thought the question was going to be. “I know the answer!” some students eagerly said as they raised their hands.

“We’re just listing what we noticed and wondered for now, we will get to the question, don’t worry” Valerie stated. I was amased how without even given a question, students hands shot up to answer what they “thought” the question may be. I feel as though this is proof that the I Notice, I Wonder activity really gets students minds going. While listing everything they notice, their minds start turning and they start wondering  about the problem.

This week I went through all of the packets I created and edited them. Besides fixing spacing and grammar issues, I also read through them and tried to make the wording easier for a primary student to understand. Doing so actually made me start thinking a lot. Besides having to teach children the fundamentals of math, these primary teachers actually need to watch their wording when explaining the problems. In many of my packets I was like “You can conlude that…” but how many first graders would use the word “Conclude?” I feel as though it is very important to know how to talk to the students when getting your information across. This goes off of my week 4 blog, which stated that elementary school teachers may actually have it harder than an upperlevel teacher. I know personally when editing my teacher packets, I had to sit there for a few minutes and ask myself “What is another way of stating this, so that a primary student could understand?” Instead of saying “We concluded that the answer was 25.” I could simply say “We got the answer to be 25.” I feel as though it is hard for a person with some english education under their belt, such as a teacher, to not be tempted to use more intricate words when explaining things.

This week was the first time us new co-ops at the math forum got to go into a school and see first hand Valerie, Suzanne, Steve, and Max at work! I’ve been working a lot with the “I Notice, I Wonder” method when making packets but never had the opportuntity to see it in action. When looking at the problem Valerie and I were going to be working with, I sat down and listed the things I Noticed and Wondered before Valerie gave it to the students. I was curious if I would come up with more notice or wonders then them or if they would have more. After the problem was handed out and Valerie listed all the notice and wonders on the board, I was amazed to see how many things the students noticed that I missed! I also found it very interesting that the 4th and 3rd graders had a lot more wonders then the 8th graders did. A lot of the notice/wonders from the 8th graders were more mathematical where the ones from the younger students would be more about the picture then the actual problem. The one problem we did with the students had to do with worms in the shape of triangles and one of the younger student asked if the plants and people would also be shaped like triangles. I feel as though the type of wonders reflect on your backround in mathematics. When seeing a worm made out of triangles, one of my wonders may be “Are those isosceles triangles, or acute?” Where as someone younger with not as much math knowledge may wonder Why triangles are being used instead of circles or if plants and people would be made out of triangles, like the one student asked. I really enjoyed my experience at the school this week and am super excited to go back!! All of the students are so eager to participate which makes it so rewarding!

Helping to create teacher packets has been one of my favorite activities at work so far! I really enjoy coming up with them however, sometimes its hard to come up with different methods. When solving a more tedious problem such as an algebra or calculus problem there are often different methods you can come up with, but when given a simple addition problem it is often hard to think of different methods. For instance when given a problem such as “John has 3 apples then his sister gives him 2 more apples. How many apples does John have now?” You think to yourself, “It’s 5! It’s 5!” You almost want to just write down, “Its 5, because it just is!” When solving these primary problems and coming up with methods, I get to put myself in a Kindergarten/ Elementary Teacher’s shoes. I was always under the impression that elementary school teachers probably had it easier then upper level teachers because the work was a lot easier and more simple. My view on that has definitely changed. Why, You may ask. Well a teacher in a middle school or highschool often knows that the students have some former knowledge of their subject, but an elementary teacher often needs to start from scratch. A middle schol teacher could be like “Well since you know 10 +10 +10 +10 +10 +10 +10 + 10 +10 +10 = 100, you can do 10 ^10 = 100 and get the same answer. Where an elementary teacher needs to show the students, WHY 10 + 10 + ….=100. They need to come up with different methods on how to get this information across to their students. They cannot simple rely on counting alone. Instead they use other methods as well such as counters, numberlines, and pictures. Without the dedication of the elementary school teachers and their various methods of teaching, these students would not know the fundamentals of math that the upperlevel teachers rely on.