Thinking Mathematically: Pages 1-25

Fictional “Case Study” relating to Mason’s Strategies

Seth is a young man in my Principles of Math 10 class. He is a nice boy, but he is sure having a great deal of problems understanding the topics that are discussed in class. Seth attentively listens and writes down notes during class. Furthermore, he works hard during the class on his homework; however, he cannot solve any of the problems. I help him as much as I can during class and he is constantly coming in at lunch and breaks for help. He understands the problems when I go through them with him, but he cannot do them by himself. Recently, I have read a book by John Mason with Leone Burton and Kaye Stacey called Thinking Mathematically. I got a lot of ideas from the first chapter of this book and I think by using some of Mason’s ideas I can help Seth improve in his math. I like Mason’s idea of RUBRIC writing. I think that this will really help Seth in math because by writing “STUCK,” “AHA,” “CHECK,” and “REFLECT” in the margins of his notebook he will be able to see what exactly is causing him problems, what he understands, and what he should revisit. I think by being able to categorize where he is having problems and what he understands, both Seth and I will know what areas in math he needs to spend more time on and what areas of math he comprehends. In addition to RUBRIC writing, I think Mason’s strategy of specialization and generalization will also help Seth improve his math skills. With the specialization strategy Seth will be able to randomly choose examples to get a feel for the problem that he is working on. I think by “playing” around with these different examples Seth will develop an understanding for the problem that he is working on. Additionally, I think that the generalization strategy, which involves detecting patterns, will also help Seth improve his math skills. Once students see patterns many of them start understanding what is going on – hopefully, Seth finds that patterns help him. Moreover I will have Seth constantly write himself notes because by doing this I think that he will not forget any of the ideas that he is thinking about and this will help him solve his problems. I think this will help Seth because many times Seth can verbally say what some of the latter steps in the solution are but when trying to think of the steps that come before these ones, he forgets the latter steps. Overall, I cannot wait to have Seth try some of Mason’s strategies because I think that they will really help him in his math. Seth is a bright young man and I think these strategies will help him express his mathematics better; therefore, improving his success in math.

Math Write-up and Poem

Math Poetry

Time Writing:

Divide:

When I hear the word divide I think about cutting some object, such as pizza, into pieces for a number of different people. This word also results in the image of splitting people into groups to do group work popping into my head. The division symbol also pops into my mind when I think of the word divide. I think back to the days when I learned long division. Unlike my friends, I did not mind doing long division. The word divide also reminds me of the night before my History of Math final in university. I had to learn this new way of dividing. I think it was a method of dividing from the Arabic mathematics. I spent hours trying to figure out how to divide using this method of division. I was very fortunate that my dad knew how to divide using this method. It took me awhile to get this method, but I finally got it. I was so happy to see a question using this method of division on the exam because I knew exactly how to do it.

Zero:

When I think of the word zero, the number zero pops into my mind. I like multiplying numbers by zero because it is easy to figure out the answer. I like when numbers or problems are all to the zero exponent because these answers are very easy to figure out. Also, when I hear the word zero I think of the zero laundry detergent box that used to be on the shelf in my laundry room when I was little. Zero soap is excellent at taking out stains in clothes. I also enjoy saying the word zero because it sounds neat. If a person really thinks about it, zero represents nothing. Temperature freezes at zero degrees Celsius. The word zero rhymes with hero, and Zero to Hero was the name of the first major research paper I ever wrote. This research paper was about how Elvis Presley became the King of Rock and Roll and I wrote it in English 11. It is my most favourite paper I ever wrote.

Poem on “Division of Zero”:

Dividing by Nothing

Division – splitting items among a number of people

Zero – an empty space that represents nothing

What happens when these two words are brought together?

You get division by zero!

But wait, this means splitting a number up into no groups.

How is this possible?

I do not understand.

How do I deal with this problem? Is there a solution?

There is a solution – it is not possible!

Oh, I see, I understand - it all makes so much more sense now.

Teacher-ly Comments on Math Poetry

Math poetry is something that I have never heard of before. I think that it is very interesting and brings out a different side of math. Math poetry takes away the emotionless that many people think exists in math. I thought it was very interesting to write a poem about division by zero. At first, I found this assignment to be very difficult because I could not remember how to write a poem – I have not written a poem since high school and writing poetry was not my favourite part of English. However, once I started writing I found that writing a poem was not extremely difficult.

I think that there exist many positive aspects to having high school students write poems about math. By doing this kind of assignment math students can see that math can be a creative subject – like many other subjects. Students also get a chance to express their feelings about a particular mathematical topic with math poetry. Another positive aspect of math poetry is that it gives students a break from just answering questions and it can result in students enjoying math a great deal more. Math poetry can also help students, who have difficulties in math, express their ideas about math or a particular math topic.

Although math poetry has many strengths, it also has a few weaknesses. Some students might not be very good at writing poems. Hence, these students would find this activity to be very difficult. Moreover, if students are having difficulties in English and math then they would find this activity to be very difficult. Furthermore, some students might not learn a great deal from math poetry; therefore, it might just be a waste of time to do. However, although there are some negative aspects to math poetry, I would love to try it in my math class at least once because it might be very fun for the students and it might help them understand the math more.

I think that math poetry can be used in any grade: grade 8 to 12. I think that students must first know how to write a poem before they are told to just write a poem in math class. However, I do not think that this would be a very big problem because many students have to take an English class from grade 8 to 12. I think that it is possible for students to write a math poem on any topic in the math 8 to 12 curriculum. Therefore, I think that it is possible to use math poetry in any math class in high school and I think that it would be very interesting to try.

Short Practicum Experience

Practicum Experience

Best Practicum Story

My best practicum story occurred on Halloween – the day I taught Math 8 for the first time. I was very nervous teaching this class because my faculty advisor was observing me and I was not sure how the students would behave because it was Halloween. Additionally, I was really nervous because it was my first day using the computer tablet. I practiced writing on the computer tablet the day before, but I was still very nervous. However, once I told the students to take their notebooks out and stop talking, my nervousness subsided and I did not even notice my faculty advisor sitting at the back of the classroom writing down notes. I was successfully able to give the students their notes on mean, median, and mode by having them participate by asking them questions and having them solve examples that I asked them. Moreover, the students were very enthusiastic about what they were learning and they really enjoyed the lesson. I also did a little class activity with the students. In this activity the goal was to determine the mean, median, and mode of the shoe sizes in the class. I had the students come up and mark off their shoe size on the computer tablet. This little task made the students very happy because they were able to write on the computer tablet. For the rest of the hour the students worked on the homework or studied for the test that they were going to have during the next portion of the class. After the students finished their tests we watched Transformers for the rest of the class. Additionally, I was very happy that afternoon because I received excellent comments from my faculty advisor for my lesson. Nothing too crazy happened during this lesson, but it was still a very memorable lesson for me because it was my first time teaching a Math 8 class and both the students and I had a lot of fun during this lesson.

Changes in my teaching as a result of the practicum

Overall, I really enjoyed the short practicum and I found it to be a very educational experience. It was very nice to actually work with high school students and see their personalities – instead of just sitting in the classroom and hearing about how high school students act and think. Once I was in the classroom teaching, I realized that I had to be very clear when giving students instructions. I could not just assume that the students would understand what I was saying, even if I thought I was telling the students something they would already know. Therefore, I learned that I have to be very clear and direct when giving students, no matter what grade they are in, explanations and instructions. Furthermore, after the practicum I learned that I have to be very commanding. I realized that I cannot just ask students to do things; instead I have to demand that they perform certain tasks. I found it very difficult to be commanding; however, as a started to teach more and more classes, I was able to become more commanding. Moreover, I think that during my long practicum I will be able to do this better because I will be teaching more often. In general, I experienced good changes in my teaching as a result of the experiences that I encountered during my short practicum.