“Math Projects” Assignment: Codes

Names: Hong Jiang, Howard Hu, Esther Yang

Grade level: Any level in high school (grade 8-12)

Purpose: The purpose is to encourage students to be creative, arouse interests, and promote analytical skills.

Original project tasks:

1. Read description of your chosen code and work to make sense of it.

2. Research more information about your code from at least 2 other resources.

3. Make a poster and teach us about your code.

4. Prepare a 5 minute presentation, include a puzzle for the class to work on as homework.

5. Take notes on other people's presentations, there will be a question on the next test about codes.

Sources: Students can use these suggest and/or other books and Internet sources on codes:

 Martin Gardner (1972). Codes, ciphers and secret writing. NY: Simon & Schuster, (J652.8 G22c)

 Fred Wrixon (1992). codes and ciphers. NY: Prentice Hall. (BUS 652.8 W95c)

Handouts, graphics, etc.

Example:

Handout #1: The Keyword cipher: substituting part of the alphabet with a keyword

To create a substitution alphabet from a keyword, first write down the alphabet. 

Then write down the keyword below the alphabet, followed by the remaining

unused letters of the alphabet.

To create a secret message, convert all letters from the top row to their corresponding letter on the bottom row.

These types of simple substitution ciphers can be easily cracked by using frequency analysis and some educated guessing.

Keyword: orange

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(might not be a good one since the last part of the alphabet has not been changed)

Keyword: zhujiang

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Try this:

Encipher this massage: vizpiuzsngrgiem

Benefits of this project:

We have found that the original project would be a great opportunity for students to explore new and interesting mathematical things, and it would be a fun project for students to try and hopefully spark some curiosity about mathematics. Through research students would realize that mathematics is not all about numbers and calculations. We think that this project would be a good way to introduce different branches in mathematics. Also, this group project will help students to develop skills in research, presentation, communication, and teamwork.

Weaknesses of this project:

The topic is a bit advanced for some grades, and some students may find it too complicated to understand some coding methods. Since every group is doing a poster presentation, it may become too routine and boring. Also, it is often times difficult for students to take notes while listening to presentations and retain information for the test question about the presentations.

Modified Project:

Grade level: Any level in high school (grade 8-12)

Purpose: The purpose is to encourage students to be creative, arouse interests, and promote analytical skills.

Sources: Students can use these suggest and/or other books and Internet sources on codes:

 Martin Gardner (1972). Codes, ciphers and secret writing. NY: Simon & Schuster, (J652.8 G22c)

 Fred Wrixon (1992). codes and ciphers. NY: Prentice Hall. (BUS 652.8 W95c)

Modified Project tasks:

Project Format (5-7 minutes long): Video or Skit

Theme: History of the code and how to use the code OR Creative presentation incorporating the code somehow

Project Requirements: Use of props, everyone must have equal act/talk time in the presentation (thus, everyone MUST participate), explanation of how the code works

Benefits: Practice public speaking, boost of confidence, memorable experience to refer to for the test question, incorporating something different into a math classroom

Marking criteria:

Rubric for the presentation (skit or video)

	5	4	3	2	1
Organization and preparation
Creative approach of presentation
Use of props effectively
Clarity and Relativity of Presentation
Ability to answer questions from audience

Response to Selter's Article

I was moved by the little Ferit’s story. Isn’t it one of the strategies people use all the time? Usually when we found an efficient way of doing one thing, we tend to stick with it (or at least try to reuse it) when we deal with another situation, especially when the two things have some common ground. As what happened in the story, sometimes it works, but many times it doesn’t. This reminds me of the math teaching. For example, providing several examples and then letting students conquer many homework questions is just one way of teaching mathematics, but it works generally, even though it might not be the best way of teaching and learning. Because this is a tradition and it is how we learned, we are familiar with this style and it is easy to use, but unfortunately, it is often overused in many classrooms. Teachers are no different than little Ferit.

All the studies are interesting and they all point to the same direction and that is, an efficient way of solving math questions involves creativity, flexibility and adaptability. It also applies to the teaching of mathematics. I think the first step is to be flexible. We have to be open-minded and acknowledge that there are different styles and opinions in the field, and our job is to find out which ones suit us the best on a particular topic. Second, we have to learn to adapt the existing material according to our teaching environment. The strategies work for other people in other classes might not be the best for us or might not fit into our classes. Therefore, it is necessary that we take what work for us and make changes. Finally, I think the most difficult part is to be creative because it takes time and effort to create something which might not be guaranteed to be successful. It also means that the teacher has to voluntarily add an extra piece on top of their already heavy workload. All these put together a dedicated math teacher who will turn math into a fun and interesting subject beyond mere strategies.

The Two Colum Word Problem Sovling

A Problematic Word Problem

I found this word problem on line at: http://www.analyzemath.com/middle_school_math/grade_8/problems.html

Q: Two different schools (A and B) have the same number of pupils. The ratio of the boys in school A and the boys in school B is 2:1 and the ratio of the girls in school A and the girls in school B is 4:5. Find the ratio of the boys in school A to the girls in school A.

Even though the problem is related to school situation (and therefore might be close to the students) and it is solvable given all the information, I will say this word problem is not practical at all. First of all, it is very unlikely that the two schools have exact same number of students. Secondly, nobody in the administration would ever do this to find out the ratio of the boys and girls in the same school (nowadays, it is just a click away). If I were to put this into a real life situation, it is like I want to go to the UBC bookstore from the Scarfe building on campus, but instead of going straight to the book store, I first go to the bus loop, taking Bus 99 to Broadway Station and then take the Skytrain all the away to Surrey, and then transfer to a bus and come back to UBC, and then get off the bus and rent a bike in SUB, and then finally bike enthusiastically towards the long desired bookstore---who would ever do this?! I think students will solely look at the numbers and do the math as in many similar cases since the problem itself is dry and not very interesting. To rewrite it, I think it would be better to incorporate something that is attracting to children, e.g., something related to animals or games or some interesting facts.

The average length of male bottlenose dolphin is around 2.5 meters, which is the same as the average length of male tiger shark. If the ratio of the length of male and female bottlenose dolphin is 11:10, and the ratio of the length of male and female tiger shark is 12:10. Which one is slightly longer on average, an average female tiger shark or an average female bottlenose dolphin? Can you estimate before calculating it?

Now I am thinking, this is not good enough, since there is a big rang when you think of the word "average"... feeling sympathy towards all math textbook writers. 

About My Short Practicum

I was placed in a secondary school in Vancouver with approximately 1700 students. My time was divided equally into Math and Mandarin. I have only one school advisor and she teaches both Math and Mandarin. It is amazing that she is fully bilingual with native proficiency in both English and Chinese. There were about 4 or 5 Ministry Designated students, mostly with learning disabilities, in each of her four math classes and only one class has a TA. As a result, the students’ levels vary greatly and the teacher has to spend time managing students’ behaviour. During my visit to the resource center, the teacher there told me that there were about 90 special need students in total and it is only considered an average in the School Board. I have noticed that the teacher had to explain and repeat many times and the students liked to ask such questions about, i.e., the homework, texts, projects, etc, because either they didn’t pay attention or they just wanted to make sure what they understood was correct, even though (to me at least) the teacher had given a very clear instruction (mostly written on the chalkboard) on what they were expected to do,   

I taught two classes in the second week, and one of the main suggestions my SA provided was to have a longer “wait time” for students to get ready, to digest, or simply to make transition. She said it might seem very long when you were standing there, but actually it wasn’t. After, I paid extra attention to her wait time and I found that she gave her students a lot of “wait time” throughout the lessons. “Thinking as a learner, not a teacher” was what she told me and also was what she did in her classroom. I think because she understood her students, she was able to establish very good relations with her students but at the same time she was able to retain her authority in the classroom. And that was why even with a number of special need students, her classes were generally well managed. As mentioned, students’ math skills vary drastically in all of her four math classes, so she had to pay special attention to those students at lower levels. For example, when she let the students work on the word problems, a large proportion of her time was devoted to helping those students individually while other students were working independently.

I observed several other classes, i.e., Socials, English, French and Japanese, in addition to my teaching subjects. To my surprise, most of the classes I’ve observed were largely structure oriented and the activities were rare and were usually arranged at the end of the class. After talking to my friends from other schools, I have a feeling that it seems to be common in practice and I am wondering why. The math classes were usually centered on providing examples and the language classes were mainly about sentence patterns and translation. Some teachers told me that since they were so curriculum driven, they simply didn’t have enough time to do the activities on daily bases, but students did have group projects which were considered activities. Overall, it was a great experience for me and I have learned a lot from my short practicum.