Fraction Manipulations Unit Plan

http://docs.google.com/Doc?docid=0AWex3nDbHmheZGZkNndkNF8wZDMyemM3ZDc&hl=en

math project (Credit Card Code (Luhn's Algorithm))

1) Sketch of the project


2) Assessment



3) Project idea: Divisibility test of numbers from 1 to 10 in base 10An enrichment project.

Grade Level: 10-12

Purpose: The students will gain better understanding of the divisibility of numbers in base 10 and the students will be challenged to think mathematically.

Description of activities: The students will first make conjectures about the divisibility for each of the numbers from 1 to 10. Then they will need to reason to themselves about why or why not the conjectures work.

Sources: N/A

Length of time project will take (in and out of class): 2 classes, 2 weeks

What students are required to produce: A poster or pamphlet of the students’ own conjectures on the divisibility test of numbers from 1 to 10 in base 10.

Handouts, graphics, etc.: N/A

Marking criteria: Number of solutions; Organization; Appropriate conjecture (i.e. not just saying to plug the numbers into the calculator…)

by Jenny Chu, Alan Hsueh, Sara Wang

Two Column Method

some memorable moments from the short practicum

First I would like to talk about the math clinic that I was participating. Basically the clinic is an after-school help for those students who struggle with math. On the day that I was helping, we had two special guests. They were two deaf students. It was my first time helping deaf students with their math homework. It was a surprise for me that they are taking math 12 and calculus. The fact that they are disadvantageous compares to other students and yet willing to take the challenge really inspired me. It is very encouraging for me to see them wanting to learn more than just what’s required. The other heart-touching moment for me was when I was observing the dance class. There’s a student with Down syndrome who was in the dance class. The teacher was teaching them how to do a full turn. This student kept on doing two 180 degrees turns instead. While it was entertaining to watch but it was the fact that he never gave up that was heart-touching. Near the end of the class, he finally figured it out. Seriously, at that moment I can feel the tears in my eyes. These were the two most memorable moments in my short practicum.

reflection on timed writting exercise

It is a good exercise if one can think of ideas quickly, but for myself, it is not my favourite.
I usually get frustrated with it because i can't come up with ideas, i feel pressured.

Strength:
-a good way to get students actively thinking about the topic
-we can get ideas from many people
-teacher get to know what those people who are little bit shy are thinking
-get the work done quickly
-we can get some dynamic ideas

Weakness:
-time pressure
-thoughts could be really wild
-frustration can come in if can't think of anything in short period of time

division and zero

Division:
-opposite arithematic operation from multiplication
-hard
-inverse
-scary
-flip
-division of 0 => yuck

Zero:
-zero could be good and bad, "no" problem or "no" clue. it could be no mistakes or 0/100
-middle of the number line, maybe that's why it's good and bad. It could go either way
-not positive nor negative
-nothingness/emptieness
-division of 0 => yuck
-freezing point

Division by Zero poem

Division by zero

What did i just wrote

teacher says no no no

division rules doesn't hold

the answer on calculator doesn't show

it does not make sense at all

thus i do what i was told

that is,

don't talk about it at all

second micro-teaching self-reflection

Due to lack of experience and time working together, I think the lesson wasn't fluent enough. It's a unique experience to do a team teaching, next time for sure though, i will need to communicate with Sara a bit more. One thing i am happy about the lesson is that we clearly indicate what we want to do for the lesson and i think our examples lead to our ultimate goal quite nicely. However, if we used powerpoint instead of the white board, it would be more clear because there're some confusions of the graphs. Also, it could be more interesting if we add some real life examples to engage the students.

second micro-teaching summary

In general, people agreed that our group has great attitude towards teaching. They also liked the participation we had in our presentation. Some concerns are the contents and the explanation of translation. We didn’t explicitly explain the idea behind translation and that may have confused some people. Also, we kind of just make an assumption about the students being able to relate translation of a graph by graphing. Another concern is that there was no graph paper provided. Some people suggested that having graph paper would have helped their understanding.

second micro-teaching lesson plan

Transformation of a Function

Bridge: Does a function transforms? if so, does that mean function is a transformer?

Learning Objective: SWBAT translate a graph vertically and horizontally

Teaching Objective: To prompt the students to observe the relationships and patterns between given graphs

Pre-Test: Does anyone know how to translate a graph?

Participatory:
- What are some questions regards to the different graphs? (What-If-Not)
- Graph y = 2x and y = 2x + 1, y = 2x - 1, y = 2(x - 1), y = 2(x + 1), y = 2(x + 1) – 2
- Ask the students if they notice patterns
- Explain how the graph transforms if students can’t find the pattern

Post-Test: Give a graph y = f(x), then give another graph on the same grid but moved both horizontally and vertically. Ask students to find the equation of the graph that has been moved.

Summary: Generalization of function; what is the equation of the function f(x) if we translate it to the right by 2? And down by 5? And so on.

citizenship education

It is important for us as educators to realize the importance of mathematical education in our society. First of all, the basic mathematics (numeracy, basic addition and subtraction operations etc.) plays an important role in our daily lives. Whether we want to or not, we are all assigned to numbers: age, height, weight, and many other attributes. So the first step I believe to develop a mathematical citizen is to teach quantitative literacy. Furthermore, “we must educate our youth, our citizens, so that they begin to understand and critique the formatting power of mathematics in society.” There are many different ways to prepare the students for citizenship; one of them is through problem posing. By encouraging students to create problems within the given problem will help them to understand the mathematical concepts behind it. Not only that, we should encourage students and explain their rationale and the mathematical concepts clearly to others. This improves their communication skills as well as helping them to listen to other opinions from colleagues. After all, math is a fundamental aspect of the society in my opinion. Thus, every citizen should have an equal chance of being mathematically educated from their school experiences.

The What-If-Not strategy

How can I incorporate the What-If-Not strategy in the micro-teaching?
Our micro-teaching topic is going to be on graph transformation. We will start by graphing some simple graphs, and ask students if they recognize the pattern or relationships between the graphs. For instance, y = 2x+2 is moved vertically upward by two units from y = 2x. From here, I can ask “what if the graph is not moved upward?” Let students explore how equations would change if the graph is moved downward or sideways and then ask students to make some conjectures about the transformation. Finally, I can ask “how would the equation change if the graph moved both vertically and horizontally?” as the “problem posing” part.

What are the strengths and weaknesses about the What-If-Not strategy?
I think the strengths of this approach are:
1. It allows students to think creatively.
2. It might lead to some unexpected and interesting questions that one may not think of.
3. It helps both “strong” and “weak” students by getting students involved in thinking about the problem not just doing the problem.

Here are some weaknesses of this approach:
1. It is very time-consuming; I personally don’t think it will work well in a regular class setting.
2. It could end up like an endless loop, as we create more and more problems.
3. It could lead to some totally unrelated topic.
4. We could scare people away from math with series of math questions.

To be honest, I think this approach works well with students who are interested in Math but not so much for those who are already bored with math and yet we throw even more questions at them. I think it works best for those graduate students or mathematicians who are looking for more ideas.

10Questions/Comments for the book "The Art of Problem Posing"

1.Do you think we should just ask for more questions from students instead of solving the question?

2.I was fascinated because how many possible patterns we can find from a table of values.

3.Is it always good to pose a problem?

4.When is the time that exact answers are not necessary? and why?

5.How do we avoid posing a bad problem?

6.What's your defination of a bad problem?

7.Since when do you think posing problems is important?

8.Did your teachers used the strategies that you suggest when you were in school?

9.What was your motivation of writting this book?

10.You said that we impose a context on the situation, how can i avoid that?

letters of good and bad

Dear Mr.Hsueh

I was your student ten years ago, the year that you had your first full time job. Your attitude towards students taught me that we should treat every individual equally and fairly. You were always caring about students, not just the academics but also their lives. You brought new ways of teaching to the school system. Instead of notes taking, we were doing some fun activities and group discussion was encouraged. The broad math knowledge you had was incredible. You were the one that I was really looked up to. I am glad that I had you as my math teacher and I will always remember you.

Sincerely,

Alphonse

I hope that my style of teaching will help students to learn better.

I want to help them both academics and some personal issues if appropriate.

Dear Mr.Hsueh

I was your student ten years ago, the year that you had your first full time job. I guess you were not well trained, as you made tons of mistakes in class. I was very confused to what you were saying, teaching. The teaching style you had was horrible; we had class discussions but usually you lost the students because students started chatting on their own issues rather than concentrating on math topics. I hope your skills of class-management improved through some experience. I can’t let you to destroy the kids of the next generations. Good luck!

Best regards,

Betty

I hope that my class-management will not be described as above.

response to Dave Hewitt's film

I thought the way he introduced pattern finding was really neat. With him tabbing the board or the wall to count numbers, students were really engaged. At first, I thought it was too repetitious. However, the video shows that some students were still not getting the concept of additions and subtractions that involved with a letter. It is important for me to think in student’s perspective, what I think is too much may not apply to students. I like how he interacted with students; it was a lot of talking and walking around the class. No notes taking was needed which could be helpful in some aspect. However, in my opinion, the traditional way of teaching still has its value. I think activities, group discussions etc. can be used as an aid to complement the traditional teaching. They add different flavours to the teaching as well as getting students involved in the learning process. Also, I like his idea of teacher not being the person with authority to do the checking. Instead, students should do the self-check so that they can gain confidence. After all, teaching or educating is all about helping students, we need to find the best ways to teach different topics so that students can learn the best.

summary and resonse to battleground schools

Since 1900, Math education in North America has been viewed in two ways namely progressive and conservative (traditionalist) views. Conservatives believe that the goal of Math is the fluency; it should be taught through presenting and students should absorb and apply the facts without questioning. On the other hand, progressive believe that the goal is the understanding of the concepts and teachers encourage students to think and question.
Public criticism of Math education in late nineteenth century led to Progressivist Reform (circa 1910 – 1940). It was the time of industrialization and urbanization, thus Math was perceived as the prerequisite for many subjects. The technique that was generally used was “programming the environment”. Students were encouraged to be involved in activities and “doing” math as opposed to sitting still and taking notes.
In the 1960s, it was the time of competition with USSR. Elite scientists were needed thus Math education became the focus of the nation. The public outcry of preparing children to become elite scientists led to the New Math movement. They were trying to rewrite the Math curriculum for K-12 level. There were huge problems as the existing teachers weren’t familiar with the new curriculum and the parents were not able to help their kids with their math homework. Due to these obstacles, the movement ended in the early 1970s.
From 1990s and onward, there’s a battle between Math curriculum and teaching methods known as the Math War. After a poor ranking in the world in Math for American eighth-grade students and detailed video analysis, the Third International Mathematics and Science Study (TIMSS) concluded that deeper conceptual understanding of Math was the key to succeed a higher ranking.
It is likely that during my future teaching career, I will come across some kind of new movement. To be able to adjust to a possible new “system”, I need to be open minded and willing to adjust to a new style. With my characteristics of caring for students and my passion for teaching, I believe I am up for the challenge.

group summary of the interview

(1) Why do you think we learn math in school, and why do you think math is an important or unimportant subject?
The general consensus is that Math is important to understand the world around us, and is a critical prerequisite to learning essential skills such as statistics, accounting, physics, poetry, etc. Additionally Math helps to develop critical thinking and problem solving skills.

(2a) For students: When learning a new material, do you tend to memorize the steps in solving a problem or do you try to understand the meaning and idea under each steps? and why do you do so?
Our students, who both struggled with Math, had differing opinions on Instrumental versus Relational understanding. The first student, who learned using a "work at your own pace" system, believed that the best method for him was 100% instrumental learning, since he viewed mathematics as an unnecessary learning exercise, and had no interest beyond passing the course. Our second student believed that if he had an Relational understanding, that it would be easier for him to develop (or "memorize") the Instrumental understanding.

(2b) For teachers: When teaching a new material, do you just work through a problem and showing all the steps in solving a problem or do you explain or try to explain the idea in each of the steps involved in solving a problem? and why do you do so?
Two of our teachers believe strongly that Relational teaching leads to a stronger understanding of the material than Instrumental teaching, which in turn allows the students to better apply their knowledge to a wider variety of problems. Our third teacher believes it is important to emphasize a variety of teaching techniques, both Relational and Instrumental, combined with classroom discussion and a final summary of the Relational concepts.

(3) What do you think of TPS (Think-Pair-Share) techniques where students break into groups of 2 to discuss the material before the class discusses it as a whole? How about groups of 5 students?
Two of our three teachers were willing to comment on TPS techniques, but for different reasons. Our first teacher believes that TPS can help both as a classroom management tool, as well as help reduce the possibility of public humiliation that occurs when a student answers a question wrong. Our second teacher supports TPS techniques because the students take a more active roll in their learning. She finds it inspires creativity in the students, improves their ability to communicate using math terms, and strengthens their understanding of the concepts.Both students believe TPS techniques would help with classroom management. One student expressed concern regarding groups of 5, where not everyone may be actively involved.

(4) Administering tests can be an effective tool in determining class proficiency before moving on to new material. How frequently do you believe tests should be administered?
Our teachers as a whole believed that constant assessment is necessary, but did not believe that tests were essential to administer frequently. They all stressed that alternate methods of assessment were just as effective. Both students explicitly stated that tests should be administered at the end of every unit, and suggested one test a week as a good pace. One of the students specified that he prefers tests to homework assignments as a means of assessment.

(5) What are your views on traditional class lecturing versus a system where students could work at their own pace and each individual could spend extra time on material they found difficult?
Our teachers agreed that a "work at your own pace" system would be nice, but is very difficult to implement due to time constraints and class management. Although not included in the written response, the one teacher, Mr. Jack French, did mention in a phone conversation that the administration and parents pushed heavily against this system due to students having to take a Grade 12 math block to finish their required Grade 11 mathematics, which by the program requirement, they eventually passed with 80% or better. One student expressed concern that a "work at your own pace" system would result in the students getting behind, while the other student was concerned about teacher unavailability.

self reflection on interview assignment

The teacher I interviewed (through email) was my high school Math teacher. When I was in high school, we did not have group discussion or in-class activities. It was basically sat there and listened to the lecture, much like the university style (for most Math class at least). So I was surprised to hear that TPS (Think-Pair-Share) technique has been adapted into her teaching style. Prior to education program, I did not believe that group discussion could be used in a Math class. I always thought that group discussion is only for Social Studies, English and literature courses. However, she has shown me that group discussion can be used in a typical Math class. I like her idea of letting students communicate their methods to peers and then she offers a formal summary of the concepts and state what she expects to see on homework assignments. All of the students we interviewed like the idea of group discussion in Math class. This again is a shock to me, because I did not think that group discussion will work well in Math class. What I learned from this interview exercise is that what I believe is right may not be the right method anymore. I must keep observing what students need so that they can get the most out of the Math class.

reflection on Robinson's article

After reading the article, it makes me believe even more that “students learn best when they are actively engaged in thinking about and doing mathematics.” I believe it is easier to remember or understand the concepts if it is learnt by guided discovery. It is also nice to know that there are teachers out there who are willing to improve themselves. It is very easy to just sit back and relax after you “get on” with the system. I thought her new versions of the quiz questions were fantastic, it encourages students to think and to support their statements or explain their reasoning. Before reading this article, I was not sure how I can lecture less during class; I found it difficult to come up with ideas to get students more involved. The author shared some of her strategies and ways to have students involved in group discussion, I found them useful and I will probably implement those ideas during the practicum. After all I think that teaching is an ongoing process, we have to adjust our teaching style if needed as we go along our teaching career.

Two of my most memorable math teachers

One of my most memorable professor in UBC is Dr.Pierce. He's really helpful during the office hour. He encouraged us to extend the concepts we learned in class and applied them in real life situations. I remember an instance that he stayed after the office hours ended and it was after six! Just to help us to fully grasp the concepts and homework problems. Dr.Pierce is just a tremendous person, i salute you!!!

The other memorable math teacher is Ms.Funk. Her knowledge of math is incredible, she answers all kinds of math questions whether it's related to school work or not. She cares about her students and helps students whenever needed. She also asked me to be her TA in the class, that was my first teaching experience and it ended up being my career path.

Looking back at these two teachers, one common characteristic is that both of them care about their students. They both have great passion about teaching math; they want to share their broad knowledge about math. They also encourage students to explore beyond what was taught in class. They have great influences in my life.

my first microteaching assessment

I didn't pick a good game to share with peers. Due to time constraint, it might have been hard for me to explain effectively the rules of the game to everyone. Also, the feedback i got from the peers was that the intro was not clearly conducted and thereby caused confusion. However, the positive feedbacks from the peers were showing passion for the game, patience in answering questions as well as hard work. The areas in which i need to improve include organization of instruction and time management. In sum, i think we all had a great time playing the game.

BOOPPPS lesson plan

B(Bridge):
Have you ever played the game called Coloretto?

O(Teaching objective):
1. Team work
2. Anaylyze the situation
3. Instant reaction
4. Have some fun

O(Learning objective):
1. Students will learn how to play the game
2. Students will learn to work together, and communicate with the team
member

P(Pretest):
No formal test

P(Participatory):
We will play a game with everyone showing their cards

P(Post-test):
Play a real, competitive game

S(Summary):
Conclude by emphasizing the importance of group work

Skemp Article

I used to believe that we learn Math by repetition. After I read this article, I still believe we learn Math by repetition but with some degree of understanding. What I did not realize was that Math learning is a life-long process. By teaching instrumentally, it is true that “the rewards are more immediate, and more apparent” and students “can get the right answer more quickly and reliably by instrumental thinking.” But without further understanding the concepts, instrumental teaching may require a lot of “new rules” as the conditions change. One may argue that “the relational understanding would take too long to achieve” but if the concepts are learnt, then it will be easier remember and possibly dig deeper into the topic. It is also mentioned in the article that “learning relational mathematics consists of building up a conceptual structure” and the author uses the analogy of a person with a mental map of a town can correct his own mistake if taking the wrong turn. It is very much the same in studying Math, if we comprehend the concepts. With “the importance of examinations for future employment” it is unfortunate that the direction of Math learning for the majority of students is to achieve good grades instead of developing a full grasp of Mathematical concepts. Therefore, I believe that relational understanding is important, nevertheless, there are still a lot of challenges faced by both students and teachers.

hello world

as above