Letters from fake students

Dear Ms. Jiang,

My name is Jane, Zhu. Maybe you don’t remember me, but I always remembered you. I am writing to you because at my 10 year graduation anniversary, you are one of few teachers I would like to thank. I am now a new Math teacher in China. I remember how terrible my math was when I entered high school. It was my least favourite subject. I was lucky to have you as my math teacher, because you were not only nice to us, but also made math fun. I remember the numerous brain tearing but interesting puzzles we did during our classes, and I remember the historical stories about math you told us in our math club after school. But most importantly, I remember you told me that, “Math is scary only if you don’t get it” and you were the one that helped me “getting” it. For all the troubles I made and all the questions I repeatedly asked, I would like to thank you for being a nice, patient and professional teacher who led me into my current well-loved career.

Please visit me when you come back.

Best,

Jane

Dear Ms. Jiang,

My name is John, Ahu. Maybe you don’t remember me, but I always remembered you. I am writing to you because at my 10 year graduation anniversary, you are one of few teachers I would like to send a letter and let you know something that I always wanted to say. I am now a successful business man, but numbers were not and will not be my favourite topic to talk about. And I want to let you know that it’s all because of you. You made me feel stupid and ashamed by asking me so many questions in front of the whole class and what made it worse was that you knew that I was never good at math. Your effort of forcing me into math only made me hate it more. I want to let you know that I was a failed math student through out my high school all because of your over-practiced teaching methods.

Best,

But I don’t want to hear from you.

John



By writing these letters, I really feel the power of a teacher (even though they are fake). Often, your unconscious gestures or even just one word will affect your students for an incredible long time in their lives, and the consequences are, sometimes good, but sometimes unfortunately very bad. I am glad that we did this activity because even though I acknowledge that a teacher takes a lot of responsibilities, but the feeling is a lot stronger when I actually put the words down.
Hong

The Battle of Mathematics Education in America (Summary and Reflection of Susan's Battleground Schools: Mathematics Education)

The battle of Mathematics education in North America has been mainly a battle between progressive and conservative approaches. The critique of math curriculum dated back in the late 19^th century, when mathematics learning was traditionally equivalent to raw memorization without understanding of how and why the procedures worked. Therefore, scholars such as Dewey advocated progressive math learning, which treated students as active learning agencies and considers math learning part of a reflective inquiry to develop scientific and democratic thinkers rather than obedient rule-followers.

The scientific and technological competition during the Cold War generated the anxieties about the lack of scientists in the US. Therefore, there was a public outcry for better preparation of American children for the future, resulting the movement known as “the New Math” in the 1960’s, which aimed at reforming math curriculum in public schools. Thus, several new concepts, such as abstract algebra, linear algebra, and calculus etc. were added in school math programs. However, this change created big problems since neither the teachers nor the parents were prepared for the new curriculum. Consequently, “the New Math” was regarded as a misguided experiment and soon discarded.

Since late 1970’s, the math teaching moved towards a ‘back to basics’ curriculum. The National Council of Teacher of Mathematics (NCTM) developed its own Standards program in the mid-1980’s. The NCTM Principles and Standards were well received by both government and teachers because of its balanced progressive approach which emphasized the development of flexible problem-solving skills, the ability of represent math in multiple forms, the use of technologies and the ability to communicate mathematically. At the same time, California state legislators also developed a new school mathematics curriculum in the similar approach.

In the mid1990’s, voice of criticizing standards-based curriculums emerged. Especially in 1996 when the Third International Mathematics and Science Study shows that American eighth-grade students ranked 28^th in the world in mathematics, anxieties roused and sparked calls for a more rigorous and traditional standards for school mathematics, although video analysis of school classes supported the NCTM and California state standards. Until now, mathematics education itself is still at the center of this prolonged ongoing battle.

This article is very informative and interesting to read. Even though it is mainly about the historical “battle” in the US, I can easily relate it to my learning experience. For example, the ideology of math education in my childhood was largely based on the conservative approach which believes that high-level abstract ability can be trained through excessive drilling. However, I feel fortunate that I had one teacher who taught math in a more progressive way. And his classes have become the most interesting and precious math moments in my memory. I have to remember that as an educator, it is my duty to give my students these memorable moments.

Assignment 1 Report (Group Members: Michelle Davis, Hong Jiang and Nadine Lundie)

PART 1 – Mathematics Teacher

We chose to ask our five burning questions to two different math teachers with varying experience. The first teacher interviewed had graduated from the UBC four years ago and has been teaching grade 11 and 12 math. The second teacher is the Senior Math Expert and has 30 years of high school teaching experience. We decided to ask two teachers with different levels of teaching experience to compare our results.

We found the answers were quite different in that the responses from the recent UBC grad were responses that we as teacher candidates might have thought of. On the other hand, the responses from the experienced math teacher were quite different and her methods unexpected. For example, we asked both teachers how they approach both the students who like math and dislike math. The newer teacher said that when she has a student who is only there because it’s a requirement to graduate and they are not interested in pursuing anything mathematical after high school then she simply tells them what they need to pass. She explains the requirements for them to get a specific grade and lets the students decide for themselves what grade they want. The experienced math teacher did not bring up the notion of ‘requirement to graduate’ and said that she shows students that math is more than computation. She believes that math is a fine art and compares it to music in saying that playing scales is not all music is. She says that she teaches from the premise that math is creative, efficient, effective and fun.  She believes that all students can and should have an appreciation for mathematics even if they never plan to pursue it.  She is not content to just let them be.

This premise also relates to how she manages to relate math to concepts beyond the classroom. She describes math as a way of thinking which helps with organizational skills, efficient procedures and problem solving. She goes on to say that this mathematical way of thinking is used even for daily things such as your cell phone plan or relationship issues.  She firmly believes that math is more than just procedures to memorize and strives to make this come across to her students.

One thing our group found interesting was how the experienced teacher incorporated topics from the real world into the classroom compared to the newer teacher. Rather than presenting or telling about real world applications, the experienced teacher posed questions or problems for the students to think about. For example, using a parabola to represent a bridge or arch she would ask the students whether they could replicate a famous structure in a different location over another river of different width or to allow for taller boats. We found this very interesting because not only is she relating math to a real problem, she is also having the students try and solve it themselves. This would be a great idea for a group project.

PART 2 – Mathematics Student

We asked our five burning questions to a high school student who likes math and a high school student who dislikes math. When considering math a mere subject, the student said that they like math because there is either a right answer or a wrong answer, and there is no maybe answers. The other student said they dislike math because they feel it is too hard for them to understand and they wait too long to ask for help until right before the unit test. Our group was wondering if perhaps the teacher was not approachable enough for extra help, or if the student already established a sense of defeat about math.

We found it interesting that the students had similar answers as to what about a specific math teacher made them their favourite. Both the students said that the teacher made math fun, used good humor and brought jokes about math into the lesson. For example, one of the students said that their teacher gave the three different forms for the equation of a line names that were funny and non-math related to help students remember. The student who disliked math said their favourite teacher explained things in the simplest and easiest way and the student who liked math said their favourite teacher did things that were hands on and interactive. One of the students also said their favourite teacher let them watch “Finding Nemo” during class.  It seems to us that it is much more about the relationship that the teacher built with the kids that made them memorable.

A few of the other comments we found interesting had little to do with the content of mathematics itself.  The student who likes math said that her teacher cared, wanted to help, and made sure that the students were doing okay, and not just in math. The student who dislikes math said that their favourite teacher had a positive attitude. We found this intriguing that these characteristics are completely unrelated to the subject. We have been learning that being a teacher is more than knowing and teaching your subject matter. It is also about caring for your students and their success.

Of course the issue of homework came up with both students.  They both said they did not much like homework, which is not surprising. The student who dislikes math said that if too many questions were assigned they would dread even getting started on it.  It’s an interesting issue; how much homework is too much?  How much is not enough?  As the teacher how do you treat homework in the evaluation process?

Conclusion

This interview was very eye opening for all the members in our group. We can relate to the answers from the newer math teacher, although we aspire to develop the methods of the experienced teacher. We believe the confidence and creativity this teacher brings to the classroom comes not only with experience but also with constant reflection and adaptation.

We gained a different perspective by interviewing both types of math students. We saw that they had different concerns in areas like what made learning the easiest, but they had the same ideas about homework and why a certain teacher were their favourite. We learned that the teacher having a positive attitude and caring about their personal wellbeing, which are both unrelated to math, are more important than we previously thought.

Reflection about My Micro-teaching

For this ten minute micro-teaching, I had a group of four and I taught them how to make origami boats. There are a lot of positive feedbacks which are very encouraging. For example, my group liked this activity, which means I chose a good topic to teach. Three people mentioned that the instructions were clear, and they liked the fact that I wasn’t rushing. Also, people like the fact that I monitored their process and made sure that the group was staying with me all the time, so that everyone made their own boat at the end. Two people suggested that I could improve on time management since we didn’t have time to complete the post-test. One person suggested that it would be better if I could show them what to make before hand (having a sample).

The comments are really valuable and beneficial to me, and I have learned a lot from this ten minute activity, so thank you, my group!

I think the biggest part that I can improve is the time management. I tried at home and it was about the right time, but when I was teaching the classmates, there were those minutes that I didn’t think of when I was doing it by myself. For example, the time to distribute paper, the time to check if the learners understand, the time to clarify, or the time to help the individual learners. Therefore, it is important to give myself extra few minutes to prepare for these things. It might be a good idea to divide the learning into different parts. For example, first to teach them how to make a basic boat, and then carry the activity into a deeper level (e.g. adding a roof for the boat), in case everything runs smoothly and we have few minutes left (therefore also need to prepare materials for extra activity). It is always necessary to have something back up, e.g., I can give them some stickers to let them decorate their boats if we still have time left.

BOOPPPS for Origami Activity

 

	What to do	How long	Materials
Bridge	Discuss a little bit about other classes or other things in the morning, e.g. do they have class blogs for other classes, etc.	≈ 1 minute
L. Objective	The learners will be able to fold a boat with a piece of rectangular paper.
T. Objective	To provide clear verbal instructions while demonstrating the steps
Pre-test	Ask them when the last time was that they made origami, what did they make.	≈ 1 minutes
Participatory	Pass one piece of white paper to each person, telling them what kind of paper is good for origami, and let them follow the steps that I demonstrate. When finish, let them unfold their boats, and re-fold it.	≈ 5 minutes	White printing paper
Post-test	Give them another piece of color paper at their choice and let them fold their own paper boats. Adding some decorations when finish.	≈ 2 minutes	Colored paper & pens
Summary	Answering questions. Emphasizing the important points, e.g. what kind of paper to choose, etc.	≈ 1 minutes

Comment on Dave Hewitt's Video

I have to say that I really like Dave’s teaching style. He did a very good job at grabbing students’ attention and engaging them in the learning process. He started from the very basic point and go step by step at a good pace which is very important when teaching a new concept to a whole class. You want to give your students a little time and some background knowledge to simply let them refresh their mind or review what they've learned. The facts that he was moving around the classroom and making sounds with his stick greatly activated the learning atmosphere. And sometimes even a little funny sound might make the seemingly dry material fun.

My Favorite Math Teacher

My favorite teacher is my grade three math teacher, Mr. Li. I moved to a new city when I was ten and I became a new student in his class while all the other children had known each other for two or three years. I thought I was good at math but very soon I found out that all my classmates were much better than me.

One day, after school, Mr. Li asked me what I had learned and what I hadn’t. The next day, he asked me to be his assistant to teach a new concept which I already knew. He explained to the whole class that there was this curriculum inconsistency between different schools and there was always something we could learn from other people. He really helped me establish my confidence in the very first week of my new school.

I learned fast and I was good at math, but there was one thing: I always made careless mistakes. For example, instead of writing ¾, I would write 30/40 as my final answer on my exam paper. What he did was to let me go through every mistake and to see whether it could be avoid if I were to be more careful. Then he let me calculate the total mark that I could save. This really shocked me after I found out that over 80% of my mistakes were due to my carelessness. Then he asked me to think about how to avoid those mistakes. So I told myself that I needed to slow down, to double check after I finished and to ask “is it the final answer?”

I really like the way that he let me teach myself instead of him telling me what to do. He tried to understand his students’ previous learning experience and he established an effective communication between his students and him. Therefore, his students respected, trusted and loved him.

Hong

Assignment 1 Questions (Hong, Michelle & Nadine)

Questions for Math Student:
1. What memorable method did a current or previous math teacher use that made the learning easier?
2. What memorable method did a current or previous math teacher use that made the learning fun?
3. Why is your favourite math teacher your favourite? What did they do differently than other math teachers?
4. Why do you like (or dislike) math?
5. How do you feel about the amount of math homework that you get?

Questions for Math Teacher:
1. How do you incorporate topics into your math class which show how the math applied to real life outside the classroom?
2. Do you include history of math into your classroom? How?
3. What types of methods do you use to ensure that the student’s homework or assignments are their own?
4. What is the most challenging part about teaching the subject?
5. How do you approach both the students who like math and students who dislike math?

Hong, Michelle & Nadine

EDCP 342: Instrumental vs. Relational

I have learnt math for such a long time, but I rarely thought about these two ways of teaching or learning: instrumental vs. relational.

I think many children at my time were taught relationally during their first couple of years in elementary, because for the things you learn, it was actually possible for you to understand why, (e.g. addition and multiplication).

However, as children get older, the math gets harder, usually because the math is “growing” much faster than children (I don’t think it has to, but it usually does). Therefore, more instrumental teaching and learning were applied. I remember the time when I was in my grade three math class learning something called “the scary pai”. My elementary math teacher told us that “you don’t really need to know why; the key is to know the formulas.” Very instrumental! But eventually I got it, after “plenty of exercises”.

I think Vygotsky’s social-learning theory might be of a good use here. There is the Zone of Proximal Development (ZPD) and for children learning something too advanced at such a young age (as many Chinese and Japanese children have experienced, even now), cognitively, they are just not ready for it. Therefore, the only way is to give them the rules and a lot of similar questions.

I have always questioned why math have to be so difficult for many children. Is it because of the children’s lack of practice or because of the teachers’ lack of efficient ways of teaching? Or both?

Thanks for reading it:)