This assignment is due Thursday, September 8, at the start of class.

**Assignment. **Choose ONE of the following two topics. Write a reply to this post, responding to the topic. Begin by telling us which topic you chose. (1-2 paragraphs).

**Topics.**

- Sometimes people can recognize a time when their opinion of math dramatically changed either for the better or the worse. If such a time happened to you, tell us about it.
- Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college). Describe what happened. Do you think you could explain it to others in a way that they could have the same flash of understanding?

**Extra Credit. **For extra credit, write a response to one of your classmates’ comments. Do you feel the same, or different? Did you learn anything? Did you get any ideas about teaching, or about learning?

** Why are we doing this, anyway?** We are following two ideas that have come up already in class — things that may not seem related to learning math, but research shows that engaging in these activities can

*dramatically*increase the amount that you learn, and change the way you learn it. The first is

**– something not typically associated with mathematics. When you express your ideas in words, it forces you to think them through very carefully, detail by detail. A great way to check and see if you really understand something is to try to explain it to someone else, either out loud or in writing.**

*writing**Example: if you know how to add fractions, try teaching it someone who doesn’t know how.*The second is called

**, or “thinking about thinking.” This happens when you think about what was going on in your head while you were working on a problem or trying to learn a new idea. What train of thought did you follow? Where did you get stuck, and what did you do next? What were you feeling at the time? and so on. Combining writing and metacognition can be a tremendously powerful tool in identifying the ways we learn best and the ways we make mistakes, and learning to improve. However, like any skill, it takes practice. That’s why we’re getting started by writing a little about our past experiences with mathematics.**

*metacognition*

Topic 1

My opinion of maths changed dramatically during my 3rd year in secondary school back home in Ireland.

Up until 2nd year, I was under the schooling of ‘ordinary’ level mathematics (which covered a whole range of topics covered, hence why I refer to the subject as ‘maths’ as opposed to ‘math’). My teacher at the time quickly realised that the topics covered in our ordinary level classes were just too easy for me and that I was outpacing the rest of the class. Our teacher and principal pulled us aside and asked if I (amongst other students) would like to move up to the higher level class and take on a much more ambitious level.

Much to my delight, I accepted the offer. My whole attitude in almost downplaying maths shifted as I entered a whole new level of complexity. It also helps that my new teacher was extremely talented at explaining core concepts. To this day, I thank my principal and my teachers for my ability in taking maths, and as a result, Calculus Honours, Calculus II and now Proofs & Logic. Even after this class, I plan to venture forth to even higher complex dimensions of mathematics, I subject that I’ve grown to love as a result of that dramatic change.

Dear Ismail,

Thanks for sharing – what a great story. I think it’s true that sometimes the higher levels of math are actually more appealing (and, though challenging, “make more sense”), because they don’t skip over the complexity. Instead, they dive right into it! This course is all about getting to the bottom of things, instead of just learning the procedures for solving problems, and (in my mind) that’s the best thing about it.

-Prof. Reitz

Topic 1

A time period where my opinion on math dramatically changed was during my experience as a math tutor and assistant. This was because during this time I noticed that some students had difficulty with math while others didn’t. This made me realize that everybody has to start learning at different levels. Some students needed more attention and/or needed to work harder with their studying. My opinion on math changed when I noticed this and watched their test scores go up while they learned more over time. I enjoyed being a math tutor because while I watched my students progress they appreciated me helping. They thanked me and had a better understanding of math because of me. This made me enjoy teaching math and during this time my opinion on math changed.

Great observations! One of the hardest things (especially in math, maybe, but it shows up in other subjects too) is understanding where students are having troubles – especially when an idea seems perfectly clear to you! I try to think about this problem a lot. A good exercise in this class is to notice the places where you are confused or frustrated, take note of how you’re acting / what you’re feeling / what you’re doing, and then try to notice those same things occurring in your own students – it can help connect your own experience to theirs. Good luck!

-Prof. Reitz

This reminds me of the difference between learning a concept and teaching it. Sometimes we take certain ideas for granted but when we’re asked to explain them, we realise it was second nature to us and that we just ‘get it’. I’d say that if you truly understand something you should be able to simplify it and explain it to someone completely oblivious to an idea. Imagine trying to teach algebra for the first time to 1st year (7th grade?) students.

Incorporating the abstract idea of letters (or variables) into a language that previously exclusively dealt with numbers and operations is a good example. We take that granted now but imagine remembering our first time in learning that process again.

Thank you Hanan for reminding me of that.

-Ismail

very great story!I bet you achieved your goal because for many teachers and professors the main goal is their students to understand what is explained to them.Moreover,it is wonderful to have great teachers who make the topics more easy in understanding them.

I’ve had this exact situation before and at times it was hard to figure out a solution. It’s very important to know the difference between a teacher and a person who lectures. I realized quickly that I was a resource to both the teacher and the students and I could explain the little things that may not have been said or that may have not been understood slower and more thorough than the teacher and I saw a big impact on student grades.

Topic 2

Math knowledge is universal language that can be understood in many manifestations in real life. I realized when I was in Bronx Community College studying Electronic Engineering Technology as a major and later I could graduate , I always wanted to find out proves for that it is worth to know Math for future application. I discovered electricity can be calculated using integration such as voltage, current,frequency to know cicle for second of light.Phetagorian theory applied for resistance, capacitor and algebra to get a Gain in transistor. I became amazed that everything can be found exactly in Math based on Phisics.My perspective on Math have been changed because is not only memorize formulas mechanically , but the utility on problem solving to take care of humanity in having a better life quality.

Electricity is one of those subjects that I’ve studied very briefly, but it didn’t quite sink in – I’d love to take the time to study it more seriously, because the math is just beautiful!

Topic 1.

I always thought that my math was in a normal level.Not a bad level,and not extremly good.Even though that for my mathteachers I was their best student,who always got good grades,worked hard and who always came well prepaired in their class, I never had that feeling that I was the best because I never had any opportiunity to show how good I was in math,except for exams and homework which were basic works for every student.But,my mind changed while I was taking Calculus ll.From more than 20 students who were in the class,professor picked me and another student and asked us to meet him after class.when we went to his office he asked us if we want to be a math tutors for fall and spring semester.That was a big surprise for me,and I felt very good that it came the time to show how good I am in Math!

Violanda you need to be confident in your abilities that God have given to you because you have purposes to become a great Math teacher with a calm personality. You are a working hard woman and wise, so you have an exceptional future to help develop children with awesome minds. Congratulations!

Topic 1

Math for me was very inspiring ever since I started from elementary school. I have remembered one time when I was at the 4th grade, where my teacher assigns us to do multiplication tables starting from 1,2,3, and so on. I had to this homework every night and I got used to multiplying basic numbers without using writing or using my fingers. Division was also another interest that motivated me to become superior. As years flew by I had actually started to do some problems for myself to solve, like if I’m testing my math abilities and I felt very happy about my results. I felt very confident that I’ve became a tutor for some students that needed help on their elementary school work. It was a success for these students that it made me want to become a tutor for the future. Not only I want to make my students to progress their needs but I would want them to see me as their progress from a great tutor!

Topic 1

Math has been probably my favorite subject for most of my life. I remember when I had first moved to the states and had started 2nd grade I was placed in the lowest class. I gradually progressed from there and somehow ended up in a gifted class for the 5th grade. When they started teaching math in that class I was totally lost and confused. My previous classes had all these confusing ways to do math like breaking down and separating numbers in all sorts of confusing ways. When my new 5th grade class had started teaching multiplications I hadn’t at that point knew that when you multiply numbers you would add a zero before you start multiplying for the second row of numbers. I didn’t even know how to divide correctly. Everyone in that class who had previously been in gifted classes already knew but I didn’t. I was able to catch up even though I was behind at the beginning and got a 4 in math which was the highest you could of got. After that class I realized how easy math is when you get the simpler, quicker ways to multiply, divide instead of breaking things down which just confuses you completely. Math is always being evolved and manipulated and I will continue to study it since it has taken us beyond and above what most wouldn’t even think to be possible.

I think one of the hardest things is asking questions about the very basic stuff – especially when it feels like everyone else understands, but you don’t (this is hard no matter how far you go in math – it’s even true at professional mathematics research seminars!). BUT these are also the most important questions to ask – sometimes, clearing up confusion about the basic things makes all the rest of it fall into place.

Topic # 1

When I was in the elementary school, my favourite subject was history because it tells you stories. I wasn’t a big fun of math, one of the reasons was elementary school math being very basic, I was able to get good test scores without putting a very much offer and I did not depth understand Math at that moment. But as time went on, Math became a lot more interesting to me in High school. There is an expression, “the penny drops”, which means that understanding occurs in a sudden burst. Sometimes you are taught things in math and it may take years before the penny drops. I started to enjoy solving math problem in my second year of high school. Whenever I overcome a challenging math problem, it gives me a pleasure that I’ve never felt anywhere else. So, now math became one of my favourite subject too.

The feeling of the penny dropping is addictive, too – it gives you something to look forward to, which can help when things feel hard & confusing!

I know how you feel about enjoying solving challenging problems. When I was in high school it felt like I accomplished something and it felt pretty satisfying. Maybe because it had really great math teachers that kept me interested in the subject, so I can say that math is my favorite subject.

Topic 1

In my opinion for me math was repetitive for me from elementary and middle school. My opinion of math changed for me when I was in high school because when I got a job being a teacher’s assistant during the summer at first I didn’t know what to do. Later on in the job I was able to learn what to do from the teacher and was able to help the students with their classwork and homework. After doing the job during the summer that I had made me realize that I would like to become a math teacher in the future.

When I was in the elementary school, I was not a big fan of math too. I felt the same way like you did: repetitive and humdrum. I also started love math during the high school too, because one of my math teacher. I enjoyed to been in her class. she showed me that math is also a very interesting subject. And I realized that a teacher not only can help student get a good grade on math but also help them become more interest in it. So, I set myself a goal that one day I can to become a teacher can make more students interesting in math.

Helping teach definitely gives a new perspective – great!

One experience I had was when I was going through my bad kid phase in Middle School and I got sent to summer school in math evem though I excelled big time. When I hit the 9the grade, I was given the challenge of teaching special ed students which I completely accomplished but I was the transition that killed me. After getting sent to summer school, I doubted my self alot and I didn’t wanna even see math anymore, so one major obstacle was to find my love for it, and thorough helping others, I regained my love for it.

They say that in order to learn a subject completely, you need to teach it to someone else – and teaching has additional benefits, too, like helping other people.

Topic #2

I recently had an experience where I understood a topic that I spent last semester a little puzzled about. During my math education class my classmate Armando showed us during his presentation of his mini lesson plan, how he would teach students how to graph the area between two curves with the use of subtracting integrals. My performance in calculus 2 was horrendous due to my lack of understanding the majority of the topics.

The way he showed it by drawing on the board and explaining step by step in very simple language helped me understand the topic a little better, hence, furthering my understanding of a topic I had trouble with last semester. The way he did it explained the meaning of the formula in detail so there is no room for error.

I think the problem with some of these classes is that the professors sometimes assume that we already know the meaning of things.

I believe that I will be able to do problems like those now, and with lots of practice I will be able to explain how to apply the formula to similar problems as well.

It can be hard from the teacher perspective to remember exactly what it feels like from the student perspective – and, especially, to remember what it is that your students do and don’t know. Try to hold on to your experiences as a student – they will help you a lot in your future teaching!

Topic 1:

My view of math actually changed last year in calc 3. Since elementary school to high school math is my best subject. To me I thought it was just simple calculations and just memorizing some theorems. But then calc 3 hit me with all these new concepts and theorems that renders the stuff I learned in the past sorta “useless”. Like having the mindset of everything to be 2 dimensional is all gone and have to put the 3rd dimension into account (which was really difficult to me). Calc 3 wasn’t a breeze. But now I see math to be an extremely tough topic and I can’t be too cocky about my knowledge. I can say it changed for the better because it opened my eyes to this new world.