This assignment is due Thursday, September 14, 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*

A time in life when I realized that was important was when I realized that math is about more than numbers. My 6th grade math teacher explained to me that math is a very systematic subject. It strengthens your logical reasoning and analytic skills.

Once I realized that math was just a form of critical thinking, I realized that those skills are necessary not just for school but for everyday survival. That changed how I viewed math and the importance of learning it for life.

I love your story, Zaniya. The intention of this class is to highlight the logical reasoning aspects of math – hold on to that idea!

The relationship between math and critical thinking can never be overstated. Fomenting the ability for critical thought in a child should be a high priority for every teacher. The fact that you understand this important relationship should help to make you a more effective teacher.

I am glad that you feel the same way like I does. I also believe that math is related to our everyday life. We solve math problem by logic reasoning, critical thinking, if one way is not working we try another way. That exactly what we does in our everyday life, Solving problems !

A time when my opinion of math dramatically changed was in freshman year of high school where I realize I had a passion for math and was able to help my classmates. During my freshman year, I realize that what you learn in elementary school through middle school, you take what you learn and build up your knowledge in math. Math is like a puzzle to me since your able to solve it in many ways. But you just have to find what works best for you or how you could remember how to solve it. I noticed that not every student in my class find math easy like I do. High school year is where I saw that some students had difficulty with math, but there’s other who didn’t. There were some many students in my class that needed so much help because they just didn’t know what to do or didn’t understand how they remember everything.

Once I finish my classwork, I would go around helping my classmates with their work and answering questions that they had, since my algebra teacher wasn’t able to get to every student. So, I would help her out. I would show my classmates ways that helped me remember what to do and/or ways that I found easy to solve problems. As the school year goes on, my classmates would thank me for helping them since they were now able to understand math more because the way I showed them made it easier for them. Honestly, I wasn’t good at math when I was young, but as I go older I started understanding math more. Which helped me changed how I see math for the better. And now, I know that I want to teach math to inspire, motivate them and show my students not to give up.

The topic I chose to write about was the second one. When I was in third grade I could not master adding fractions. During third grade, I was battling with personal problems at home that made me miss a lot of school days thus missing valuable information. So when I came back to school, we were in the middle of learning to add fractions. I had never seen fractions before so nothing seemed to make sense in class. It also didn’t help that my teacher would yell at me when I didn’t understand what was going on. It wasn’t until when my second teacher (I had two teachers in my class) took the time to teach me the concept from the beginning. She used pie charts and other diagrams to demonstrate what a fraction was and what was the purpose of it. From then on, she began to build on the concept of a fraction. She demonstrated how to add fractions by illustrating each fraction. After each session, everything seemed to connect. Using diagrams and/or drawings to explain a concept is definitely helpful for students, especially if there are visual learners. If I were to teach this concept to someone who was struggling with fractions, I would definitely use some sort of diagram to help them visualize the fraction. It might help the student see the problems in a different way.

Dear Evelin,

Let me start off by saying that I could relate to teachers yelling at me and/or my classmates for not knowing a material. I feel like teachers shouldn’t be blaming students for not knowing something. I Love your little story, I didn’t really understand fractions when I was young too, but I do now and I hate it. But the ideas your second teacher used to help you understand fractions is something I would take with me, so I would have another way of teaching someone fractions, especially those who are visual learners.

Evelin,

I also relate to being behind on some subject material. I too often miss class because I have an autoimmune disease called Lupus. It’s so important to have those great teachers who take the time to work with you instead of just yelling at you to make sure you understand!

This story hits me right in the heart! I appreciate that, as a future math teacher, you already have a sense of empathy for the challenges your students face – this will certainly help you in the classroom and out of it.

I time my opinion for math changed was during my junior year. I have always loved math since Elementary School but like one of my classmates said I saw it as a bunch of numbers that combined together gave you an answer and I honestly believed that it would always work. And it did work until, I got to high school and was taking Trig. I think this is were my real passion for math came in. My 11th grade teacher made it a big deal for her students to see that math was a huge puzzle and when put the pieces together you would make a beautiful picture. And since then even though I have had difficulties with my college math, I always try to remember that math is a huge puzzle and every class I take is another piece to that puzzle that will eventually make a beautiful picture.

Awesome. Puzzles are the reason I love math!

Math is something I like even though I can’t even remember how, maybe it is something I loved since I was born. Math just turned to be my passion in life, although sometimes I got struggles with some practiced problems. However, these struggles built me up for better. I remembered the way my siblings talked about math like it was the horrible thing in the world when they saw me struggles. At school also some students had a negative perspective about math, and I usually told them that math was the same as all the other subjects if they wanted to succeed they needed to have the will to practice because saying that math was worse would not change nothing for them instead that would make it worse for them to understand and also to work on it. Their ideas did not stop me instead it pushed me to go further for what I want. For me math is the subject I can spend the whole day working on without having any problem, and I really enjoy doing the problems. I know it is something that will stick with me because I learn to know that as a human being I can never finish to learn in life, the more I learn the better I will be, and the more I will want to know.

I can relate to your story so much. I also had friends that were very negative towards math, but as you mentioned that didn’t stop me from working hard in math. Those negative comments didn’t stop me from working hard.

Miralia,

When I read your words, I felt you are talking from my perspective. I enjoy math especially if there is a challenging problem. I think we will keep hearing negative thoughts about math, but that encourages us to be math majors.

I choose topic number one.

The second topic

Since middle school I’ve learned many math concepts, but never go deeply into most of them until I started college.

“Pi” was one of these concepts that I have heard many times. I have learned pi is approximately 3.14. I knew it is related to the circle, but I didn’t know the kind of relationship until I started this semester. Taking this class-proof and logic- along with math education class (MAT 3011), I realized that pi is the ratio of the circumference of any circle to the diameter of that circle. No matter how big or small the circle is, this pi is approximately 3.14. That makes me more curious to learn math even though math is already my favorite subject since I was a little kid.

What I like about this is that important part is the connection to a simple picture – something everyone (even folks who lament their problems in math) have a good sense of. Mostly, math is simple once you understand it – but can be terribly confusing when you don’t. Hold on to this idea if you find yourself struggling – a simple idea like “circles” may be just around the corner!

As a MEDU student I always be aware of how people think about Math, By years of my observation I notice that Math is not favored by most of the people, And I did some research online. I found that Math is often right on the top of list of “top10 most boring class in the school.” People commend: “Something dies in me when I enter Math class” or “We should only learn the basics of math not function, factorials, polynomials… What for? I don’t wanna be a engineer so I think I really don’t need to study all thous useless stuff!”

I was shocked when I saw these comments, I start thinking what Math had done that makes it become the least papular class in the school. And if I become a teacher one day, how can I make sure my student does not feel something dies in them when they step in class, or how can I convince them that Math is useful you then they think?

With these questions I began to think back than when I was in the elementary school and start learning math. To be honest, I wasn’t a big fan of Math during that period of time. But I had a great math teacher, Because of her, I was able to keep my grade above B+. Unfortunately, when I start middle school I had to change my school, I remember that at beginning of the first semester with unfamiliar environment And unfamiliar math teacher.We start to learning more advance math, I felt that I am bout to go down. And I did after a while. Middle school math require us to memorize tons to formula. I have a bad short term memory. And It didn’t work very well when I was try to memory the formulas by write them dome hundred times in my notes book. So, I started to feeling that math is just memorization of formulas. And I am not good at that. therefore, I started to falling my math class.

I start fleeing that math is boring too, but because of the bad performance on my exam, My parents send me to after school. At that after school I met a great teacher call Kang. She showed me a different way of memorize that formulas, Which is understand the concept of the formula. In another word, if you son’t understand the connection between meaning and formula, you’r brain will not be able to see connections and you are likely to quickly forget what you have leaned. I feel so stupid that I was try to memorize the formula by sit at my desk and attempt to learn them without fully understanding the meaning behind them.

I start see the beauty of math, after I knowledge the “trick” ofit. Math is challenge but interesting. it is about logic reasoning. Which we need to use in our everyday life.when ever I successfully solve a problem make me happy and exiting. finally, I found the joy of doing math.

Lastly, I think math is like a introvert person, it not easy to become her friend, but if you spend some time with her and understand her. You will fall in love with her.

I love your final paragraph, Sonam. An introverted friend, indeed!

I agree with you Sonam, a that’s a very interesting story.

The best way to learn is to visualize and be able to clearly translate. Then you can derive the formulas instead of memorizing them.

Another benefit is that you will know your derivation may be more reliable then your memory.

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.

While taking math and science classes in highschool together… I saw the same techniques being used to solve a wide variety of problems. From that moment forward I wanted to learn all the different techniques.. Cause Each technique means hundreds if not thousands of applications.

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?

Once when determining triangle congruence I visualized the the angles and determined why certain properties such as SAS ASA have to indicate congruent triangles. If a single angle or side length is changed it changes the whole triangle. I believe this is very easy to show to others using a chalkboard or even a model of sides with hinges to demonstrate varying angles.