OpenLab #2: Mathography

This assignment is due Thursday, September 13, 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.

  1. 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.
  2. 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 writing – 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.  Example: if you know how to add fractions, try teaching it someone who doesn’t know how.  The second is called metacognition, 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.

23 Comments

  1. Junior

    Topic 2

    I’ve always been good at math and always learned quickly. I never really had to try hard or practice lots of problems to solve the question asked or understand the question. Then came along the semester I took calculus 2. I came in thinking it would be an easy class, after all I passed calculus 1 with little to no effort. I didn’t care much about the homework or anything. I could just scrape by right?
    The answer was, no. Before I knew it we were half way into the semester and i was failing. I had no idea what was going on in the class. It was only then I made the choice to go to office hours for the rest of the semester. My professor was really helpful and enjoyed helping out students in office hours. Through hard work and lots of practice problems, along with asking questions on how, and why we do this. I eventually grew to perfect my integrating techniques and was enlightened on how easy it cold have been. I feel like I can guide others on the steps to integrate and explain it very clearly now. I learned a lot from this major experience. Never leave everything to the last minute, always ask and look for help, and most importantly students learn mathematics best by doing homework and reiterating the concepts.

    • Jessie

      Yes! I agree 100%. I never understood when professors use to say “For every hour of math class you should be studying 2” until I reached calculus II. This was the first class that forced me to do math homework and I also learned that Practice definitely makes permanent.

    • Rachel

      I can relate to this so much! Calculus II was my first math class in college, and I don’t think that I was really prepared for how difficult it would be. (Calculus I was a breeze after all.) I didn’t have such a helpful professor as yours, but I definitely learned a lot of the same lessons, especially about doing the homework to practice the concepts.

    • Jonas Reitz

      I believe Calc II is the most difficult of the Calculus sequence (and I had a similar experience with it in college – the class is a challenge!).
      -Prof. Reitz

  2. jesstopal

    I hated math when I was in the third grade. One of the reasons I feel this way is because of my own experiences. I studied in Turkey, where education is very traditional. When I was in the third grade, my teacher called my name, without me having raised my hand, to solve a problem on the board. I still remember the panic I felt. My body froze, and my voice got wobbly because I did not know how to express my thoughts, so my teacher punished me in front of my classmates instead of explaining how to solve the problem. I was very embarrassed, started to hate math, and thought that I was not good at math. I always passed my math classes when I was in school, but I never paid attention to or understood the concepts because my bad experience had created unnecessary stress for me at school. However, when I came here, I decided to be a nurse. While taking a math class, I realized that I loved math; I did not hate it anymore. My professor had a passion for explaining things that I didn’t understand. I started to learn more about math, and I decided to be a math teacher because I like to teach, and I have a passion for teaching. Over the years, I have learned that it is important to embrace different learning styles because people have different ways of absorbing and processing knowledge, and a good teaching strategy should embrace these differences. My plan is always to make sure that all of my students connect the subject matter with real-life concepts. If they understand how something applies to them and why it is important for their everyday lives, they will be motivated to be attentive and learn.

    • Aleks

      I can relate to the fact that the teacher did not approach you in a way that would help you out in learning. There’s many different ways to go about teaching and there is not just one way to learn. I don’t agree that you should have been put on the spot but in the end you grew from it and growing is always good.

    • Danping Zhong

      I agree that teachers impact their students in different ways. Students like the subject or not really depends on if they like the teacher. Any one who want to be a teacher should know that teaching is not just a job. I’m so glad that you changed your opinion on math when you met a great professor.

  3. Aleks

    Answering to topic 1: Prior to starting high school I did not enjoy math. The topics started to become complex and the teachers style of teaching was not reaching me. I thought the next level, being high school, would be terrible. My first math teacher changed all that and I couldn’t believe why I could not do these prior problems. Math was explained with a different style and from then on my confidence in the subject increased and my past did not matter anymore.

    • Silvana

      I agree, there is a variety of teaching styles. However, once we find a teacher that can change it all, understanding the concept becomes much easier.

    • Samantha.C

      Hey Alex!
      A lot of people I know that struggle with math just didn’t enjoy it because of the teachers style of teaching it. I actually had a difficult time enjoying calculus 2 because of the style the professor taught made me lost and confused. But I gotten help from a tutor and then I started to feel much better about calculus 2. I truly feel that every student can enjoy math as long as it is taught in a way where student can enjoy it and still learn at the same time.

  4. Silvana

    Topic #2

    I had taken Geometry in high school and we were learning how to write statements and reasons to prove triangles. This topic became difficult for me because of two reasons. First, my teacher would use problems from the book and copy the steps without explaining much. Second, since I didn’t understand from the beginning, as we went on I lost track of what was going on.
    In my school we had two semesters and would switch teachers for the second semester. My new teacher was completely different. She would explain everything in detail, made us practice with various problems and offered help. The moment I realized I was fully understanding the topic was when I scored higher on a test than my friend. She would always get the highest score but she asked me to explain to her certain questions she did not understand. Because of my new teacher I was able to fully understand and help my friends understand as well.

    • jesstopal

      Dear Silvana,
      I think everyone can be a teacher, but not everyone can teach! Some teacher is choosing to the easy way and doesn’t want to put effort into their student’s learning. However, some teachers put their attempt to make sure that their students learn and understand everything. I am glad that you met one of that teacher in your life.

  5. Jessie

    Topic #2
    I Loved When I began learning how to differentiate in Calculus I. It was new , different and interesting. Then we got to the chain rule and I was LOST! The concept for every other rule was straight forward but with the chain rule multiplying the derivative of the outside function by the derivative of the inside function was confusing with out any organization. On occasions the difficult part was identifying the inside from the outside and when I finally got through with that part I would forget to multiply Because I was already flustered and just happy to have differentiated the two. Triple composition was even worse. One day I found the solution to my disorderly madness; organizing the inside and outside function by substitution. I never forgot to multiply the two again. The chain rule became one of my favorite problems to do that semester and I am confident that I can explain the concept to anyone at this point.

  6. Danping Zhong

    Topic 2.
    I like math since I was little, and it’s a fun subject to me. Every time when I solving a math problem, it’s like playing a puzzle game. It could be challenged, but also interesting. learning new math concepts is challenged, specially when it goes to high level math, because most of the definitions are abstract and confusing. When I learned a new concept, sometimes I didn’t understand at the beginning, but later when I did the exercise or homework, I suddenly understood. I enjoy the flash of understanding, and math is the only subject that gives me that feeling. In the proof and logic class, I also had one flash of understanding in day two. When I learned about the Cartesian product of sets, it seems simple when all the sets only have finite elements. For example, if two sets are containing finite numbers, the Cartesian product of these two sets is a set containing order pairs which is form by elements of these two sets. But when I did the Example 5 exercise, to find [1,2]x(3,5), I was confused at the beginning. How to find the Cartesian product of two intervals? It’s difficult by looking at the problem. But when I look at the definition of Cartesian product again, I suddenly notice that RxR=R2. If two sets contain real numbers, then the Cartesian product of them are order pairs. So I though one set can be consider as one dimension and the Cartesian product of two sets can be consider as two dimensions, and so on. Then I sketched [1,2]x(3,5) in x-y plane, and got a rectangle with two open sides as the solution.

    • Jonas Reitz

      We’ll be spending some time working on puzzles in this class, especially in the project, but also throughout the class. I also think of most math in terms of puzzles (maybe we should rename the homework problems as “homework puzzles”?), and I really like the satisfaction of figuring them out!

  7. Samantha.C

    Topic#2
    Mathematics from a child has always been something that I grasped pretty easily. You show me the steps to answer a problem and I can do it, no problem. But I never understood where did these math theories and formulas come from. Until I took professor Rojas class. Learning how to teach middle grade mathematics open my eyes to why math is so wonderful. One day at class professor Rojas asked why is that 4-10=-6. From what I was told back in middle school, is that you take the sign of the larger number. Which is not the correct; we learned about the zero property. If a + -a =- a + a = 0 then a and -a and -a are additive inverse or opposites of each other. When I learn the true meaning it made me understand it better. The activities we did to visulaize the additive inverse helped me see why we get negative numbers.I was truly amazed by this, because of how simple it was to get the answer for me, I still was wrong in knowing the true reason to why we get negative numbers. I feel more comfortable to teach the proper material to students but i also what to provide the profs in the theories and formulas. just providing them with these things just like I was won’t help them understand the true meaning of it all. Math is a powerful thing to learn and I think the more I learn to understand math the better I can teach it.

    • Samantha.C

      Want*

    • Jonas Reitz

      I am a big fan of asking “why”, and in a sense that is the entire purpose of this class, figuring out why the mathematics that we know works in the way it does. Great!

  8. Rachel

    Topic #1

    My love of mathematics began with learning how to count. I would line up all my toys and count them in different ways; four red toys, three Barbies, etc. When I got to school and started learning how to add and subtract, and later to multiply and divide, my love of math grew even more. We could use counting to solve a problem! However, in the third grade, my teacher passed out the class’s first ever timed test and I began to hate math just as much as I had once loved it.

    Timed tests became the bane of my existence. I’d never been good at memorization, and that seemed to be the trick to completing these quizzes. While everyone was flipping their papers over to show they’d finished, I was still working my way to the halfway mark, counting with my fingers or trying to picture arrays like I had been taught to figure out the multiplication. Eventually, though, these timed tests helped me to memorize the basics, something I had thus far been unable to do. After a few very stressful months I no longer needed to use my fingers to count or picture arrays, I was able to remember everything. I was completing the entire timed test like everyone else, and I was getting all the correct answers. The whole experience changed my view of math for the worse — I realized mathematics would require much memorization in the future. And to be honest, I still hate having to memorize equations or trigonometric identities. My love of math has since returned, thanks in large part to the teachers I’ve had who have helped me to understand equations, not just to memorize them.

    • Jonas Reitz

      I definitely sympathize with this. Although it’s true that there is some memorization required in math, it’s never been my strength either – I find that I remember things much better when I learn the concept (and then I can usually figure out the corresponding formula, even if I don’t have it memorized).

  9. yvan gohourou

    Topic#2
    I used to be really bad in math back in the day. I was struggling with derivative and integral when i was in high school *(I did my high school in France and we pretty much cover most of the topics of calculus I) ,and I had that feeling of doing things without knowing what they were used for. I used to think that I wasn’t built to understand math. But since I moved in the us couple years ago, I really became better. I found myself enjoying the classes that I was taking and my comprehension of the different concepts got better. I can do know problem that i did not understand four years ago and my opinion on math really changed.

  10. Jaroslav E Sykora

    Topic#1
    Math was always a kind of enigma and mystery for me to which I have been driven my whole life. I understood Math to be the purest science, the queen among others, the elevated goddess, the uplifted sage, unshakable and omnipresent. Although I got tons of Math during my HS-years [program of civil engineering], which, in theory, could motivate me to apply for studies of theoretical Math at a college in Prague, but when the time came, I decided to study Philosophy and Religious Science [finished with a PhD degree]. Moving to the US, the challenge to become marketable and earn some dough, made me abandon my “American dream” of becoming Prof of Religious Science in the New World, and focus on issues of the super real, American life. Thanks to God, the enigma of Math reappeared in my heart and brain, and I, finally, after looong time, began to study Math. It does not go that well anymore [I am too slow to get things and to old to remember the theorems] but I LOVE IT!

  11. Franklin Ajisogun

    Math has always been a part of me. When I was a child, my mom always gave me math problems to solve or a math puzzle to do. I remember one time that my mom got me my first toy and it was the rubik’s cube. I think this is the moment that I realized that I like math. Not sure why or how it happened but once I started playing with my rubik’s cube I was hooked so much that i was finding different way to rearrange and solve it again. Finding different ways to solve the cubes seemed like a fun thing to do.
    I can still remember my first attempt to solve the rubik’s cube. I would sit at my desk at home and develop methods to solving it and I also tried to visualize the various outcomes of certain moves. After weeks of learning, the rubik’s cube it began to make sense when I finished solving the rubik’s cube. Conquering a puzzle had never felt so

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