OpenLab #2: Mathography

This assignment is due Thursday, September 10, at the end of the day

NOTE: Normally, OpenLab assignments are due on Thursday at the start of class. However, Thursday, 9/10, runs on a Monday schedule, so our class does not meet.  Instead, this assignment is due at the end of the day.

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.

38 thoughts on “OpenLab #2: Mathography

  1. Trigonometry in general was a difficult subject and senior year of high school was when my perception changed. Basically for years our teachers taught us to memorize equations and concepts but you cant just memorize 50 equations throughout the years. This one teacher Mr. Schneider showed me where sin cos and tan derived from and how to always remember there values in both radians and degrees. He taught me about the unit circle and the whole “everything is over 2” trick. I believe I can explain the way he did to others, its a matter of how clear you speak.

    1. Hi Joe, I agree that being able to articulate yourself is an important aspect toward achieving the person’s understanding. I actually came across the “everything is over 2” trick after I had completed high school trigonometry and found in intriguing. What my high school teacher pointed out was that the values repeat and you could simply remember the order and find tan buy setting sin/cos. I actually taught an introductory to trigonometry over the summer and introduced the different ideas and tricks to the students in order for them to have different ways of understanding incase they forget or don’t fully understand one way.

    2. Trig was the math course that changed my perception too! I’m not sure what it is about that course. It just seems soooo much more difficult than other math courses. I rather take calculus again than have to do trig.

      1. Hi Sanaya1.

        My college years ended in the early nineties, or so I thought. My high school experience with trigonometry was long ago. Coming to City Tech going into a program with heavy trigonometry, I signed up for a algebra/trigonometry class.

        The teachers use a different method of teaching trigonometry now. They used a method called SOCATOA (I hope this is right). It was very confusing. I tried and when I did, much of the time, I got the sine, cosine answers wrong. Converting between radians and degrees seemed more difficult than I remembered.

        I went back and re-learned to draw and label the “Unit Circle” using radians and degrees, converting between the two. The teacher when sitting with me noted and agreed the Unit Circle is much easier, however, she said, “it’s old school.” You will show your age. She also noted I was using derivatives on the basic trigonometric functions making problems more difficult to solve than necessary.

        Returning to school after being out for so long, retreading in mathematics has been a challenge. I agree that the trigonometry at City Tech can be difficult. Relearning the Unit Circle made trig more fun and a lot easier.

    3. Hi Joe,
      This is a great example. I was just talking to a friend about the fact that I don’t have the values of sine and cosine memorized, even for “easy” angles – but I do know the unit circle picture, and I use it to figure them out as needed. Much easier than memorization for me – I’ve always been lousy at remembering facts!
      -Prof. Reitz

  2. Math among my friends is a very disliked subject. One finds it very challenging to have a hunch of number makes sense. Well I use to be one those students too, un till my opinion changed. I never liked math, I thought it was pointless. The main reason how ever was I just could not understand it. But then something happened. I realized in my junior year of high school that I was learning something, I was liking math. It was becoming quite easy for me, & that’s when I realized I loved math. To my more powerful discovery, I discovered that it was not my fault I could not understand, how ever that is sometimes the case for the students, but more importantly it was the teachers fault. I realized that before my junior year, I had not come across a teacher that can actually teach the lesson. My junior year teacher, he was marvelous! He made me and my peers understand everything. Further most, he taught us that math does not come easy. It takes patience and questioning. If one is not patient with a problem, they will not understand it. I learned that’s some problems, might look easy but in actually it takes trial and error. I learned also that questioning is the way to go. There are many formulas and part to math, so if one does not understand such a formula, ask-ask-ask! To really truly understand the topic being taught, one has to bug there instructor its questions to fully implement the topic. As the days went on after my junior year of high school, I kept falling in love with math. I fell in love with the simplicity of it, and the logical aspect of it. Hence, now I want to be the teacher that I had in my junior year. To change if not all, but at least one students mindset and opinion of math, like mine did.

    1. Rahat, I agree with your opinion about how a good teacher changes a student’s interest in that subject he or she is teahcing. From your experience, I think that when I became a Math teacher, I must make my lessons understandable so that the students could catch up with the course and love doing the problems related to math. Even though it is not an easy task, it is the path that every teacher has to go through. Students go to the class to learn, and it is teachers’ responsibilty to make them understood and transfer their ideas to students in a different and acceptable way.

    2. Rahat,
      I’m sure you are looking back on this experience often as you progress through the Math Ed program – I wish you the best in your journey to become a great teacher. You’re off to a good start.
      -Prof. Reitz

  3. topic 1
    When I was a freshman in high school, math was a most difficult subject to me. I passed all courses except math. I always got 55 on my report card. math was awful subject that kept pulling down my averaged score each marking period.I used to hate math at that time and it all blamed my math teacher, she was a worst teacher that I ever had. her lecture was confused.she always skip important material. during the exam, I see some of the problem, she never taught in the class. math had driven me crazy during the freshman year. I became a student that really didn’t care math and I finally give up.
    In my sophomore year, I loved math because I met a great excellent math teacher who really cared his student.he made me feel math is easier than ever.I can clearly understand his lecture. he changed my views on mathematics for the better. he was always reassuring students that math wasn’t hard and that we could get through it. That was first time I felt math was a super easy course. I believe when you’re good at something, you automatically become a fan. I strongly agree with it. nowadays, math become my favorite subject. That’s why I major in math education. I want to be a good teacher. I can’t say I’m very good in math but I can learn it and understand it easily. every time I struggle with math problem, I would watch YouTube video. In college, math become easier course to me and I got all A on my previous math class.

    1. Xiong,
      I love your description of the “excellent math teacher who really cared [about] his student” – I think the interpersonal aspect of teaching, the relationships between student and teacher and between students, are such a significant part of the process of teaching and learning. Great!
      -Prof. Reitz

  4. topic1: 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.

    I was raised by a scientist dad. Math was important and nothing made my dad prouder than to see A grades in all my STEM classes. I was in advanced math and was frequently bored. I complained that my math teacher let another student zone out in class and she kept calling on me every time I zoned out too. I decided in my senior year to not take AP Calculus but instead to take AP Statistics and Probability, a choice primarily to avoid the above mentioned teacher (I am an adult now I can admit it). I loved AP Stat and came home with the so loved A and top scores on the AP exam.

    Then I went away to college at Smith, in the engineering school. Everyone in my freshman class of engineers had taken calculus. They were advised to take calc to prepare for engineering. I was a freshman sitting in calculus based physics for 4 hours directly after I sat though 2.5 hours of calculus, calculus for the first time.

    My father convinced me that I was a math head and that I could do it! I frequently slept in late, or fell asleep in my 8am calc class (being taught by a 1st time professor a few years older than us in class). Being totally lost in calc class in the morning was bad enough but physics class was worse. I took physics in high school, but all the math in this physics class was calculus!

    It took me 7 weeks to actually speak up and find help. That’s after exams in both classes were returned with Ds. I had never gotten a D before in any class especially math or science. The whole experience of not just taking a while to understand the material but being truly lost was a humbling experience and has changed my approach with all my college school work since that first semester.

  5. It was said by one of my professors that, middle school is the point where one decides whether or not they consider themselves to be good at math and I fully agree with this statement. I was privileged to have great instructor for math in the sixth grade. This instructor was creative and assigned us projects we could work on in order to better enhance our abilities to comprehend the material. When learning transformations, he brought in mirrors as a manipulative so we could visually see the reflection the images cast over the x-axis and the y-axis. Another activity I remember doing was using bags of skittles and spreading the colors into groups. After this we tallied the amount number and constructed a variety of different graphs and tables using Microsoft Excel. From these projects I started getting a new perspective on math and developed further understanding. On the homework assignments, he would include a question that was slightly more challenging. One day he accidently assigned a challenging problem we hadn’t really gone over and I was the only one who had completed the problem. At home while I attempted to solve the problem I felt stuck but continued trying to come up with ways of solving it until I came to one final conclusion. To my surprise, I had successfully solved it and my teacher congratulated me. I felt invigorated and proud of myself for pushing myself and successfully solving the problem that my other classmates did not attempt.

    1. HI Irania, I agree with you it really feels good when you solve a challenging math problem, and it is true middle school where a lot of student start either to hate or like math, a lot of my friend gave up on math early, they would make a lot excused just to avoid solving a challenging a question. and good job you solved the challenging problem.

    2. I wish I had had your sixth grade teacher! It strikes me that the things you remember are the things that weren’t in the book – the mirrors, the Skittles, and so on. Keep this in mind when you are doing your own lesson planning – it’s very easy to fall into the habit of just “following the book”, but those extras that you add on your own can have the greatest impact.
      -Prof. Reitz

  6. I would like to talk about Topic#1. I started intern from Fall 2014 semester in remedial math at BMCC. I assisted professor with students’ homework assignment in class, also I helped some of them after class if they needed. The reason I think it dramatically changed my opinion of Math because it was really not easy to teach even it was a remedial math class. It focuses on real life problem solving, such as mileage of cars, dimensional analysis based on daily groceries like galons for milk, how to know if a person drinks one bottle of beer is allowed to drive under the law, etc. I remember the first semester I did not perform so well, and students kind of disbelieve my thoughts and rechecked my answers with the professor. I felt embarrassed when people refused to get help when I asked them. Then, I sat on my chair bahaved like I was also a student of the class. In fact, I was the tutor for them and was responsible for their questions. I was happy that there was a student who was already 42 years old and still loved study a lot. He had a hard time in passing the class, and he also failed once.
    Based on the fact that he had a job and it was a night class, I asked him to come earlier so I could help him with problems from the homework. I found that he got nervous and sweat a lot when he could not come up with a solution. I told him to calm dowm as he could avoid that problem if he could solve it before the exam. He almost came to see me every time before we went to class. I was glad that he told me he passed the class with 71. It was disappointed that some others had problem with the course, but he did not seek for help. Even though I was not the best one, I would like to do my best to help them.
    I learned a lot from the internship because it helped me understand how hard it is to do education but also how rewarding when I found a person could do better because of me. I could say all these due to my strong basis of math. That is how math changed me dramatically at some point.

    1. Dear Mei,
      I love your response. It has so many things that ring true to me as a math teacher. You’re right, it’s frustrating when people need help but won’t ask – and a big, tough part of the job is to keep finding new ways to encourage them to ask for help when they need it! Good luck.
      -Prof. Reitz

    2. Hi Mei,

      What a wonderful story! I like the fact that you help the student when he needed your help. I respect when I see people are helping each other. Three years ago, when I was a high school student and did not know how to speak english, I had received a lot of help from my teacher. By the way, I am starting an internship as a High School Teacher Assistant and your story helps me to recognize the experience and the responsibly that is expected from a teacher assistant. Thank you!

  7. Topic 1

    Trigonometry was definitely the hardest class I’ve had in high school. I found it extremely difficult to the point where I didn’t even want to class since I couldn’t understand anything at all. But then I found out about tutoring, I went there every day after class and ask for help. At first, I couldn’t understand anything no matter how the teachers explained it to me. But they were really patient with me, explaining everything over and over again in details. As I get more and more practice, I started to understand how to do the problems. They really helped me a lot. I would have never thought I would be able to pass the regent exam before going to tutoring, but I managed to score a 75 on the exam. I was really happy and started to like math.

  8. topic 2:
    bringing back memories, in my first year of high school we got introduced to the first degree equation with a single variable x, I remember everyone was doing good at math until we got to that equation. before that equation we were just doing addition, division, all other natural numbers operations and a little geometry. Introducing variable x in math confused everyone, student start to hate math but for me it was a different story I liked how we have to find that x, I understood the concept very well, I knew that we are just looking for unknown number who will balance the equation. unfortunately a lot of my classmates couldn’t process that transition even though my math teacher was really good explaining it. I remember he used an example of a scale he drew it in the board and start putting different weights units. he would put 5kg ( kg is the unit we use in morocco instead of pound 1k = 2.206 pound ) in one side and 2kg in the other side and asks how many kgs we have to add to the second side to be equal to the first side. it was really fun and creative. equations really easy if you know the concept behind and I think I will definitely explained to someone who he is a start up in math.

    1. I also tend to remember key mathematical concepts through images (like your example of weights on a scale) – I find they stick in my mind much easier than equations or numbers…

  9. Topic Number #1

    Generally all my life I have been good at math, or at least I would like to thinks so. For the most part, I always got an A in my math classes which led me to believe that I had a good understanding of mathematical concepts. Because of my success in my math courses, math became my favorite subject up until I took Trigonometry my 10th grade year. Between the teaching style of the teacher and the complexity of the topics, I couldn’t seem to get a grip on understanding the material.For the first time I actually began studying for my math exams. But no matter how much studying I did or how prepared I felt, when the results came back, my grades were always mediocre. My performance in this math course really made my confidence, as far as math is concerned, drop dramatically. I used to pride myself in being an excellent math student, but after taking that course it took a while for me to get my “mojo’ back. I reevaluated my career choice. It really took a toll on me and how I felt about my math ability.

  10. Topic 1
    If someone asked me during my Junior year what my opinion on math was I’d say I love math. I find it easy and fun in every way. Algebra, Geometry, trigonometry you name it. If you asked me during my senior year in high school on my opinion on math I’d say I hate math. It’s hard and not fun at all.
    That year I ended up taking Calculus I and II. A lot of new vocabulary was presented that I couldn’t comprehend as quickly as I did in my other math classes or any of the concepts. Instead of seeing 90’s on my test papers I was seeing 60’s. It wasn’t till the end of the year that I finally came to a better understanding in calculus and meeting the borderline of an 80.
    Now that I’m in college and surpassed this challenging moment I find math to be both fun and challenging.

    1. Great! Everyone reaches this point eventually (for me it was Abstract Algebra, a class I was not prepared for as an undergraduate) – but overcoming it gives you the confidence to carry on in the face of future challenges. Good job!

  11. Topic #1

    When I was in middle school, the most major subjects were Math and English. There was always a debate between me and my friends as to which subject is better. I favored Math over English because of its one definite answer. In English and writing, essays are your answer to a provocative questions. However, it’s usually graded upon how well you support and compose your idea. Then, there’s grammar, punctuation, vocabulary etc. I enjoy Math because of its simplicity. There is one answer but multiple methods. Even if you were given a seemingly complicated Math problem, you can break it down into a number of small and simple steps. That is Math’s greatest appeal to me.

    1. Hi Chen, I enjoyed reading your post especialy the “There is one definite answer” , this is true to me always favourated math over any other subjects similar to you but for me it was french at that time. when I was in high school in morrocco we had to write essays in french and it was chalenging because there is no definate answer like math.
      And yes math problems can be break down in to steps and thats the beauty of it.

    2. I find this appealing also – it such a satisfying feeling when a complicated (impossible-seeming!) problem gets broken down into pieces, and I see how I can find my way through each one. Great!

  12. Topic 1.
    When I first taken MAT 2572 Probability and Statistics I, it was one hardest math class I ever taken in my life. I was struggling in the beginning trying understand logic behind some these situation we given. The hardest part is professor I had didn’t go by textbook telling you use formula, he wanted everyone learn the chart in finding probability. So basically your fail safe textbook not going help you earn your medal in this class. One day I got home, I went over the notes that I copy from board and try like what call reverse process to figure it out and backfire nothing make sense. I was staring at the charts that professor did about pulling red or white ball from urn, then realize those number were sequence if probability for pulling that color ball. the given information for chart was like “Pulling three random ball from urn that have 3 red balls and 4 white balls with replacement meaning you return ball back into urn to draw again. What probability drawing a red ball out of those three balls. ” The one three ball with sequence white, white, red; so order numbers “(4/7) (4/7) (3/7)” for probability, because the whole urn only had 7 balls and drawing from it so if pull white probability pulling white ball is number of white balls divide by total number of balls in urn and since there was two white meaning you have two “(4/7)” this also same case for red ball “(3/7)” is number of red ball divide by total number of balls. This wasn’t finish part you had taken the factor of when you may pull red ball, so it mean if order changes like “(3/7) (4/7) (4/7) or (4/7) (3/7) (4/7) and one given (4/7)(4/7)(3/7)” meaning we had 3 combination so multiple 3 onto our number so have “3(4/7) (4/7) (3/7)= .419 or simply 41.9%. After discover this was what it meant, my understand what happening in situation for these problem and simply logic and math increased. So that experience learning Probability and Statistics, I wish luck and do your best when taking that class.

    1. Probability is full of strange and wonderful things – I’m always surprised at how simple (and obvious) things turn out to be wrong! And complicated things turn out to be simple at heart. I highly recommend this subject – it keeps you on your toes.

  13. Topic 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.

    When I was in second grade, I was sent to a boarding school where I was not taught any math. I only studied Quran for four years staying at the school. Then, I was registered in six grade by skipping the Third, fourth and fifth grade. I saw a new language of Math which I never learned. At the first year, my math teacher tried to help me to understand the math and solve the problems, but I was unable to understand him clearly. Math became the major problem for me. I started to do worst and worst in the test. When the final test arrived, I could not pass the test and neither the math class.

    But, the following year, I had the most incredible math teacher. His name was Abdul Malik. He explained the math very clearly and creatively. I started to understand the math and solved the problems. As I solved the problems, I felt the joy inside and started to like the math. I began to do well in class and finally passed the math class.

    1. There is a common idea that math is like a language, and it has some truth to it. It definitely becomes unfamiliar when you don’t practice it! But it’s satisfying to find that practice allows you to make progress, even in the most difficult problems. Congratulations on your persistence!

  14. My answer is a combination of both 1 and 2.

    As a mid-career adult, one who spent close to 1.7 decades in the professional world, it’s hard to remember when the “math light-bulb” lit up. When I was in High School, I was in an honors Math Program with a course outline of Algebra I & Geometry; freshman year, Algebra II & Trigonometry; sophomore year and Pre-Calculus junior year.

    Attending school in a southeastern state town, black students were not expected to excel in mathematics. My mother made sure I took the appropriate math classes to give me an entry into college.

    I took Calculus I and Calculus II in my Freshman Year of college (as well as calculus based Physics I along with Chemistry I and II), and it was difficult. I took Calculus III during my third semester, and I couldn’t believe how simple it seemed after the 1st two courses. We used Larson, Hostetler and Edwards, (math teachers at City Tech say they are best), the most difficult problems were always part of the assignment, and variations of those on our test. I was happy to get Bs in I and II, but thrilled to get that A in III.

    I transferred to a major southern institution and encountered non-english professors for the first time in courses like topography, advanced algebra and the dreaded differential equations. Speaking dialects of the all non-American professors (who excelled at Math) made the coursework extremely difficult. I survived and upon exit, was hired into the Engineering Management world into Project Management.

    Now, I have spent time in the Engineering Management Field. Some of my assignments have been in Chemical Manufacturing, Environmental Cleanups, (Investment Banking) Technology, Aviation and Mass Transit. These were all design projects when finished are usually constructed if financially feasible.

    Currently, most Engineers are foreign nationals in the United States. Project Managers are the go-betweens between executives and the pure science technical engineers and designers. As an assigned PM specialist, it was my my job to explain (logically break into work packages, assign time and money as well as graphic curve explanations using sequel based software) to executives the technical pure science material.

    I am grateful for the difficulties in understanding the dialects in addition to the difficult concepts. For my time in industry, comprehension of pure science to discuss in basic english is an art that must be mastered. Without the experiences dealing with foreign nationals, I am sure I would not have had the great career experiences I’ve encountered.

  15. I remember very vividly in high school being bored one day in my pre-calculus class. The teacher was writing something on the board and instead of paying attention I started playing with numbers in my notebook, looking for patterns. I would do this frequently with dates and times of the day, just trying to find a way to relate all the numbers to each other with math. The teacher had mentioned odd and even number earlier in the period, so I was just playing around, grouping odds and evens together. I then started adding odd numbers together. I found that adding the consecutive odd numbers starting at one gave us the consecutive perfect squares. I thought this was the coolest thing in the world.

    I was incredibly proud of myself and immediately told my teacher when the bell rang. He wasn’t even upset that I was daydreaming during class. It was the first real discovery I made in mathematics. I have always enjoyed math, along with other subjects such as poetry, but this was a new feeling of pride and accomplishment. I felt this way because I had discovered this on my own, without any direction from someone else.

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