If mathematics is language that we use to describe our world, then we should not be surprised when it pops up in arenas other than the explicit study of math. Consider a time that ways of knowing you employ in your math studies came to bear in another realm. First, extract a knowledge question from the math moment, then explain how that math knowledge intersected with another area of your studies, and wrap it all together by applying the knowledge question to the other area of knowledge and answering the KQ. Consider why the answers may be different in the two different situations, and how different perspectives change the knowledge. Please post your response by the end of Sunday 10 July.
Here's a great old number to help you get in a mathy mood: The Magic Number
By taking Cornell's Robotic class, I am feeling how useful math is now. As a class, now we are learning to use Arduino to do some coding; for me, it is all about memorizing the codes, but there are some tricks in there. 1024, for example, is using in code [analogRead(pin)].Because 1024 is referenced with ten binary switches. I am not a math person, but some stories related with math can easily attract me. Thus, this fact let me think if studying mathematics is bias where emotion and sense perception are tightly bonded.
ReplyDeleteThen I realized that the science class that I am taking-Chemistry is just corresponding with math. I do the same calculations, but seem indulge with repeating calculations and memorizations. For me, I feel it is fun and easy, therefore, I don't really like math and chemistry, but I don't hate them. So I know both math and chemistry mediocrely. To answer my question, I found not biases in studying in mathematics, because as learners, we are all unique.
In mathematics, I primarily use memory and reasoning to solve problems. One example was when I was using the discriminant in order to figure out how many roots a quadratic equation would have. In order to recall which answer of the discriminant equation would code for how many roots there were required memory. The answer was 0 and that meant that the quadratic equation had one root.
ReplyDeleteKQ: How can memory be used as an aid to reason when understanding mathematical knowledge.
This situation ties with one moment in my science class. We were learning about processes in cell respiration. We had to act the process out in class. My part was to explain that oxygen is the last electron acceptor. I had not prepared fully for the presentation but I remembered that oxygen was the terminal electron acceptor and led me to reason that oxygen was a strong oxidizer and will take in electrons easily so that cell respiration can continue. It is evident that my knowledge of one thing led me to reason even further. The knowledge question is applicable to both areas of knowledge and both, from my opinion, require memory to understanding that content and reasoning to solve, analyze, or investigate that problem.
The ways of knowing I use in my math studies, are memory, reason, sense perception and intuition. While being faced with problems to solve, I use memory to remember what I have learned and apply this to the problem, reason to see if i think what I am doing is right, and sense perception to see the problem. KQ: How does reason affect a knowers ability to solve a math problem? This ties into my science class, which I have noticed involves a lot of math, and I use the same ways of knowing in both of these areas of studies. Back to my knowledge question, reason has affected the way in which I respond to a prompt in my ESS class. The reason I use shapes my answer in many ways. This is both good and bad, because my reasoning could be correct as well as very incorrect, so reason inevitably decides wether or not I am right or wrong. This knowledge question although was initially targeted towards math, could be used for both of these areas of knowledge due to the fact that reason is being used in both of these knowledge areas. And for both of these areas of knowledge, reason affects the way you solve a problem the same.
ReplyDeleteIn order to solve a math problem, I use memory, intuition and reason as ways of knowing. Being a person who tends to memorize things, I rely more heavily on memory than the other two. KO: How can memory as a way of knowing aid or hinder a knower's ability to correctly solve a math problem? While being able to remember past solutions to or steps from past problems similar to a math problem can be very useful at times, I find it more of a hinderance as memories tend to change over time and the information recalled might not generate the desired answer when applied to the new problem. In German class however, the art of memory as a way of knowing and memorization in general comes in much more handy than it does when solving a math problem. Since German is less exact than answers in math, not remembering exact steps to exercises is less of a problem. Therefore, only using memory as a way of knowing is much more of a hinderance in mathematics than it is in German class.
ReplyDeleteI use reasoning and the intuition as ways of knowing when I study math. In IB math, I did a research on the correlation coefficient which is an unit statistic that measures the strength of association between two variables. Before I calculated association between the value A and B, I used my intuition and predicted that they are not strongly associated. However, when I checked my assumption by reasoning, I realized that I was wrong. KQ: To what extent, using both reasoning and the intuition as ways of knowing make one’s knowledge certain.
ReplyDeleteNow I’m attending to a summer camp where I’m studying globalization. When a professor asked me what I think is the effect of the open trade to a country’s economy, I answered that it can potentially hurt it. Because I thought that people would buy cheaper products imported from other countries more than the domestic companies’ products. However, the reasoning supported by a graph and statistics proved that I was wrong.
In both math class and globalization course, my thoughts lead by intuition were wrong, and that were proved by the reasons. However, I actually think that these different thoughts make my knowledge more certain. It is because admitting that I’m wrong gives me a huge impact and makes me think more about the reasons. Predict knowledge by intuition and correct it by reasoning is a great combination to make the knowledge certain.
Memory and reason have always played a key role in my mathematical learning; my memory retains many important mathematical rules/equations that I can apply to solve problems. For example, when I did an ACT practice test, I encountered a logarithm problem that required me recalls what I had learnt last year. In this moment, my reasoning was extracted from my memory of previous lessons. Although my reasoning in math is always obtained from factual evidence, I wonder what the difference is between a knower accumulating reason from personal experience versus factual evidence. Chinese and math to me are similar in the sense that they both involve my usage of memory and reasoning; in chinese, likewise to math, I use my memory of factual evidence to build upon my reasoning. Chinese also has many rules: the order of a character stroke, tones, grammar etc; these are all rules that have existent long before my life and are not tangible. My understanding of the chinese language is derived from its historical make-up and hence is the foundation to my growth in chinese. Chinese, however, has always been significantly easier than math because it surpasses math with emotion; to me, the more ways of knowing are involved in my education, the more knowledge and tools can be absorbed in various ways to make this knowledge more impactful. In chinese, we often learn poems to expand our vocabulary and enhance our sentence structures. As these poems have very profound meanings, we associate many of the emotions triggered with characters; as a result, not only are the characters in our memory for future reference, but they are engraved by the emotion attached to them. Finally, in regards to my knowledge question, I often try to look at the poems differently to see how different sentence structures affect the emotional effectiveness of the poems. In all cases, the correct sentence structure always has the most powerful emotional impact on me, thus leaving its mark in my memory which will be easier to access for future reference. In this way, evidence from personal experience is more profoundly engraved in my memory as a result of its emotional richness, whereas factual evidence exists more superficially in my memorization.
ReplyDeleteMemory and reason have always been important for me in my math studies. This year in math I memorized the formulas for circles and spheres it was easy to memorize these formulas because I was able to see why they worked using reason. When I was taking the ACT, during the math section I used memory and reason to solve the problems on the test. KQ: In what ways can memory enhance mathematical knowledge? This year in Biology we had to use math to figure out conversion of measurements with magnification. Because I was able to memorized the the conversion patterns it was easy to solve the problems. Memory enhances mathematical knowledge because you are able to recall things that you have already learned and apply them to other equations and problems.
ReplyDeleteReason and memory are the primary ways of knowing I employ in my use of mathematics, as they are key in the understanding and application of mathematical principles. However, I also find that emotion plays an important role in my attainment of mathematical knowledge: my curiosity to know more or to understand drives me to learn. That being said, the main thing driving me to do math is usually school, but my own curiosity is still always present. I wonder, how great a role curiosity as an emotional way of knowing plays in my ability to learn mathematical knowledge. When I was studying the mathematics behind the RSA encryption method for a class project, I was able to process a large amount of new information in a fairly short amount of time (a time period that was of course not shortened by my great skills in procrastination, that most definitely played no role). I believe part of the reason I could do that was that I was naturally curious about my topic; I had the desire to know it and hence the emotional portion of myself as knower was open to the attainment and retention of this new knowledge. This is true in other areas of knowing as well, in fact all of them. For example, in literature if I am reading a book my curiosity to understand the characters and the rest of the plot drives me to finish the book and acquire that new knowledge. Yes, I can still read the book if I am not curious about the ending and have no interest in it, but I would argue without this base curiosity not only will I complete the task much slower but I will not retain the majority of the information. I believe curiosity as a way of knowing is a fundamental component in the majority of the acquisition of new knowledge, not only in math but in all areas of knowing.
ReplyDeleteI always use my memory, intuition and reasoning when I study math. I usually use my own reasoning combined with memorized formula when I solve a math question. One I was doing a math problem during in math class, I used my own reasoning which was a little bit different from the teacher's way. It made a lot of sense to me, but the answer that I got was wrong, and the teacher told me that my reasoning is wrong. KQ: To what extent can one's own reasoning affect one's accuracy when solving a math problem?
ReplyDeleteWhen I do ACT readings practices, I also tend to use my reasoning to choose the answer that seems correct to me. However, I always choose the wrong answer, because I "think too much". I always use reasoning too much while the question is only asking for a little.
During both of these situations, my reasoning led me to the wrong answers. However, they are kind of different. For math, to a big extent can one's own reasoning affect their accuracy when solving a problem, because people's own reasoning can lead them to different understandings of the question and the ways to solve it, and these are the keys to solving a math problem.
Meredith writes:
ReplyDeleteIn my opinion, Chinese and math are very similar in the ways of knowing a knower must employ while studying these subjects. While in math class, the two main areas of knowledge that are in use are memory and reason. I must use my previous knowledge in my memory to draw on while learning new material. Along with having to memorize new formulas and concepts constantly in order to further my progress in mathematics. Secondly, I use reason to grapple with complex mathematical concepts and know if I am doing the problem correctly. This begs the question, how does reason and memory affect a knower's ability to solve a math problem. The study of mathematics has always been similar to the study of Chinese for me. The knower must memorize characters and sentence structures in order to be able to speak and write proficiently. Additionally a knower uses reason to understand whether the words they or a peer are speaking or writing is correct. Clearly, Chinese and math are two very different subjects so while math is much more analytical and has one correct answer, Chinese more often has several different answers.
I always use memory and reasoning as ways of knowing in math. There are always a lot of formulas that I need to memorize in math. During school year, I found it easy to memorize those formula because I can understand them using reasoning. In contrast, when I was preparing for SAT math subject test, I had to memorize some formulas that I didn't learn. I found it hard to memorize, because I can't understand them through simple reasoning.
ReplyDeleteKQ: How does reasoning and memory affect each other？
This also happens to me a lot in biology. When I was preparing for the final exam, there are a lot of metabolic process that I have to memorize. Once I understood the process, it was much easier for me to memorize those process, and details. Therefore, reasoning can significantly help a knower to memorize knowledge, and memory provides the basic evidence for a knower to reason.
I went to a restaurant with my friend last year, and it was one of the first times I had gone to a restaurant without my parents paying (I know it’s pretty pathetic). So my friend and I figured out the bill and split it. She then placed the folder thing upright and in response to my confused expression, explained that it was a signal to the waiter to take the bill. Seconds later the waiter swooped the bill off of the table. Incredible right?
ReplyDeleteThe next part was trickier though, we had to figure out the tip. This has always been an area that has confused me. My equation is give 15-20% of your bill, but what if the waiter was rude? Or if they screwed up the order or if the wait was too long? In this situation, it was all three of these circumstances which made the tip figuring come complicated.
KQ: How is understanding and application of a mathematical system affected by mood and emotion (Situation)?
In this situation, the simple equation: .15 * [bill] = tip was clouded by negative feelings surrounding the experience. We still ended up giving a tip, it was just not 15%. So apparently, there is a qualitative direct relationship in place: if the service is great, then the tip may increase from the set amount, but if it is subpar, then the tip may decrease. However, the nature of emotion is that it is impossible to quantify and predict results because every person and situation is different. Other people in the same situation may not have reduced the tip, which suggests an alternative answer to this KQ, that mathematical systems are not affected significantly by emotion.
The answer to this KQ would change again, when placed in a situation involving culture (indigenous knowledge systems), because if this situation took place in India, there would be no tip given. I can point to multiple outings which I can remember that there was no tip given. Therefore the answer to the KQ would be that mathematical systems (only the bill) are not affected by emotion. At the same time, there may be some Indians who tip waiters, and this would change the answer to this question within this situation also: mathematical systems can be affected by emotion.
Three ways of knowing that I know I use both during my math studies and in other situations in the real world are memory, reasoning, and faith. When solving math problems, memory is used after trials of repetition when doing math problems, reasoning is used to figure out which method would work best in order to answer the question, and faith if you try to find other ways to solve a problem that is not standard. KQ: How can memory and reasoning limit the amount of faith a knower can use in order to solve a mathematical problem?
ReplyDeleteI remember the first time that I took the train on my own and had to use the three ways of knowing that I listed above. I had to use my memory to think about how I used to get around the stations when I was with my mom. I used reasoning when I had to decided on which train would be smarter to use to get to my destination and where I should sit that would not put me in an uncomfortable position. I used faith to believe that I would make it home safe and that nothing extreme would happen during my journey. My ability to use faith in this situation was limited because which the strong memory I had of using the train system with my mom, I was more focused on the process of getting to and from home. Also, using reasoning allowed me to keep myself out of immediate danger and uncomfortable positions.
This would be a different case if I had no memory of traveling in the subway with my mom because it would then be a new experience and I would have nothing to look back to for references, so faith would play a much larger role as I would be using that almost completely.