Comments for On Teaching and Learning Mathematics
http://blogs.ams.org/matheducation
Fri, 28 Apr 2017 15:50:12 +0000hourly1https://wordpress.org/?v=4.7.4Comment on Creating a Classroom Culture by Jacob Koczwara
http://blogs.ams.org/matheducation/2016/04/18/creating-a-classroom-culture/#comment-574
Fri, 28 Apr 2017 15:50:12 +0000http://blogs.ams.org/matheducation/?p=1229#comment-574I think this is a very insight blog post and I commend you for posting it. I believe it is extremely important to create a classroom culture at any level of teaching. It is of the utmost important to make sure students feel comfortable with their professors/teachers and are able to talk with them about the problems they have. A student will not be able to perform at their highest capacity if they don’t feel comfortable asking questions. This is a problem I’ve seen with a lot of my fellow classmates at my university. I see many of my fellow students struggling with the more difficult subjects and they are just unable to ask the professor for help because they don’t feel comfortable doing so. Thankfully I never have this problem because after my schooling experience I am completely comfortable asking questions when I don’t understand something but my fellow students always seem to have issue doing so. It’s sad when I see so many students dropping courses they need to take or failing a course just because they don’t feel comfortable asking questions about things they don’t understand. It’s such an easy thing to do for teachers to promote students to go to their office hours or go see the ta but I see only a few teachers who actually make the effort to do so or even try to make sure the students understand the material. In my opinion my favorite professors I’ve had are the ones who do put the time and effort into making sure their students learn and master the material and I appreciate those teachers so much more for doing so.
]]>Comment on The Inefficiency of Teaching by Jacob Koczwara
http://blogs.ams.org/matheducation/2016/09/06/the-inefficiency-of-teaching/#comment-573
Fri, 28 Apr 2017 15:41:02 +0000http://blogs.ams.org/matheducation/?p=1393#comment-573I think the biggest inefficiency in teaching at least at my university is that professors accumulate a set teaching style after teaching the same course year after year and never change their approach even if it’s not the best one. The professors rarely ever adapt their teaching style at all after years of teaching the same course. I have friends who have already graduated in my major and they have told me that the professors have taught the courses the same exact way when they took them as when I took them. I feel like this is inadequate. Professors need to adapt to the change in technology and new advances in mathematics. They need to adapt their teaching style to reach the whole class if they see most of the class struggling to understand a concept. I feel like the professors job is to make sure the entire class understands the concepts and is prepared for the higher level courses that the class they are teaching is a prerequisite for instead of just teaching the material and hoping they reach at least the smart students in the class. In my case I don’t have this issue because I’m always one of the smartest students in my class but I see other students struggling and I think it’s unfair to them. Especially at college where we are paying 10s of thousands of dollars to attend the university and take the courses I feel like the students should at least understand the material. I mean those students can just go see the professor during their office hours to be fair but some of the professors I have are intimidating and make the students not want to do that or don’t even go to their office hours which is extremely frustrating.
]]>Comment on The Second Year of “On Teaching and Learning Mathematics” by Jacob Koczwara
http://blogs.ams.org/matheducation/2016/07/11/the-second-year-of-on-teaching-and-learning-mathematics/#comment-572
Fri, 28 Apr 2017 15:30:45 +0000http://blogs.ams.org/matheducation/?p=1343#comment-572I like how you kept track of what happened while you were teaching. I think one of the things teachers fail to do in general is keep track of how what they are teaching, how they are reaching the students and interacting with them. I think it critical for any teacher who is just starting to keep a journal of what they think is going well, what they think didn’t work as well, and how they think they can improve. It’s crucial for teachers to do so just for their own improvement so that they can become better teachers. I think that when I become a math teacher I’m going to keep an audio journal on my phone. I plan on each morning when I drive into work talking about what I’m going to do, what my plans are for class today, and how I hope I can reach and interact with my students and in the evening when I drive home from work I’m going to make an audio log about how my plans went, what my plans are for tomorrow, and what I’m thinking about doing tomorrow. After each month I’m going to listen to the audio logs on the weekends and see how I’ve improved and what I still need to work on. I think this is important so I don’t get lost in the teaching process and so I can continually improve and become the best teacher I possibly can be.
]]>Comment on Proportionality Confusion by Dick Stanley
http://blogs.ams.org/matheducation/2014/11/20/proportionality-confusion/#comment-571
Fri, 28 Apr 2017 14:38:23 +0000http://blogs.ams.org/matheducation/?p=491#comment-571Thank you for your comments. Picking up on one thing you said, I have also long felt that it is important to make a rigorous definition of what is meant by a comparison. And I like the idea that it must be concrete. With this basis, students will understand the formulas better when they are introduced.
]]>Comment on Creating Momentum Through Communicating Mathematics by Jacob Koczwara
http://blogs.ams.org/matheducation/2016/10/17/creating-momentum-through-communicating-mathematics/#comment-570
Thu, 27 Apr 2017 02:09:15 +0000http://blogs.ams.org/matheducation/?p=1445#comment-570I think it extremely invaluable to discuss mathematics with younger students. High school level students that have an interest in mathematics but aren’t necessarily sure that’s what they want to do with their lives should be pushed towards the field. To continue progress with mathematics and expand our understand of the field itself and to expand our understanding of the world around us we need fresh minds and new perspectives. New students who are interested in mathematics are critical for this to continue. While the current mathematicians and professors are continuing to expand the field a large number of new minds studying and expanding the field would be invaluable. This is because with new perspectives we can continue to push the boundaries of what we know and what we understand. What we know and what we don’t know will be expanded with these new minds. We never know who will be the next Newton or the next Gauss. Young students and their minds are our most valuable resource to continue pushing the boundaries of the field of mathematics and if we can interest them in pursuing careers in mathematics that would be amazing. These able new minds might give us invaluable insists into our universe and the world we live in and that would be invaluable to the field of mathematics and the human race in and of itself.
]]>Comment on More Linear Algebra, Please by Jacob Koczwara
http://blogs.ams.org/matheducation/2016/09/19/more-linear-algebra-please/#comment-569
Wed, 26 Apr 2017 20:06:25 +0000http://blogs.ams.org/matheducation/?p=1406#comment-569I agree completely. While I went to an IB high school and took HL math so I was experienced with matrices, vectors, and imaginary numbers i.e. Euler’s form and imaginary algebra my linear algebra skills weren’t as good as my calculus skills. As a math major in college I feel like my education has been more heavily weighed towards calculus. I am a graduating senior this year and I have taken Calculus 1-3, Differential equations and advanced calculus 1 and 2. Whereas to this day I have only taken 1 Linear Algebra course and a Modern algebra course. I feel like this hasn’t prepared me as much as I wish it had for the field of jobs I want to go into. As a future data scientist I know Linear Algebra will factor in much more heavily than Calculus will. To be honest I wish we had had more mandatory Linear Algebra courses. While I feel prepared and am not struggling in my higher level courses I feel like some of my other classmates are. Not everyone has the strong mathematics background and so I feel like the rest of my class is struggling somewhat. Even in Advanced calculus sometimes I feel like I’m one of the few people who fully grasp the material and that the rest of my class is just nodding along in agreement. I feel like extra linear algebra courses would help in this effect and it would definitely help with taking Modern Algebra because while the courses isn’t extremely difficult it would be a lot easier if we were taught more Linear Algebra and if the prerequisite courses were more heavily focused. So in that respect we are in agreement that Linear Algebra should be more heavily focused in undergraduate mathematics degree programs in universities in the United States.
]]>Comment on If You Don’t Talk To Your Students About Math, Who Will? by Jacob Koczwara
http://blogs.ams.org/matheducation/2016/12/12/if-you-dont-talk-to-your-students-about-math-who-will/#comment-568
Wed, 26 Apr 2017 16:29:35 +0000http://blogs.ams.org/matheducation/?p=1558#comment-568I agree with your point. It’s imperative that teachers talk about mathematics with their students. It not only facilitates assistance for their students but it is also imperative to focus the students who want to pursue higher levels of mathematics to do so. Talking mathematics also like you said encourages students to think from multiple mathematical perspectives which is imperative for finding multiple solutions to a problem. In my opinion the more ways students know how to solve a problem the easier it is for them to master the material. Another issue I find with pursing a degree in mathematics is that I see many of my classmates struggling with the harder material and refusing to go and get help to understand it. It boggles my mind why they would rather fail exams and not do well in classes they are paying for instead of just going to ask for help. The professors I have had have greatly appreciated the fact that when I have a problem I go and ask them for help. It shows that I am taking the course seriously and that I am actively trying to master the material and do well in the course. I think if students are struggling to understand the material and they refuse to go to office hours or go get help for it, the teachers should offer incentives. Like for instance if they go and get help on material from the professor’s or TA’s office hours if they are struggling it would be beneficial to give them an extra point on an exam or on a homework assignment. Like you said students are human beings and in my experience human beings are most invented to do things because of rewards. They are more willing to go the extra mile if it benefits them in some way. I think it’s sad that most students don’t think doing as well as they possibly can in a course is an incentive but for those students I think professors need to put in that little extra effort. While it’s not mandatory for professors to do so because they obviously have many more things to be doing with their time I think the policy I stated would help motivate the students who aren’t doing as well as they could in the class to do better and to further succeed. The point I’m making here is that some students need to be incentivized because they simply don’t care enough. I believe it would be beneficial for professors to give them a reason to care besides doing as well as they can just to give the students who are lazy and don’t want to put in the effort the extra push to do as well as they possibly could. I believe the first step in this is like you said talking mathematics with the students and further increasing their interest in the subject matter.
]]>Comment on Integrating Computer Science in Math: The Potential Is Great, But So Are The Risks by Jacob Koczwara
http://blogs.ams.org/matheducation/2017/01/09/integrating-computer-science-in-math-the-potential-is-great-but-so-are-the-risks/#comment-567
Wed, 26 Apr 2017 15:51:48 +0000http://blogs.ams.org/matheducation/?p=1571#comment-567I agree completely. I believe that it is extremely important to integrate computer science with mathematics. It not only helps display and show the mathematical process at lower levels of mathematics course but it is infinitely helpful at higher levels. This semester one of the courses I’m taking is theory of numbers. In it we are learning RSA encryption using modular numbers. At extremely high numbers it becomes extremely difficult to use successive squaring to solve the problems. The fact that Mathematica, a math based coding program, allows us to use the PowerMod function to calculate these extremely large number modular encryption makes it so much easier to understand and do. I am also taking a mathematical inquiry course this semester which is why I’m doing this blog post in the first place. But anyways in it we are tasked with figuring out ways to further reach and promote mathematical skills in High school or lower level math courses. My idea which is the one you brought up is to use technology and coding. The ability to plot graphs and images I think makes it much easier to reach students. They not only get to listen as I explain the topic to them but they also can see images of the graphs to help them further digest the material. In my opinion the integration of computer science and coding is integral to the teaching of mathematics to further generations. It allows access to many more tools to help teach which is critical to the process in and of itself. The mathematical process must adapt and utilize all the tools available to them to advance and I believe this integration is key to doing so.
]]>Comment on Aspirations and Ideals, Struggles and Reality by Jacob Koczwara
http://blogs.ams.org/matheducation/2017/02/06/aspirations-and-ideals-struggles-and-reality/#comment-566
Wed, 26 Apr 2017 15:42:52 +0000http://blogs.ams.org/matheducation/?p=1610#comment-566I agree with you. I think one of the biggest things preventing students from pursuing the field of mathematics is they are afraid of failure and of making mistakes. One of the many reasons that I went to an IB high school was that I had the ability to take Higher Level mathematics. In that course over the two years of taking it I learned to not be afraid of making mistakes and being wrong about things. It’s part of life. Everyone makes mistakes. As long as you realize it’s a mistake and you try and correct it you end up learning more in the end. This had lead to a policy I apply to my college level courses. It’s okay to be wrong. It’s not the end of the world. It’s human and acceptable to make mistakes. This had lead me to actively participate in classes when I don’t have a complete idea of what we are discussing. I always try my best and give the best answer I can and if I’m wrong so be it. The fact that I still try even if I don’t completely know the answer shows my professor I care and I am trying. This is by far the most important thing. As long as you show your professors you are making an honest attempt they are much more willing to work with you and further explain so you can master the material. Which is critical to success in any field. Success doesn’t always happen right away and as long as you put the work in you will succeed. This has become my mantra and one that I am extremely happy to have.
]]>Comment on Six Ways Mathematics Instructors Can Support Diversity and Inclusion by Jacob Koczwara
http://blogs.ams.org/matheducation/2017/03/06/six-ways-mathematics-instructors-can-support-diversity-and-inclusion/#comment-565
Tue, 25 Apr 2017 22:28:01 +0000http://blogs.ams.org/matheducation/?p=1627#comment-565I completely agree with your ideas. The problem with teaching mathematics is that the students who take the courses are split into two groups. The ones that enjoy mathematics and take the courses because of their interest and the students that are forced into taking mathematics course to fulfill their major requirements or have to take the courses to graduate like in high school. The problem with this is that you have to find a balance between helping the students that want to continue with mathematics and push them forward in the field, and reaching the students who are only there because they have to be there. The trick is assisting both groups of students within the necessary time limit i.e. the semester or during class itself. With this in mind I really like your idea of varying mathematical assignments to reach the students who don’t necessarily want to be there. I agree completely that the best way to reach the kids who don’t want to be in the class is by varying the problems to reach their interests. It’s absolutely necessary to promote the mathematics process because whether or not the students want to admit it or see it, mathematics models into almost every aspect of life or higher education.
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