Week 4: Why Teach Anything? The Point of Teaching Math

This week, we read an article and listened to a podcast that detailed much of what we read. It dealt with reason and sense making and why we need to focus on it. There were ideas of how to incorporate it into the curriculum, but the largest issue might be that reasoning is not something you can teach. It’s like the saying goes, “You can lead a horse to water…”. Making sense of problems and approaching them from a logical angle could work, but reasoning is a whole other creature.

In a perfect world, we  could insert reasoning and sense making without an issue. However, it is not a perfect world. They do bring up great points, and I think the main takeaway is that something has to change and the only way to kick-start that change would be for everyone to work together and address the issues at hand with regard to mathematics at the high school level.

There was one particular idea that I’m glad they brought up. High school students come from a variety of backgrounds. Every classroom is different, containing varying levels of abilities and students from different backgrounds. Some students, especially minorities, will be placed in lower level math courses under the assumption that they may not be attending college. Therefore, they do not receive the same opportunities to learn as another student in a higher level course. The idea of equality in the classroom in reference to obtaining the same learning opportunity is spot on. Otherwise, we will continue to perpetuate an idea of a “math type”. (Sort of like setting “math people” aside, continuing this idea that you are inherently good or bad at math.) Such attitudes need to be turned around, at least in my opinion. It is not fair to strip educational opportunities from anyone regardless of race, ethnicity, or socioeconomic status. Education is not an exclusive club.

I came across a post this week about why we should teach mathematics. Mostly, it was a conversation starter. The author gave their own reasons, but also inquired about other reasons from the readers. Mostly, I believe we should teach math for the sake of teaching it. I feel like we have taken a turn for usefulness. We only care about those things that are completely useful to us. If we cannot instantly benefit, then we don’t care. Learning for the sake of learning seems to be a thing of the past. For example, why do we read Shakespeare? Why do we read Huck Finn? Why do we read Frankenstein? Why do we read anything? For the pure enjoyment of it. For the culture that surrounds it. For understanding. The same thing goes for math. We should teach it because it offers another dimension to understanding the world around us. It doesn’t exist to torture unsuspecting students. We should teach it for the beauty of it. That may not be enough reason for some, but it is for me.

It really got me thinking about what other people might think about why we teach math. I think this question resides on more of an individual level.

Here is the link to the article, (with my comment toward the bottom):

http://davidwees.com/content/why-teach-math

Continuing with the equality idea, I saw a few things that I liked on Twitter dealing with gender bias in STEM classrooms. And, being a female in math, I agreed with many points. The most important part, though, was the fact that we think this bias is dwindling with our generation, but it is just as present. (And history repeats itself.) Though, I’m also inclined to be wary of the article, if only because it was a woman who wrote it. So, the article about bias is, potentially, biased. In any case, I present you with the article:

http://www.vox.com/2016/2/17/11030292/male-classmates-smarter-women-stem-sexism

I believe that is all for this week! Let me know if you have any thoughts!

 

 

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Week 3: Blog Comments & Tweets-“Would a Grade By Any Other Name Work as Well?”

Have we lost focus on the point of education? Series of tests, quizzes, papers, standardized tests weigh heavy on our minds. Many times we remember taking the test: “It was hard; it was easy; everything I studied wasn’t on the test; everything I studied was on the test.” An exchange of phrases whizzes by, the only remnants being a grade you file away in a folder that you may never see again.

Why is this important? When are we going to use this? Why do I need to know this formula? Why doesn’t ‘X’ solve its own problems? I have my own to worry about. Students are not the same. As individuals, we have different interests. Therefore, we value different things. We shouldn’t be expected to pursue interests that are not our own. Sure, being educated on basic concepts is a great idea, but ‘why’ knowing such concepts is a great idea is the question. Too often, the answer of why becomes getting good grades, because it’s on the test, you just have to know it, it’s on the MCAS or the SATs, and so on. There is no real purpose. There is no drive. Grades as motivation is a surefire way to burn out fairly quickly. Personally, I think it limits potential and creativity. Too often, we look for the instructor’s approval over our own thoughts and ideas. Reading people and giving them what they want is easier than thinking for oneself. I find that to be a huge issue.

What if we just trashed grades? ANARCHY?! No. Let’s actually think about it for a second. Maybe another minute. Grades are like trophies. Trophies serve as a ranking mechanism. Sonner or later, everyone will want a trophy. Trophies then become everything. Everyone gets one and the meaning of a trophy becomes tainted. What once meant to serve as a ranking system, a means of motivation, has become tainted like little league sports. Grades seem to be the only reason to do anything. It has become a threat. If you get a bad grade you will not get into a good college, unless, perhaps, you slip the interviewer a twenty under the table. Jokes aside, even if we don’t throw away grades, I think the whole system needs to be revised.

I read a few articles this week, but one in particular stood out to me. It was about grades and if colleges should stop giving them. I thought many points were valid and that it was a good idea to experiment with. There was a plan as well, and although it may have holes, I think it is a great outline for how we could work around and tailor a schedule to the student and their interests which they are allowed to explore with. Most students now do the bare minimum to pass, but what if they were given the opportunity to pursue their interests without being chained down by a major from day one. They might be able to find something that they love without being pressured to choose as soon as they are thrown into a college environment.

Anyway, before this gets too long, I think it is worth the read and offers some pretty good ideas that we could experiment with. No grades could offer an increase in productivity, creativity, and overall performance, given other motivators. (No grades does not mean no work. You still have to work hard to keep your place within a class. If you don’t want it, then you are in the wrong class.)

Link to Blog: Grades Post

Here is my post on the Blog: “Thank you for this post! I completely agree that grades need to be looked into. This seems like a great solution to something that I have lived through. Grades are the “be-all, end-all” for most students. Things would be much different if students, including myself, weren’t so focused on getting good grades over completely understanding a topic. I think this system is absolutely brilliant, and I would love to see it implemented at some point. It would be a great experiment. I think we have lost sight of what education is, and it would be a good idea to start revising the system to optimize learning. I truly believe that, if given the chance, students will find that motivation to explore and discover their interests on their own. It’s sort of like asking, “What would you do with a million dollars?”, except it’s, “What classes would you take if grades weren’t an issue?”. It is an extremely liberating notion for students. Granted, there may be some unforeseen issues with an ungraded system, but I see more merit in working hard for something and pursuing interests despite failure. In all, I think it would be a great idea to experiment with and see the results.”

Also, I had a few Tweets/ Retweets. I was mentioned in one about growth mindset, which you all should take a look at. Growth Mindset is a great concept. And I tweeted a few links about growth mindset as well.

I still haven’t quite figured out that copy and pasting deal with Twitter….so this might be the best I can do for now:

<blockquote class=”twitter-tweet” data-lang=”en”><p lang=”en” dir=”ltr”>More on Growth Mindset! Take a look! <a href=”https://t.co/b2yCSgQooP”>https://t.co/b2yCSgQooP</a></p>&mdash; Rebecca Pereira (@rpereira418) <a href=”https://twitter.com/rpereira418/status/698315809953869825″>February 13, 2016</a></blockquote>

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<blockquote class=”twitter-tweet” data-lang=”en”><p lang=”en” dir=”ltr”>I keep soming across &quot;Growth Mindset&quot;, and I quite like the idea. <a href=”https://t.co/IGT8W9hoxn”>https://t.co/IGT8W9hoxn</a&gt; <a href=”https://t.co/piBNZdIQpd”>pic.twitter.com/piBNZdIQpd</a></p>&mdash; Rebecca Pereira (@rpereira418) <a href=”https://twitter.com/rpereira418/status/697798428185722880″>February 11, 2016</a></blockquote>

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<blockquote class=”twitter-tweet” data-lang=”en”><p lang=”en” dir=”ltr”>Should colleges stop giving grades? <a href=”https://t.co/UyemyIbVj9″>https://t.co/UyemyIbVj9</a></p>&mdash; Steve Shea (@SteveShea33) <a href=”https://twitter.com/SteveShea33/status/696762880096600064″>February 8, 2016</a></blockquote>

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Week 2: Blog Posts/Tweets

http://www.nctm.org/Publications/Mathematics-Teacher/Blog/Focus-on-Learning,-Not-Grades/#.VrSzkAnPPfo.twitter

This week, I saw a few articles I really liked, but I want to share this one because I have seen and heard a lot of things related to grades lately. Also, in my experience, grades have been detrimental to learning. Personally, I just want to learn. I want to know everything. Realistically, that is not really possible, but I like learning for the purpose of learning. The first question in any class seems to be, “when is the test?”. When the test day nears, the question becomes, “what is on the test?”. Once answered, students are scrambling to cram only the essential test material into their brains.

In essence, they are not learning. They are studying those few problems only to forget them a day after the test. This is temporary knowledge.

Last semester, I had this really great professor for my course in Logic. He told us we would have three tests. He also told us that we didn’t need to worry about them. Not once did he discourage us. From week 2, there were help sessions. We did problems every class. Not only that, we had discussions on other topics related to philosophy and the breakthroughs that are occurring within the field, especially in relation to mathematics and physics. I enjoyed going to every class. Every topic built on the last. Memorizing the rules were not required, but we did them so often that they became second nature. On my own time, I would do the homework problems and familiarize myself with the operators. If I was unsure, I would ask the professor and he was always glad to answer the question. In a class with over 30 males and 3 females, I felt comfortable to answer questions and go to the board to answer my own question sometimes. (He would help if I got stuck.) Here’s the thing, the homework was not graded. When it came time for the test, I didn’t feel pressured. I knew everything I needed to know. He did not place emphasis on the test. He cared more about us learning and thinking for ourselves. He created the perfect environment for that, and I learned so much. Also, if you asked me to solve questions now, I could probably do them without much of a problem.

The whole point in what I’m trying to say is that grades should not be the first priority. Learning should be the most important part. Creating an environment in which learning can take place is very important. Practicing and making students want to practice on their own time might help facilitate learning. We should not emphasize grades as much as we do. I saw a post that gave mathematicians grades, and I couldn’t help but laugh. (I’ll find it and post the link below.) We need assessments, but not at the expense of grades and learning. Students will take the initiative if encouragement is thrown their way. I am willing to experiment and see how not placing grades on my students’ quizzes helps or hinders them.

Report Cards for Famous Mathematicians

I was also able to have a conversation over Twitter with another person that I re-tweeted, and I shared the article I read with him because it was related to what he posted. He tweeted the article out to his followers.

That’s about all for this week!

Week 2 Reading: What Makes it a Proof?

“The very function of proof is not to prove the obvious in order to meet some sophisticated and purely professional standards and goals, but to prove what is not obvious.”-Morris Kline

This is how most people are inclined to think, at least in my opinion. But, the question here lies in what is considered to be obvious. What assumptions are we allowed to make? Obvious varies from person to person, from audience to audience. What is obvious to a nuclear physicist might not be obvious to your everyday lawyer.

Most students, especially early on, are not typically strong with proof, (if I’m honest, I’m not strong with proofs either). This might be due to levels of exposure, or the fact that they might think certain things don’t require proving. Also, throughout the article, many of them believe proof is by example. They show an example, and there is the proof.

I think that might be a start. It’s like the basis step. For example, is what they are giving me even true for a few cases? If it is, then they can move on to generally applying what is given by using prior/existing knowledge and assumptions. I would have started by looking at a few examples and seeing some kind of pattern. Since the proof gave a hint, I would have started looking at the hint first, expanding it and seeing what it is telling me. Then I would have proceeded from there. These students all seem to have the same idea, but they don’t have a strong background in proof or even the basic concepts. (At least not enough to make the connections.)

As teachers, we should work on providing an exploratory environment where students can think and make connections. We need to give students more tools that they may be able to use in coming up with ideas. Create an open classroom focused on thought an interpretation and making the rules of the game clear. Explain what proof is. Explain different types of proof. Explain that math is connected and not this distorted group of topics that have no relation to one another. The goal is to make deeper connections, but the question is how, and I think more experimentation and research is needed on that front.

More focus needs to be on the student and their understanding and the article seems to fall short on explaining itself. Though, it does make some useful points and brings up an issue that students are having. Yes, we should analyze student work, but we also need to expand student knowledge and encourage deeper understanding through inquiry and study. With that being said, we might want to try to discourage teaching strictly for the test. Students will never learn if they study for the one grade and never go back to the material. Maybe we need a strong use of cycling within the classroom. So, go back to old topics and show how they might be connected to the new ones. Topics in the classroom are not isolated. There is a connection. And students need to see that. It’s like history. dates are chained together, and one event may be connected to another event resulting in this domino effect. Math is the same way. There are chains, links, between topics.

In all, analyzing students work is helpful and seeing where students need help, but applying that knowledge to helping students root their understanding in the best manner is the issue that needs more research. What ways can we help our students?