“When we label some students “gifted,” … what message are we sending the other kids—the “un-gifted” ones?” http://tntp.org/blog/post/when-we-label-some-children-gifted-what-does-that-say-to-the-others …
What does the Celsius thermometer show when it’s 41 F? Which approach do you prefer and why?
A circle sits insides a triangle which sits inside a square of side length 1. What is the largest possible radius of that circle?
What could f(4) be? How do you know?
5 Questions to Ask Yourself About Your Unmotivated Students via
Top 5 Learning Strategies to Master Math and Science
“Do not loose faith in our public institutions, our schools, because they serve the kids with the greatest need.” ~
Proofs are hard to understand, never mind teach. This week we read and discussed “Proof for Everyone” written by Eugene Olmstead. The trouble with learning proofs is sometimes students are not taught the right tools to understand them, let alone use them.
From my experience, I was not taught any rhyme or reason. Freshman year of high school, I was thrown into generalizing geometric proofs, which was the first time I even knew what a proof was. My teacher at the time kind of just did a bunch of proofs on the board and thought that was teaching us. In fact, he did it in so many different ways. I remember looking at my notes thinking to myself, “what does this even mean.” Needless to say, my test scores showed it. I was then terrified by the word proof until I needed to give it another shot in college.
There is a rhyme and reason to proofs, the problem is that every one has their own way of proofs. Some professors and teachers accept proofs when they are as detailed as can be, and others don’t mind if it’s not. What frustrates me is having to change the way to present proofs for each professor. There needs to be some sort of structure to follow and stick to it.
As far as this article goes, it makes sense, however the example throughout gets confusing when looking at the graphs and figures. But, I understand the point of it all.
This week we read the article “Produce Intrigue with Crypto” by Avila and Ortiz. We discussed how intriguing it is to students in middle school to learn cryptography. They are curious when trying to figure out messages rather than answers to formulas, however it can help with algebra. Using games, like cryptography games, help student engage more inside the classroom. However, it is difficult to do these activities with time restrictions and teaching restrictions. We also did our own cryptography that Professor gave us to decode. We also got into the discussion about technology and if it should be implemented in classroom activities as well as homework. My opinion on this is it should be. Technology is very important in our society, and world that we live in. Many college courses in various majors, as well as, job opportunities, require the use of technology. So to be exposed to it early would be beneficial in the long run since technology is just becoming more and more useful.
Lately, we have been discussing using multiple representations in algebra, which ties into how to generalization problems and the issues that people have with it. The idea that students learning multiple representations will enhance their abilities to solve algebraic problems is true, however, the question proposed in class was, how can this be done? Many students stick to the representation that they feel most comfortable with. It’s like trying to break a habit, it’s not an easy thing to do. This does propose an issue when trying to generalize problems.
In the article, “Developing Algebraic Reasoning through Generalization” Lanin provides an example and explains the strategies used to generalize it. But, the issue is that many students are not asked to generalize the problem and explain it the way they would do it, teachers look for specific methods when asked to solve a problem, especially by the way the problem is proposed. Problems are proposed in a way that students only see it in one way, so using multiple representations is out of the question since students generally use the method that works best for them, which is usually the first method they are shown that is successful. By presenting problems in a more general way will help lead students to generalizing it in multiple ways.
This week, I found this blog post very interesting, especially since I read some of Andrew Hacker’s excerpts. A lot of people, including me at one point in high school and I love math, found algebra useless in most cases, and still do. However, they only think of algebra in the way Hacker does, which is “the inane study of parametric equations, polynomial functions, and vectorial angles,” I really like the analogy used at the end of this blog about algebra relating to a chapter of a book.
This week, we read Teaching strategies for “Algebra for all” by J.R. Choike. I really enjoyed this article. Choike brings up very good points about the problems with teaching mathematics. For example, the point about eliminating complicated numbers and being more specific with wording. Confusing students right off the bat is not a way to help them learn the bigger picture of the idea or concept being taught. I can remember many instances in my education where I was confused by details in the way the problem was presented. Also, showing multiple ways or representations is important and making word problems relate to students in a way that they are interested in the outcome. Although it is done already in math education, there is never a connection shown between all of them. I understand all of the points Choike presents are difficult to achieve because of the restriction of time in each class meeting and also because teachers are pressured into teaching by the book and for the standardized tests. However, that means that something has to be changed in order to improve the math education.
I did not do much on Twitter last week. But I did comment on my first blog post shown below:
“I really enjoyed reading this. It is not everyday you hear a student wanting to do more math problems. The use of algebra in division is a great idea so that there are multiple ways to show how you can divide and students can choose which strategy works for them.”