Math Teachers At Play #10

Welcome to the tenth edition of Math Teachers At Play blog carnival! Here with the heat of the summer, "less is more". We concentrate on teaching issues, but also get to "play" a bit with binary numbers, geometry, integers, and an optical illusion.


What's a math teacher going to do with Wolfram | Alpha ?

In case you haven't heard... Wolfram|Alpha is a new, computational search engine. And if you're a math teacher, you should be aware of it.

Collection of Web Freebies discusses Wolfram|Alpha as your Personal Free Online Math Assistant.

I wrote an introduction to Wolfram|Alpha as well. I feel it can both be a benefit and a drawback to math education - a benefit because it can free us from routine calculations, and a drawback because students still need to learn to do those, but how can you easily enforce that?

W|A presents a dilemma to math teachers... because it can solve SO MUCH. It can solve just about any routine type calculation in algebra 1 or algebra 2 or calculus courses. So what can a teacher do? Jason, The Number Warrior wonders how we can be Teaching to the Limits of Wolfram Alpha. In essence, should teachers strive to find problems that cannot be solved with Wolfram|Alpha?

What's a math teacher going to do with homework?

I have checked these answers 3 times and I think you got #10 wrong.
Photo courtesy of Vicki's pics
Another, an age-old, dilemma for math teachers. What is the best way to assign, grade, and check homework? Sam Shah conducted an unofficial survey on the matter and presents the Homework Survey Results.

I glanced over the survey results, and found one response that really "struck" me as a "sweet" solution to the homework problem. It is from a 5th grade teacher, and I apologize for taking so much space for it here but I just feel it was really good (and if the person feels I shouldn't quote this, please let me know). Emphasis mine:

"I work hard at the beginning to set up a culture of responsibility for themselves. They are responsible for making sure they understand, for asking questions, for asking for more practice or another example.

When we come into class, we check the answers together. I will solve a problem or two on the board that I have learned over the years is confusing. Other than that, I expect them to ask for clarification if a problem is wrong.

They "grade" their own. If it's wrong, they are expected to take a minute right then to figure out why it was wrong. Usually it's a silly mistake. If not, they bookmark it to ask questions during our next work time.

I don't give any grades. I don't assess it. The final test/quiz is their grade. The homework is just them figuring out how to do the skills. They know they won't be graded on it. They know they won't be penalized for getting it wrong. They know that the whole point of the homework is to figure this math stuff out. If they get it wrong, they know they haven't mastered it and need to get help.

On the opposite side, if a student doesn't do their homework, I don't get too upset. We have a talk about how they hurt themselves, because now they don't have an accurate measure of if they can do it on their own. I can't help them because they didn't get the opportunity to make their mistakes before the test. However, I have a few who don't need to do homework. They still earn A's on the final test. They learned it by being in class and paying attention.

With those who obviously do need the homework practice, but aren't doing it, I problem solve that on a case-by-case basis.

It changes the whole culture of learning and mastery in the classroom. But it is VERY important to set up that culture at the beginning."
Now, I'm not claiming that middle and high school teachers could easily transfer these ideas to their classes... but perhaps they can, at least somewhat. Please discuss homework at Sam Shah's post.

A teacher's problems do not end with homework. Can you believe that TEACHING as a profession is so difficult in today's world that sites exist solely to help new teachers to SURVIVE their first year? That's exactly the word that is used. Teaching has compiled a list of 100 Helpful Websites for New Teachers, and the list includes new teacher "survival" sites, teacher video sites, freebies, inspirational sites, and several other categories as well.

Some Math As Well

At Exploring Binary blog we find an EXCELLENT way to explain binary numbers that he found when he taught his mother binary numbers . It's true, once you struggle at explaining a concept to someone who's not a math whiz, you really get to the brass tacks of the matter.

Denise from Let's play math! has some geometry challenges for us, some of which are from ancient Egypt. I solved the puzzle under the title "Can You Explain This?", using fractions (and not avoiding them as it tells you to do). I also pondered number (2) but couldn't find an immediate (easy) way to find an answer. I don't think she ever posted answers to those.

spiral illusionJohn Cook from The Endeavour blog shows us an optical illusion that is so fooling that I couldn't believe my eyes at first. Quite amazing. He also makes an analogy from the optical illusion to a "mathematical" illusion within his own work.

Dr. Jeff is asking us to fold a humongous piece of xerox paper and see how many folds reach to the top of mount Everest or the sun, among other things. You probably won't believe the answers!

If you're into 5th-7th grade math, please check also my videos about integer subtraction.

This is where to send your submission for the next carnival on July 10th at Math Mama Writes. Happy summer, everyone!


Colin Beveridge said…
I found a nice explanation of the triangle problem. Let one of the fixed-length sides be the base, and the other go in any direction you like. Since the area of the triangle is (base * perp height)/2, you want the perpendicular height to be as great as possible - which happens when the second side is at 90 degrees to the base.

(Sadly, I solved it with calculus before I figured out why).
Student Talk said…
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Anonymous said…
Thank you for doing the carnival, Maria! My blog reading time has disappeared along with my writing time, so all of these articles are new to me. I will definitely take some time today to go browsing...
Ron Smith said…
Nice article..

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