Tag: learning math

Posted in Math blogs

Math Teachers at Play blog carnival #50

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When I sign-up to host the May edition of Math Teachers At Play blog carnival organized by Denise of Let’s Play Math blog, I didn’t know it will be its 50th edition. Wasn’t I lucky? It’s a milestone for MTAP. Kudos to the organizer and supporters of MTAP. But I got one little problem. It is a tradition in math blog carnivals to always starts with saying something mathematically significant about the n in its nth edition! Oh dear. Things I associate with the number 50 are mostly non-mathematical  like golden anniversaries!

the number 50

Wikipedia to the rescue:

Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: 50 = 12 + 72 and 50 = 52 + 52. It is also the sum of three squares, 50 = 32 + 42 + 52.

And I didn’t know that until I hosted this carnival! I’m a teacher I have to ask: “So what’s the next bigger number to 50 that is the sum of two non-zero square numbers in two distinct ways?”; “What are other numbers that can be expressed as a sum of the squares of consecutive numbers?”; “What about those numbers that can be expressed as sum of cubes?”;…  There is always something to investigate in math. One of the major objectives of school math is to get students into this thinking habit without us telling them to do so but I’m digressing from my topic now. Let’s get to the great posts submitted for this edition.

1 – How many bricks are in this building? Says its author Paul Murray: This is an activity I’ve used for years and recently wrote up for a class.  It integrates many problem-solving methods, multiplication, addition, and place value concepts, estimation, and organization of data.   It also takes the students outside with a clearly defined task to accomplish.

2 – Wolfram Alpha. Says it author Coleen Young: This page is from the student version of my blog and has several slideshows showing the syntax for WolframAlpha including a fun show at the end on the sillier questions one can ask! I started this student version because they can just be given the link. One of my former students emailed me recently to tell me how much she was using WolframAlpha at university.

3 – New intuitive ways of learning math by Mohamed Usama. Says Mohamed,  “I am a student and I love game programming. CREVO is just my virtual startup where I publish all my ideas and other news. Math Operations is a game that won local game development competition. That time, I developed this game in Flash. It was just a 48 hour competition but still idea was executed well. At the time when I was receiving my prize I announced that soon, I’ll publish it for all Android devices and here it is. I finally developed this game for all Android & Amazon Kindle Fire devices. Designed graphics (SD & HD) for tablet as well. Last week I published my new version 1.5 and its available on Google Play (Amazon is still reviewing it). I hope you people will love it. I need high support because I really want to make games for kids, education sector is what my target is.

4 – Guess my rule says its author John Golden is a story of an algebra lesson based on a simple, common social game.

5 – You Want School Reform?  Brace Yourself…. submitted by Matt Wilson. Writes Matt in the post “Anybody building a house needs to start by building a foundation, but our system is teaching foundation building without ever teaching anyone what a house actually is…”

6 – Missing Angles says the author of Five Triangles is a non-trivial math problem for middle school students requires some actual thinking.

7 – An elegant solution: An algebra problem from 1798 by Dan Pearcy. Says Dan, I stumbled across this great little problem on John Cook’s blog (The Endeavour) during the weekend. The reasons that it’s so great are two-fold: (1) Most people think they’ve solved it when they have four solutions from their equation when in fact they have not considered that the equation could be written in four different ways. (2) The solutions are so elegant. Possibly because they are all based around the golden ratio.

8 – More on Microsoft Equation Editor says John Chase is a follow-up and more in-depth discussion of http://mrchasemath.wordpress.com/2012/03/15/microsoft-office-equation-editor/.

9 –  Sidewalk Math: Functions. No name was supplied but its from a blog called “The Map is Not the Territory”.

10 –  9 TED talks to get your teens excited about math shared by Caroline Mukisa. A great collection.

11 – Thinking (and teaching) like a mathematician. Says Denise, “Being ‘good at math’ means much more than being able to work with numbers. It means making connections, thinking creatively, seeing familiar things in new ways, asking “Why?” and “What if?” and “Are you sure?” If we want to teach real mathematics, we teachers need to learn to think like mathematicians. We need to see math as a mental game, playing with ideas.”

12 – Tiger’s Mum presents Geometry: 2D and 3D posted at The Tiger Chronicle.

13 –  Another Proof of the Sum of the First n Positive Integers and  The Mathematics of the Poles shared by Guillermo Bautista. The first shows a geometric proof and the second post is a discussion on the connection among poles of the earth, the latitudes and longitudes, and the polar coordinates.

14 – Planning and Analyzing Mathematics Lessons in Lesson Study by Erlina Ronda (that’s me). This is a powerpoint presentation for researching lessons with your colleagues.  Lesson study is schools-based teacher-led professional development model.

15 – The nature of math vs the nature of school math. This is my top post this month. Everybody is concerned about the great divide between math and math education.

The next MTap Carnival will be hosted in  Math Mama Writes.

 

Posted in What is mathematics

The fun in learning mathematics is in the challenge

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Just like the games we play, the fun in learning mathematics is in the challenge. In the post Math is not easy, I argued that we love a sport because of the challenge it presents, the opportunities it gives us to make prediction, analyze, strategize, make our stand and defend it, etc and not because it is easy to play! Learning math is like playing our favorite sport. I shared that post in Math, Math Education, and Culture community in LinkedIn and I got interesting comments and insights.

  1. Andrea Levy • If a game is too easy, it no longer is fun! That is why kids move on to more and more challenging games. Math is fun when it is challenging, but not overwhelming. Chess is a wonderful game because the rules are simple, but the game is more challenging when you play with people who are at, or within a certain range, of your own abilities. If you play with someone who is too far below you in understanding strategy then the game is boring. If you play with someone too far advanced, then the game is frustrating. Learning math is similar. Our challenge as teachers is to find a way to make math challenging without it feeling overwhelming. And yes it can be challenging and fun. Most students learn best through social interaction. We need to provide opportunities for students to struggle individually with an interesting problem, share with a small group their thinking and try to move forward in their understanding of the problem, and then share as a class the different processes and solutions. Then math can be challenging and interesting (fun.)
  2. Jeffrey Topp • I think the problem is more fundamental than math, the challenge is getting students to look for challenges and see conquering those challenges as being fun because ultimately life is about finding out what we are made of. I have always been good in math but received poor grades in high school and didn’t learn anything until I realized that the challenge of solving difficult problems was actually fun. Once I realized that, everything fell into place.Math is a great venue to teach this concept because, frankly, thinking is challenging. As a country, though, we are getting lazy and rather than accepting that there are students who won’t spend the time thinking we change the material to require more memorizing, or process following. This hurts everybody.
  3. Sheldon Dan • I don’t know if math should be “easy,” but it should be understandable. I have taught developmental math at a community college in Memphis, and one of my goals is to help people understand a subject that many fear, especially my students who have not been in a math class in many years. Therefore, my concern is more for them to know why they are doing something as well as how to do it. “Fun” is not really a consideration, and I don’t think it should be. I think if the concepts can be taught in an interesting way, say by the use of manipulatives, that is a bonus, but we can’t lose sight of the fact that there are some things in math which will not be “fun” and they are still necessary in our classes.