My Reflection on Math Myths

April 4, 2008 at 7:50 pm | In Goals, Module 5, algebra | 4 Comments

I’ve encountered several of these myths throughout the years.  The one that stands out the most is “Math requires a good memory, and memorizing formulas and rules is the best way to learn it.”  My high school geometry teacher made us memorize everything!  While my friends in the other section got to have a cheat sheet for tests, my section had to memorize all of the theorems and postulates!   I don’t think any of us understood them any better because we had memorized them.  Many people failed her tests because they hadn’t memorized them even though they probably could have USED them correctly to complete the proofs if they were given a list.  This experience has definitely had an impact on how I teach.  There are some formulas that students should KNOW because they are so common, but a student should never have to sit and memorize a formula because they might need it on a test.  I always supply students with a formula sheet or individual formulas as needed.  Even for the PSSA, students are given a formula sheet and not expected to memorize everything!  I think (hope) my general attitude towards this is apparent to students and will help dispel this myth.

The other myth that hits home with me is “There is a math mind – some people have it and some don’t.”  I think many people to this day believe this myth.  I know my friends thought this in school, many students still do today, and most parents believe it.  I even hear teachers saying it.  This is one of the myths that most effects girls, because “girls don’t have the math mind.”    For me, some of the most logical concrete thinkers are the ones who struggle most with math when it really counts, because they can’t problem solve.  I always tell my kids that someday a potential employer won’t care that you can solve a page filled with equations if when it comes to writing and applying an equation she has to give you the equation before you can solve it.  If she has to give you the equation, she might as well solve it herself!  Some of my students who are the most creative are the best problem solvers in math even though they are stereotypically thought of as “non-math people.”  I think I was fooled by this myth when I was younger because I had many friends who despised math.  However, being a teacher has really helped me to see otherwise.  I think that I help my students avoid this myth be encouraging problem solving and applications of skills instead of rote memory.  I can further help by encouraging and praising all students, including girls!

Non-Linear Pattern Web Quest

April 4, 2008 at 6:14 pm | In Module 5, Patterns, algebra | Leave a Comment

I started by searching “Fractals” and “Nature” and “Patterns”.  I like fractals because they can be so complicated yet start with such a basic concept.  I love the phrase “pattern of chaos” because it just seems so ironic to me.  This first site I liked because it goes through many types of fractals: simple, natural, etc.   You can click the links at the topic to see the different categories of fractals.
http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html

I liked the Wikipedia entry for Fractals because it provides animations for both the Sierpinksi Triangle and Koch snowflake.
http://en.wikipedia.org/wiki/Fractal

This third site I enjoyed because it looks into many topics in Science that involve Fractals.  These topics would be a great way for math and science teachers to collaborate.
http://kluge.in-chemnitz.de/documents/fractal/node2.html

Then I searched “Fibonacci” and “Phyllotaxis” and “Prime Numbers”.  This search did not lead me to nearly as many useful sites as the one above, but I did really like this Prime Factorization Machine, because students could use it to check their answers.
http://britton.disted.camosun.bc.ca/jbprimefactor.htm

I also found this site helpful for Phyllotaxis since I wasn’t familiar with that term really at all.
http://en.wikipedia.org/wiki/Phyllotaxis
Questions:

1. Were there ideas or concepts you were not familiar with? What were they?  I really had not heard of Phyllotaxis before, so that was the most foreign to me.  Nature is so interesting!

2. What images did you find particularly striking?  I liked the interactive images of fractals, because they help students visualize what’s going on.  I also really enjoyed the fractals in nature, because they are so amazing!

3. Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?  Our schedule this week at school for PSSA testing was definitely nonlinear!  Additionally, the activity in my bank account lately has been nonlinear with preparing for a baby.

4. How can you adapt this webquest activity for your classroom?  In order to do a web quest with my seventh graders, I would have to provide specific sites for them to visit and specific questions or guidelines for them to explore.  I would probably also let them work in partners.

My Definition of Linear Patterns

April 3, 2008 at 1:13 am | In Module 5, Patterns, algebra | Leave a Comment

A non-traditional pattern is one that does not have consistent recurring set of events.  It does not have to be repetitive or symmetrical.  It may have segments that have patterns, but most are irregular.  These include family trees and concept maps.

A linear pattern is one that has a repetitive format.  It has the same rate of change between any two events.  The pattern may be increasing or decreasing but must increase or decrease the same amount in each interval.  Linear equations form straight lines when graphed because they have a constant rate of change between points.

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