• Describe your blogging experience in this course. Do you think you will continue using your blog? Why or why not?
  • I found the blogging component of this course to be very frustrating.  The writing component was good; it was the blogging service itself that was bad.  I have been blogging for several years and have never used wordpress.  With that said, wordpress is the most cumbersome and least user-friendly logging service I have ever used.  One other note I might make and maybe I am missing the point but I feel we could get the point of journaling just as adequately by simply using the message board that is standard to blackboard.  Journaling is a great tool in the mathematics classroom but not all students have access to a computer on a regular basis so the focus on journaling by using a blog specifically only targets a percentage of students and teachers.  I believe I would continue to use a blog in a mathematical context I just would not use wordpress. I think it would be important to have something available for students to access and respond to teacher thoughts and reflections on math.
• What did you learn about yourself and your abilities or interests in Math or Algebra?
  • I learned that concepts are more important to my math development then mechanics and mathematical formality.  I also learned that I tend to look at concepts very abstractly and do not tend to focus on the concrete connections with which concepts apply.
• Did you learn or discover anything you found particularly interesting through your course actives or your own internet research? Describe one interesting discovery and why you found it fascinating.
  • In the webquest activity I was intrigued to find out how many places fractal patterns occur.  I knew that fractal patterns occurred in nature I did not realize that humans unknowingly used fractal patterns in construction and architecture.
• Do you think you will use journals with your students? Do you think you will use blogs? Why or why not?
  • I have already started using journals with my students as a result of this process.  I do not believe that I will use blogs with my students at least until I can assure that the students will have regular access to computers with network capability.

Paraphrasing factoring a quadratic:

1)      First the quadratic should be in standard form

2)      Look at the constant term and break it into its pairs factors

3)      Look for a pair of factors that sums to the linear term

4)      Write the quadratic in factored form (the product of two binomials where the x terms have an exponent of 1) using the factor pairs you identified in the previous step.

5)      Check by using the foil method

Questions:

• Did paraphrasing the words help you internalize the concepts more?
  • Paraphrasing does help internalize the process. However, I would not say I internalized the concept any more then I had before. 
• How can you apply this type of exercise in a lesson for your own students?
  • I would use this exercise as an informal assessment to determine if students understand the process of factoring basic quadratics.

I found a great cross curricular lesson that deals with writing recursive formulas.  The goal is to find out how many handshakes occur when the Supreme Court justices meat and shake each others hand. As part of the lesson there is a neat applet that creates a tree diagram depending on the number of people involved.  The applet is not filled with bells and whistles.  In fact it is extremely simple.  It is for that reason it is so powerful in helping students make connections.  If the applet is so complicated that students need a tutorial in the applet then they will probably fail to see the mathematics the applet is trying to address.

Getting the same gear ratio between two bicycles

Gear ratios are calculated by using a formula that calculates something called gear inches ((Diameter of drive wheel in inches × number of teeth in front chainring) / number of teeth in rear cog).  I have several bikes that I race in various competitions and types of circumstances. Sometimes I find a gear ratio that I really like on one bike.  I want to have the same ratio exist on all my bikes.  Unfortunately they are all different.  One has 20 gears and 700c or aprox. 27” wheels, another has 18 gears and 700c or aprox 27” wheels, and the last has 27 gears and aprox. 29 inch wheels. So if I know the number of teeth on the front chain ring and the number of teeth on the rear cog in addition to the wheel size I can create a proportion based on the info I know from another bike and find the number of teeth I need to have on the real cog.

 For example I like the 48 tooth chain ring 23 tooth cog combo on my road bike that has 27 inch wheels. So I want to duplicate that gear on my mountain bike which has a 42 tooth chain ring and 29 inch wheels so the proportion would look like this;

(27”X48)/23 = (29”X42)/?

1296/23 = 1247/?

1296(?) = 23(1247)

1296(?) = 28681

? = 28681/1296

? = 22…… or 22 tooth cog

Example #2

Calculating fuel efficiency between two camping stoves

An ongoing project/hobby of mine is making ultra light backpacking stoves that burn denatured alcohol.  One problem that has come up is what if you want to cook for more then one person?  The stove that I carry for myself is tiny and would not be practical for cooking much food.  So if I double the volume of my stove but keep the design the same it would be reasonable to think that the cook time would be twice as long as well.  To test the theory I would time how long it would take to burn 1oz of fuel in my personal stove.  I would then time how long it takes to burn 2oz of fuel in the larger stove. 

Ex. 1oz fuel/15 minute burn time = 2oz fuel/?

Clearly ? = 30 minutes if it does then great if it burns longer that is even better and if it burns les then I scrap the stove and start again.

$.75 = 3 quarters or $2.00 = 20 dimes.

=

Let’s say you are buying cd’s at $15.00 a piece shipping is $4.00 per order. If you spend 64 dollars the equation you would use to find the number of cd’s would be 15(x) + 4 = 64 where x is the number of cd’s.

Functions- A mathematical statement in which every element in the domain is paired with only one element in the range. So if you think about it like a key board if you press the “J” key you will only get a “J” on the screen, you won’t get a “J” sometimes and a “W” others. Or as one teacher said about their infant son they feed it one thing and something comes out. So if I want a function for my cd example above y = 15(x) + 4 where y is the amount of money I spend depending on the number of cds I buy. A useful function might be written for the following certificate of deposit information from first citizens bank.

1 Year Fixed rate guaranteed to maturity.
(If rates go up, you may convert every 90 days to a higher rate.)

Myths: It’s always important to get the answer exactly right, it’s wrong to count on your fingers.

• • Did you encounter any of these myths in your own experience with Math education as a student? If so, which ones?

I experienced both of these myths as a student. I never got the answers right and thought I was a terrible math student. I also used my fingers but made sure no one could see me.

What has happened since to dispel or perpetuate your understanding of the myth?

When I was in college I had a professor whom I respected highly who used his fingers all the time since then I have no problem using mine.

Since leaving a very small high school (my graduating class had 48 kids) and going to college where I was exposed to so many more mathers, I have come to realize getting the almost right answer is a skill that can save huge amounts of time. I also know now that counting on your fingers is a simply using a very convenient resource and resourcefulness should be rewarded. The problem comes when using the fingers becomes a crutch instead of an aid.

• • How can you help dispel any of these myths for your students?

I think the best way to dispel the myth is to teach them how to effectively do both. Clearly a teacher is not going to teach a students to do something that they think is absolutely wrong.

            http://www.contracosta.edu/math/pentagrm.htm

•  
  1. Were there ideas or concepts you were not familiar with? What were they?

a)      I was not aware that the golden ratio appeared when comparing consecutive elements in certain sequences like Fibonacci sequence.

•  
  1. What images did you find particularly striking?

a)      I found a image of a pentagram developed from the golden ratio inset in a parallelogram in such a way that when certain portions were shaded it created another parallelogram that conformed to the golden ratio.

•  
  1. Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?

a)      I often ride an indoor trainer this time of year when I can’t ride my bike outside. The device works in such a way that as the wheel speed increases the resistance also increases but it increases exponentially

•  
  1. How can you adapt this webquest activity for your classroom?

a)      I would give students specific items to look for and give them a choice of websites to visit so as not to ovewhelm them with the vast amount of info out there.

 Fractals and Nature

            http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html

http://www.ted.com/index.php/talks/ron_eglash_on_african_fractals.html

•  
  1. Were there ideas or concepts you were not familiar with? What were they?

a)      I was not aware that many African villages were built using a Fractal model.  I was also surprised to learn that even human thought process may have a connection to fractals relationships.

•  
  1. What images did you find particularly striking?

a)      I was struck mst by a drawing of an African village that looked almost identical to a very common Fractal pattern.

•  
  1. Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?

a)      As I look at my desk I see a fractal pattern.  My desk consist of a table and underneath and to the far right side is a smaller table.  Underneath and to th far right side of the smaller table is a stack of books.

•  
  1. How can you adapt this webquest activity for your classroom?

Linear Pattern- A pattern that shows a repetitive linear relationship. In other words a pattern that behaves in such a way that changes between elements in the pattern are uniform and calculable. The method for calculating the change between elements does not include any computation dealing with powers larger then one.

Formal definition-

www.mathsteacher.com.au/year8/ch15_graphs/02_linear/patterns.htm

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The biggest difference between my definition and theirs is that I did not make reference to a graph. The graphical representation is definitely helpful for the visual learners. I would help students learn the definition by having them 1) identify linear patterns form non linear 2) have them create their own linear patterns, and finally create their own definitions of linear patterns.