Reflections on Blogging
May 3, 2008 at 12:04 pm | In Uncategorized | 3 CommentsTags: Module 9
* Describe your blogging experience in this course. Do you think you will continue using your blog? Why or why not? I had used blogs before in other online classes, but never on WordPress. It was a bit challenging to get use to the interface at first, but it didn’t take long to get comfortable using it. I got very frustrated a few times with trying to format. I couldn’t figure out how to underline text or insert tables. I also had difficulty inserting images, but that may have been an issue with my MAC and not with the blogging. I’m not sure about continuing this blog yet. It’s very difficult to require students to do a technology activity frequently unless the mobile lab would be available and I could fit it into class time. It is almost easier just to have students do writing on paper.
* What did you learn about yourself and your abilities or interests in Math or Algebra? It was interesting to see how much easier it is to write about a skill or concept that I already enjoy teaching. It was much harder to write about one that I don’t like which makes me wonder if these “emotions” come across in my teaching. It is something to consider, because I don’t want my students’ learning to be affected by my feelings on a topic.
* 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. I was really fascinated by the web search I did on fractals. The animations were so cool. I never realized there was so much information out there including the animations of Sierpinski’s triangle and Koch’s snowflake.
* Do you think you will use journals with your students? Do you think you will use blogs? Why or why not? Again, I totally agree that journaling is an excellent experience for students, but I am not sure about using the blogs to do it. Most of students have Internet and I could require them to do blogging at home, but for some, they would have to make time to do their blogging at school. Another option is to let those students do their entries on paper, but then the whole feeling of community and sharing is lost.
Factoring Quadratic Equations
May 3, 2008 at 11:48 am | In Uncategorized | 2 CommentsTags: Module 9, Quadratic Equations
Instructions for factoring a quadratic equation in the form ax2+bx+c=0:
1. First look at the factors of the constant value, c.
2. Factor the first term, ax2. This is very easy when a = 1 since the only option is x * x.
3. Determine which combination of factors have a sum/difference equal to the coefficient of the middle term, b.
4. Write the factors as the product of two binomials: (x + f1)(x+f2).
Questions:
* Did paraphrasing the words help you internalize the concepts more? I think it’s very difficult to put something like this in your own words and generalize it. It is much easier to describe the steps as you do some example problems. It’s easier to describe how to factor a basic quadratic equation with a = 1 and plus signs, but when you combine a variety of a values with some minus signs, now it is much more difficult to describe. I don’t actually feel that paraphrasing this concept in words help me to internalize it.
* How can you apply this type of exercise in a lesson for your own students? Although I didn’t feel paraphrasing this concept was very helpful for me, it is an exercise I do with my students often. I usually would have students paraphrase a new skill or concept as their closure or bell-ringer.
Evaluating Your Own Definitions
April 13, 2008 at 8:07 pm | In Uncategorized | Leave a Comment* After reviewing your classmates post, would you alter your definition? Why or why not? Would you provide different examples?
It was interesting to see the different ways to word the definitions, but overall I felt they were pretty similar. I would probably use the words input and output in my function definition if I had to write it again. I don’t feel any need to change my examples.
* How can you evaluate whether or not your students grasped the difference between the two?
I think having the students come up with their own examples of each is the best way to see if they really get it. When we first start functions, I like to have the students draw relations that are functions and some that are not. I actually had my students this year make the questions for the chapter test. I of course chose some of the better ones they made up. As far as linear equations go, there is only one type of linear equation that is not a function (vertical lines). In Algebra I, we spend quite a bit of time examining the special types of linear equations (horizontal and vertical) and in our discussion we examine which type would not satisfy a function and why not. Of course we mention that all linear positive and negative equations are functions and then look at them in function form. I have a writing prompt from one of my books, which makes students explain this in their own words. For my lower level classes I just provide them with a word bank for their writing, but they always surprise me how detailed their explanations are.
Applet Review
April 13, 2008 at 3:07 am | In Uncategorized | 3 CommentsFrom the NLVM site, I really like the “Grapher” applet.
http://nlvm.usu.edu/en/nav/frames_asid_109_g_3_t_2.html?open=activities&from=category_g_3_t_2.html
This applet is fantastic, because it just like students having a graphing calculator at their house (as long as they have internet). I love using the graphing calculators in class, but I can’t let students take them home, so that makes it very difficult sometimes to incorporate them into different lessons, chapters, assessments, etc. I actually like the applet better than the graphing calculators in some ways. It is easier to learn to use, has a bigger screen, and the graphs are color-coded. They can trace the values on three functions at a time and compare them right away.
I could definitely use this applet to have students investigate families of graphs. They could look at parallel lines with different y-intercepts. They could look at lines with the same intercept, but different slopes. They could even look at perpendicular lines with opposite reciprocal slopes. Students could play with using parameters, using them as slope and/or y-intercepts, and then changing the parameters using the sliders. This feature makes it easier to investigate families of graph using the applet than a graphing calculator!
Magic of Proportions
April 13, 2008 at 1:14 am | In algebra | Leave a CommentTags: Module 6, Proportions
Problem #1:
Julie is creating a scale model of her bedroom to help her decide how to rearrange her furniture. Her actual bedroom is 12 feet by 15 feet. She has a shoebox that is 4 inches wide that she can cut to be the correct length. She plans to use the following proportion to help her figure out how long to make the shoebox:
Feet 12 = 15
Inches 4 x
Then Julie uses cross multiplication to find the equation 12x = 60. She solves it by dividing both sides by 12 which produces x = 5. She should cut the shoebox to be 5 inches long.
Problem #2:
Mrs. Boyer has to drive to Lancaster to visit her grandmother. She has a map with scale 1 cm: 10 miles. She measures that it is approximately 10 centimeters from Lewisburg to Lancaster. She uses the following proportion to help her figure out how far it is:
Centimeters 1 = 10
Miles 10 x
Then she cross-multiplies to get the equation x = 100 which tells her that it is 100 miles to Lancaster. Then she knows that her car gets 23 miles per gallon, and gas is currently $3.35 per gallon. She wants to estimate how much it will cost her to drive to Lancaster, so she uses the following proportion:
Miles 23 = 100
Gallons 1 x
She cross-multiplies to get the equation 23x=100. She divides both sides by 23 to find that she will use about 4.3 gallons of gasoline. Then she uses the following proportion:
Dollars 3.35 = x
Gallons 1 4.3
She cross-multiplies to get x=14.405, so she knows it will cost about $14.41 to buy gas for her trip to Lancaster.
My Definition of Equations and Functions
April 11, 2008 at 8:49 pm | In algebra | 1 CommentTags: Module 6
Equation – a mathematical sentence where two expressions are set equal to each other
For example: 3 + 2 = 5
(3)(2) = (6)(1)
x + 6 = 12
x + y = 12
Function – a relationship between two sets of numbers, called the domain and range. Each element in the domain is paired with exactly one element in the range.
For example: set of ordered pairs: {(-2, 1), (5, 2), (3, 4)}
Table:
x y
-2 1
5 2
3 4
* Functions can also be represented as mappings and graphs, but these wouldn’t copy from my microsoft word document
Functions as equations – equations that represent functions can be written as function rules. Function rules can be written with function notation.
For example: a function rule: y = 2x + 3
Function notation: f(x) = 2x + 3
My Reflection on Math Myths
April 4, 2008 at 7:50 pm | In Goals, Module 5, algebra | 4 CommentsI’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 CommentI 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 CommentA 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.
Return to Earth
March 29, 2008 at 12:29 pm | In Activities, Module 4, Ratios, algebra, seventh grade | Leave a Commenthttp://www.nasa.gov/audience/foreducators/topnav/materials/listbytype/Space.Shuttle.Glider.html
This link is to a hands-on activity where students create their own Space Shuttle Glider that is a scale model to the actual U.S. Space Shuttle Orbiter. This activity caught my attention because it is hands on and seventh graders love to build things! I also think it’s really neat to learn something about the orbiter while practicing math skills, specifically ratios and proportions. Project materials are included in the downloadable PDF file. Some additional materials must be supplied.
The project challenges students to follow directions to build an accurate glider that will “take flight.” Then students have to apply ratios and proportions to find the scale factor between their glider and the real orbiter. Next students find the glide ratio (height to distance) of their glider as they launch it horizontally and it makes a safe landing on the ground. This will lead students to research and compare the glide ratios of other aircraft. Lastly, students use a fishing line guidance system to simulate the landing of an orbiter on the airstrip.
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