Blogging Experience

• Describe your blogging experience in this course. Do you think you will continue using your blog? Why or why not?

I have never blogged before, so it was a great experience for me. It really opened my mind to Web Tools. I do not think that I will continue to blog on this site, but I may create a blog to communicate to my lacrosse team that I coach. It is a fast way to communicate to a bunch of people.

• What did you learn about yourself and your abilities or interests in Math or Algebra?

I learned that I still love to learn about math. I love learning about how to teach in interesting ways to my students. I do not want to get stuck in a rut with my teaching style.

• Did you learn or discover anything you found particularly interesting through your course activities or your own internet research? Describe one interesting discovery and why you found it fascinating.

I really like the Applets that were shown in this course. It is definitely something that will be interesting to the students and useful within our lessons that we learn within the classroom. I also think that they can be used as a great differentiation piece with students who are ahead of behind the rest of the group.

• Do you think you will use journals with your students? Do you think you will use blogs? Why or why not?

I do not think that I will use journals or blogs in my classroom just yet. I have too many different subjects that I teach. If I had one  subject to focus on it may be easier to maintain.

Factoring Quadratics

How to factor a quadratic:

1.  In order to factor a quadratic equation you want to have it in the form of

2. You first will look at the c term in the quadratic. What are all the possible factors of c?

1, 2, 4

3. Next, you will have to figure out what factors of c will add together to get b. (Make sure you are paying attention to the signs. )

1, 4

4. If a is 1, you will not have to worry about it when you are factoring into two binomials. If a is prime then you will have the number and 1 in your two binomials. If the number is composite, then you will have to play around with the factors of a and the factors of c to make their products add together to get b.

A is prime, so the factors are x and x

5. Place the factors of the a term first in the binomial and then the factors of the c term second in the binomial.

(x + 1) (x + 4)

6. Test your work by multiplying the binomials together using FOIL to see if you got the answer you started with.

F:  O: 4x  I: 1x  L: 4

 

 

–>Paraphrasing someone else’s directions does not help me internalize.  I get too caught up in the fact that I am copying their work or that I am going to miss something that they put in their directions.

–> I would try this activity by asking my students to write down the 6 steps of factoring quadratics by themselves first. I would then give them my directions and see if they have hit all the key points in the directions.

 

5-D-2: Applet Review

http://illuminations.nctm.org/ActivityDetail.aspx?ID=160

This Applet is called, Mean and Median. It allows students to create box and whisker plots. We do plenty of work with box and whisker plots and measures of central tendencies when we review for PSSAs. This would be a great tool for us to do after we talk about measures of central tendencies.I usually will depict how to make one on the board and then we will do one together. After that I would give them a set of points and they had to create box and whisker plots at their seat. I think using this Applet instead of making them do it on paper would be a fun way and hopefully would grab interest from more of them.

Evaluating our Definitions: Equations and Functions

• After reviewing your classmates post, would you alter your definition? Why or why not? Would you provide different examples?

I would alter my definition of equation a little. I would state that an equation could contain a variable. Equations do not always have to have variables. I still like the examples that I used. Pictures help me visualize what the word means.

• How can you evaluate whether or not your students grasped the difference between the two?

If I asked the students to show me examples of the concepts of equation and function, I would be able to see if they grasped the difference between the two. Sometimes it is hard for students to put their understanding of concepts down in words. I am going to add on my tests this year that they may define or show by example the understanding of vocabulary.

 

5-A-3: My Definition of Equations and Functions

An equation consists of a variable, an operation, quantities and an equal sign. An equation is used to set two statements equal to each other. The difference between an algebraic expression and an equation is that there is an equal sign in an equation. An equation defines the line.

Example:

y=mx+b is the equation of a line.

The equation of this line is y=4x – 2.

A function is a fancy way of defining the input-output method. You plug a value in for the variable in the function and you obtain an output value. It creates a set of coordinate points; (x,y). A function is usually written in the form of f(x)= …

Example:

References:

http://www.coolmath.com/algebra/15-functions/02-function-notation-01.htm

http://hotmath.com/help/gt/genericalg1/section_5_4.html

5-B-1: The Magic of Proportions

My Reflection on Math Myths

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

• I encountered the myth, “In order to find the right answer you must always know how you got that answer.” It happened frequently in calculus. I could figure out what the answer is supposed to be, but some times could not actually do the problem correctly. I also encountered, “Boys are naturally better at math than than girls.”

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

• My husband and I have been together for 11 years, so we have had much experience together with math, since he was also a math major. I have always had the impression that boys were better at math than girls, but I have realized that I have just matured a little later than him. I have revisited the math the “I was not good at” and have a better understanding now that I am “ready” to learn.

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

• I try to make sure that I help all students why they are doing individual work not just the students that I think are really struggling. I try to “pump-up” their confidence in the problems or concepts that we are working on.

Pascal’s Triangle

Pascal’s Triangle is a triangle made up of numbers generated from the row directly above the current row, i.e row 5 is generated from row 4. The triangle is bordered by the number 1. The inner numbers of the triangle are generated from the numbers directly above to the left and right.

Non-Linear Pattern Web Quest

This is a picture of a fractal in the forest in Southern Spain from the website Fractals in Nature.

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

• There is an equation that describes magnetic phase transitions (an ising model). It is so interesting to me that there are equations to represent things that happen in science.

2. What images did you find particularly striking?

• I found the image above particularly striking. It is a picture of a forest in Southern Spain. Nature does crazy things on its own.

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

• At my home, there are nonlinear patterns outside in my flower garden. My pictures on the wall are also in a nonlinear pattern in my family room.

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

• I would love to do a webquest activity for unit prices where students have to search the web for different uses of ratio, rates and unit prices. There is a huge emphasis on this on the State Assessments.  I think that my two year advanced students could actually take interest in a webquest activity exactly like the one we did for this online class. They would be interested in taking a look at Fibonacci, the Golden Ratio and Fractals in Nature and seeing the connection to math.

Working with the Definition of Linear Patterns

Non-traditional pattern: pattern that does not repeat or follow a linear pattern

Linear pattern: (kid definition) a linear pattern is an equal-interval step of numbers

Linear pattern: (formal definition) A linear pattern is a set of point locations, all of which lie on a straight line.

• What is the difference between your kid definition and the formal one?
1. My kid friendly definition seems to be a little wordier than the formal definition. I wanted the students to understand that there would be equal intervals or differences amongst the numbers in the pattern in order to make it linear.
• Explain how you could help students learn the formal definition without having them memorize it.
1. I definitely think having a picture along with the pattern will help the students remember the formal definition of linear patterns. They will be able to connect the two and grasp the idea.