Reflection on Blogging
- Describe your blogging experience in this course. Do you think you will continue using your blog? Why or why not? I really enjoyed the blogging experience in this course. I have never blogged before and I was honestly very scared to blog. It was very overwhelming at first but now I feel like a pro at blogging. It was great to read stories that everyone wrote and get to know my classmates and get ideas from them. I do not think I will continue to blog at this point in time. After reading another classmate’s blog, I did like her idea as it being a resource for my parents, but for now, I think blogging is not for me. I have a hard enough time keeping my facebook up to date. I did enjoy blogging and did it at ease, so maybe one day in the future I will come back to it.
- What did you learn about yourself and your abilities or interests in Math or Algebra? I learned that I had a lot to learn about math and algebra. Just because I teach this subject doesn’t mean I know everything. I realized that I just teach a lot of these concepts to my students mostly for them to just get it, not to fully understand it. This course allowed me to break down the concepts and truly understand them by re-writing concepts and ideas in my own words.
- 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 learned some really neat things. The one thing I found really fascinating was the Golden Ratio. After I read about it and wrote my blog I was more aware of my surroundings and found the Golden Ratio in my everyday life. I would notice something and yell out “OMG, the Golden Ratio”. My fiance thought I was nuts (well, I am). I discovered all of the wonderful tools that internet has to offer as well. Many times, my students need that change of scenery or pace of concepts. The websites allowed for a games, colors and applications that I could never offer them.
- Do you think you will use journals with your students? Do you think you will use blogs? Why or why not? I do currently use journals in my class and will continue to use them. They reflect, write math papers and solve some open-ended questions in there. I would love to use blogs with them, but currently our technology at my school is under par. We have one wireless laptop lab that is ridiculous to sign out and our computer labs are only currently for the computer class. Once the technology becomes more available, I can start blogging more often along with my students.
2 comments July 23, 2009
Factoring Quadratics: In My Own Words
Steps to factoring a quadratic:
1. List the factors of the third term (c) They can be both positive or negative, or one of each
2. Once you have all of them, figure out which set has the sum of the middle number (b)
3. Now you have the second numbers in each of the binomials, to find the first term check out the number A. Find the factors of term A. If just “x”, then “x” is the first term in both binomials.
4. Put one of the factors that was determined in step 2 into the first binomial and the second factor into the second binomial and then keep the first term in both binomial “x”
Did paraphrasing the words help you internalize the concepts more? Yes and no. It does help but this is a concept I am very familiar with. This may help my students understand it better, because sometimes the steps listed from a textbook are very wordy and do not get straight to the point.
How can you apply this type of exercise in a lesson for your own students? I would definitely help explain this concept to my students using my paraphrasing. Something that I could do with them is once they get familiar with the concept of factoring, they could come up with their own steps or drawings on how to factor. The “kid” language helps them, and then in the following years, I could show new students the last year’s class perspective on factoring.
Add a comment July 23, 2009
Tags: Quadratics
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? Yes, I would. I would add in the definition of equation that it has one or more operations along with an equal sign. Many of the definitions were extremely similar and that is how they should be. The more complex one makes a definition, the harder it is for students to understand. The examples given were great. I love how someone put the input/output table as the example. That I feel is the best way for students to visually see a function.
How can you evaluate whether or not your students grasped the difference between the two? I feel that is very tough to understand if students have grasped the difference between the two. Just by seeing students solve the problems properly doesn’t necessarily mean they know the difference between the two. The thing that is hard is that an equation can be a function. For something to solely be a function, they must understand that each number put in will result in a number exclusively to that number. That may not always be the case with an equation.
Add a comment July 2, 2009
5-A-3: Vocab in my own words
Equation: numbers or variables that equal another set of number or variables. Must include an equal sign. 4+6=10, 4+6=x, 3x+7=7+3x
http://numberjugglers.com/images/equations.jpg
Function: Every input has one output. The input is usually represented by x and the output is usually represented with y.
http://www.grc.nasa.gov/WWW/K-12/rocket/Images/function.gif
Add a comment July 2, 2009
Exploring the World of Applets
One of the items I must teach to all my levels is interior angle measures. This is one of the “biggie’s” on our state tests as well. The applet I absolutely loved was titled “Angle Sums”. It is awesome! First off, it is super colorful. I love colors. When I teach this to my students it can get boring. This applet allows students to see and hear the different angle measures. It gives you triangles up to octagons. The triangle for example has 3 angles that total 180 degrees. It starts by having each angle be 60 degrees. There is a picture of this and a chart. Each angle is a different color and is represented by that same color on the chart. If I took say angle A and moved it, all the angles would change accordingly so it still equaled 180 degrees. What I thought was great was that it showed students that no matter what the triangle looks like, regular or not, the angle measures inside will still be 180 degrees. Something that was also neat was that with triangles and quadrilaterals, it showed that corners of a triangle, make 180 degrees and four corners of a quad. make 360 degrees.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=9
Check it out!!!!
Add a comment July 2, 2009
The Magic of Proportions
I went to visit my parents this past weekend in NJ. They live 147 miles away from where I live in PA. I always try to figure out how long it will take me to get there. Most of the the drive is on the PA turnpike and I195, therefore, I can travel at least 65 mph. I usually drive an average of 75 mph (oops). About how long should it take me to get there? I know that I can go 75 miles in one hour. There for I can go 150 miles in 2 hours. Since I am going 147, my answer will be close to 2 hours.
My friend Kelly and I went out for sushi today. We had a total of $30 and it was $4.95 per sushi roll. How many rolls of sushi could we get? How much would we have left over? This is definitely a problem I would round. Here is how we solved the problem.
Because the $4.95 does not go into $30 evenly, we round down. Therefore, Kelly and I can get 6 rolls of sushi, 3 each! This will cost us $29.70. $.30 left over.
Add a comment July 1, 2009
Tags: Proportions
Post 4-C-3: Formal Math Language
Pascal’s Triangle includes many non-linear patterns that can be seen throughout algebra today.
When we find combinations we use the formula nCr. With a combination, the order does not matter when ordering 3 or more objects. How combinations of 2 letters can we form from the word CAT? CA, AC, TC, CT, AT, TA. Half of the pairs are crossed out because CA and AC are the same pair. We can see that there are 3 pairs of two. 3 C 2 = 3.
The same can be said for Pascal’s Triangle. To find the number of combinations of two objects that can be taken from a set of three objects (2 letters from 3, just like cart), all we need to do is look at the second entry in row 3. Remember, it starts with entry zero, then one, then two. The the second entry is really the third term in row 3. When you look at the triangle, the second entry in row 3 is 3. 3C2. Using the combination formula can help you explore the entire triangle, especially as it grows. Row 10, term 4. (really term #3 since zero is first). 10C3=120.
This allows students to see connection between combinations and Pascal’s Triangle.
Add a comment June 25, 2009
Tags: Pascal's Triangle
Non-Linear Patterns Webquest
For this webquest, I decided to search “The Golden Ratio” and the “Pentagram”. I chose these words for a very specific reason. Up until recently, I was not familiar with either of these words, let alone their relationship.
Before I even conducted my search online, I must put in a small anecdote. I love Disney movies, and I am a member of the Disney Movie Rewards. Each time I buy a Disney DVD, I register online and earn points. One day, I saw I had enough points to buy a new Disney movie. Awesome right? Along with this movie came a free gift, the Donald in Mathemagic Land DVD. No one would be interested in this DVD except a math teacher and I was so excited. When it came in the mail I turned on the movie and watched the 1950′s cartoon of Donald in the land of math. Within the DVD it talks about the golden ratio and how Greeks used it to create their buildings and statues to proportion. I never new that!! It also shows the pentagram (star) and how its proportions are found in many things we see everyday.
If you haven’t seen this one yet, it is a math must.
As seen on the left, one can see the golden ratio in the rectangles throughout.
The pentagram is what we call our polygon the star (decagon). Inside the pentagram, one can make a regular pentagon and as you can see from the picture, the pattern can continue indefinitely. 
As you can see, the pentagram on the left has colored line segments. The four lengths are in golden ratio to one another. Red/green=green/blue=blue/purple=phi or the golden ratio. The four lines seen in the pentagram to the left can be seen throughout nature. In spirals, trees, and flowers. 
1 comment June 24, 2009
Tags: WEBQUEST
Math Myths: Reflection
Below are two of the myths that I have personally seen during my short two year teaching career. I have encountered more than just these two, but these were the ones I felt I could reflect the best on.
To solve a difficult problem, work intensely, and don’t stop until the problem is done
I encounter this myth almost every time I give a lengthy assessment. As I pace around the room checking my students as they work on an assessment I always find a student who is just staring at a problem with nothing written below it. I pat their back and tell them they are doing a good job. A few minutes later I come back to the same student and low and behold, they are still staring at the same problem. I say “how about we skip this one and come back?” They always listen, complete the assessment and then go back to the problem. Guess what!? They do fine on the problem when they come back to it. For some reason, most of my students are very sequential and hate going out of order. They listen to me when I suggest the change of path but most of them need my direction to get there.
As I saw this happening, I had to change the way my students thought. I had to honestly re-program their brains on how to answer questions. I actually starting giving “random” practice problems. I would give each student 3 index cards with word problems on it and tell them to start the problem on the top of their pile. I did not give them enough time to finish the problem. After one minute, I told them to flip that card to the bottom and then start the next problem. The sequence went on again with card number 3. After they started each problem, they then were on their own to finish all three problems. The result: all the students were able to finish their problems, in different orders, but with the same results. It is nice to get students out of their comfort level and still see them succeed. It also is that “aha” moment for some of them.
It’s wrong to count on your fingers.
I HATE this myth. I am the first to admit that sometimes I need to use my fingers. (I know right, a math teacher?) When I teach my IEP students, I can see them struggling on something as simple as 5 + 2. I tell them, use your fingers to help you. They immediately say “Miss Z, that’s for 5 year olds or I don’t want to”. I then proceed to ask them, if you are doing a problem at your seat by yourself, who else sees you besides me. They can never answer that one.
I remind my IEP students and all my students for that fact that there is no right or wrong to solve a simple math problem. Since they are “afraid” to try this simple method, I try to model it to them as much as possible. I even use my fingers when I multiply small numbers to show them it is ok. By getting them comfortable with using their fingers inside class, this will help them on their state tests (especially on the parts where they can’t use a calculator) by being comfortable with the method. Sometimes blocks and counters just aren’t available, but your fingers are always there.
1 comment June 24, 2009
Working with the definition of linear patterns:
Non-Linear Pattern (used my brain for this one): any sequence that does not follow a repetitive pattern or a symmetrical pattern.
Linear Pattern (8th grade definition): any object, shape, or number that repeats in the same order.
Linear Pattern (official definition): Linear patterns repeat indefinitely in either direction along a line. Beads on a necklace, the weave of a fabric or basket, wallpaper borders, stripes on clothing, zippers, walking footprints, musical rhythms, the meter of poetry, the passage of a day, and the changing seasons are all examples of linear patterns that are created or extended by the regular repetition of units, sounds, or events.
(http://www.brooklynkids.org/patternwizardry/pattern_linear.html)
The definition I found online was from the Brooklyn Kids Museum Website. I loved this definition because even though this is the formal definition, I feel that students of any age could relate to this definition. What I love about it is it gives non-traditional examples of linear patterns (music beats, seasons).
I think both the definitions are very similar. Both are very age appropriate but the formal definition explains that patterns can go indefinitely in both directions. Many students only think a pattern can go “forward”.
I feel that students do not have to memorize the definition of linear pattern. By finding patterns inside the classroom (cinder blocks on the wall, tiles on the floor) and reminding students that though simple, these are all examples of linear pattern, the definition will stick with them more and the real life examples will make it more meaningful to them.
1 comment June 22, 2009
Tags: Linear Patterns
