Reflections on Blogging

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

Blogging is a great tool for reflection.  I’m not sure that I will continue to use this specific blog; however, I have set up a blog that I will be using next year.  The goal of this blog is to increase parent involvement by posting a daily agenda, daily activities, worksheets, resources, and homework in one central location.  This way students and parents have access to everything 24 hours a day.  I feel this will spark interest in the students and help improve make-up work as well.

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

This course made me feel good about some of the things I am currently doing in the classroom.  It is nice also to get a refresher and several different perspectives on all of the topics that were presented.

• 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’m a big fan of integrating technology into the classroom so I was really interested in all of the web applications and software used throughout the course.  I see myself using virtual manipulatives like the function machine, and I will also be incorporating FreeMind into the classroom.

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

I would like to use journals and have before; however, it is one of those “time” consuming tasks.  There never seems to be enough time to do it effectively.  I would like to use blogs, but I’m afraid of what students might try to post to the internet.  It would be important to be able to moderate before they are live.

9-b-1 Factoring

Instructions for factoring a quadratic in the form ax^2 + bx + c = 0 where a = 1.

1. Examine the factors of c.
2. Choose the two factors whose sum is b.
3. Both binomials will start with x. (because a = 1)
4. Each binomial will be the sum of x and one of the factors of c.

 

• Did paraphrasing the words help you internalize the concepts more?

Yes.  Putting the definition into your own language creates a stronger connection and personalizes the concept at hand.

• How can you apply this type of exercise in a lesson for your own students?

I often have my students state or write methods/vocabulary in their own words.  It makes the lesson more meaningful and creates ownership of the task.

Evaluating Definitions

After reading everyones definitions, it seems that we are all on the same page.  If I was presenting these to my class, I would be sure to include examples.  I would also be sure to define range and domain as well.

My defintions of Equation and Function

Equation – a math sentence that states two expressions are equal.

Function – a rule or formula that matches each member of the domain to only one member of the range.

Function Machine

I wish I have been introduced to this resource just one week sooner.  This would have been a great tool for my level 1 co-taught classes.  Last week we were working on finding, completing, and writing rules for patterns.  This would have been a great activity for the students to sit on their laptops and complete.  After a short discussion about patterns I would have turned them loose on this site.  Since there is no way of keeping track of how many they did or how they are doing.  I would have provided a sheet complete with blank tables and a space to write the rule for the pattern.   All they would have to do is complete the tables on the computer, transfer it to the worksheet, and write the rules.  I really like that the site provides instant feedback.

6-B-1 The Magic of Proportions

This is rather ironic because I actually had my students complete this activity earlier in the year.  I had them create a real life application for proportions using indirect measurement.  They had to write their own problems and provide an illustration.  I found this to be extremely beneficial.  If your school subscribes to united streaming there is also a very good clip that shows how Lance Armstrong and his team rely on indirect measurement to help them calculate distances and race.  I used this as a basis for my discussion along with the scenario of finding the height of a very tall apartment building that the students can see from the windows in my classroom.  I hold a 25 foot measuring tape in my hand and ask them how we can calculate the height of the building.  I pray for a sunny day so that we can see the shadows!  We then measure the height of a student, their shadow, and the buildings shadow.  Next, setup a proportion being sure to keep everything in order and solve using cross multiplication.

 

Another activity that we do is called “left handed learns.”  In this scenario we talk about sampling and how we can get a rough idea of the number of left handed, right handed, and ambidextrous students in the school.  The students have a couple of days to sample students in each grade.  We set up proportions using the data they have found and I provide them with the number of students in each grade.  They must then calculate the left, right, and ambidextrous students for each grade.  Since the numbers often differ by a little bit, this is a great chance to ask them how the polled the other students and talk about biased sampling.  (note:  They are not allowed to sample students that are in the same math class)  This is a great activity that opens the door to sampling in the real world.  Students discuss where sampling can be applied elsewhere along with why and how it is done outside the classroom.

6-D-2 NLVM

I’m a big fan of NLVM.  I actually want to share two that I’ve been extremely happy with the results that have produced in the classroom.  The first is the algebra balance scale.  I have used this to introduce the whole idea of balancing and solving one and two step equations.  What is nice is that you can “create” or enter your own problems.  I also use the newest version of IE so that I can have different problems set up and ready to go in each tab.  Then I simply set it up to my digital projector and instruct the class using the manipulative.  I have also let the students get out their laptops and practice solving equations.  It is nice that they are able to see how they are affecting the equation.  The other I would like to share is the geoboard.  I have used this to discus both similar and congruent figures.  One neat feature is the ability to color the shapes.  This could also be used to discus properties of polygons, area, perimeter, ect.  The best part is those “perfect” junior highers won’t be able to make fun of your artistic ability on the board when you are creating regular polygon. 

My Reflection on Math Myths

• Did you encounter any of these myths in your own experience with Math education as a student? If so, which ones?
• What has happened since to dispel or perpetuate your understanding of the myth?
• How can you help dispel any of these myths for your students?

 1.  For the most part I had an outstanding math education; however, I did have a teacher that believed three of the myths:  “there is always one best way to do a math problem, to solve a difficult problem, work intensely and don’t stop until the problem is solved, and math requires a good memory and memorizing formulas and rules is the best way to learn.”  This year was rather annoying, and honestly I didn’t get much out of the class.

2.  I had some great teachers before and after this horrible 8th grade year.  These teachers felt much differently when it came to learning and completing the work.  Method and meaning were both discussed, and the understanding of mathematics came more evident in the years that followed.

3.  To help my students from feeling this way, I work strongly towards an understanding of why we need math and how to apply it.  I typically do not have “strong” student so it is key for them to make connections and relate the material to prior knowledge.

Patters WebQuest

“Fractals” and “Nature” and “pattern”

 

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

 

http://math.rice.edu/~lanius/frac/

 

http://discovermagazine.com/2001/nov/featpollock

 

 

I was pretty excited when I found the second link.  The mathematics side of fractals can be rather complicated; however, this site does an outstanding job of relating the material to younger students.

 

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

2.       What images did you find particularly striking?

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

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

 

1. I was partially familiar with fractals.  We probably all know what fractals look like; however, I wasn’t 100% familiar with their properties.  The second website above does an outstanding job of outlining fractal properties.

 

2. Pictures of fractals can be quite mesmerizing; however, I was taken back by the edible fractal in the bowl.  It turns out it was a nice big bowl of fractal cualiflower.

 

3.  I would have to say that this week of work was the most nonlinear it has ever been.  Our testing schedule was so crazy that some students managed to accidentally make it through the day without taking their test. :-/ 

 

4.  My students really enjoy webquests; however, it is important to narrow the search for them.  I would be afraid to have them go to a search engine and type in a few words.  Instead, I would limit them to 4 or 5 outlined websites for them to examine and even play with fractals.  Like this activity it is important for them to have a focus and self guided questions.

 

5-A-2 My Definition of Linear Patterns

Non-Traditional Pattern – a series that does not follow any consistant sequence or have a distinct repetitve nature.

Linear Pattern – a never-ending series that follows a distinct repetitve rule.