Math: Final Reflection

I have learned a lot from our math class this quarter.  One of the biggest things I learned was that much of what we use in the elementary grades can be applied to middle school.  For example, using manipulatives.  As teachers we need to consider that each student has a different learning style that they prefer, and many children are hands on.  That doesn't change whether they are 5 or 35.  I know that for myself, hands on and practice is the best way for me to learn any task.  We need not ditch the manipulatives just because the students are performing higher level math.

It was a huge wake up call this quarter to talk so much about discussing the logic and reasoning behind a process.  I grew up only learning the process and memorizing formulas.  That said, I disliked a lot of math because it was all memorization.  I remember when I would break out in cold sweats before a test anxiously waiting for the teacher to hand out the test so I could hurriedly write down all of the formulas before I forgot them.  What did that teach me?  Only that I could memorize formulas, but I never knew WHY they worked.  I don't remember one single time when something as basic as "carrying the one" was ever called by what it really was, "carrying the ten."

This class has also fueled my desire to use both group work and technology in my classroom.  Four minds are definitely better than one, so why not work in groups?  Just about everywhere except school people have to collaborate, so why not start early?  I know that I was much more comfortable doing tasks in this class, such as tangrams, when I had the support of my group to help me.  It is also amazing how much technology is out there, and there are so many applications for it to be used in the classroom.

I end this quarter feeling more confident in math and equipped with many strategies to help my students to feel successful.

Math Class #7

I learned a lot in class today, some specifically about math, and more about teaching with technology in a classroom.  For math, I learned about measurement and how you can use anything to measure with.  It was also so cool to see the wolframalpha site in action. 

What really resonated me and will most affect my own teaching is what we talked about with technology.  Part of what was bothering me with implementing technology in the classroom and assigning technology as homework was that some students may not have access to a computer or the internet at home.  What Robin said today about how students 20years ago had to go to the library to do research for projects was an "a-ha" moment.  I was one of these students, and it did not seem out of the ordinary to do this.  This is the same for the students who now do not have access to technology at home.  They have a wonderful resource nearby: the public library.  Or alternatively, they can use a classroom computer before or after school, or a library computer at recess. 

The more we talk about technology, I wonder how technology will continue to change the teaching and learning in the public schools.  When I was in high school and took the SAT, we had to do all of our calculations by hand.  A few years after I graduated, students were able to use calculators.  How important is it for us to teach the "long way" of performing math calculations, etc. vs. letting the students use the technology?  In the near future will there be an app that measures items, as Robin suggested?  Will rulers go the way of protractors?  I wonder if math curriculum will change or if we will continue to teach antiquated methods.

Math Class #6: Making Geometry & Data Tables Fun

So last week I talked about how I really struggled with the tangrams, and that I am not good at geometry.  This week we got to play with Geometer's Sketch Pad.  So I am still not good at geometry, but I had fun with it this week.  I learned a lot about shapes and how to manipulate them to make objects.  It also reminded me of the importance of seeing problems multiple ways.  Many of us used different shapes to make the pieces needed for the face.  So there are ways to make pieces of math that students' may dislike fun for them.

I love the technology piece, but I am struggling with how to get it into the classroom.  In my main placement classroom, the teacher has a computer and there are two other computers that I have never seen used.  Computer Lab time is a rarity and it is usually for praticing typing.  How do I bring a cool program like Geometer's Sketchpad into the classroom for all the students?  I don't think it would be beneficial unless they all could "drive" the mouse and have the hands on experience with it.

I see the implications for these tools in my future practice.  Geometer's Sketchpad would work if we had a larger amount of computers in the class, or if we took turns on the computers while the other kids worked on a different aspect of math.  I would like to use Fathom to make graphs and tables using students' own information so that it is relevant to them.

Math Class #5: Cotton Ball Frogs & Tangrams

Monday's Math was a session filled with fun manipulatives.  The first was constructing frogs out of cotton balls and making them hop by launching them off of paperclips.  From this lesson, I saw again the value of having the kids compile their own data in a fun way.  We all had a blast making our frogs jump and recording the distance. 

For me it was fun playing with the tangrams until we had to construct the giraffe.  This further reinforced for me that I am not a spatial visualizer (Good thing I never went into the field of ultrasound tech like I had once thought about!)  This assignment brought up my frustration level, but also made me realize that most people have strengths and weaknesses when it comes to math.

My question is: how far into frustration do you let a student struggle?  Should the group members jump in to help, or should a student have to try and work it out on their own?

The applications I see for my class are making math fun!  Students won't even realize they are learning because they are so absorbed in a fun activity.  Also, I want students to see their math strengths.  Even if they think they aren't good at math, there should be an area that they feel confident in.

Math Class #4: Oh no, not geometry!

So as Robin has mentioned multiple times, when you ask someone about math, they have a strong reaction.  As for me, I really enjoyed math to a certain point.  Algebra made complete sense to me and I liked to do it.  But if you say the word...ge-om-etry...I'm going to freak out!  I am not one who can mentally picture 3D items; my nemesis on tests are those problems that give you a 3D item unfolded to a 2D item and you have to be able to visualize it in 3D.  Not happening. 

In class I did learn to fold the 3D box, as well as to face my fear of geometry and folding.  I also saw the implications for classroom practice which was the power of showing someone step by step and working together.  If you give me a set of written directions to fold an object such as a paper crane, I will fail every time.  If you actually demonstrate it step by step, I will be able to do it.  I know this applies to my students also.  Each of my students has strengths and weaknesses in math, and it is my job to help them to be successful. 

Class #3: Gapminder

This week in Math we were able to finish and view everyone's Gapminder posters.  I learned so much about presenting data in different ways, and also how everyone's interpretations and presentations were different.  For instance, I enjoyed graphs that were basic and provided all of the information.  I would get overwhelmed on the posters that were very busy.  But that is just my style, everyone has their own preferences. 

The question I have is: How much time would you have a Gapminder project go on with elementary or middle school students?  How do we fit in a lenghty project like this when we are given a math pacing guide that tells exactly which lesson you should be on each day?

I see this as a useful project to use in a classroom.  When viewing the standards for 5th grade, line graphs is among them.  I believe that using Gapminder would be a memorable experience and would give more ownership and meaning to the data and graphs the children produced. 

Class #2: Positive & Negative, polynomials with manipulatives

This week I was amazed at the alternative ways to teach by using manipulatives.  When I learned about positive and negative numbers and multiplying polynomials when I was in school, we had to memorize a process, but were never told the logic behind it.  In class this week I was able to see why these processes work.  It was so much easier for me to visualize adding and subtracting the positive and negative numbers with the two different colored beans and making pairs.

The question I have is how long to use the scaffolded methods before moving to teaching the students the theorem or process to use?  For example, my daughter who is in 4th grade came home with homework for multiplying two two-digit numbers together.  The method that was being shown was the grid where you multiply each number by the others and add up the sums.  Two of her friends had shown her how to skip this step and set up an equation like:
  42
x37

Now that she was able to do it the quicker way, she no longer wanted to do homework that took much longer.

The implications this class session had for classroom environments were very clear.  I think it is important that the kids know why a process works and that they can visualize it.  By using the manipulatives, the kids can see and understand why the math works.  It is also best to have multiple ways to explain a problem so that every child can understand.

Math Class #1: Snakes, Gardens, and Rivers

This week I learned more about finding relationships between different situations.  I have always had a hard time with these types of problems, because I don't do well with visualizing situations.  I do better with looking at a sequence of numbers and figuring out how to move from one to another.  It was helpful to have practice with these types of problems and have manipulatives to use to figure them out.

My question is about Cohen's group method.  How often should this approach be used vs. individual work?  Are there times when individual work is more valuable?

The first implication that this class had for our future classrooms was the group work.  I really liked that each person had to be accountable for knowing how to get the answer so each person knew how to solve the problem.  Another implication was having students use manipulatives to show the class how they found their answer, and seeing multiple ways to do the problem. 

Snow Math

So all this snow had me thinking about the addage: "no two snowflakes are alike."  Is this really true?  Are there really an infinite amount of snowflakes that never repeat?  Luckily, I have the internet to consult.  After reading a few different reputable websites (http://www.its.caltech.edu/~atomic/snowcrystals/alike/alike.htm
http://www.sciencebase.com/science-blog/are-all-snowflakes-different.html)

The answer appears to be that no two larger snowflakes are alike.  Wow!  That really boggles the mind! 

Math is Fun!

This video is just one of the many that is on YouTube by the group They Might Be Giants.  They put out a Friday night podcast of videos done to their educational songs.  These videos are a great way to get kids excited and interested about math.
The songs are catchy, and the kids love to sing along.  I was introduced to these in my dyad class, and have since shown them to my girls.  They cover different subjects such as math, science, and art.  

I really like bringing multimedia into the classroom, and I look forward to using it into my class.  One obstacle I see if that our district blocks the use of YouTube, so I don't know how they can be downloaded.  One possible option is to have a blog of videos to use in the classroom.  I think it would also be fun to have the kids create their own music videos about math.