Week Five 1510

Oh how I love Minnesota Summers!  Blue sky, green grass, birds chirping, and people out and about.  As a family, we enjoy camping, swimming, biking, and traveling during the summer months.  I have recently taken up walking as my form of exercise and stress relief.  I was an avid runner for almost 25 years, and about 2 years ago I started to feel my knees "give out" after a run.  So, in an effort to remain sane and healthy I began to walk; I feel great and there is no more pain in my knees.  And, walking is something that my husband and I can do together and actually hold a conversation!  He is 6'5" and I am 5'4" so any running we may have done in the past was a sprint for me and a jog for him.  So now, we walk together and soak in the great outdoors.

A few mornings ago, as we were beginning our walk, we noticed another couple beginning their walk about 6 blocks ahead of us.  (It is important to note that the path we walk is a basic rectangle.  I am a creature of habit and I have been running/walking this particular path for years.)  As we progressed down the first lag of the route, I started to hope that this couple would turn a different direction than the way we were going to be turning; at this point we had closed the gap to about 3 blocks.  (Please keep in mind that they have no idea we are behind them.)  They ended up turning the same direction that we would soon be going as well.  It was obvious that we were going to catch up to them!  My mind started to race as to how to pass two people that were walking when we too were walking!  It is one thing to pass a walker if you are biking or running, but walking?  How is this done?  When you pass do you yell "Coming up on your right!"  Or does one pick up the pace to the point of hyper extending your knees?  Call me crazy, but these are the things that swim through my mind when confronted with a pressure situation, such as the one we were about to encounter.

Pretty soon, I could hardly take the anxiety, we were right on top of them!  It was at that same moment that I remembered certain math formulas and how to pass these people without them knowing!  Just yards ahead of us was the high school athletic field; tennis courts, a soccer and football field, and a running track, and at the corner of that field, straight ahead, was the 2nd turn in the path.  As all of us approached the last intersection before the 2nd turn, we needed to make our move!  This was our opportunity to beat this couple by letting them go straight while we took an immediate right turn.  Now, I know that the shortest distance between two points is a straight line, we however, had no straight line to walk.  Remember, there was an athletic field blocking the logical path to the opposite corner!  There was no way to cut through, this required speed and concentration!  The only way we were going to beat this other couple distance wise and end up ahead of them on the other side, was to pick up our speed; I mean drastically pick up our speed!

My husband thought  I had lost my mind, I was laughing and sweating profusely trying to beat this unsuspecting couple to the opposite side of this giant athletic field!  My husband kept saying, "You know, they have no idea that we were even behind them."  And I would reply, "Faster man!  We must beat them!"  (In hindsight, maybe the sun was starting to "get to me!")  Well, I am happy to report that our tenacity got us ahead of the other couple.  In fact, when we reached the opposite corner, they were almost a block behind us now!  This made me very happy and I laughed at how ridiculous and goofy I can be at certain times in my life.  But hey, I enjoy a challenge!

The path we walked is 2.7 miles in distance and we had completed it in 40 minutes.  This means that we walked at a pace of approximately 4 mph.  The pace we were walking at was 15 minutes/mile.  I used to run a 10 minutes mile, so this isn't too bad!  Remember, always keep your eyes open for living, breathing math situations and see how determination and a little fun can make a rather routine habit exhilarating!

Week Three 1510

My assignment this week was all about cooperative learning.  Here is a You tube video that sums up the idea of cooperative learning:

Cooperative learning is an excellent tool for students, of all ages!  This past semester I was able to observe excellent teachers in the classroom.  I was surprised to see the constant movement in the classroom compared to what I grew up with almost 30 years ago.  Classrooms are mobile and active, which is something that is exciting to see.  I was able to watch these master teachers take students of all ability levels and create an environment that allows every student to excel.  In the elementary school that I have been observing in, there is a high population of ELL students.  I noticed that many of the ELL students that spoke no English would sit quietly in class, taking in all the sights and sounds of the classroom and then work the best they could on the assignments.  When the teacher or specialists spent extra time with the ELLs there was a greater opportunity for deeper learning.  However, with 25+ students in a class, it is easy for the quiet students and ELLs to get overlooked.  This is where cooperative learning is a great benefit for all students.

My mentor had great success with Think-Pair-Share in his classroom.  He used this technique daily and several times within each lesson.  I watched as quiet students came to life when they were given the time to think about an idea, share with their fellow classmates in a small group setting, and then present to the class as a whole.  I marveled as students encouraged each other and politely challenged some thoughts and ideas.  The students who were higher achieving always took the time to listen and offer any suggestions and the students who tend to struggle always listened closely.   There were times that I could literally see new ideas form as two or three students talked about concepts and ideas. 

This type of learning gets me very excited!  I look forward to observing over the next several years as I finish up my own education, and take all these ideas and concepts into my own classroom.  I can already see that cooperative learning is an incredible tool for every classroom.  I get excited watching students work together and understand ideas rather than "just learn it."  As students go into to the world and continue in their education and become employed, this teaching tool will prove beneficial in daily living.  You can't get much better than that!

Week Two 1510

This week in Mathematics for Elementary Education Teachers, I am learning about "Sets and Whole-Number Operations and Properties."  That is a mouthful and the information that follows is just as jam-packed with great information.  Last week, I felt that most the information presented was more of a refresher for me.  However, this week there has been far too may "what?" moments rather than "aha" moments.  What I found the most challenging was the information presented on Numeration with the included information on the "base-ten place-value numeration system."

This YouTube video does a good job giving a basic background for the reasoning behind base-ten.  As a substitute teacher, I am familiar with the schools using blocks and charts to help students comprehend the value of a unit.  Being able to see a relationship between units will help students understand and visually see that math is a part of everyday life and not secluded to the classroom.

The lesson in our text continues further into different bases and learning how to get from, for example, base six to base eight.  As I am still grasping the idea behind the different bases, I was able to watch this video that helped me learn how to go between the bases.

I have to admit that I have mastered the mathematical equations involved but I have failed to fully grasp the concept of base-ten numeration.  This course will move quickly and I am hoping that I will be able to fully understand concepts as they are introduced.  This is one that I am going to need to look over to be able to know the reason behind this type of teaching.

Week One 1510

This week in Mathematics for Elementary School Teachers, I was reintroduced to communicating and reasoning mathematically and problem solving.  Thankfully much of the information was a refresher but at the same time, I was challenged in my thinking when I read through the material titled "Reasoning Mathematically."  As I continued to read, I came across terms like "converse statements," "inverse statements," and "contrapositive statements."  What?  This threw me for a loop and took extra time to grasp.  I found this clip from YouTube rather helpful:

A friend of mine is a high school math teacher and I have recently found out that he creates math songs and videos to help his students.  I listened to it a few times and began to realize that math really is as easy as it appears at times; I need to stop over thinking things.

When reading further in the text, I was able to draw on the words themselves to help me understand the meaning of them.  For example, when I have a conversation with someone, we are speaking back and forth to each other.  Likewise, the converse of a conditional statement is formed by interchanging the hypothesis and conclusion.  Back and forth.  Another everyday example is found in my laundry room.  When I invert my childrens' clothing before washing them, I am turning them inside out (or really right side in!)  Again, the inverse of a conditional statement is formed by negating (opposite) both the hypothesis and conclusion.  Finally, and probably resounds with many of you with teenagers, is when my children contradict every idea I may have.  In essence they are attempting to have the same effect as the contrapositive of the original statement (idea).  Not only are they telling me my idea isn't any fun, they are turning my idea around.  The contrapositive of a conditional statement is formed by changing both the hypothesis and the conclusion and negating both.

This is what has helped me rejoin the math world and begin to understand mathematical vocabulary, which really is a part of my everyday life.  Understanding the root of a word helps me to further comprehend the mathematical concept that lies behind it.  After much studying and reviewing and watching videos, I am happy to say that I understand these terms and the logical reasoning attached to them.  This week turned out to be a brainteaser for me until I was able to see the terms from real-life situations.