Week Six 1510

This weekend turned out to be a very hot and humid weekend.  We started Friday off with thunderstorms and ended the day with almost 7" of rain in a flash storm that lasted about 2 hours!  That is a lot of rain in a short amount of time.  Interstate 90 runs through Austin, MN and actually is perpendicular to the end of our block that we live on, and the city closed Interstate 90 for a few hours due to flooding!  We have lived here for 15 years and although the interstate gets closed several times during the winter season, this was a first for us.  Austin, MN made the Twin Cities news because of the closure, that is always fun!  When we started our day on Saturday, we could tell right away that the heat was going to overtake the cool aftermath of a thunderstorm.  My kids got the idea to set up an ice tea stand at the end of our block and they asked me to bake chocolate chip cookies to sweeten the deal :)

Ironically, this particular week in Mathematics for Elementary School Teachers, fractions was the topic of learning.  Baking is filled with fractions and is always a great teaching tool for my kids when we get the chance to do it.  By the time I began baking, the temperature outside had reached the low 90s and even though the air conditioning inside was perfect, turning on the oven was pure madness!  However, when it comes to creative ideas and the kids getting along, I will help them out with just about anything.  They braved the heat and set up their stand and sold $23.00 worth of ice tea and chocolate chip cookies at $0.50 for both.  They had a blast and Chris and I enjoyed peeking out the window of the air conditioned house to watch them flag down customers and see the smiles on their faces when they would make another sale.

Here is the recipe for these delicious chocolate chip cookies:
Oven at 350 degrees

1/2 cup softened butter (not margarine)
1/2 cup shortening
Beat these two together in a large mixing bowl, set aside
2 1/2 cups flour
1 cup brown sugar
1/2 sugar
2 eggs
1 teaspoon vanilla
1/2 teaspoon baking soda
Combine into separate bowl and mix generously
1+ packages of semi-sweet chocolate chips for baking

Take approximately 1/3 of the flour mixture and add it to the butter/shortening and mix.  I use and electric mixer.  Once blended, add another 1/3 and mix, and then add the remaining flour mixture and combine until all blended.

I listed 1+ packages of chocolate chips to the ingredients because we love chocolately cookies.  I have made this recipe for years and I have never had a complaint about them and pretty much everyone we know loves them.  So here is my secret:  I add one full package and about 1/4 of another package and hand mix them into the cookie batter.

Drop tablespoon size balls onto cookie sheet, I can get 8 on a jelly roll size pan.  Bake 10-12 minutes but keep an eye on them.  My first batch always takes longer.  And here is part two of my secret:  Take the cookies out just as they are slightly brown around the edges.   This particular recipe does well with a slightly underbaked cookie.  Even though the cookies rarely make it two or three days after I am done baking, on the off chance there are a few left, they are still soft.  If you leave the cookies in the oven until they are browned, they will not be as delicious as they really can be! :)

So this is what our weekend was all about, ice tea, chocolate chip cookies, and extremely hot temperatures!  I love that I was able to take time away from school to be a part of this fun activity with my kids.  My daughter would run home every so often to cool off and on one such visit, she exclaimed that a woman had just given her and her brother $1.00 each without wanting any tea or cookies solely because this woman had done lemonade stands as a kid and it made her happy to see them out having fun!  Now that is pretty nice!

Math really is a great subject and, as you can see, is a part of daily life.  Baking is a great activity for kids to learn about fractions and reduce recipes or doubling them.  In the classroom, it is great to have manipulatives for students to continue to have the hands on learning that is such a vital part of the school day.  I look forward to more baking and teaching as summer will pass and the frenzy of the holidays approach.

Week Six 1512

When my husband and I decided to start a family, one very big decision to make was in regards to childcare.  Do we do daycare or does one of us stay home?  Hands down we chose being at home and I was beyond thrilled to be a stay-at-home mom.  It was hard work but very rewarding.  I took part-time jobs here and there to help out with bills and to have some extra money.  I ended up getting a job as a server at Applebees about 8 years ago.  I worked nights while my husband worked days teaching 2nd grade.  It worked perfectly for our family and we all got used to the schedule.  A few years ago, I started to feel that a change was needed.  Our kids were getting to the age of being more independent and we were finding our summers being gulped up by camping and family activities.  Being a server has its perks, but weekends and holidays off is not one of them.  I had graduated in 1996 with a BS in Corporate Wellness and was not seeing that as the career to re-enter with.  With much discussion, we decided that going back to school to get my teaching license was the best fit for our family, and I was very excited about this! :)

The first step in starting a Teacher Licensure Program is to take the MTLE, Minnesota Teacher License Examination, in the areas of reading, writing, and math.  Now, I hadn't cracked a textbook in over 15 years and this turned out to be quite a test!  Thankfully, I have a husband who teaches and a few friends who are excellent in math, an area I have struggled with.  I studied for a month or so and went and took the test.  It turns out that I didn't pass the math portion.  Ugh.  That was a little hard to swallow but I kept a positive attitude and was happy that I was close to passing after being away from school for as long as I had been.  I have rescheduled the math portion of the MTLE for August 19th and after taking Mathematics for Elementary School Teachers this summer, I am confident that I will pass the exam!

The final chapter in our text is all about Algebraic Equations and Coordinate Geometry, all of which is a huge portion of the MTLE.  I found this particular chapter the most exciting chapter out of the text mainly because I know this is helping me tremendously for the upcoming exam.  As I read through the text, I was thankful that many of the equations and problem solving techniques were familiar to me and that I was actually able to understand them.  The terms slope, linear function, quadratic equation, factorization, midpoint, distance between points on a graph, and circle equation theorem sprinkled the entire chapter.  Any fear I may have had for math has been squished!  This course has helped me see that math is filled with equations and formulas, all of which are very logical and basically easy to input and solve once the time is taken to understand all that is taking place.  I am excited to get back into the classroom for observation with my mentor and help students with math with a confidence unparalleled to 3 months ago.  The culmination of this class has further confirmed that choosing a teaching path has been the right decision for me and my family.

Week Five 1512

I am an avid couponer :)  I love finding great deals and then add a coupon or two to it and make the deal even better.  I have to admit that with the amount of time I am spending on school this summer, my couponing has taken back seat to homework.  But, that doesn't mean that I have lost my touch at finding sweet deals.  Recently our grocery store, HyVee, had the sale of the century on Hormel Cheese Wranglers.  Now, if you have never had a Cheese Wrangler before, I highly recommend purchasing a package and trying one for yourself.  I am not sure what Hormel has done to create such a delicious hot dog, but they have outdone themselves with the Cheese Wrangler.

A package of Hormel Cheese Wranglers normally sell for $4.49 per package.  At the same time, I have never seen a coupon from the Hormel company offering even $0.25 off this delicatessen.  Now, if you enjoy hot dogs in general, you know that this is an outrageous price for an American treat.  But, it is a favorite at out house and so I purchase them for special occasions.  This particular 4-day sale offered Hormel Cheese Wranglers for $2.25/package!  This is a great sale!  It is almost a BOGO, buy one get one free, sale.  When I saw the sale ad, I almost did cartwheels!  I am glad that I didn't do any acrobats, I may have been laid up for weeks :)  My husband and I began to clean out our freezer in anticipation of some new product filling it up.  We decided that we could fit 48 packages of hot dogs in our freezer and be set with Cheese Wranglers for at least a year, probably 2 years.  We would have to eat a package of hot dogs per week to eat them all by next summer and that won't be happening.  I like them, but not that much.  This type of purchase is more of a "stock up" sale rather than a weekly dinner item.

I called ahead to the meat department to make sure we could purchase what turned out to be 4 cases of Cheese Wranglers, there are 12 packages in each case.  That is 48 packages of hot dogs, and each package has 8 hot dogs.  All in all we purchased 384 hot dogs and paid $108.00, instead of $215.52, which is a savings of $107.52, close to 50%!  That is alot of money!  It also turns out that each hot dog ends up costing us $0.28 per hot dog which is a cheap lunch in the summer when kids and friends come over!  I was very pleased with my purchase and these Cheese Wranglers will take us into next summer and beyond.  My advice to anyone wanting to save some money.....never pass up a good deal especially Hormel Cheese Wranglers!

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 Four 1512

I am going to start with a memory that I have of Geometry as a freshman in High School.  I was not very good at sitting and watching my teacher explain angles and lines and degrees on the chalkboard (Yes chalkboard.  I used to clap erasers as a chore after school!).  I distinctly remember taking a test that had 25 questions on it.  I did all the homework, I studied from the text, and then took the test.  I ended up getting 13/25 on the test.  I was devastated!  After class, I approached my teacher, practically in tears, and asked "what now?"  He looked at me and said "I have no idea, but you would have done better had you just guessed the answers rather than tried to figure them out."  Ugh!  That was not the response I was looking for.  I walked away from class that day telling myself that I have no ability in math and my teacher doesn't have much faith in me either.

As I reflect on that day, I know that my teacher didn't mean to crush my hopes of becoming an excellent math student.  Math tends to be difficult and requires extra effort for a person, like me, who doesn't see the equation or the answer or the reason for the answer.  I have no ill-feelings toward my teacher and I do remember that he had me come in after school for about a week as he helped me, but I was already mentally checked out.  Note to self:  as a teacher, never use sarcasm.

All of that to say that I was interested to read about the NCTM Geometry Standards for grades 3-5.  (National Council of Teachers of Mathematics).  As I scrolled through the information, I noticed how much the concept of visualization and relationships between shapes is stressed in the Standards.  "The study of geometry in grades 3-5 requires thinking and doing.  As students sort, build, draw, model, trace, measure, and construct, their capacity to visualize geometric relationships will develop."  (NCTM)  As I think about teaching, I am thankful that the standards are explicit in their objectives.  I see the standards that are written for all the subjects as a great tool and assurance that students are getting the best possible education they can get.  I look forward to challenging my students in their educational goals and will guard my tongue against the kind of "knee-jerk" remark that was said to me.

Week Four 1510

This week in Mathematics for Elementary School Teachers, I was able to read a vignette titled "Number Sense in the Classroom" (pages 18-22).  This was written by a college student studying to be a teacher, like me :)  The vignette opens with a conversation between Ms. Davis, the 4th/5th grade math teacher, and Rhonda Cane, the student intern.  They were speaking about an upcoming lesson in division and this particular response by Ms. Davis caught my attention:  "I want the children to be able to develop and modify an algorithm and to root the work in reality."  "Root the work in reality."  I really like this statement.  Teaching math is exciting and when students get the chance to apply what they are learning immediately, their potential for learning is dramatically increased.

The mathematical equation that was written on the board the next day in class was 126/9=?  The classroom was divided into two groups to test their theories.  Did someone say cooperative learning again?  This is incredible that students are given the opportunity to talk with each other and figure out real life situations in which this problem can be solved!  The students talked about candy and baseball cards and how to divide these items up equally.  Manipulatives were used to physically represent the candy or baseball cards and then begins the process of division, well sharing, in their case.  During this time that the students are teaching each other, Ms. Davis and Rhonda take time to walk around the room "eavesdropping and asking questions."

Eventually, the students become the algorithm to solve this problem.  After spending time letting the students share how they discovered the answer and comment on each other's work, Rhonda stated "it is interesting how the children forgot to use the manipulatives after a while."  I find it fascinating that the students forgot to use the manipulatives as they began to think through a real-life situation.  This shows me that the more I can give my students the chance to apply their learning, the more likely it is that my students will gain a deeper understanding of the concept being taught.  I was given the opportunity to observe excellent teachers this past semester, and I know that the time I spent in the classroom solidified all that I was learning as a student.  Applying what is learned to something you already enjoy, the candy or baseball cards or teaching, for me, is really the way to "root the work in reality" like Ms. Davis so eloquently stated.

In closing, I found this video on YouTube and found it appropriate for this scenario.  This video is showing a constructivist approach to a math class.  "Constructivist perspectives focus heavily on the role of students as active learners and also see learning as a social and collaborative process" (Pickle, 2010).   Cooperative learning is one of many techniques that are at the heart of constructivist teaching.

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 Three 1512

This week in math, I was given the opportunity to take a closer look at a problem presented in our textbook Mathematics for Elementary School Teachers.  The idea behind the discussion was to get our class thinking more critically about math and the various directions a math lesson can take.  I found this assignment to be enjoyable and yet challenging at the same time due to the lack of classroom time I have had.  I started back in school this past January and have had only one semester of classroom observation, so I find questions that put me in the position of teacher rather challenging.  However, I am up for the challenge!

The math question was given to a 4th grade student.  The topic is on probability.  Here is the question posed to the 4th grader:

The gum ball machine has 100 gum balls; 20 are yellow, 30 are blue, and 50 are red.  The gum balls are well mixed inside the machine.
Jenny gets 10 gum balls from this machine.  What is your best prediction of the number that will be red?
Student Answer:  5 gum balls
Explain why you chose this number:
     Because red has the biggest number 50 and 10 divided by 2 is 5 so 30+20=50 and the rest would be blue and yellow.

The following is the discussion that followed for me:
How is this fourth-grade student's reasoning?
Although I have not had enough experience in a classroom, I am taking an educated guess that the student appears to be creating an equation using all the numbers available to solve the problem.  The reasoning is more based on the need to make a math equation.
Do you think that this response is typical or rather advanced for a fourth-grader?
Again, I have not had personal experience with 4th graders in a math class so I am not sure if this is typical or not.  As I read and re-read the explanation to the problem, it looks as though the student does understand how to solve the problem but lacks the vocabulary to explain why.  When the student said "10 divided by 2 is 5" I saw that as the solution but the student failed to give the reasoning behind how they came to get that equation.  I asked my 6th grade daughter to solve this problem and she came up with the correct answer but was unable to give a reason behind the answer.  I also asked my soon-to-be 4th grade son and he came up with the correct answer as well.  However, he too was unable to give a coherent reason behind his answer.  Both of my kids kept saying there are more red gum balls but didn't say there are 2x as many red as other colors.  It makes sense in their heads but the reason gets lost in translation.  I look at this 4th grade student and think the same thing.
What percent of fourth-graders would you expect to get this item correct?
I would imagine that most, if not all, students would get this correct.  (80%-100%)  If this lesson is fresh in their head, I would guess that they would quickly look at the information presented and draw their conclusions and get the answer correct.
What percent of you classmates do you think would get it correct?
I think all of us would get this correct! :) 100%.  Although, I have to admit that when I stopped and looked at it, I freaked out slightly due to the massive amounts of information swimming around in my head right now!  All the recent formulas that I have been learning is causing me to second guess a seemingly easy question.  When I have stress or an overload of information, I struggle with obvious answers, so if anyone else in class is on overload, this problem may appear overwhelming at first.
I suppose to a 4th grade student who may be under stress from changes in their life or just unable to concentrate, this problem may appear overwhelming as well.  As a teacher, I need to remember that my students will encounter problems in school academically and personal issues that can effect the outcomes of school work.




After spending time re-reading this problem and reading insight from my classmates I have learned that math is so much more involved than just teaching the concepts.  Students come to school with several different learning styles and issues that face them daily.  As a teacher it is critical to take the time to learn about my students and understand their strengths and weaknesses.  Math is math and several paths will lead a person to the correct answer, but to go a step further and explain how you got to the answer will drive home critical thinking in my students, which is critical in itself.

Week Two 1512

With two full weeks of math completed, I feel that this is a good time to share a fun website that my children go to and play cool math games.

Cool Math Games: Bloxorz

The game Bloxorz uses visual/spatial reasoning and logic to solve each puzzle.  As a future teacher, this website offers an excellent variety of school appropriate games for students to play.  Leaning is fun when kids don't even realize they are learning :)

Now back to reality.....this week math was all about analyzing data.

As a product of the 1990s, The Far Side was one of my favorite cartoons to look at in the Sunday paper.  This particular cartoon always puts a smile on my face.  There are many instances that I will go through my day and not pay attention to any new detail that may be staring me in my face.  For instance, there have been several times that I have gotten in my car to go to the grocery store only to end up in the parking lot of Applebees (that is where I spent the last 7 years of my life)!  When I finally would realize that I am not at the grocery store, I would laugh at myself and try to pay better attention to where I need to go.  Paying attention or not paying attention appears to be a critical theme in the math world, or at least my math world.  From this cartoon I feel it is easy to say that you can never take for granted an obvious obstacle.  Take the time to read the directions and do as it says and you will never go wrong. 

I found this chart and thought it was a great visual for information about the virtual world we live in today.  At the same time, I would like to point out that in this particular study, it is obvious that no one contacted me to be a part of the data.  My time spent on facebook (only an open tab while studying hard) far exceeds the information presented.  Does this mean that I need to get off facebook and start browsing Yahoo sites more often?  That is debatable however, this is the joy of a chart or graph.  The information is presented in a manner that allows the person viewing the information to draw their own logical conclusions and make future decisions from a more educated standpoint.  Charts and graphs offer so much to the viewer and it is important to take the time to look at the legend and become familiar with the information that is jammed in there.  These tools are excellent for quick glances and intelligent conversation but be careful not to draw inaccurate conclusions because you didn't take the time to look at all the information presented.

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 1512

This week in Mathematics for Elementary School Teachers, I learned about "Proportional Reasoning."  This topic was rather exciting to learn about; I am finding that math really is enjoyable and interesting to learn.  The big challenge this week was Compound Interest!  Wow!  I am not sure if learning the formula or figuring out how to use graphing calculator was more challenging!  The two ideas in this particular area of the text involved simple interest and compound interest.  Calculating simple interest really is simple: i=prt.
the amount of interest (i)=the amount of principal (p) x the annual rate of simple interest (r) x the number of years (t).  Quit simple :)

Now enter compound interest!  This equation is rather detailed and when I first looked at it, I was overwhelmed to say the least.

A=the total amount of principal plus interest
P=the principal
r=the annual rate of interest (although in our text, an "i" is used)
n=the number of times the interest is compounded per year
t=the number of years

As I learned these formulas and began to understand the difference between simple interest and compound interest, I was pleasantly surprised, again, that math is basically straight-forward.  I feel that the most difficult portion of this lesson was learning the formulas and how to correctly input the numbers.  Once it clicked, I was able to fly through this information and get it drilled into my head.

My ultimate goal of this math course is to really understand why things work the way they do and not just memorize formulas.  When I look back on my education, especially in elementary and middle school, I feel like I memorized everything without understanding anything.  With the Internet and all the tools that are available within these confines, it would seem that learning math skills should be easier this time around.  I have found YouTube to be very helpful with resources from people who eat, sleep, and breathe math!  Simple and compound interest are now part of my repertoire of valuable information tucked into my brain soon to be used in my own classroom!

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.

First post 1510/1512 (General)

I am two weeks into math and I have found the information thus far to be both challenging and exciting.  I am looking forward to "fine-tuning" my math skills as the class progresses.

The first week of class presented the challenge of time management.  Becoming organized is a key component to being a successful student and I was finally able to see the big picture of all that is required before the end of July.  I also enjoyed the articles "A Coherent Curriculum: The Case of Mathematics" by Schmidt, Houang, and Cogan and "The Mathematical Miseducation of America's Youth" by Micheal Battista.  I appreciated the challenge of seeing math from different viewpoints.  I value information that gets me thinking outside the box.  These articles showed me that math is more involved than memorization and the students need to understand why they are solving problems, not just how to do them.  These ideas challenge much of what I grew up with; rote repetition.  That will be an obstacle to conquer for me during this class; don't just memorize it, comprehend it as well.   Finally, after spending time in the local schools observing classrooms, it is obvious that math is much more involved than I ever realized while at the same time, it can be as simple as it appears.

A frustration that I have when it comes to math is homework; not mine but my childrens' homework.  My daughter Abigail just completed 6th grade and my son Toby, just finished up 3rd grade.  Homework, homework, and more homework.  A huge part of our school night routine was obviously homework.  Both the children always had math homework every night and inevitably, I would be more confused than they with the "how to" of their math homework.  Thankfully, my husband, a 2nd grade teacher, is very familiar with all the "ins and outs" of the math curriculum and he was able to explain equations and techniques in a way our children could comprehend.  I would sit and listen and watch him teach and wonder when I would be able to be that fluent in math.  I was always happy that he was able to help, but at the same time I would be frustrated that I didn't know what a math tree was and the point of it.

As a student, I intend to soak in as much information as possible.  I look forward to learning the "ins and outs" of math in order to gain a greater knowledge for a teaching career.  Furthermore, I look forward to the time I too will be able to sit at the table with my own children and be able to explain math to them in a way they will comprehend.  I have quickly become aware of different learning styles in students from observing in the classroom this past semester.  In my own children, I can see that my daughter is one to get frustrated immediately and my son is one who will sit and work a problem until he fully understands it.  My daughter does well with repetition and my son learns better with visuals.  When I become a teacher I know that the students in my classroom will be diverse in everything including learning styles.

I am looking forward to the challenges and triumphs of this class and I look forward to reading and learning tips and tricks to math from my fellow classmates.