Mathmaticious

Okay, so this was quite humorous haha. I felt I needed to share this.

Reflection on Math 107

     Overall this past semester, Math 107 has been a challenge.  Coming into this course and knowing the name of the course (Elementary math), I thought it was going to be a piece of cake.  I took Math 100 last semester and I feel like it had nothing to do with Math in this previous course.  However, it was good to see a math course last semester considering it had been a few years since I have seen math.

     I feel that I have learned a lot this past semester.  It was a challenge, but for the most part I made my way through.  I did fairly well on most of the quizzes and take home assignments.  I did struggle with the tests but did corrections for 4 out of the 5 tests.  I found the test corrections very helpful this past semester.  Not only did it help better my grades but it also helped me understand the material better.  I also liked the quizzes because they were short and showed what I was able to do before a test.

     Another difficult part of this course was not being able to use a calculator.  I understood the reasoning for it but it was something that I just wasn't used it.  I noticed throughout the course how many silly errors I made just from doing simple calculations.  With that being said, it is very important to double check your work, even if it seems to be an easy problem.  

     Looking back and learning about bases, at the time I found it to be very difficult.  Now, I don't feel that way at all.  If anything, that topic isn't at the top of the list for most difficult.  I'd say I struggled with factoring like I always have.  Ever since factoring was introduced to me in the 10th grade I was never good at it.  I definitely need to spend a lot of time reviewing before the final arrives.

     Math is the only subject I struggle with.  I don't know if it runs in the family, but the majority of my immediate family isn't too great at math.  I am not putting the blame on my genes though! There have been times this past semester I could have studied more.  It's funny because I am not used to studying.  The other course I take I do not have to study for.  So, when I study for math I spend usually 30-45 minutes.  Now that I think about it, that's not much time at all.  

     My feelings about math definitely changed.  I no longer despise this subject.  I feel that I have come a long way and regret putting it off for so long.  I haven't missed a class yet and I am glad.  I need all the time I could get.  

Mean, Median, and Mode

  We have recently discussed mean, median, and mode.  Based on the notes I took in class, mean is the average of a group of given numbers.  First, you would add each of the numbers together.  You then take the sum and divide it by the amount of numbers you were given originally.  For example, 1,2,2,3,4,4,4,5.  Add 1+2+2+3+4+4+4+5. This equals 25.  Take your sum (25) and divide by 8 (amount of digits show).  The mean (average) is 3.125 or if you decide to round 3.13.   Median is said to be the "middle" number.  We already know 8 digits exist.  Being that there is an even number of digits we will have to take two digits from the center. 3 and 4.  Since there isn't a number exactly in the middle, you need to add 3 and 4 and divide by 2.  3+4=7.  Then 7 divided by 2 is 3.5.  Your median for the following numbers 1,2,2,3,4,4,4,7 is 3.5.  Mode is the number of times a number appears.  In this case, in the example above, the mode will be 4. By looking at 1,2,2,3,4,4,4,7 you can see 4 occurs three times.  

     I find this topic one of the easier ones in math.  I have seen it multiple times and I realize the importance of it now.  You can apply this to your classroom to find where your students scores stand.  Another part of this chapter I found interesting was standard deviation.  When the term was mentioned I didn't really remember what it was.  I found a simple explanation of what standard deviation is on Wikipedia.  I know Wikipedia isn't the best source but after reading some of the text it was similar to what was discussed in class.  

Standard deviation is a widely used measurement of variability or diversity used in statistics and probability theory. It shows how much variation or 'dispersion' there is from the 'average' (mean, or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data is spread out over a large range of values.

As you can see, it is exactly what was discussed in class and I wanted to provide the few graphs we saw as well.  

Each graph above should look familiar.  As a teacher, you would want your students to be on the same "page".  This is why, standard deviation plays a major role and can help a teacher discover where her students stand. 

Graphing

     One of the most recent topics we discussed in our course was graphs.  We went through a small packet that included a variety of graphs.  We looked at the bar graph, histograms, line graphs, pictographs, circle graphs, and pictorial embellishments.  I personally forgot there were even that many types of graphs.  I haven't deal with this topic for quite a long time.  I always enjoyed constructing graphs to show data.  Graphs are used widely throughout businesses and it is an important concept to know and understand.  

     When I am a teacher one day, I find graphs are a good thing to incorporate in a classroom.  They can be fun and provide a positive learning experience.  In my classroom, I will make a graph of the kid’s heights.  I will collect the data and have them make a graph of their own.  They can decorate their personal graphs and compare and contrast one another’s heights.  This is a good math lesson and can only benefit them later in life.  Unfortunately, some people have the wrong idea of creating a graph.  

      There are graphs out there that have misleading information.  How a graph is created really affects how people perceive the graph and some may see data in a different way then how it really is. Below, I found a graph that doesn't show the data in the best way possible.  It is nice there is a title, but if you look at the scaling on the vertical axis, you will see how it can be difficult to read the information given.  Europe has this 3D effect that looks distant from the scale.  Due to the way this graph has been established, you will not be able to get certain points properly.  Yes, there are positives to this graph such as the coloring and labeling, but I think a line graph, not shown in a 3D form, would be more suitable for information containing a comparison of river runoff through the 20th century.

 

   A more appropriate graph, in my opinion, is shown below. 

 

    I like this graph because it is clear and concise.  You can easily pinpoint certain data you'd like to find and everything is labeled.  There is a legend available consisting of the different color scheme and shapes which makes it easier for the reader.  This graph would have been a better fit for the other graph above.  Even though each graph deals with different types of information, the data can still be portrayed in similar ways.

      

     

Change in Mathophobia...

     So it has been quite awhile since my last post.  My first blog was about mathophobia and how I felt about math.  Since then, I am proud to say my feelings about math have changed in a positive way.  I do not despise this subject anymore.  At first, I didn't even want to give it a chance.  I kept putting off the course until the very end.  Now here I am, admitting that I do not mind learning and doing math.  I know I am not the best at it, but I have come a long way.  I am now open to new concepts.  I have learned and refreshed my memory in different areas that we covered in the course this semester.  

     At one point, I thought it was funny that we were going to be adding, subtracting, multiplying, and dividing fractions.  It came to my surprise that I didn't remember how to do problems so well.  The past few years I have been using a calculator.  I did all of my operations through the use of a calculator.  It made me become rusty.  Now, I can do operations by hand and I find it much easier.  I have been doing better on the quizzes and take home assignments.  My test grades are not the greatest but they aren't terrible.  My average in test grades seems to stay in the 60's.  It's as if I am close to doing well but seem to be on the border line.  Yes it annoys me, but I always try my best.  My mathophobia on tests seems to have changed as well.  I don't worry so much anymore.  I spend time studying and looking over my notes and doing practice problems that are given to us in class.  I always do the test corrections and I find it very beneficial.  I like the fact that out teacher allows us to do them because instead of just looking at the grade, I actually spend the time to go back and correct errors.  Some errors I notice are silly and careless.  Other errors I learn from and can acquire a better understanding of the material. 

      I just don't mind math anymore and it is a good feeling.  I never realized in how many ways math can be used.  Math is used in everyday life.  I could be out shopping and see that a clothing item is 30% off.  Many people don't know how to compute that and it is good to know.  I am glad the course is as it is.  The material covered is important and can be applied to everyday life.  There are going to be instances where children ask questions and I need to be able to answer them.  I am going to be a teacher one day and to say "I don't know to a child" isn't the best thing to say.

Prime Factorization, GCF and LCM

   I was relieved to know we were moving on to this topic in chapter five.  I didn't enjoy our first chapter, sets and shading etc.  I absolutely hated that chapter and it even showed on my test.  Therefore, I am thankful we have test corrections in our class.  I am not going to lie, I was surprised when I realized what we were going to be doing.  I haven't heard of prime numbers, GCF and LCM in a very very long time which means I haven't done it. 
  I am expecting to do much better on this upcoming test.  I feel that I know and understand the material much better than last unit.  I don't mind doing the factor trees and figuring out problems.  I hope to do much better on the true or false section on this test. 
  What I really like about this unit is that there is a choice of methods to use to figure out the GCF or LCM.  I mentioned above that I don't mind the factor trees, which is one of the theorem's to choose from.  I am not a fan of the set intersection method for finding GCF.  It it too time consuming and there is always the possibility of missing a factor.  It can also be difficult for someone who doesn't know all the factors of different numbers, I am one of those people. 
  Another theorem I consider using to find the GCF is the subtracting method.  This method is good to use especially when the numbers aren't too large.  To start out it'd look like this GCF (350-250,250) and one would continue that until there are two similar numbers in the parentheses.  There is another theorem that deals with long division.  I personally haven't done long division without a calculator since elementary school.  I don't really bother with this method which is why I'm glad there's a choice. 
   It's always important to know that GCF, with prime factorization, needs the lowest exponent with only COMMON numbers.  Where as LCM needs the highest exponent with ALL numbers. 
  The prime factor test is the main thing I struggle with in this unit.  I confuse some of the rules to determine whether or not a number is prime.  I know how to figure the square root in that first step, which is why it's important to know all the numbers up to 100.  I know I have to test primes up to the first number.  From there I just seem to get confused.  I will just have to practice more on that part of the unit.  This time around I am not worried about this test and seem pretty confident.  I just hope my mathophobia doesn't kick in once I receive the test.   
    
  

Piaget

    The following article "Applying Piaget's Theory of Cognitive Development to Mathematics Instruction" by Bobby Ojose, discusses concrete stages of cognitive development in children.  Jean Piaget is a primary focus in children's psychology and has contributed a great deal of information in that field.
    All together, there are four primary stages of development.  They are sensorimotor, preoperational, concrete operational, and formal operational.  Some of this information is a summary to me because I have taken two psychology courses here at Dutchess Community College.  Each course discussed Piaget and the stages that were mentioned above. 
    The sensorimotor stage is “characterized by the progressive acquisition of object permanence in which the child becomes able to find objects after they have been displaced, even if the objects have been taken out of his field of vision”.  This stage is also important for a child to link numbers to objects. It’s interesting to know children at such a young age are able to have this concept of numbers and counting.  Mathematics starts early and it is just the beginning.
    The next stage is the preoperational stage.  Now, children engage in problem-solving tasks. Children can use materials such as blocks for building and sand and water for measuring. 
    The third stage is the concrete operations stage.  Cognitive growth in this stage is remarkable.  Hands-on activities are great because they have mathematical ideas and concepts which is useful for problem-solving.  Manipulative materials include: pattern blocks, Cuisenaire rods, algebra tiles, algebra cubes, geoboards, tangrams, counters, dice, and spinners.  These are all great items to contribute to growth in mathematics. 
    The last stage is the formal operations stage.  Children develop abstract thought patterns where reasoning comes into play.  Such reasoning skills include clarification, inference, evaluation, and application. 
    With these stages, teachers have the opportunity to develop lesson plans based on where a child stands.  Teachers are able to know what children know math wise and can provide proper materials that children will know how to use.  At certain stages, I would only focus on what type of growth is occurring.  For example, in the sensorimotor stage, one can read books to the children that show objects linked to numbers.  There could be a picture of three dogs with the number three right next to them.  Children could easily begin this concept and make the necessary connections. 
    I always wonder where things would stand if people like Jean Piaget never discovered stages of development in humans.  Piaget made it possible for teacher's to teach math at a proper level to children. This was an interesting article and it really refreshed my memory. 

Visual Learner

     Everyone prefers a specific learning style.  A person can choose from over three learning styles when dealing with a subject.  These styles include visual learning, auditory learning, and kinesthetic/tactile learning. In math, I consider myself a visual learner.  I need to see examples and pictures drawn.  This way, I am able to make more connections and have a better chance of remembering the material.  Being a college student, I take many notes from lectures and I prefer those notes to be written by the professor on a blackboard.  I feel more confident by this because when test time comes around, I know I have material ready to be reviewed.   

     All teachers are different and I never know what to expect on the first day of class.  Some teachers prefer to talk the full hour and fifteen minutes while students jot down facts/statements that have been said.  Others make use of power points and blackboards for students to copy from.  In math, visuals are a must.  It's easier to make graphs and draw diagrams to figure out a problem. 

     The following article "Learning Styles" is a good way for someone to figure out which type of style is strongest.  I pretty much answered yes to all of those questions in the visual learner section.  I like to see things written in order to read it as many times as I need to.  Which is why I prefer written instructions as opposed to oral instructions.  I know where to look and don't have to bother asking over and over.  When I study, I rely heavily on notes that I've taken in math class.  I write down everything that's written on the board.  It could be a number of examples and terms, as soon as I see them, I write them down.  Later on, I know exactly where to look and can remember what we did in class. 

     During math lectures, I don't doodle or have my mind elsewhere.  Knowing that math is my weak subject, I focus and am too busy writing as well as looking at the examples.  I give a lot of credit to those who are strong in auditory learning.  In one lecture alone, a lot of material is covered and a ton of information is said.  Those who can listen a great length of time and be able to remember the information, are not simple tasks.  That is just my opinion, like I've said above, I need to write notes in order to remember information.  In a sense, I can see how auditory learning could be helpful in some aspects.  One being, saying words or terms aloud over and over.  That is something I do when I am really struggling to remember something.  It sinks in more this way, but overall I am a visual learner and I will continue with writing notes, using pictures and looking at my math book. 

Mathophobia?

  About five years ago, mathophobia entered my life.  It is the only subject I struggle with and I have been holding back from it.  I remember I was in the tenth grade and I was not understanding the new material.  Everything kept building up and I became more and more stressed.  Luckily I made it through to the eleventh grade math (Math B).  I passed eleventh grade math, by one point! I struggled...terribly. My junior year I was going to math labs, receiving help from friends.  I even felt more discouraged because I had a terrible teacher.  Let's just say, he resigned, but would have been fired.  I had two other math teachers that same year, a teacher would come and go.  I never felt comfortable with that course and it was never steady.  

   I took an online math course last semester, Math 100.  I needed to refresh my memory and re-learn how to do many things.  I found it very helpful and it prepared me for an upcoming math course, Math 107.  I will be honest, I am not thrilled I have to do another math course again this semester, but it is an important requirement.  I'm taking a different approach this time around.  I am going to have a fresh start and attempt to learn this math to the best of my ability.  I want to succeed. I have never failed a course in my life and I always get A's and B's.  This is one course I will have to spend more time on.

    In class recently, everyone took a quiz that would tell them if they had mathophobia or not.  According to my score, I was in the category for mathophobia.  I knew I had it before I even took the quiz as I've mentioned above.  I get nervous when I have to take a quiz or test, and nerves cause loss of memory! So this semester, I plan to take many notes, focus, study, and ask questions.  I want to do well and be prepared for what is to come.  I don't want to be one of those teacher's that show children I hate math.  I will pass that point and continue to move forward.  I think that every person has the capability to succeed.  Math comes easier to others which I find is unfair by the way!  But oh well.  I will be someone who needs to spend extra time, have more examples, and study.  Like I said before, I am going to have a fresh start.