Mth/157 Research Paper

Reflective Paper
Maurice Young
MTH/157
September 15, 2013
Evan Schwartz

Reflective Paper
Mathematics for Elementary Teachers is a two- part course designed to prepare potential educators the mathematical concepts need to teach to elementary schools students K-8. The two-part course also addresses the relationship concepts to the National Council of Teachers of Mathematics Standards for K-8 instruction (Billstein, Libeskind & Lott, 2010). This semester, which presented the second half the two-part course, the MTH/157 curriculum gave appropriate statistical methods to analysis data, applied basic concepts of probability, applied and identified geometric figures and shapes for problem solving, and identified applications of measurements. This class introduced very interesting, exciting
and fun ways how to teach the above mathematical concepts like probability in the form of games. There are several types of probabilities: Theoretical Probability and Experimental Probability. Theoretical probability examples can be used to illustrate the predictions of the “Coin Flip” or “Dice Roll” probability games. Yang’s example: If there are n equally outcomes and an event A for which there are k of these outcomes, then the expression of the probability that the event A will happen looks like this P(A) = k/n (p. 283, para. 4). What I experience while playing the “Coin Flip” game was that the probability of flipping the coin and it turning up heads was P (H) = ½. To include, the probability of flipping the coin and it turning up tails was P (T) = ½. So, if the chance of the coin flipped and turning up heads is 0.50 then the probability of two coins coming up heads is 0.5 x 0.5 = 0.25. What I experience while playing the “Dice Roll” game was that with both dice being rolled the outcome, sample space and events of the probability could be many. Rolling the two dice there would have been 36 different ways to predict the outcomes. I decided to roll one die instead of two dice so that I could fine the probability of the die turning up an even number which resulted P (E) = 3/6 = ½. When dealing with real life situations, it is impossible to use the theoretical probability method. The experimental probability method is best used in these instances by performing an experiment or survey. The experiment is used to predict occurrences that will happen in the future (Yang, 2012). Probability of independent and dependent events might be the most difficult concepts for students to grasp. Independent events are those where the outcome of one event is not affected by the other, and dependent events are events where the outcome of one is affected by the other. The formula for these events could cause the student to become confused if not learned correctly. The course introduced the concepts of geometry in a fun way by giving me the opportunity to modify a geometry manipulative activity. My activity was to show kindergarten thru first grade students how to identify three geometric shapes and how to select and count a specific shape out of a mixed group of shapes. The student will trace on the colored paper the example of the shape on the blackboard which will be displayed one at a time by the instructor. Each time that the example shape is placed on the blackboard the student will call out the name of the shape. The instructor will then hold up that specific shape and its color so that the student can call out both the shape and its color to trace. After the student has identified and traced all of the shapes on its specific colors, the instructor will place on the student’s desk 10 cut out shapes consisting of 3 red circles, 5 yellow squares, and 2 green triangles. The instructor will ask the student to place all of the different shapes in 2 lines consisting of five shapes (assistance might be needed). While the instructor is observing each line of shapes, the instructor will ask the student to put all of the same colored shapes together in the lines. The instructor will then ask the student to count and to tell the instructor the number of each shape that is in the mixed group of shapes. After the first question is answered correctly, the instructor can then ask question like: “Are there more squares then circles in the first group or second group? “Or “How many more squares are there then triangles in the first group or second group of mixed shapes?” and “Tell me what shapes is closest to the squares?” MTH/157 not only introduced a curriculum that would help potential math teachers how the above mathematical concepts to elementary students, it also teaches the math teacher what concepts that the students might have difficulty with and gives information on how to help that individual student to grasp the concepts.
In my opinion, the best way to make sure that every student learns any mathematical concept is to make it “fun and game” learning. In this way, students are more successful in clearly understanding and comprehending the fundamentals of the subject and have a better chance of not forgetting, at least, the beginning steps. I have learned from this class that the above is very vital to achieve the characteristics of a professional mathematics teacher. If I were to recommend anything in the way to add to the course curriculum, it would be very little because I felt like the course was designed for someone like me an individual who has always found math courses to be very difficult. This course has been simplified to a dream that has influenced my ideas philosophy of teaching and that is that “the most difficult can be fun
learning!”

References:
Billstein, R., Libeskind, S., & Lott, J. W. (2010). A problem solving approach to Mathematics for elementary school teachers (10th Ed.). Boston, MA: Wesley
Yang, Rong. (2012). A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra, Publisher, A-Plus Notes Learning Center. Los Angles California