On Effectively Teaching Geometry, Probability and Statistics

Recently I was exposed to the concepts of interior and exterior angles. We learned to very beneficial formula of 180(n-2) for interior angles. In many education environments you take the formula and simply plug in the corresponding numbers. Instead, we took time to process that the  subtraction of 2 accounts for the two triangles that can't be formed in the process of triangulation, due to being adjacent sides to a vertex in a polygon. I believe triangulation is extremely beneficial to visual learners who need to visually process the amount of triangles; and thus interior angles, in a given polygon. The concept of interior and exterior angles amounting to a supplementary angle of 180 degrees is also greatly beneficial. Through our recent geometry activities, we have been exposed to a great deal of helpful teaching manipulatives. We were exposed to one technology that enables teachers to guide a powerpoint presentation on students individual tablets. This innovative teaching I thi

This last week was an introduction to shapes and angles and everything to do with them. We started with a fun activity of the Angle Finder. The angle finder was simply a index card that naturally lent itself to 90 and 180 degree angles. This opened my eyes to see how heavily reliant modern architecture is on 90 degree angles. We also reviews the relationship amongst line and line segments into different categorizations. Parallel lines, if continued indifferently , would not interest. Intersecting, lines on the contrary do intersect. There is even a more highly specific word of perpendicularity which implies a 90 degree intersection. Then, there are skew lines that don't interest and aren't parallel because of where they lay on their corresponding planes. We also submerged ourselves to the world of shapes and angles. We most dealt with triangles and quadrilaterals since those are the shapes that serve as the building blocks for all others. Triangles can be broken into characte

When learning about statistic measures of spread we fell on a very important subject as a class, standard deviation. A subset within standard deviation that I think is even more vitally important is normal distribution, or a bell curve. Having an understanding on this concept is vital to connecting knowledge of statistics to the world around you. For instance IQ is heavily based on how many standard deviation off the norm you stand. The average IQ score of 100 for example, represents a score in which 50 percent of the population scores higher than, and 50 percent scores lower than. Nature pretty accurately results in the bell curve as well. For instance a population has a wide array of outcomes in something such as eye sight, some members have perfect vision while others are left blind, but of course a majority lie somewhere in between. A helpful hint as to the percent of a population within the subsets of a a given standard deviation is 68/95/99.7 , What these values represent is ho

This is an example of the M&M graphing activity and the bottom shows conversion to a pie chart utilizing Microsoft Excel.

This last week we have immersed ourselves into the different types of graphs that we are likely to encounter. Pictographs, Bar Graphs, and Circle/ Pie Charts were introduced together as an effective means of displaying different types of categorical data. Separately we encountered a real graph while doing an M&M activity. It was considered to be a real graph because we were categorizing the color of our M&M based on the real sample size we had available in front of us, modeling it with the actual item we were measuring. Numerical data is better served by the following graphs: dot plot, histogram, and stem and leaf. Highlighting between discrete(each data entry unique) and continuous (data isn't nessecarily separate) data should also be emphasized. My criticism of the stem and leaf graph is that it really has no transferrable use outside the use of educational environments. In the M&M activity I also appreciated how the manufacturing statistics out of the factory in Hack

This showcases how odds are used in a real world application.