Overcomplicating Mathematics

            Throughout the third week of class, we focused on making two concepts in math become more visual to the students.  These two concepts can often be tricky to learn in math especially when it is taught using traditional schooling methods.  I believe like most subjects that math should not just be taught from the textbook.  Often times the textbook leaves out information that leads to poor understanding from the students.  Essentially, the textbooks often try to “make concepts easier” by using different language or situations but this usually results in confusion when students attempt to read the question.  Looking at the picture below, I am still very confused as to what the question is asking and this is from a grade 5 math textbook.  I was reading an article written by Gina Cassini found here http://toprightnews.com/priceless-student-sums-common-core-math-idiocy-single-word/ and I believe it truly sums up the downside to overcomplicating mathematics  Essentially, this style of learning has been put into place in many math textbooks to try and look at another approach of solving the problem.  This is a great idea in theory but it is not always a plausible method of looking at a problem.  I believe that something like arithmetic which is vital in mathematics should not be over complicated to the point of extreme confusion.  Now I am not saying that we shouldn’t be looking at mathematics (specifically arithmetic) through multiple perspectives.  I am saying that if one way at looking a problem makes you scratch your head 10 times over than perhaps that is not an effect way for students to learn.  This is why if you are trying to teach a lesson from a different perspective than the "norm" that it is important that this lesson is still clear to the students.  Often times this can be achieved by reading over your lesson plan to make sure it even makes sense as clearly whoever wrote this question must've not checked their plan. 

Source:  http://toprightnews.com/priceless-student-sums-common-core-math-idiocy-single-word/

                I believe that a solution to the textbooks is visualizing mathematics.  In class we used a variety of methods to visualize patterns and algebra.  Each student in the class made their own patterns and displayed a picture of it on the projector.  This allowed us to individually go through each of our pattern creations and work together to try and solve the recursive formula.  I believe that interact visual methods such as these are beneficial to improving learning as these combine student’s imagination with learning.  You would be quite surprised to see what some students might come up with in their pattern.  Moreover, we used algebra tiles that make learning the dreaded concept of “algebra” seem less threatening.  I similarly thought that using these was an interactive method that could be applied to a variety of problems including: factoring, completing the square, expanding binomials etc.  Overall, I am excited to see what we are going to learn next week in class as this class really makes me observe mathematics with a critical lens.

Rote Learning

Throughout my academic career, I knew I could always achieve above average grades as I had a of traditional education “studying system” down to an art.  I found this was prevalent especially in high school math courses.  I always knew that every unit in high school always had a "unit test" that incorporated a few chapters of the textbook. Although most of the time I didn't participate much in terms of the daily lessons I always knew that if I just study those chapters the day before that I will be able to do well on the application and knowledge portions of the test.  This is because the questions on the test were essentially questions found in the textbook just with the numbers altered.  The only section of the test in which I would do poor on was the thinking and inquiry section.  These sections were designed for you to not just regurgitate formulas or theories but to apply your knowledge gained throughout the unit to real world situations.  I could never fully understand these questions and often would leave them blank.  Looking back, I see my troubles with this section is actually because I never applied my mathematics skills through different applications.  I would rarely practice or challenge myself using online resources, activities etc. to put my mathematical skills to the test.  In class, we did the leap frog game which used various elements of mathematics (spatial awareness, estimating moves, patterns etc.).  This was one of the first times where I felt challenged in mathematics as I had to look at the problem from multiple perspectives.  I had to try several different ways to actually get the result I wanted.

url:https://www.bing.com/images/search?q=Rote+learning&view=detailv2&&id=9F4B7800CA4CC46B3F7652C846A229E34418B529&selectedIndex=12&ccid=%2b5zg%2bvwA&simid=608029299970869429&thid=OIP.Mfb9ce0fafc00eef5b2b4d83861ab8f3do0&ajaxhist=0

In looking at the picture above, you can see that memorization and regurgitation does not equate to true knowledge of the subject.  In the picture you can see a drawing of a person who states “memorizing is great! I don’t know why; I just memorized it”.  This is all related to the term “rote learning” which is greatly incorporated in traditional education settings.  Although “rote learning” is necessary in some cases when it comes to education I truly don’t believe it should be the foundation of which all learning is conducted.  Essentially, just like the leap frog game, there is other ways to apply and challenge somebody’s knowledge and produce a much more enriching learning experience.

           In closing, I know that we as future educators must keep mathematics fun, fresh and interesting to the students.  We should try to incorporate as many online resources, games and activities into our lessons so that it keeps math interesting and challenges students.  Lastly, we should be moving away from the “rote learning” and make math something that is not just memorized but is fluently learned in all aspects.