“When are we ever going to use this in the real world?” The words escape from a student in the back row, and all across the room heads nod in agreement with his perplexity. The teacher rolls her eyes in frustration after hearing this very question for the millionth time. This is the question voiced on a near daily-basis in math class, and while it has almost become a cliche, the inquiry expresses a significant concern. Is math really important, or should students be exempt from learning math skills that would not be practical in their daily lives? With the idea of using my knowledge of math to teach younger students, I first wanted verification that this work would be worthwhile. I wanted to know that the subject I would be teaching would benefit my students in the long run, for that one simple question echoing from the back of the room had me questioning whether math was important at all.

   In seeking evidence of the importance of math as a whole, one fact was consistently enforced through my research: America is falling behind. In the article “Americans Are Bad at Math, but It’s Not Too Late to Fix,” writer Carl Richards (2014) expresses his concern for our nation’s suffering from an ailment he calls innumeracy, which he defines as, “the mathematical equivalent of not being able to read” (pg 1). The article goes on to state that, “A 2012 study comparing 16-to-65-year-olds in 20 countries found that Americans rank in the bottom five in numeracy,” (pg 1), and “On national tests, nearly two-thirds of fourth graders and eighth graders are not proficient in math,” (pg 1). It was particularly alarming to see our nation’s shortcoming in numeracy when compared to countries considered far less developed. Even just focussing within the US, the inadequacy of math education nationally proves to be a significant concern. While my intentions for teaching were to help students achieve an understanding of math beyond their grade level, I realized that accelerating math education across the country is necessary to bring our students up to standards. This issue became a much broader concern after seeing the weakness of American students in the subject of math.

   Now I knew that as a nation we were falling short of where we should be. Though our national averages suffered, I had yet to see the effects that studying mathematics would have on an individual learner. The practicality of the knowledge beyond national rankings was still in question. Delving deeper into the idea that math is an important subject to learn, whether your career involves specific math concepts or not, “Mathematics Education in the United States: Past to Present” (Woodward 2004) explores the effects math has on a developing young mind. Woodward describes a shift in math teaching methods, beginning in the 1980s, to include a larger focus on problem solving as a “central theme in mathematics education,” (pg 6). This shift was aimed to develop students in a way that surpassed rote memorization of steps or mindless computations. The problem-solving factor helped develop the students’ information processing abilities. Some of the advancements through problem solving were, “the organization of information in long-term memory, the role of visual images in enhancing understanding, and the importance of metacognition in the problem-solving process,” (pg 6). Metacognition is described in the article as “reflective intelligence in mathematical understanding,” (pg 6). This new strategy in math curriculum was not only adding to a preexisting “bank of knowledge” that the students had. It was rewiring the way they organize and store information. It was translating to the enhancement of understanding through visuals, which would connect the problems they were solving to a whole different realm of sensory detail and bridge them to real-world problems. A different kind of intelligence was being developed through learning these abilities that extended beyond being able to solve a math problem. Developing the way the students process information provides a skill that is indisputably beneficial across many subjects. The question, “When are we ever going to use this in the real world?” becomes irrelevant when the problem in front of you is designed to pave a complex way of thinking that helps a student to better assess all problems.

   The strong focus on the benefits of specific problem solving abilities in math expressed in “Mathematics Education in the United States: Past to Present” (Woodward 2004) helped direct my lesson plans for the program. Centering my teaching towards building up simple math skills to solve math word problems would develop the complex paths of thinking highlighted in the article. The use of word problems that require the students to assess each problem and apply the concepts they know in order to solve it would train and strengthen these important problem-solving abilities.

   This particular article also brought an important idea to my attention; each student is unique in his or her own learning process. The students would be developing a new way of storing and accessing information through the problem-solving process, but each student would have to learn to pave these new paths individually. The article states, “Mathematical knowledge- both the procedural knowledge of how to carry out mathematical manipulations and the conceptual knowledge of mathematical concepts and relationships-is always at least partly “invented” by each individual learner,” (pg 7). This shows a new level of connection and retention by students learning math because it goes beyond mechanical absorbtion of information and accesses a personal understanding by each learner. Adjusting to word problems like the ones I would be teaching would result in new abilities and understanding that would otherwise be absent in these students. The true importance of the math-learning process went beyond simply retaining the material. This idea of individual development encouraged me to strive for every student’s full understanding of each concept and helped me to focus on pacing to ensure every student could forge crucial connections in their minds.

   I now knew the great importance for each student to learn mathematics and develop a new way of thinking, but I wondered how I would be able to use my teaching to effectively guide this development. I furthered my research to not only focus on the students, but on myself as a teacher. Since I had never taught before, I began to search for the most effective strategies to aid me in advancing my students’ math skills. In an article by David Bornstein (2011), “A Better Way to Teach Math,” emphasis is placed on the importance of breaking large concepts down into small steps and organizing information in a way that makes it easy to keep track of mentally. In describing a teacher’s discoveries, he states, “To be effective he often had to break things down into minute steps and assess each student’s understanding at each micro-level before moving on.” While I may be familiar with a math concept, it may be a completely new concept to my students. Breaking each piece down into small steps allows students to master a lesson by ensuring thorough comprehension. It also makes it easier to identify where the students are struggling and what pieces are hindering them from being able to understand a concept. By breaking problems down, I would be able to gauge how well the students are grasping the information, and this would help me to optimally pace my lessons.

   This article also provided interesting insight on the opportunistic effects of math learning. “A Better Way to Teach Math” (Bornstein 2011) explains, “As the children experienced repeated success, it seemed to Mighton that their brains actually began to work more efficiently. Sometimes adding one more drop of knowledge led to a leap in understanding.” This idea added an interesting dimension to my work; knowledge builds on itself. The information I would be teaching would be used as stepping stones to understanding an even more vast array of information. The concept of repeated success also brought about the psychological effects of this education. A factor of confidence and excitement stems from small accomplishments, and this could propel the students further forward as they learned. The domino effects of both gaining information and the feeling of success would be keys in keeping my students engaged and motivated. As a teacher, I would have to pay careful attention to the difficulty of problems I was choosing in order to keep the students challenged and improving, while still allowing them to feel accomplished.

   My research was able to provide me with a firmer understanding of how my service work would have rewarding effects on young students. Learning math would open a new way of thinking and understanding that would benefit the students academically and extend beyond the math classroom. My plans for how I would carry out my lessons were shaped largely by my new understanding on the developmental nature of problem solving and the beneficial teaching tactic of breaking large concepts into small steps. In understanding how important learning math truly is, it became important to me to be an effective teacher for my students, for math has lasting effects not only on one’s academic abilities, but also one’s confidence. “A Better Way to Teach Math” (Bornstein 2011) provided light for the greatest influence I could hope to have on my students when it states, “For children, math looms large; there’s something about doing well in math that makes kids feel they are smart in everything,”