Thursday 23 October 2014

Why math matters

In our current academic climate, it is understandable to question the role of mathematics education in school and what it should resemble. We are growing into an ever-changing age where the ability to memorize does not necessarily guarantee an equivalence with intelligence. The age of “information deprivation” and encyclopaedias as the “all-knowing” entity is over. The age of “information surplus” has shattered our notion of what it means to be intelligent. Not only does this uneasy footing bring into question what formal education should entail, but it begs for a close examination of the role of subjects like math, which for many years, has been questioned for its relevance. If we truly aim to understand the value of mathematics education, we need to clearly define what mathematics is and what the intent of learning math in school is; only then will we be able to understand math’s purpose and begin to build a framework to create a meaningful vision for universal instruction.
A single definition of mathematics tends to be highly debated, and therefore uncertain. While a complete definition may never be hardened, it seems fair to say that, at its core, mathematics is the interpretation and understanding of quantity. This “quantity” may be variable or concrete, but the logic, rules, and axiomatic laws that govern these quantities are to be without debate. Although subjective-based fields have merit, they are susceptible to continued change based on the lens they are viewed through because they typically require interpretation.  The structure that underlines mathematics is its greatest strength as many other disciplines can only offer “exceptions” when things cannot be explained. The language of math continues to be applied in an effort to decode and interpret concepts which beg for understanding. Even subjects like Chemistry and Physics require assumptions that are not yet understood which leaves math, in its purest form, as the only footing of guaranteed confidence. In a head-address speech at the University of Chicago, Physicist Albert Michelson (1894) discussed the end of learning about Physics when he said:
"The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote..."  
Nine years later, Alberta Einstein would publish his Special Theory of Relativity, essentially claiming all that was understood in Newtonian Physics must be rethought. How can an entire field go from knowing everything, to questioning almost everything? This is the result of fields which offer explanations through a process of inductive logic and speculation. By learning math, it offers people a chance to explain, through logic and deductive reasoning, undeniable answers. Whether it is a mechanic needing a wrench that is an eighth of an inch larger, a server calculating a bill total, a physicist determining the work done through integration, or an engineer quantifying a relativistic time-adjustment, confident answers only result because math offers that possibility. It is a language with varying complexity that offers solutions to our quantitative questioning. This basic yet broad form of definition makes room for the simplest rules like addition to be considered mathematics, but also allows for complex and abstract reasoning to fit. Even Gates (2003) recognizes that math has a broad definition but it is used by everyone:
First, (math) trains the mind to be analytical and critical, with skills needed to solve problems and to sustain life-long learning efforts….Second, it provides ordinary citizens with quantitative tools needed to function competently in today’s complicated economies, essentially helping each citizen to make sound decisions. (pg. 46)
If math offers a foundation for our world to communicate through, then the ultimate goal should be to impart this language in everyone so that they may utilize it in whatever path they take in life. Being math literate not only implies confidence in the laws of managing numbers, but is a precursor to skills like critical-thinking and problem-solving. If classrooms, which used to rely on a teacher and a set of encyclopaedias for information are now flooded with “facts”, then the ability to reason and think critically is growing ever more important.
There is a constant struggle with a growing number of students who fail to see an implicit value is attending school and learning math. Many students have simply accepted the “fact” that math is not for them and a dawning culture of failure becomes acceptable; these students refer to their inability of math with certain pride. How do we convince students there is value in outcomes like “completing the square” if we cannot articulate it ourselves? It is fair to assume that most people agree there is a need for education but the focus of this learning and what results has often been challenging to verbalize. Is the purpose of attending school entirely social - to create well-rounded individuals with enough of a foundation that they are ready to become functioning members of society? Or is it simply an academic pass/fail test to see whether students are capable of higher education?

The reason for attending school most likely lies on a spectrum between the two sides. As the philosophy behind in loco parentis in schools becomes more necessary, teachers need to continually balance instilling moral values and citizenship while developing strong academic students. Curriculum experts need to find this balance, especially considering the more defined opposing skills that are being expected of students. At a time when industry and technical schools are short of skilled labour and pertinent (practical) knowledge, universities and grad schools are searching for students who are capable of deep thought, complex reasoning, and critical thinking of abstract concepts. Considering the polarising needs that society requires filled, students need to be prepared for life after school. This becomes the goal of education - preparing students for whatever path they may take. It becomes a challenging task to select the academic and social goals for a complex group of individuals; but we must find a way to impart practical outcomes into one student body while exposing a different body to a world of analytical thinking, capable of becoming expert learners? If we don’t stratify our learners, we simply have a group of learners incapable of meeting the diverse needs that society expects. To spend 12 years of a student’s life directing them towards a path that they will never take is simply bad planning.
A qualification in mathematics seems to be considered as vital for many careers as it is for entry to university, even when the subject to be studied bears little connection to mathematics”. It is generally understood that there is value in mathematics, but perhaps over many different curricula and philosophies, this significance has become lost to the learner. If a clear pedagogy in a meaningful curriculum were established, people should be less hesitant to question why they are learning math. There are curricular factors that need to be in place before the mathematics education is accepted without question. For it to be relevant to the student, though, it needs to be meaningful. First curriculum experts need to understand there is a common domain in which all students exist and need to work in. This “world” needs a common set of skills (not outcomes) based on number sense, estimation, and problem solving involved in quantitative analysis. Every student should finish their formal education confident in solving life’s essential numerical challenges.  Whether a student attends university or enters directly into traditional employment, they both encounter similar challenges that involve quantities. No person should lack confidence when doing taxes, dealing with percentages, measuring, or dealing with money; yet, there is a general disconnect that “math is foreign” to many people. Beyond this common foundation of skills, the future paths that students take should determine specific outcomes, skills, and to what depth. Despite clearly omitting common skills that all students should have upon completion of high school, the Alberta government has created a fairly smart interpretation of how to properly stream students in math. The university-bound students in 30-1 and 30-2 are clearly distinct visions from math 30-3, which is suited for entry into the work-force and trades.

The significant divergence of streams by the end of high school is essential because the expectations beyond core programming are opposing.  The minority of students that attend post-secondary require a great ability to reason and problem-solve in any material that they are presented with. The curriculum that these students must take needs to be concentrated and focus on creating critical thinkers. More important than the outcomes will be their ability to face anything presented to them. Students should be confident in their problem-solving skills and knowledge of the axiomatic laws that govern quantitative analysis. If they know how to learn and what conditions govern that learning, then they are prepared for whatever future they may encounter. This ambiguity of expectation is very different than the more confident understanding of what will be required in the workforce. By giving trades and work-bound students the required outcomes that are more understood, we can validate industry’s expectations. A curriculum designed for a specific group of students not only prepares them for their future, but also aligns nicely with the type of learner that each path often attracts. 

The only challenge with extremely divergent streams is focused on students who do not know their futures. Often, students will “keep doors” open and attempt the most challenging and academic route. This not only results in students who may not fully feel invested in a course, but it can result in a student inadequately prepared for their future career because they took the “wrong path”. Many curriculum designers try to balance the divergent streams with student indecision by offering parallels like Alberta did with 30-1 and 30-2.  This balance waters-down an effective model of stratified streams, but is required due to the great amount of indecisions that exists in high school students’ futures.
Gates (2003) argues that “mathematics is often still associated with ‘giftedness’ by parents and pupils, by teachers and politicians, making it an exclusive discipline...as long as a social focus on the ‘gifted’ persists, the majority will not be educated appropriately” (pg 34) Our schools need to build an understanding that leads as far from this ideology as possible. Math exists in every person’s life. Gates (2003) continues:
“many mathematicians and mathematics teachers would see their discipline as an important means through which individuals can make sense of the world; that mathematics is an empowering force in solving life’s problems” (pg 31)
Once we understand how clean the definition of math can be and that those essential foundations need to be imparted with great confidence in all students, the curriculum can start to take shape. If a well-defined curriculum pertinent to what post-secondary requires is outlined, yet still offers meaning to each individual, there will be more student-investment and less questioning of why math is taught. The streams that stratify the extremely diverse needs of society create the paths that students must become experts in. The foundations that root these streams become the language of confidence which define the world we live in. When students fluently articulate that language, they are more likely to be life-long learners in it.




REFERENCES

1.      Gates, P. (2003) Is Mathematics For All? Second International Handbook of Mathematics Education, 15(3), 3-73.


2.      Stantic, G. (1992) Mathematics curriculum reform in the United States: A Historical Perspective. International Journal of Educational Research. 17(5), 407-417.