The Problem with Mathematics Today
If we were to think about what consists of a classic education: reading, writing, and mathematics, we might reflect upon our own educational histories and best view these three pillars as separate, but equal. Educational psychologists will assert that two of these factors (reading and writing) are grounded in left brain activity, while mathematics is grounded in the right brain. This has always assisted students who were more inclined toward operating in a given sphere of the mind. To extrapolate the argument further, the majority of male students operate from that very section. However, the two solitudes of language arts and mathematics have experienced a higher than normal convergence during the last couple of decades. Of course, mathematics always had some degree of language integration in the form of decoding questions and arriving at a result from the analysis of a word problem. That was fair game. Math students knew that questions would not always be presented in pure numerical fashion, and word problems existed to challenge them and integrate some “real life” scenarios into the program. Their teachers knew that some math competencies required language such as ratio, per cent, problems, and time. Some of our parents’ generation had trouble in understanding what was known as the “new math” and could aid us only to a certain level. The problem today is that the new math has become “new and improved” (to borrow a trendy tagline), and now both parents and students are caught in a system that values less accuracy, places little emphasis on basic fundamentals, and seeks to explore reasoning, rather than results.
Most of the mathematics programs that are being delivered in Ontario are faulty. Examine the following EQAO results from Grade Six: 2005 (60%); 2006 (61%); 2007 (59%); 2008 (61%); and 2009 (63%). The per-cent results indicated how many students across Ontario were meeting provincial standards. Boys are generally performing 2 – 4% worse than girls, in a field they once dominated. In terms of gender, all of our students need to be doing much better! So what is wrong? Let us begin with an examination of the structure of the textbook itself. Math texts are generally divided into self-contained units. Students know that if they are not good at geometry or fractions, they can “run out the clock” and not see these units until the following grade. There is little or no building of competencies across a wider length of time, a critical tenet in producing unshakeable foundation from which a future math scholar might be forged. If textbooks were to be reorganized into short lessons that introduce new concepts, while continuously revisiting past skill sets, this incremental approach would produce highly skilled students. Thus, what has been taught in Lesson 14, will still have representation in Lesson 135. Discover the research surrounding Saxon Math and Singapore Math, two non-unit, incrementally based systems, and their ability to fashion students who retain a great deal more knowledge at the conclusion of the school year.
Many of the Math textbooks used in Ontario are too colourful and look like magazines. They ask questions that are deemed, by many students, as unnecessary and frivolous. It is without question that the process of how an answer is achieved must be evaluated and part of student learning. However, the essence of mathematics and its attraction to it, by students, is the nature of its pure right and wrong clarity. Using elaborate language to explain how an answer was arrived at, but not knowing the basic functional skills to achieve the answer, is a waste of time. Teachers need to evaluate the “showing of work” through calculation, which employs methods/formulas. They do not need to ask students how they felt about the problem or how to formulate in words basic mathematical processes. The ironic tragedy, regarding elementary and middle-school mathematics is that, once students enter secondary school, many of these core skills they will need to succeed are either are absent, or severely lacking. Secondary level education assumes that basic competencies are known to the students, and that they are capable of solving the two-to-four-step solutions with some degree of automatic competency. They do not have the time to draw diagrams and work with manipulatives in the ninth grade, while offering their insights in journals into their feelings and motivations arriving at a numerical answer.
Parents should take note from the best practices of the tutoring centres in Toronto. They should begin the process by having their children learn their times tables cold: no figures, no manipulatives, straight old school rote memory. It might be a tough battle, but the skill set will last them a lifetime. You and your children must discover what they can and cannot do by reviewing their textbook. Turn to each page, and simply perform a yes or no diagnostic. Upon completion of this process, create a top-ten list, and work through each skill set over a timetable that is appropriate for the family’s particular set of circumstances. The sobering conclusion is that the textbook is not the whole story. There are some excellent publications that narrow in on specific skills, and through clear explanations and repeated practice (frequency of examples is greater), you can cross them off your list. It has been my experience, that if there is a partnership between the home and the school, and a recognition that one can share in the work of the other, together they can achieve success. Mathematics is akin to basic life skills and higher intelligence. Bloom’s Taxonomy suggests a foundation is required to reach the ability to analyze, synthesize, and evaluate. The major disconnect with mathematics in elementary school and, subsequently, in secondary school, appears to be the nature and quality of the foundational intelligences required to reach up to the upper echelons of achievement.
About the Author: Manfred J. von Vulte is the Director of Development and Vice Principal of Northmount Independent Boys Catholic Elementary School in Toronto. He is the published author of two books (history and children's) and numerous articles in various publications. His interests include writing about education as it pertains to students, family life, and improving their experience with learning. He has been teaching for eleven years and resides in Toronto. He is a graduate of Francis Libermann Catholic High and York University. Visit his website at www.northmount.com.