• by Paula Martin Johnson, M.A. • IDRA Newsletter • April 2011 •
Mathematics literacy is essential for any child to be prepared for the future. The National Mathematics Advisory Panel asserts that we can no longer accept that a rigorous mathematics education be reserved for those who intend to enter science, technology, engineering and math (STEM) related fields (2008). Gauging student success in mathematics, however, goes far beyond state exams, aptitude tests, college entrance exams and international assessments.
The manner in which we teach must address more than the content alone. There are three major components of a high quality mathematics curriculum: quantity, sequence and rigor. We must prepare learners for the potential application of mathematical concepts, problem-solving and high cognitive thinking that will be crucial in a technology driven society. The national workforce of future years will surely have to handle quantitative concepts more fully and more deftly than at present.
Past president of the National Council of Teachers of Mathematics (NCTM) Cathy Seeley suggests that, when a school’s or district’s mathematics performance differs significantly from group to group, the system has a problem not with an underachieving group but with its mathematics program (2009). Furthermore, in order to reach our full potential, we must take a hard look at reality. To launch today’s student into the expanding digital generation, math curriculum must adopt a new format and method of delivery for instruction.
We live in an innovative world, the Information Age. The number of vocations that demand a high level of aptitude in the use of mathematics, or mathematical modes of thinking, has flourished with the progress of technology. Yet in this time of ever-advancing technologies, we fall short as a nation in our effort to develop a culture of individuals capable of sustaining and continuing this growth. This country is accustomed to being a world leader in innovation. However, the last decades have proven that we are in fact losing the battle to maintain that position in the economic and education communities.
The Trends in International Math and Science Study (TIMSS) was designed to evaluate student performance worldwide on traditional classroom content at targeted grade levels in math and science. U.S. eighth graders placed ninth overall in 2007, rising from 15th in 2003.
In contrast, the Programme for International Student Assessment (PISA) exams, first given in 2000, aim at measuring literacy of 15-year-old school students in math, science and reading. Based on assessment results, the United States’ ranking in mathematics has fallen from 24 in 2003 to 30 in 2009.
What to teach…
Contemporary U.S. education systems build curriculum programs that incorporate numerous concepts over a short amount of time. Broad topics within narrow time frames, sometimes referred to as a “surface” approach to instruction, follow an “inch deep, mile wide” pattern. Topics that are launched at too early an age then with too little depth are not cemented into the learner’s understanding.
The preferred approach would pursue an enriching “inch wide, mile deep” philosophy, providing students with the needed time to be introduced to, process and apply new concepts. This is imperative to nurturing a community of problem-solvers.
The trend in the highest-performing countries on TIMSS (Singapore, Japan, Korea, Hong Kong, Flemish Belgium, and the Czech Republic, sometimes called the “A+ countries,” is to cover fewer topics in greater depth over the course of an academic year (NMAP, 2008). The primary challenge is to determine which elements of each course are considered interesting but not useful; those that are useful but not critical; and finally the attributes that are critically important to the development of a student’s mathematical reasoning, thinking and self-evaluation skills. With this achieved, educators can design a syllabus allocating suitable amounts of time for each area of focus. These actions enable learners to gain higher-order knowledge as they progress in their sequence of courses.
…and when do we teach it?
Progressive instruction runs concurrent with the selection of vital subject matter. Research has found that, in comparison to our “A+” counterparts, topics in the United States are not presented in a logical, step-by-step order (Hook, et al., 2007). Content tends to be introduced in isolation, without relating items to components found in other areas of the mathematical sequence, minimizing concepts’ connectedness.
This is most influential in elementary school, where teachers do not usually have advanced education in mathematics. They are inclined to rely on prescribed textbook scope and sequences to determine the curriculum calendar, rather than on a foundational understanding of the mathematics series.
Common among many U.S. schools, our intended content is highly repetitive. We introduce topics early and then repeat them year after year (Schmidt, et al., 2002). To make matters worse, very little depth is added each time the topic is addressed because each year we devote much of the time to reviewing the topic. The results leave us with curriculum that is not very demanding by international standards. This is especially true in the middle school years, when the relative performance of U.S. students declines. During these years, the rest of the world shifts its attention from the basics of arithmetic and elementary science to beginning concepts in algebra, geometry, chemistry and physics.
In the end, how are we going to teach what we have deemed imperative? TIMSS has observed that even when teachers begin with a challenging student task, they frequently provide excessive guidance or intervene at the first signs of difficulty. We must, as a community of educators, realize that we can guide students’ learning without doing so much of the work for them, spoon-feeding information. As it is when babies learn to walk, students must learn to problem-solve by trial and error. Seeley purports that we should teach in ways that present students with challenging problems, help them build perseverance, and develop their creativity and mathematical perspective (2009).
Greater consistency and quality across schools and districts in the United States can be achieved through a common, coherent curriculum. As found in A+ countries, virtually all students through the eighth grade have a common curriculum, independent of their socio-economic status, location, race or gender. The children of this nation deserve the greatest exposure to a rich, sequential, and rigorous curriculum that will broaden their minds and prepare them for the technical workforce of the future.
Resources
Hook, W., & W. Bishop, J. Hook, J. “A Quality Math Curriculum in Support of Effective Teaching for Elementary Schools,” Educational Studies in Mathematics (2007) Vol. 65, 125-148.
Mullis, I.V.S., & M.O. Martin, G.J. Ruddock, C.Y. O’Sullivan, C. Preuschoff. TIMSS 2011 Assessment Frameworks (Chestnut Hill, Mass.: TIMSS & PIRLS International Study Center, September 2009).
National Mathematics Advisory Panel. The Final Report of the National Mathematics Advisory Panel (Washington, D.C.: U.S. Department of Education, 2008).
Organization for Economic Co-operation and Development. PISA 2009 Results: What Makes a School Successful?: Resources, Policies and Practices (Volume IV) (OECD Publishing, 2010).
Seeley, C. Faster. Isn’t Smarter: Messages About Math, Teaching, and Learning in the 21st Century (Sausalito, Calif.: Math Solutions, 2009).
Schmidt, W., & R. Houang L. Cogan. “A Coherent Curriculum – The Case of Mathematics,” American Educator (2002) Vol. 26(2), 3-18.
Paula Martin Johnson, M.A., is an education associate in IDRA Field Services. Comments and questions may be directed to her via e-mail at feedback@idra.org.
[©2011, IDRA. This article originally appeared in the April 2011 IDRA Newsletter by the Intercultural Development Research Association. Permission to reproduce this article is granted provided the article is reprinted in its entirety and proper credit is given to IDRA and the author.]
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