The manner in which the mathematics curriculum has been organized shapes learners’ opportunity to study. Algebra learning and teaching are possibly best studied in specific mathematical contexts and domains, but there might be facets of algebra learning and teaching that are increasingly general and may be learned across multiple contexts and domains. Where systematic analysis focused on learning explicit areas of algebra has been executed previously, for instance, research on students’ early study of numbers, subtraction, addition, the payoff for learning and teaching has been significant. This experience implies that it may be productive to focus the coordinated investigation on how students study within other contemporary domains of school math. Algebra would be defined broadly to embrace the manner in which it evolves right through the kindergarten to 12th grade (K–12) curriculum and its correlation to other algebraic topics on which algebra develops and to which it is linked(Bergstra, 2011).
Algebra as a School Subject and Mathematical Domain
Algebra is fundamental in every area of math since it grants the tools such as the structure and language for analyzing and representing quantitative interaction, modelling situations, solving problems, as well as for stating and establishing generalizations. A central facet of algebra in contemporary math is its capability to offer general and unifying algebraic concepts. This capability is a powerful source for building connectivity and coherence in the school math curriculum, in all grade levels, as well as across algebraic settings (Broué, 2011).
Historically, algebra started with the establishing of letter symbols in math expressions to symbolize names of uncertain quantities. These symbols may be unknowns in an algebraic equation that needs to be solved or variables in a functional correlation. As the uses and ideas of algebra expand, it has now included structural imagery of number systems as well as their generalizations, as well as the fundamental concepts of functions and their purpose in modelling empirical phenomena, for instance, as a method of encoding developing patterns observed within data. Algebra organizes the structure and analysis of formulas, equations, as well as functions that structure much of arithmetic as well as its (applications Narode, 2006). Algebra, as a mathematical domain as well as a school subject, today embraces all these themes.
Numerous researchers have already proposed several recommendations concerning the suitable curricular focus in regard to school algebra, and what represents proficiency in the K–12 algebra. Universal to the majority of the recommendations are the expectations associated with algebraic proficiency. These expectations are as follows.
- The aptitude to work meaningfully and flexibly with algebraic relations or formulas to utilize them in representing situations, manipulate them, as well as to solve the differential equations they symbolize.
- A structural comprehension of the essential operations of mathematics as well as of the notational depiction of numbers and algebraic operations, for instance, exponentiation, place value, and fraction notation.
- A strong understanding of the concept of function, together with symbolizing functions, for instance, analytic, tabular, and graphical forms. Having a fine repertoire of the fundamental functions including quadratic and linear polynomials, rational, exponential, as well as trigonometric functions. Employing the functions to learn the change of a given quantity with respect to another.
- Knowing the way to classify and name important variables to model quantitative context, identifying patterns, and utilizing symbols, formulas, as well as functions to symbolize those contexts.
The above recommendations also necessitate the theories of algebra to be rationally linked across the primary and secondary school and for teaching that builds these linkages. These are consistent with the direction of national and state structures and standards, and the evident trends in teaching materials utilized across the U.S. (Leykin, 2011).
Positive and Negative Impacts of Current Trends in Algebra Instruction
It is essential to mention that algebra is essential for investigating the majority of areas of science, engineering, and mathematics. Algebraic thinking, concepts, and notation are central in numerous workplace contexts as well as in the analysis of information that persons obtain in their everyday lives. Another reason for choosing algebra as a primary subject of focus is its formidable and unique gatekeeper function in K–12 schooling. Devoid of adeptness in algebra, students would not access a full assortment of career and educational options. Consequently, students would have narrow likelihood of success. Failure to study algebra is prevalent, and the penalty of this failure is numerous students become disenfranchised (Borasi & Smith, 2006).
This restriction of opportunity is most prevalent in groups that are underprivileged and exacerbates contemporary inequities in society. According to NCTM (2009), algebra ought to be considered as the latest civil right available to every U.S. citizen.
It ought to be noted that, numerous U.S. high schools currently require their students to display extensive algebraic proficiency prior to graduation. These requirements originate from the advanced standards for math that are currently adopted by the majority of states including the state of New Jersey (Smith, 2009). This is due to the universal public pressure for advanced standards and related accountability systems. The current “No Child Left Behind” legislation reinforces these moves. The considerable increase in expectations in regard to performance in algebraic proficiency connected with these standards inflicts challenges for teachers and students alike. It is evident that, in the near future, the absence of strong and functional research in favour of instructional development in algebra is prone to cause policy and interventions decisions that would be unsystematic and fragmented.
Such interventions would be susceptible to the polemics of a discordant political environment. In the long term, research and development in addition to trials and evaluation are obligatory to generate new instructional skills, materials, and programs that would facilitate the attainment of advanced standards for algebraic proficiency. There is a need for a tactical choice for dealing with equity concerns in algebraic education (Welchman, 2011).
Focusing on algebraic instruction brings concerns connected to the structure of the instructional curriculum in U.S schools, and New Jersey in particular. These concerns relate to the requirements for course options and high school graduation, as well as the uses of appraisals for functions of accountability that bear comprehensive consequences. Consequently, research is essential for a better understanding of the implications as well as results of diverse policy options and the range of structural and curricular choices. This is in relation to when algebra should be learnt, and who should learn it. In the middle school and high school curriculum, algebra is characteristically treated as a detached course, and presently the largest part of the material in the course is new to the students. On the contrary, math in elementary schools normally merges experiences of the student with a number of different algebraic domains. Such traditions have been subject to challenge by analyses that demonstrate that secondary curricula in many countries do not detach algebra in a course except for other subject areas. The U.S. requires taking a close look at the concern of algebra instruction and learning in the fragments of the population whose rate of success in learning algebra is below expectation.
Bergstra, K. (2011). Real-Time Process Algebra. Formal Aspects in Computing, 3(2):142-150.
Borasi, R. & Smith, C. (2006). Using Reading to Construct Mathematical Meaning. Communication in mathematics K-12 and beyond. Reston, VA: NCTM.
Broué, M. (2011). Journal of Algebra. Journal of Algebra Production. 25:2, 134-143.
Leykin, T. (2011). D-modules for Macaulay 2. Mathematical Software: ICMS 2002, World Scientific, 63:2, 69.
Narode, R. (2006). Communicating Mathematics through Literature. Communication in Mathematics K-12 and Beyond. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (2009). Curriculum & Evaluation Standards for School Mathematics. Reston, VA: NCTM.
Smith, D. (2009).The Math Curse. Rutherford, NJ: Viking Press.
Welchman, R. (2011). How to use children’s literature in Mathematics Instruction. Reston, VA: NCTM.
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