The context, content, cognitive and effective components of numeracy try to explain the capabilities of an individual in the aspect of problem solution. The context, as part of the component of numeracy, deals with the reason for dealing with the task depending on the mathematical demands, while the content deals with the essential mathematical capabilities for the confrontation of the problem. Consequently, the cognitive and affective components are basic processes that form interconnections between the content and the framework. These components could be helpful in determining the level of numeracy of problem solvers, where the example of children camping out with a pack of unopened marshmallows is essential in ascertaining the literacy in numeracy depending on the solutions (Gal, 2002).
Depending on the level of numeracy, the algebraic problem has trivial solutions, where the mode of approach is the constant for this proportionality. The personal approach to the problem gives 18 as the total number of marshmallows present in the unopened tin, which is a solution, presented by a student in category 4-6. This is varied from the solutions given by three of the members as solvers of the problem, where the first, second and third solvers got 27, 21 and 15 respectively. The variations in the trivia emanate from the conceptualization of the rules of algebra, where the final solution depends on the literacy of components of numeracy. This implies that differences in understanding of the rules applicable in algebra also determine the variations in the mathematical literacy, which is synonymous to the elements of numeracy. The first solution proves to be the correct solution, where application of the rules of algebra are to the latter, while the other three solutions lack the procedural application of the rules of algebra. The wrong solutions emanate from omission of some processes of problem solution, which is a factor underpinning numeracy (Woodhead, 2003).
The solutions depict a variation in the procedural knowledge, where 18, as a solution to the problem, results from the fact that the content of procedural knowledge was well expressed. By consideration, if one child wakes up and eats ¼ of the marshmallows, ¾ of the total number would still be left in the tin. If the other child wakes up and eats 1/3 of the remainder, then he or she consumes 1/3 of ¾. This also elucidates the assignment of the original number of marshmallows as an unknown number say x., the resulting sum between the first and the second consumption gives the total number of marshmallows consumed, which is 2/4 of the unknown. The difference from a whole number gives 2/4x, which represents 9 marshmallows. Calculation of the unknown in the resulting equation gives 18 as the original number of marshmallows in the unopened tin, which is the product of the reciprocal of the whole number 9 and the remaining fraction. The mode of approach in this synthesis follows the rules of algebra, where there is proper articulation of the procedural knowledge. Conversely, the solutions depicted by other solvers contravene articulation of procedural knowledge (Gal, 2002).
The conceptual knowledge in the numeracy skills shown by the solvers differs, where in some cases the element of ignorance is the force of drive towards obtaining wrong solutions. For instance, the conceptual knowledge of the second solver other than the other two solvers made up of the fraternity of friends as evidences of experimentation of numeracy reveals a descending level of conceptualization of knowledge. The first friend solver simply took the given fractions of consumed marshmallows as the total number of consume marshmallows. The total number was then obtainable through finding the product of the reciprocal of the two fractions by the remainder, which gave 27. This shows that the solver had the capability to articulate conceptual knowledge in numeracy, where a form of rectification could lead to the correct solution. The other two did not bear the conceptual knowledge of numeracy and problem solution, since they did not apply the theories of algebra as a fundamental concept in mathematical literacy as a synonym for numeracy (Kaufmann, Handl, & Thony, 2003).
The metacognitive behaviors as factors underpinning the process of acquaintance of numeracy skills are defined by the ability to recall the process that leads to the problem. Here, the articulation of knowledge in the problem through recalling the influence of the children on the unopened marshmallows forms the definition of the metacognitive behavior. The application of metacognitive skills would result in recollection of all the ideologies presented by the problem, leading to the best solutions (Huizinga, et al., 2009). This is evident in the synthesis of the solution to the problem under context, since the other three friend solvers did not correctly apply their thoughts to what happened and to the consequent source of the problem.
For instance, the third friend solver assumed that the total number of fractions represents the total number of consumed marshmallows. The figure of the total number of marshmallows was then obtained by this solver through finding the product of the reciprocal and the total sum of the given fractions. This gave rise to the variation in the solution, which implies that he lacked the capability to apply the thoughts as the elements forming the metacognitive behaviors of problem solution (Huizinga, et al., 2009).
The level of numeracy depends on the procedural knowledge through articulation of the rules of problem solution, the conceptual knowledge through recollection of the elements happening that lead to the problem of synthesis and the metacognitive behaviors, which determine the articulation of thought as an element of revelation of the hidden ideologies in the problem, resulting in the correct solutions to problems.