Application of proportions
Proportions are arguably the most applied mathematical concepts in the real world. People apply the concepts of the ratios and proportions in various aspects of life. However, these concepts are not introduced to students in the lower elementary grades but in the middle school grades. This because they involve fractions which are quite difficult for the lower elementary students to understand. Fractions are touched upon in lower elementary curriculum but students don’t engage in calculations. It’s believed that students in lower elementary grades have not cognitive ability to develop proportional reasoning. Instead, the teachers are more focused on natural numbers and additive concepts. When they reach the middle school grades, they can effectively shift from natural numbers and addictive concepts to ratio numbers and multiplicative concepts. Besides, the students in lower elementary grades cannot master the use of calculators, drawing graphs or working out various proportional problems. Teachers should stick to natural numbers and additive concepts to prepare them for more complex mathematical concepts in middle school grades.
Jitendra, A. et al. (2011). Improving students’ proportional thinking using schema-based instruction, Learning, and Instruction, 21: 731- 745.
The concept of proportions
The concept of proportion and rations usually involve the use of fractions. These concepts are introduced in middle school grades (5-8 grades) because they have the ability to reason proportionally. These students are able to easily comprehend the concept of ratios and use such reasoning to solve problems. Proportion and ratio concepts require maximum attention because of its centrality to mathematics. The students in the lower elementary grade cannot understand fractions effectively and don’t have much concentration on complex mathematical concepts.
Introduction to additive concepts
In the pre-school classrooms, the students are taught how to count items as the teachers introduce them to additive concepts. In lower elementary grades, they continue learning natural numbers and additive concepts which prepares them to shift to proportion and ration concepts in middle school grades.
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