Assessing Conceptual Understanding of Rational Numbers and Constructing a Model of the Interrelated Skills and Concepts
Students continue to struggle to understand rational numbers. We need a system for identifying students’ strengths and weaknesses dealing with rational numbers in order to jump the hurdles that impede instruction. We need a model for describing learning behavior related to rational numbers – prerequisite skills and development of rational number sense – that is dynamic and allows for continuous growth and change. It would inform us of the important background knowledge that students bring with them and the prior experiences that influence their level of understanding. It would further enable us to assess students’ current levels of understanding in order to prescribe the necessary instruction to continue forward progress. Designing a method for assessing students’ conceptual understanding of rational numbers that has this potential is a challenge. In this paper, I will discuss where the call for conceptual understanding stems from in the recent past, what has already been done involving assessment of conceptual understanding, what reach has revealed about acquiring skill and number sense with rational numbers, and describe a plan using this information for developing a continuum of rational number skills and concepts.
Background on reform in mathematics as it relates to conceptual understanding:
National assessments and reports often act as a jumpstart for research agendas, curriculum development, and professional development training. Analysis and assessment of student learning weaves its way into all three categories as the message of current reform in mathematics becomes clear. Assessment is not somethi...
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, the value of teaching subitizing skills in the classroom is clear. This ability provides a visual tool to young students as they develop a basic understanding of numbers and one to one correspondence, and it establishes a firm foundation for the future skills of addition and subtraction facts. Possessing the knowledge of how and when students develop the cognitive understanding of this concept can drive a teachers instruction so that the students find greater success in the lesson. Knowing that comprehension of number conservation does not occur until age 5 or 6 will definitely have an effect upon early teaching of number sense.
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