Alternative Mathematics Assessment: A Case Study of the Development of Descriptive Problems for Elementary School in Korea

Abstract

A focus on mathematical understanding and problem solving in math education has developed a need to implement alternate ways of testing to better assess the students' understanding and problem solving skills. The seventh national school curriculum (MOE, 1997) for mathematics in Korea was revised to the current curriculum (MOEHRD, 2007) to emphasize alternative assessment methods and particularly the descriptive assessment method. However, the implementation process has been slow due to the lack of support to help teachers to prepare, develop and grade the new descriptive problems. In order to help teachers implement the new assessment framework, we carried out a study with students of grade 2, 4 and 6 to test and refine a framework for developing and grading descriptive problems. Analysis and comparison of the data showed that the grading rubric based assessment of the descriptive problems revealed useful information about the quality of problems and the level of understanding of the students. The study showed that a structured approach to descriptive problem assessment can be a powerful tool for improving math education in the elementary school.

Three Foci of Mathematic Teachers' Considerations in Evaluation of School Students' Achievements

“…These two foci of consideration characterize, to a great degree, the discipline of mathematics and should be taken into account when planning and conducting the evaluation. It is possible to respond to this variety of difficulties by assessing the learners using a combination of alternative assessment alongside the quantitative exams (Silver & Mills, 2018), as the advantages of qualitative assessment is the possibility it gives teachers to verify by providing feedback even in the learning stages (and not just feedback on the final product) that the students understood the questions and assignments, because they know and have mastered the formal language of mathematics and its unique expressions, they have formulated their work with the proper meticulousness and precision, and that the ways to solve the problems presented to them and completing the assignments are clear and appropriate, namely, to receive a comprehensive, in-depth, and accurate picture (Cai et al, 2020c. Kim & Noh, 2010Kulm, 2013;Shahbari et al, 2018;Silver & Mills, 2018;Veldhuis & van den Heuvel-Panhuizen, 2020).…”

“…Alternative assessment methods in mathematics are diverse: descriptive assessment, which includes open questions or a requirement that students detail the problem-solving process, so that teachers can analyze the way students resolved (and not just the end result), and accordingly -help them understand their learning and improve it (Cai et al, 2020c;Kim & Noh, 2010;National Council of Teachers of Mathematics, 2000). Other alternative assessment methods in math are oral exams and interviews (Kulm, 2013;Watt, 2005;Zhao et al, 2018).…”

The Study of Constructed-Response Assessment of Elementary Mathematics Education in Korea

“…The developmental process of a constructedresponse assessment problem and rubric was designed, as shown in Figure 1, from a comprehensive point of view of preliminary studies (e.g., Cho Kim, Kwon & Noh, 2008;Kim & Noh, 2010). According to the developmental process, the developed preliminary items were examined for content validity, term relevance and field applicability of items by elementary math education experts as well as by teachers with extensive teaching experience.…”

Algebraic Thinking Profile of Junior High School Students with Reflective Cognitive Style in Solving Mathematics Problems

“…It is a competency that must be learned by students because it is a provision for the benefit of the development of knowledge and technology [2]. It serves as a mathematical tool to represent and analyze quantitative relationships, model situations, and solve problems [1] [3][4]. It is a skill that involves understanding different representations, such as equations, graphs, and solving problems using symbols in the form of letters as a representation of unknown values [5][6].…”