• The Mathematical Education
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• v.53 no.2
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• pp.163-184
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• 2014

The purpose of this study was to develop the assessment tools using graphing calculators for the assessment of the mathematical process which was emphasized in 2009 reformed mathematics curriculum. In this paper, we presented three sample calculator-based test items for the assessment of students' mathematical process abilities and scoring rubrics for the paper and pencil assessment and assessment based on observation on each item. In order to improve mathematics teachers' understanding of the assessment tools using graphing calculators and to show the procedures of assessment using technological devices, we also drew up assessment guidelines. We hope the results of the study contribute to the promotion of assessment environment encouraging the use of graphing calculators in assessments.

• School Mathematics
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• v.1 no.1
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• pp.123-133
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• 1999

For an appropriate assessment in mathematics, students should play an active role in their learning by becoming aware of what they have learned in mathematics and by being able to assess their attainment of mathematical knowledge. The process of actively examining and monitoring students' own progress in learning and understanding of their mathematical knowledge, process, and attitude is called self-assessment, Researchers in mathematics education have found some important facts about the meta-cognitive process which is related to self-assessment : i. e. meta-cognition progress is composed of being aware of ones' own personal thinking of content knowledge and cognitive process(self-awareness) and engagement in self-evaluation. Tipical method for self-assessment in mathematics developed upon above finding about meta-cognitive progress is describing about students' knowledge and their problem solving strategies. In the beginning of the description in mathematics about themselves, students are required to answer which part they know and which part they don't know. Self-assessment of students' attitudes and dispositions can be just as important as assessment of their specific mathematical abilities. To make the self-assessment method a success, teachers should let students' have confidence and earn their cooperation by let them overcoming fear to be known the their ability to other students. In conclusion, self-assessment encourages students to assume an active role in development of mathematical power. For teachers, student self-assessment activities can provide a prism through which the development of students' mathematical power can be viewed.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.553-571
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• 2014

Mathematical process is an issue in current mathematics education. In this paper discuss how to assess the mathematical process using essay type questions. For this we first suggest the concept of Mathematical Process Oriented Question which is an essay type question and possible to assess mathematical processes, that is, the mathematical communication, reasoning, and problem solving as well as mathematics knowledge. And we develop a framework for developing the mathematical process oriented question and rubric, examples of assessment standards and those questions containing rubric for assessing mathematical processes. The results of this paper can serve as basic data and examples for follow up research about mathematical process assessment.

• Journal of Educational Research in Mathematics
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• v.22 no.3
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• pp.401-427
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• 2012

The recent Korean mathematics curriculum stresses to teach mathematics focusing on mathematical process composed of problem solving, reasoning and communication. To be successful in applying the rationale of the process-focused mathematics education, the assessment practice in classrooms should be also centered on mathematical process. In this study we conducted a large-scale survey on teachers' perspectives about the process-focused mathematics assessment. First, we surveyed teachers' opinion on current assessment practices in school mathematics related to regular school exams and performance assessments. Second, we investigated teachers' perception on mathematical process components such as problem solving, reasoning, and communication regarding how they should be assessed. Finally, we examined the difference of teachers' opinion according to their teaching experience, city size, and the type of school. Based on the results, we discussed implications for mathematics assessment and process-focused mathematical assessment.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.541-563
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• 2014

The purpose of this study is to investigate how the curriculum, in which pre-service teachers experience mathematical process and develop assessment items and standards through the process experience in a mathematical essay course, affects the pre-service teachers and suggest its implications for teacher education. Fourty nine pre-service teachers, registered at a mathematical essay course in a K university in Seoul, developed mathematical essay problems and their assessment standards, and their developed processes were analyzed. According to the analysis results, first, mathematical essay problems developed by the fifty students reflect components of mathematical processes. Especially, one characteristic in revising assessment items shows that pre-service teachers considered not only justification process through different levels of difficulty and mathematical reasoning, but also logical descriptions through problem solving, when they worked on group discussions and examined middle school and high school students' responses. Second, while pre-service teachers developed rubrics for their assessment items and revised the rubrics based on students' responses, they established assessment standards which employed mathematical process by focusing on problem solving process rather than results and considering students' unexpected problem solving. The results imply a concrete method in planning and executing a mathematical essay course which makes use of mathematical process in teacher education.

• East Asian mathematical journal
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• v.36 no.4
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• pp.515-535
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• 2020

The 2015 revised mathematics curriculum had newly introduced the term 'process-focused assessment'. The official document, however, did not offer an explicit definition of the new term, but only by virtue of narrative. This has encouraged practitioners and researchers to figure out themselves what it is and how it differs from those in use, formative assessment and performance assessment in particular, in use. In consequence, many versions of interpretation, all of which are not necessarily consistent, have been developed and implemented in schools, This, in turn, still has created a chaotic situation carrying out the process-focused assessment. This study attempted to make the meaning of the process-focused assessment more explicit by conducting a comprehensive review of the related literature, for implementing it in its intended way.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.581-609
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• 2013

Students' learning processes and mathematical levels should be correctly diagnosed in many different methods of assessment to help students learn mathematics. The study developed the model for the process-based assessment while using manipulatives in the middle school in order to improve problem solving, reasoning and communication which are emphasized in 2009 reformed curriculum as the areas of mathematical process. Identifying the principles of assessment, we created the assessment model for each area and carried out a preliminary study. Based on this, we revised the representative items and the observation checklist and then conducted a main study. Through the results of assessment, we found that students' thinking processes were well presented in scoring rubric for their responses on each item. It meant that the purpose of the assessment as a criterion-referenced test was achieved.

• The Mathematical Education
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• v.43 no.1
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• pp.70-85
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• 2004

Comparing to the other subject, hierarchy among mathematical contents is strong from the perspective of knowledge order as grades go up. That is, the knowledge that students already have learned, are learning and will learn are closed related from grade to grade. We expect students to be proactive and creative in studying mathematics, which is the goal of 21th century, analyzing their. knowledge structure based on the hierarchy of knowledge through assessment. Especially, using computer system we provide students with substantial feedback for the assessment as well as objective validity is increased along with speedy and exact process in a bid to help students' mathematical understanding grow. This paper seeks to analyze the assessment data by applying knowledge spaces to computer system and develops efficient methods based on the analyzed results, to diagram each student's knowledge structure.

• The Mathematical Education
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• v.50 no.1
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• pp.13-25
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• 2011

The Goals of mathematics education for the lower grades of primary school is to shape the basic concepts and the skills of mathematics. To achieve this goal, it is necessary an assessment which is able to help the students' learning activities by precisely diagnosing their basic mathematical capability. It should lend the students an assistance in diagnosing and revising their problems throughout teacher's cognitive participation in the process of mathematical problem solving. I would like to suggest the dynamic assessment as one of these kinds of approaches. In order to prove the utilities of this way, it was examined the necessity of dynamic assessment on the basis of the Vygotsky's theory after looking into the characteristics of the contents and methods of the mathematics education for the lower grades of primary school. Next, I researched the principles of the dynamic assessment and embodied the assessment tool to evaluate the mathematical achievement of the lower grades of the primary school. Lastly, it was provided the examples of the dynamic assessment tool in order to assist the practice of it.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.