• The Mathematical Education
• /
• v.62 no.2
• /
• pp.211-236
• /
• 2023

The purpose of this study is to derive implications of preservice mathematics teacher education in Korea by analyzing the case of edTPA used in the preservice teacher training process in the United States. Recently, there has been a growing interest in promoting professional competencies considering not only the cognitive dimension related to knowledge development of preservice mathematics teachers but also the situational dimension considering reality in the classroom. The edTPA in the United States is a performance-based assessment based on lessons conducted by preservice teachers at school. This study analyzes the professional competencies required of preservice mathematics teachers by analyzing handbooks that described the case of edTPA in which preservice mathematics teachers in the United States participate. The edTPA includes planning, instruction, and assessment tasks, and continuous tasks are performed in connection with classes. Thus, the analysis is conducted on the points of linkage between the description of evaluation items and criteria in the planning, instruction, and assessment tasks, as well as the professional competencies required from that linkage. As a result of analyzing the edTPA handbooks, the professional competencies required of preservice mathematics teachers in the edTPA assessment were the competency to focus on and implement specific mathematics lessons, the competency to reflectively understand the implementation and assessment of specific mathematics lessons, and the competency to make a progressive determination of students' achievement related to their learning and their uses of language and representations. The results of this analysis can be used as constructs for competencies that can be assessed in the preservice in the organization of the preservice mathematics teacher curriculum and practice training semester system in Korea.

• Communications of Mathematical Education
• /
• v.31 no.3
• /
• pp.257-277
• /
• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• Journal of the Korean School Mathematics Society
• /
• v.3 no.1
• /
• pp.149-163
• /
• 2000

The Ministry of Education have had us practice the performance test as a substitute proposal, however, all the more for the idealistic purport, our education front does not have such a sufficient condition as to practice the performance test for many classes and miscellaneous duties and over-populated class, and that practice has been enforced so abruptly without any drastic preparation and has caused much confusion from the beginning of that enforcement. Thus, these problematic concerns are remained as the tasks of the teachers to be solved by themselves in the front of education, and herein I came to do this research. The followings are the conclusions that I got as the results of the research (1) Performance test style should be applied in consideration of the students' achievement level and the gap of the teachers' recognition; descriptive test, portfolio assignment and formative test styles were proper for the students lacking basic study ability. (2) Descriptive test should have its beginning with the question items to which students can write the problem solving procedure logically rather than those to evaluate the creation ability and thinking ability: and putting down specifically the assessment standard could prevent students' confusion and scheme the impartiality of the assessment. (3) Portfolio assignment evaluation should be given with as interesting and suitable amounts as possible so that the students can do by themselves. (4) Utilizing the performance test table enabled easy management of documentary evidence. And it is needless to say that the success of the performance test should have preceding conditions like the teachers' understanding and their positive participation. Therefore, I'd like to give suggestions herein like the followings; (1) The performance test should not always be made into grades, and there is a need to develop the test gradually in the condition that the education surroundings permit by checking time, frequency, ratio and contents of the test while practicing the multiple choice writing test. (2) As long as the performance test has the aims of improving the studying and learning activities, any performance test only for the sake of making numerals with the thought that assessment is the disposal of the grades should be avoided, and the change of the lecturing styles and development of various assessing types and studying materials should be endeavored to confirm with the aims.

• Communications of Mathematical Education
• /
• v.29 no.4
• /
• pp.625-642
• /
• 2015

The purpose of this study was to develop and verify the feedback-enhanced performance assessment model through a variety of assessment strategies focused on the development of students. In order to achieve the purpose of this study, we analyzed the achievements of the sixth grade curriculum standards and set the central achievement standards in core competencies. We then established an evaluation plan to take advantage of a variety of methods and develop an assessment tool for process-based evaluation during lessons. We applied this assessment model to 6th grade students while teaching and learning mathematics in the classroom. The result of applying the performance evaluation model showed the improvement of students' reflective thinking ability. Also, some students who was not achieved at the level of 'N' could develop to the level of 'N + 1'. A long term research using various assessment strategies should be continued for effective help of students' mathematical development.

• Communications of Mathematical Education
• /
• v.30 no.3
• /
• pp.393-418
• /
• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Journal of Elementary Mathematics Education in Korea
• /
• v.13 no.1
• /
• pp.115-140
• /
• 2009

Freudenthal has advocated the mathematisation theory. Mathematisation is an activity which endow the reality with order, through organizing phenomena. According to mathematisation theory, the departure of children's learning of mathematics is not ready-made formal mathematics, but reality which contains mathematical germination. In the first place, children mathematise reality through informal method, secondly this resulting reality is mathematised by new tool. Through survey, it turns out that area unit of Korea's seventh elementary mathematics textbook is not correspond to mathematisation theory. In that textbook, the area formular is hastily presented without sufficient real context, and the relational understanding of area concept is overwhelmed by the practice of the area formular. In this thesis, first of all, I will reconstruct area unit of seventh elementary textbook according to Freudenthal's mathematisation theory. Next, I will perform teaching experiment which is ruled by new lesson design. Lastly, I analysed the effects of teaching experiment. Through this study, I obtained the following results and suggestions. First, the mathematisation was effective on the understanding of area concept. Secondly, in both experimental and comparative class, rich-insight children more successfully achieved than poor-insight ones in the task which asked testee comparison of area from a view of number of unit square. This result show the importance of insight in mathematics education. Thirdly, in the task which asked testee computing area of figures given on lattice, experimental class handled more diverse informal strategy than comparative class. Fourthly, both experimental and comparative class showed low achievement in the task which asked testee computing area of figures by the use of Cavalieri's principle. Fifthly, Experiment class successfully achieved in the area computing task which resulting value was fraction or decimal fraction. Presently, Korea's seventh elementary mathematics textbook is excluding the area computing task which resulting value is fraction or decimal fraction. By the aid of this research, I suggest that we might progressively consider the introduction that case. Sixthly, both experimental and comparative class easily understood the relation between area and perimeter of plane figures. This result show that area and perimeter concept are integratively lessoned.

• Education of Primary School Mathematics
• /
• v.16 no.2
• /
• pp.123-145
• /
• 2013

This study was expected to yield the meaningful conclusions from the experimental group who took lessons based on inductive activities using GeoGebra at the beginning of proof learning and the comparison one who took traditional expository lessons based on deductive activities. The purpose of this study is to give some helpful suggestions for teaching proof to mathematically gifted elementary students. To attain the purpose, two research questions are established as follows. 1. Is there a significant difference in proof abilities between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? 2. Is there a significant difference in proof attitudes between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? To solve the above two research questions, they were divided into two groups, an experimental group of 10 students and a comparison group of 10 students, considering the results of gift and aptitude test, and the computer literacy among 20 elementary students that took lessons at some education institute for the gifted students located in K province after being selected in the mathematics. Special lesson based on the researcher's own lesson plan was treated to the experimental group while explanation-centered class based on the usual 8th grader's textbook was put into the comparison one. Four kinds of tests were used such as previous proof ability test, previous proof attitude test, subsequent proof ability test, and subsequent proof attitude test. One questionnaire survey was used only for experimental group. In the case of attitude toward proof test, the score of questions was calculated by 5-point Likert scale, and in the case of proof ability test was calculated by proper rating standard. The analysis of materials were performed with t-test using the SPSS V.18 statistical program. The following results have been drawn. First, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in proof ability than the comparison group who took traditional proof lessons. Second, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in the belief and attitude toward proof than the comparison group who took traditional proof lessons. Third, the survey about 'the effect of inductive activities using GeoGebra on the proof' shows that 100% of the students said that the activities were helpful for proof learning and that 60% of the reasons were 'because GeoGebra can help verify processes visually'. That means it gives positive effects on proof learning that students research constant character and make proposition by themselves justifying assumption and conclusion by changing figures through the function of estimation and drag in investigative software GeoGebra. In conclusion, this study may provide helpful suggestions in improving geometry education, through leading students to learn positive and active proof, connecting the learning processes such as induction based on activity using GeoGebra, simple deduction from induction(i.e. creating a proposition to distinguish between assumptions and conclusions), and formal deduction(i.e. proving).

• Journal of Elementary Mathematics Education in Korea
• /
• v.20 no.3
• /
• pp.431-456
• /
• 2016

The purpose of this study is to investigate the appropriate time of introduction and the usage of the number line, in order to suggest the right point of learning the number concept to the elementary school students. For the efficient achievement of this purpose, we investigated the mathematical models for constructing the number concept such as number line, empty number line and double number line, counting and development of number concept. Then, we conducted case study on the time of introduction and the usage of the number line. Finally, we analyzed the result. First, there is need for adjustment to conduct the introduction of the number line from the second year of elementary school, so to help the students understand the continuing number concept through the understanding on the metaphorical concept of the number line. Second, there is the need of positive introduction and the use on the mathematical models; empty number line which helps to draw various thinking strategy visually through the process of operations such as addition and subtraction; the division into equal part and division by equal part in which multiplicative comparative situation or division takes place; the double number line which helps to understand the rate or proportional distribution. Finally, when adopting the number line, the empty number line, or the double number line, we suggested the necessity of learning about elaborate guidance and the usage in order to fully understand the metaphorical concept of the number line.

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.1
• /
• pp.87-103
• /
• 2013

This study was investigated to examine the effects of writing activities based on Polya's Problem Solving Stages on Learning Accomplishment and Attitudes. A total of 54 students were selected from two Grade 6 classes of P Elementary School in G City to form an experimental group(n=27) and a control group (n=27). The experimental group was applied to a class which was creating writing activities according to Polya's Problem Solving Stages to problem solving and inquiry activities. The control group was taught by the traditional method to the same activities. The five questions for each area were selected as a descriptive assessment of the second semester of Grade 5 in the area of the Academic Achievement pre-test, developed by the G Education and Science Research. The post-test was selected by a descriptive assessment of the content of the first semester in Grade 6. The same questions were posed for both the pre-test and the post-test of the Mathematical Attitudes assessment. We examined the pre-test at the beginning of the school term, then the students were re-examined after one semester, using the same questions as the pre-test. This research showed that there was a meaningful difference in Learning Accomplishment as a result of T-test in the 5% level of significance. Secondly, there was a meaningful difference in the Mathematical Attitudes as a result of T-tests. It shows that writing activities based on Polya's Problem Solving Stages have an influence on improving Learning Accomplishment and Attitudes.

• Journal of Elementary Mathematics Education in Korea
• /
• v.15 no.3
• /
• pp.559-577
• /
• 2011

The purpose of this study was to investigate the effects of discourse-based math instructions on the students' mathematical attitudes and learning achievements by providing fifth graders with an opportunity to take active part in learning during math classes and applying discourse-based math instructions, which are to expand the speaking experiences as the most fundamental way to express ideas in communication. Those research efforts led to the following results: First, the discourse-based math instructions turned out to have positive influences on flexibility, will power, curiosity, reflection, and value of mathematical attitudes. When the results were reviewed before and after the instructions without considering the subvariables of attitude, there were statistically significant differences(p<0.01), which indicates that the discourse-based math instructions exerted very positive effects on the students mathematical attitudes. Second, there were no statistically significant effects in learning achievements between the experimental and comparative group, but the experimental group, which recorded low mean scores in the pre-test, increased their mean scores by 3.81 points in the post-test, which suggests that the discourse-based math instructions had positive influences on them. Third, the subjects' responses on the questionnaire on discourse-based instructions reveal that the discourse-based math instructional provided them with an opportunity to explore solutions in various ways. In short, discourse-based math instructions have positive influences on mathematical attitudes and are effective in increasing communication ability.