• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.457-484
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• 2015

This study aims to investigate an approach to teach proportional reasoning in elementary mathematics class by analyzing the proportional strategies the students use to solve the proportional reasoning tasks and their percentages of correct answers. For this research 174 sixth graders are examined. The instrument test consists of various questions types in reference to the previous study; the proportional reasoning tasks are divided into algebraic-geometric, quantitative-qualitative and missing value-comparisons tasks. Comparing the percentages of correct answers according to the task types, the algebraic tasks are higher than the geometric tasks, quantitative tasks are higher than the qualitative tasks, and missing value tasks are higher than the comparisons tasks. As to the strategies that students employed, the percentage of using the informal strategy such as factor strategy and unit rate strategy is relatively higher than that of using the formal strategy, even after learning the cross product strategy. As an insightful approach for teaching proportional reasoning, based on the study results, it is suggested to teach the informal strategy explicitly instead of the informal strategy, reinforce the qualitative reasoning while combining the qualitative with the quantitative reasoning, and balance the various task types in the mathematics classroom.

• Proceedings of the Korean Society for Cognitive Science Conference
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• 2006.06a
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• pp.125-130
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• 2006

원활한 의사소통을 위해서는 문장들을 연결하여 흐름을 조직하고 말로 산출하고 전체적인 의미를 파악할 수 있어야 한다. 이야기는 이러한 문장들이 연결되어있는 것으로, 종속적이거나 나열적인 이야기 특성은 의사소통장애인의 이야기 이해와 산출의 수행에 영향을 미칠 수 있다. 본 연구에서는 이야기 특성에 따른 유창성 실어증환자의 이야기 이해 및 산출의 능력을 알아보고, 이해과제 수행이 산출과제에 미치는 영향을 분석해보았다. 이야기 종류로는 시간적 나열 이야기와 인과적 관계 이야기, 유머가 있는 이야기를 사용하였으며, 사실적 정보, 텍스트 추론, 빠진 정보추론 등 세 가지의 이해과제를 통하여 이해 능력을 측정하였다. 산출능력은 이해과제 전과 후에 CIU 비율로 질적인 측면을 측정하고, 분당어절 수를 이용하여 양적인 측면을 분석하였다. 그 결과 이해측면은 세 가지 이야기 모두 사실적 정보에 대한 이해 능력이 상대적으로 좋았으며, 오류의 형태는 추론오류가 가장 많이 나타났다. 산출에서는 인과적 관계이야기에서의 CIU 비율이 가장 높았고, 이해과제 전, 후의 차이를 비교한 결과, CIU 비율은 변화하지 않았으나, 분당 어절수에서는 증가하고 있음을 보여주었다. 이야기의 종류에 따라서 유창성 실어증화자의 산출과제의 수행수준은 다르게 나타났다. 그리고 이해과제의 수행이 산출과제에서 양적인 증가는 가져왔으나 질적인 수준에는 아무런 영향을 미치지 않았다.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.57-79
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• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• School Mathematics
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• v.18 no.4
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• pp.819-838
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• 2016

This research analyzed proportional reasoning abilities of the 5th grade students who learned only the basis of ratio and rate and 6th grade students who also learned proportion and cross product strategy. Data were collected through the proportional reasoning tests and the interviews, and then the achievement of the students and their proportional reasoning strategies were analyzed. In the light of such analytical results, the conclusions are as follows. Firstly, there is not much difference between 5th and 6th grade students in the achievement scores. Secondly, both 5th and 6th graders are less familiar with the geometric, qualitative and comparisons tasks than the other tasks. Thirdly, not only 5th graders but also 6th graders used informal strategies much more than the formal strategy. Fourthly, some students can't come up with other strategies than the cross product strategy. Finally, many students have difficulties in discerning proportional situation and non-proportional situations. This study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: focusing on letting students use their informal strategies fluently in geometric, qualitative, and comparisons tasks as well as algebraic, quantitative, and missing value tasks focusing on the concept of ratio and proportion instead of enforcing the formal strategy.

• School Mathematics
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• v.18 no.4
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• pp.749-771
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• 2016

The purpose of this study is to analyze mathematical tasks of Korea and the USA textbooks focused on conditions for parallelograms. In this study, structures of task, types of proof and reasoning, and levels of cognitive demand are investigated. The conclusion is as follows: First, with respect to structures of task, structures presented in the USA textbooks are more diverse. Second, with respect to types of proof and reasoning, Korea and the USA prefer IC task and DA task. And task types presented in the USA textbooks are more diverse. Third, with respect to levels of cognitive demand, in both Korea and the USA textbooks, PNC task and PWC task account most. And compared to the USA, Korea prefer algorithms. In addition, we find out implications for reconstruction of Korea textbook. It is as follows: First, with respect to structures of task and types of proof and reasoning, the diversity of composition needs to be raised. Second, with respect to levels of cognitive demand, the concentration in PNC task needs to be declined. And levels of cognitive demand on types of tasks need to be reconsidered. Third, with respect to tasks' topic and material, internal and external connectivities of mathematics need to be strengthened.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.505-516
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• 2013

The purpose of this paper is to analyse the essence of proportional reasoning and to analyse the contents of the textbooks according to the mathematics curriculum revised in 2007, and to seek the direction for developing the proportional reasoning in the elementary school mathematics focused the task variables. As a result of analysis, it is found out that proportional reasoning is one form of qualitative and quantitative reasoning which is related to ratio, rate, proportion and involves a sense of covariation, multiple comparison. Mathematics textbooks according to the mathematics curriculum revised in 2007 are mainly examined by the characteristics of the proportional reasoning. It is found out that some tasks related the proportional reasoning were decreased and deleted and were numerically and algorithmically approached. It should be recognized that mechanical methods, such as the cross-product algorithm, for solving proportions do not develop proportional reasoning and should be required to provide tasks in a wide range of context including visual models.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.227-246
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• 2024

The purposes of this study were to analyze the levels of cognitive demand and questioning types in tasks of 'Data and Chance' presented in elementary mathematics textbooks in Korea, the United States, and Australia. The levels of cognitive demand of textbook tasks were analyzed according to the knowledge and process and thinking types required in the tasks. The tasks were also analyzed for questioning types, answer types, and response types. As a result, in terms of knowledge and process and thinking types in tasks, all three countries had something in common: the percentage of tasks requiring 'representation' and process was the highest, and the percentage of tasks requiring 'basic application of skill/concept' was also the highest. From a thinking types perspective, differences were found between textbook tasks in the three countries in graph and chance learning. The results of analyzing questioning types showed that in all three textbooks, the percentage of observational reasoning questions was highest, followed by the percentage of factual questions. The proportions and characteristics of the constructing questions included in the U.S. and Australian textbooks differed from those in the Korean textbooks. Based on these results, this study presents implications for constructing elementary mathematics textbook tasks in 'Data and Chance.'

• Journal of the Korean earth science society
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• v.33 no.2
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• pp.170-182
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• 2012

The purpose of this study was to develop learning materials based on the Kepler's abductive reasoning and to identify high school students' rule-inferring strategies on the law of planetary motion. The learning materials including the concepts of solar magnetic field, conservation of figure skater's angular momentum and Kepler's polyhedral theory were developed and the questions about Kepler's 2nd and 3rd law of planetary motion were also created. The participants were 79science high school students and 83general high school students. The patterns and properties of their abductive inference were analyzed. The findings revealed that the students showed 'incomplete analogy abduction', 'analogy abduction' and 'reconstruction' to generate the hypotheses concerning the Mars' motion related to the solar magnetic field. There were more general high school students who showed the incomplete analogy abduction than science high school students. On the other hand, there were more science high school students who showed the analogy abduction and reconstruction strategy than general high school students. Also, they showed 'incomplete analogy abduction', 'analogy abduction' and 'model construction and manipulation' to generate the hypotheses concerning Kepler's second law. A number of general high school students showed the incomplete analogy. It is suggested that because the analogy of figure skater cause the students' alternative framework to use, more detailed demonstration is necessary in class. In addition, students combined Kepler's polyhedral theory with their prior knowledge to infer Kepler's third law.

• Journal of The Korean Association For Science Education
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• v.19 no.1
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• pp.29-40
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• 1999

The purpose of the present study was to test hypothesis that, because it uses tri-dimensional sensory pathway which have been showed a higher rate of neural activities than uni- or bi-dimensional's, lab-activity-based instruction is more effective teaching strategy in learning science than verbal-based instruction. In the present study, manipulative teaching strategy that uses visual, somatosensory and auditory information pathway was regarded as a mode of tri-dimensional sensory inputs. In addition, verbal teaching strategy that uses mainly auditory and a little visual information pathway was used as a mode of bi-dimensional sensory inputs. Fifty-six students who failed to successfully solve two proportional reasoning tasks (i.e., pouring water tasks) were sampled for this research from a junior high school. The subjects were randomly divided into a manipulative or a verbal teaching group, and given manipulative or verbal tutoring on the use of proportional reasoning strategies and a test of proportional reasoning during instruction. The results showed that manipulative group's performance on the test of proportional reasoning during instruction showed significantly higher performance than verbal group's (t=2.45, p<0.02). The present study also discussed some educational implications of the results.

• Journal of Korean Home Economics Education Association
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• v.35 no.3
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• pp.21-45
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• 2023

The purpose of this study was to analyze the curriculum competencies of relationship-forming ability and practical problem-solving ability reflected in the activity tasks corresponding to the content elements of 'Love and marriage', 'Preparation for parenthood', 'Pregnancy and childbirth', 'Child care', and 'Family culture and intergenerational relationship' in the 2015 revised high school technology & home economics textbooks. The data are 330 activity tasks from 12 kinds of high school technology & home economics textbooks. The sub-factors of the relationship-forming ability were selected as Respect for Diversity, Consideration and Care, Family Relationship and Community Spirit, Empathy Ability, Conflict Management, and Communication, and the sub-factors of practical problem-solving ability were selected as Practical Reasoning, Decision Making, Value Judgment, Critical Thinking, and Executive Power. Based on the analysis criteria, the results of the two analyses and the expert review are as follows. First, regarding both the core concepts 'Development' and 'Relationship', the share of relationship-forming ability was relatively higher than practical problem-solving ability, and conflict management and executive power were the least reflected. For the core concept 'Development', Family Relationship and Community Spirit and Critical Thinking were the most reflected sub-factors, and for the core concept 'Relationship', Consideration and Care and critical thinking were the most reflected sub-factors. Second, in the case of the relationship-forming ability, the examples of activity tasks across sub-factors of each subject competency were devised to understand diverse opinions and sentiments and to develop competencies to care for each other and maintain healthy family relationships. In the case of practical problem-solving ability, the tasks allowed students to objectively analyze the socio-cultural background underlying the real-life problem, explore alternatives, and apply in their own lives.