• The Mathematical Education
• /
• v.62 no.3
• /
• pp.363-380
• /
• 2023

This study analyzed the difficulties and mathematical modeling knowledge improvement that an elementary school teacher experienced in modifying a mathematics textbook task to a mathematical modeling task. To this end, an elementary school teacher with 10 years of experience participated in teacher-researcher community's repeated discussions and modified the average task in the data and pattern domain of the 5th grade. The results are as followings. First, in the process of task modification, the teacher had difficulties in reflecting reality, setting the appropriate cognitive level of mathematical modeling tasks, and presenting detailed tasks according to the mathematical modeling process. Second, through repeated task modifications, the teacher was able to develop realistic tasks considering the mathematical content knowledge and students' cognitive level, set the cognitive level of the task by adjusting the complexity and openness of the task, and present detailed tasks through thought experiments on students' task-solving process, which shows that teachers' mathematical modeling knowledge, including the concept of mathematical modeling and the characteristics of the mathematical modeling task, has improved. The findings of this study suggest that, in terms of the mathematical modeling teacher education, it is necessary to provide teachers with opportunities to improve their mathematical modeling task development competency through textbook task modification rather than direct provision of mathematical modeling tasks, experience mathematical modeling theory and practice together, and participate in teacher-researcher communities.

• School Mathematics
• /
• v.16 no.3
• /
• pp.445-469
• /
• 2014

This study aims to examine secondary mathematics teachers' understanding of the levels of cognitive demand on mathematical tasks suggested in mathematics textbooks. The study also attempts to investigate whether the teachers are able to characterize the tasks accordingly and to change low level tasks to high level ones. For this purpose, we developed a survey and 50 secondary mathematics teachers participated in the survey. The findings from the data analysis suggest that 59 percent of the teachers selected high level tasks as appropriate for achieving the national curricular goals, but about 1/3 of the teachers identified PNC tasks as high level ones. The results also reveal that more than half of the teachers were not able to transform low level into high level tasks and only 4 teachers out of 50 were able to transform successfully. The teachers seem to find difficulty in transforming low level tasks into high level ones.

• Communications of Mathematical Education
• /
• v.29 no.3
• /
• pp.281-300
• /
• 2015

The purpose of this research is to analyze cognitive demands, answer types, and storytelling types on the basis of mathematical tasks in five different mathematics textbooks based on 2009 revised curriculum in order to suggest directions for the development and use of storytelling mathematics textbooks in school. Results show that first, PNC (Procedures without Connections) task was the largest category in cognitive demands of all mathematical tasks, Low-Level task was larger than others in cognitive demands of mathematical content tasks, and High-Level task was larger than others in cognitive demands of mathematical activity tasks. Second, a short-answer type was the largest category in answer types of all mathematical tasks, the majority of mathematical content tasks were a short-answer type, and the majority of mathematical activity tasks were both short-answer and explanation-answer types. Finally, storytelling connected to real-life was the largest category in storytelling types, and the number of mathematical activity tasks was less than that of mathematical content tasks. However, in the tasks reflected on storytelling, the percentage of mathematical activity tasks was higher than that of mathematical content tasks. Based on the results, while developing storytelling mathematics textbooks and using storytelling textbooks in school, it suggests to consider the need for balance and diversity in cognitive demands, answer types, and storytelling types according to mathematical tasks.

• The Mathematical Education
• /
• v.63 no.3
• /
• pp.527-547
• /
• 2024

It is difficult for mathematics teachers to develop mathematical modeling tasks and implement mathematical modeling lessons for their students. These difficulties serve as a reason why mathematical modeling lessons are not implemented well in school mathematics. In this study, we aimed to examine how preservice mathematics teachers (PMTs) modify mathematical modeling tasks in mathematics textbooks as a way to develop mathematical modeling tasks and how they implement the mathematical modeling lesson. In particular, we focused on how the openness and reality reflected in the task and the mathematical modeling process change as PMTs modify the tasks. We collected data through PMTs' evaluation reports on analyzing textbook tasks, task modification, lesson plans and implementations, peer evaluation, and self-evaluation. Then, we analyzed these data according to the case analysis process. The findings revealed that when PMTs modified the textbook task, they focused on and improved the openness and the defining variables and the model stages of mathematical modeling process. However, when PMTs implemented lesson, the openness and the defining variables and the model stages of mathematical modeling process were restricted again. PMTs did not focus on other stages. Based on these results, the theoretical and practical implications of the study was discussed.

• Communications of Mathematical Education
• /
• v.33 no.2
• /
• pp.123-139
• /
• 2019

This study analyzed how problem-posing tasks included in Korean middle school mathematics textbooks were distributed in terms of content area, task type, and context of task to investigate that the mathematics textbooks are giving students ample opportunities for problem-posing activities. The analysis of 10 mathematics textbooks for first grade in middle school according to the revised mathematics curriculum in 2015 found that the problem-posing tasks contained in the textbooks are insufficient in quantity and not evenly distributed in terms of content areas. There were also more problem-posing tasks with relatively moderate constraints than those with strong or weak constraints in terms of mathematical constraints. In addition, there were more problem-posing tasks that were not requiring students to make a new context, and more often camouflage contexts were used. Based on this, implications for improving mathematics problem-posing tasks in mathematics textbook were suggested.

• Education of Primary School Mathematics
• /
• v.18 no.2
• /
• pp.155-173
• /
• 2015

The purpose of this study is to offer the implication for elementary school mathematics teaching by analyzing teachers' reflection on the cognitive demands of mathematical tasks they give in class. During the setup phase and the implementation phase in math class, the researchers analyzed the change of cognitive demands on mathematical tasks and the factors which had influence on such changes. After teachers' reflection on teaching, the researchers analyzed the change of cognitive demands on mathematical tasks and the factors which had influence on such changes in math classes. As a result, before teachers' reflection on the cognitive demands of mathematical tasks, the higher-level demands of mathematical tasks had a tendency to decline. However, after teachers' reflection on the cognitive demands of mathematical tasks, higher-level demands of mathematical tasks were maintained.

• School Mathematics
• /
• v.15 no.1
• /
• pp.37-59
• /
• 2013

The purpose of this study was to examine and analyze the mathematical tasks in the high school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the textbooks. We adopted the framework for mathematical task analysis suggested by Smith & Stein (1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at low level and the rest at high level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures.

• School Mathematics
• /
• v.14 no.2
• /
• pp.213-232
• /
• 2012

The purpose of this study was to examine and analyze the cognitive demand of the mathematical tasks suggested in the middle school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks on function in the textbooks. We adopted the framework for mathematical task analysis suggested by Stein & Smith (1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at low level and the rest at high level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures. In particular, the high level tasks were presented at the end of each chapter or unit for wrap up rather than as key resources.

• Journal of the Korean School Mathematics Society
• /
• v.22 no.2
• /
• pp.95-113
• /
• 2019

In this paper, we analyzed the levels of cognitive demand of the tasks for developing t he mathematical core competencies presented in the "Mathematics" textbook of the first y ear of high school developed according to the 2015 revised mathematics curriculum. "Mathematics" textbook included 4999 mathematics tasks, of which 703 were tasks for developing the mathematical competency. Analysis of 703 mathematical tasks according to the analysis framework of Stein, Smith, Henningsen, and Silver (2000) showed that 61.5% of students required high cognitive levels, 38.5% required low cognitive levels, and the types of tasks were as follows: Low-M 1.0%, Low-P 37.5%, High-P 57.8%, High-D 3.7%. It w as found that most of the tasks for the purpose were tasks that led to understanding mathematical concepts, principles, and processes along procedural processes.

• The Mathematical Education
• /
• v.60 no.1
• /
• pp.61-76
• /
• 2021

The purpose of this study is to analyze the errors and difficulties which pre-service secondary teachers shows during the task modification in consideration of the cognitive demand and to provide significant implications to the pre-service teacher education program related to the modification of the mathematical tasks. In the pursuit of this purpose, tasks were selected from perpendicular bisector units and 24 pre-service teachers were asked to modify the tasks to higher and lower level tasks. After the modification activities, opportunities for reflection and modification were provided. The findings from analysis are as follows. Pre-service teachers had a difficulty to distinguish between PNC tasks and PWC tasks. Also, We identified the interference phenomena that pre-service teachers depended on the apparent elements of the task. Pre-service teachers showed a tendency to overlook the learning objectives and learning hierarchy during the task modification, and to focus on some types of task modification. However, pre-service teachers were able to have meaningful learning opportunities and extend the category of tools to technology including Geogebra through self-reflection and correction activities on task modification. The above results were summed up and we presented the implications to the task modification program in the pre-service secondary teacher education.