과제 상황의 구조화 정도에 따른 초등학생들의 문제만들기와 뇌 활성의 변화 탐색
Exploring Changes of Problem-Posing and Brain Activity of Elementary School Students According to the Degree of Structure of the Task Situation
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The purpose of this study is to develop and apply a problem-posing program for elementaryschool students according to the degree of structure of task situations in the area ofgeometry and measurement, and to compare its effectiveness to provide implications forproblem-posing instruction. In the process, changes in brain activity were analyzed togetherto verify the effect of the problem-posing program on the brain and provide empiricalevidence. For this purpose, the experimental group performed the problem-posing programin an unstructured situation and the control group performed the problem-posing programin a structured situation for 8 sessions, and evaluated the change of abilities in problemposingmade by students during the class according to analysis framework. We found thatthe students further developed their problems following the learning steps in the problemposingprogram. In particular, the experimental group showed higher improvement inthe level of problem-posing and showed significant activation on the brain areas: thefrontal regions, the right VLPFC area, and the DLPFC area. These results suggest that it isnecessary to increase the reflection of problem-posing tasks in unstructured situations inthe curriculum, develop and apply various task types, and present systematic learning stepstogether.
Abstract
The purpose of this study is to develop and apply a problem-posing program for elementaryschool students according to the degree of structure of task situations in the area ofgeometry and measurement, and to compare its effectiveness to provide implications forproblem-posing instruction. In the process, changes in brain activity were analyzed togetherto verify the effect of the problem-posing program on the brain and provide empiricalevidence. For this purpose, the experimental group performed the problem-posing programin an unstructured situation and the control group performed the problem-posing programin a structured situation for 8 sessions, and evaluated the change of abilities in problemposingmade by students during the class according to analysis framework. We found thatthe students further developed their problems following the learning steps in the problemposingprogram. In particular, the experimental group showed higher improvement inthe level of problem-posing and showed significant activation on the brain areas: thefrontal regions, the right VLPFC area, and the DLPFC area. These results suggest that it isnecessary to increase the reflection of problem-posing tasks in unstructured situations inthe curriculum, develop and apply various task types, and present systematic learning stepstogether.
참고문헌 (91)
- Arsalidou, M., "Brain areas associated with numbers and calculations in children : Meta-analyses of fMRI studies", Developmental Cognitive Neuroscience, 30, pp.239~250 (2018)
- Aziz-Zadeh, L., "Exploring the neural correlates of visual creativity", Social Cognitive and Affective Neuroscience, 8, pp.475~480 (2013)
- Babai, R., "Persistence of the intuitive conception of living things in adolescence", Journal of Science Education and Technology, 19, pp.20~26 (2010)
- Bae, J. H., "The Effects of Reflective Problem Posing Activities on Students’ Problem Solving Ability and Attitudes toward Mathematics", Journal of Elementary Mathematics Education in Korea, 20, pp.311~331 (2016)
- Baumanns, L., "Rethinking problem-posing situations : A review", Investigations in Mathematics Learning, 13, pp.59~76 (2021)
- Baumanns, L., "The process of problem posing : Development of a descriptive phase model of problem posing", Educational Studies in Mathematics, 110, pp.251~269 (2022)
- Bicer, A., "Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity", Educational Studies in Mathematics, 105, pp.457~485 (2020)
- Brown, S. I., "The Art of Problem Posing" (2005), Lawrence Erlbaum Associates. Psychology Press
- Cai, J., "Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design", International Journal of Educational Research, 102, pp.101404~ (2020)
- Cai, J., "Mathematical problem posing as a measure of curricular effect on students’ learning", Educational Studies in Mathematics, 83, pp.57~69 (2013)
- Cai, J., "An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks", International Journal of Science and Mathematics Education, 15, pp.1521~1540 (2017)
- Cai, J., "Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing", The Journal of Mathematical Behavior, 21, pp.401~421 (2002)
- Cai, J., "Learning to teach through mathematical problem posing : Theoretical considerations, methodology, and directions for future research", International Journal of Educational Research, 102, pp.101391~ (2020)
- Cai, J., "Mathematical Problem Posing:From Research to Effective Practice", pp.3~34 (2015), Springer
- Choi, Y. S., "Effects of Teaching with Problem Posing on Mathematical Problem Solving Ability and Attitude in Elementary School Mathematics", Journal of Elementary Mathematics Education in Korea, 8, pp.23~43 (2004)
- Crespo, S., "Learning to pose mathematical problems : Exploring changes in preservice teachers’practices", Educational Studies in Mathematics, 52, pp.243~270 (2003)
- Crespo, S., "What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems", Journal of Mathematics Teacher Education, 11, pp.395~415 (2008)
- Cui, X., "A quantitative comparison of NIRS and fMRI across multiple cognitive tasks", Neuroimage, 54, pp.2808~2821 (2011)
- Desco, M., "Mathematically gifted adolescents use more extensive and more bilateral areas of the fronto-parietal network than controls during executive functioning and fluid reasoning tasks", Neuroimage, 57, pp.281~292 (2011)
- DeYoung, C. G., "Personality neuroscience and the biology of traits", Social and Personality Psychology Compass, 4, pp.1165~1180 (2010)
- Dunst, B., "Neural efficiency as a function of task demands", Intelligence, 42, pp.22~30 (2014)
- English, L. D., "The development of fifth-grade children’s problem-posing abilities", Educational Studies in Mathematics, 34, pp.183~217 (1997)
- Guidelines for Question Generation Shared Task Evaluation Campaigns. In The Question Generation Shared Task & Evaluation Challenge Workshop Report, "Graesser, A", University of Memphis, ~ (2008)
- Halmos, P. R., "How to write mathematics", Ĺenseignement Mathématique, 16, pp.123~152 (1970)
- Han, H. S., "A case study on mathematical problem posing in pre-service mathematics teacher education", Journal of the Korean School Mathematics Society, 21, pp.63~89 (2018)
- Herff, C., "Mental workload during n-back task—quantified in the prefrontal cortex using fNIRS", Frontiers in Human Neuroscience, 7, pp.935~ (2014)
- Hong, J. R., "Difference of working memory according to academic achievement with college students; functional Magnetic Resonance Imaging", Journal of the Korean Society of Radiology, 6, pp.173~182 (2012)
- Huh, N., "Elementary teachers’ perceptions and applications about problem-posing in the mathematics instruction", Journal of the Korean School Mathematics Society, 14, pp.539~564 (2011)
- Kang, M. J., "Brain activation with fnirs in children’s transformational geometry problem solving:Using tangram", Brain, Digital, & Learning, 10, pp.485~497 (2020)
- Jung, J. H., "About problem setting and teaching=learning(1)", Journal of the Korean Society of Mathematical Education, 31, pp.55~62 (1992)
- Jung, S. G., "The effects of the mathematical problem generating program on problem solving ability and learning attitude", Journal of Elementary Mathematics Education in Korea, 14, pp.315~335 (2010)
- Kilpatrick, J, "Cognitive Science and Mathematics Education", pp.123~147 (1987), Erlbaum
- Kim, G. T., "An analysis of problem posing in the 5th and 6th grade mathematics textbooks and errors in problem posing of 6th graders", Journal of Elementary Mathematics Education in Korea, 17, pp.321~350 (2013)
- Kim, K. O., "The effects of the situation-based mathematical problem posing activity on problem solving ability and mathematical attitudes", Journal of Korea Society of Educational Studies in Mathematics, 11, pp.665~683 (2009)
- Kim, J. K., "An effect coming to the problem solving ability from the problem posing activity by presenting the problem situation", Journal of Elementary Mathematics Education in Korea, 5, pp.77~98 (2001)
- Kim, S. J., "The effects of open-ended problems on mathematical creativity and brain function", Journal of Elementary Mathematics Education in Korea, 14, pp.723~744 (2010)
- Ko, J. H., "The analysis of problem posing activities and students’ performance in the 4-1 textbook and workbook", Journal of the Korean School Mathematics Society, 18, pp.103~122 (2015)
- Kuk, H, "Study on brain activation characteristics in solving physics problems", NPSM, 72, pp.135~141 (2022)
- Lavy, I., "Problem posing via"what if not?"strategy in solid geometry—A case study", The Journal of Mathematical Behavior, 22, pp.369~387 (2003)
- Lee, K. M., "The analysis of the 5th graders’ responses on problem posing", School Mathematics, 14, pp.431~443 (2012)
- Lee, D. H., "An analysis on the students’ mathematical creativity in problem posing activities", Journal of the Korean School Mathematics Society, 15, pp.411~428 (2012)
- Lee, D. H., "The analysis of problem posing cases of pre-service primary teachers", School Mathematics, 19, pp.1~18 (2017)
- Lee, H. Y., "A comparative analysis on the mathematical problem posing according to the tasks with different degrees of structure by the gifted and non-gifted elementary students", Journal of Elementary Mathematics Education in Korea, 22, pp.309~330 (2018)
- Lee, J. H., "The development and application of posing open-ended problems program with renzulli’s enrichment triad model for mathematics gifted elementary students", The Mathematical Education, 55, pp.209~232 (2016)
- Lee, M. H., "Analysis of abduction in mathematics problem posing and solving", Journal of Educational Research in Mathematics, 30, pp.89~110 (2020)
- Lee, Y. J., "An Analysis of Students’ Mathematical Problem Posing", Master, pp.2013
- Leung, S. K. S., "Teachers implementing mathematical problem posing in the classroom : Challenges and strategies", Educational Studies in Mathematics, 83, pp.103~116 (2013)
- Lin, K. M., "Using problem-posing as an assessment tool", 10th Asia-Pacific Conference on Giftedness, pp.1~15 (2008)
- Manuel, D., "Differentiating instruction using a virtual environment : A study of mathematical problem posing among gifted and talented learners", Global Education Review, 4, pp.78~98 (2017)
- McLaughlin, N. C., "Differential contributions of lateral prefrontal cortex regions to visual memory processes", Brain Imaging and Behavior, 3, pp.202~211 (2009)
- Meidenbauer, K. L., "Loaddependent relationships between frontal fNIRS activity and performance : A data-driven PLS approach", NeuroImage, 230, pp.117795~ (2021)
- Meier, M. A., "Interference between naïve and scientific theories in mathematics and science : An fMRI study comparing mathematicians and nonmathematicians", Trends in Neuroscience and Education, 29 (2022)
- Ministry of Education, "2015 Revised Curriculum for Mathematics (Ministry of Education Notice No. 2015-74)", ~ (2015)
- ), , 2022
- Ministry of Education & Human Resources Development, "Revised Curriculum for Mathematics(Ministry of Education & Human Resources Development Notice No. 2006-75)", ~ (2006)
- ), , 2011
- Na, G. S., "Examining the problem making by mathematically gifted students", School Mathematics, 19, pp.77~93 (2017)
- National Council of Teachers of Mathematics., "Professional Standards for Teaching Mathematics", National Council of Teachers of Mathematics, ~ (1991)
- National Council of Teachers of Mathematics, "Principles and Standards for School Mathematics", National Council of Teachers of Mathematics, ~ (2000)
- Neubauer, A. C., "Intelligence and neural efficiency", Neuroscience & Biobehavioral Reviews, 33, pp.1004~1023 (2009)
- OBELAB, Inc, "NIRSIT Channel Information", ~ (2022)
- Olson, J. C., "When a problem is more than a teacher’s question", Educational Studies in Mathematics, 83, pp.27~36 (2013)
- Park, A. R., "A case study on the students’ characteristics toward mathematics with problem posing activities", Journal of Elementary Mathematics Education in Korea, 22, pp.93~114 (2018)
- Park, H. M., "Analysis of students’ responses according to the types of problem posing tasks in mathematics textbooks of grade 3-4", School Mathematics, 25, pp.83~112 (2023)
- Park, J. H., "An analysis of problem posing tasks in 5th and 6th grades mathematics textbooks", Journal of Elementary Mathematics Education in Korea, 25, pp.465~488 (2021)
- Petrides, M., "Differential activation of the human orbital, mid-ventrolateral, and mid-dorsolateral prefrontal cortex during the processing of visual stimuli", Proceedings of the National Academy of Sciences, 99, pp.5649~5654 (2002)
- Pinti, P., "The present and future use of functional near-infrared spectroscopy(fNIRS)for cognitive neuroscience", Annals of the New York Academy of Sciences, 1464, pp.5~29 (2020)
- Prado, J., "Developmental dissociation in the neural responses to simple multiplication and subtraction problems", Developmental Science, 17, pp.537~552 (2014)
- Sheffield, L, "Creativity in Mathematics and the Education of Gifted Students", pp.87~100 (2009), Sense Publishers
- Shin, S. J., "An analytic study of mathematical problem-posing activities for twohour classes-focusing on 3rd grade elementary school children", Journal of Elementary Mathematics Education in Korea, 14, pp.43~64 (2010)
- Silver, E. A., "On mathematical problem posing", For the Learning of Mathematics, 14, pp.19~28 (1994)
- Silver, E. A., "An analysis of arithmetic problem posing by middle school students", Journal for Research in Mathematics Education, 27, pp.521~539 (1996)
- Silver, E. A., "Assessing students’ mathematical problem posing", Teaching Children Mathematics, 12, pp.129~135 (2005)
- Silver, E. A., "Thinking through Mathematics: Fostering Inquiry and Communication in Mathematics Classrooms" (1990), The College Entrance examination Board
- Singer, F. M., "Proceedings of the 7th Conference of the European Society for Research in Mathematics Education (CERME 7)" (2011), University of Rzeszów
- Singer, F. M., "Problem-posing research in mathematics education : New questions and directions", Educational Studies in Mathematics, 83, pp.1~7 (2013)
- Soltanlou, M., "Applications of functional near-infrared spectroscopy(fNIRS)in studying cognitive development : The case of mathematics and language", Frontiers in Psychology, 9, pp.277~ (2018)
- Stanic, G., "Historical perspectives on problem solving in the mathematics curriculum", The Teaching and Assessing of Mathematical Problem Solving, 3, pp.1~22 (1989)
- Stoyanova, E., "A framework for research into students’ problem posing in school mathematics", Technology in Mathematics Education, 4, pp.518~525 (1996)
- Sung, C. G., "Analysis of problem posing activity of fifth grade students", C-Education of Primary School Mathematics, 20, pp.193~204 (2017)
- Toepper, M., "Functional correlates of distractor suppression during spatial working memory encoding", Neuroscience, 165, pp.1244~1253 (2010)
- Van Harpen, X. Y., "Creativity and mathematical problem posing : an analysis of high school students’ mathematical problem posing in China and the USA", Educational Studies in Mathematics, 82, pp.201~221 (2013)
- Watt, H. M., "Attitudes to the use of alternative assessment methods in mathematics: A study with secondary mathematics teachers in Sydney, Australia", Educational Studies in Mathematics, 58, pp.21~44 (2005)
- Xia, X., "Research on mathematics instruction experiment based problem posing", Journal of Mathematics Education, 1, pp.153~163 (2008)
- Xie, J., "Examining interactions between problem posing and problem solving with prospective primary teachers : A case of using fractions", Educational Studies in Mathematics, 96, pp.101~118 (2017)
- Xu, B., "Teachers’ predictions of students’ mathematical thinking related to problem posing", International Journal of Educational Research, 102, pp.101427~ (2020)
- Yang, Y., "Prefrontal structural and functional brain imaging findings in antisocial, violent, and psychopathic individuals : A meta-analysis", Psychiatry Research : Neuroimaging, 174, pp.81~88 (2009)
- Yao, Y., "Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving", ZDM–Mathematics Education, 53, pp.937~949 (2021)
- Yoon, S. A., "A study to improve teaching methods of mathematical problem posing in elementary mathematics", The Journal of Korea Elementary Education, 21, pp.25~47 (2010)
- Yun, M. R., "The effects of problem posing program through structure-centered cooperative learning on mathematics learning achievements and mathematical disposition", Journal of Elementary Mathematics Education in Korea, 12, pp.101~124 (2008)
- Zhang, H., "Teaching mathematics through problem posing : Insights from an analysis of teaching cases", ZDM–Mathematics Education, 53, pp.961~973 (2021)
