مروری نقادانه بر آزمون های سنجش حس عدد
محورهای موضوعی : روانشناسی تربیتی
حمیده یزدی
1
(دانشجوی دکتری روانشناسی تربیتی، دانشگاه الزهرا، تهران، ایران)
مریم محسن پور
2
(گروه روانشناسی تربیتی ، دانشکده علوم تربیتی و روانشناسی، دانشگاه الزهرا، تهران، ایران)
کلید واژه: سنجش, آزمون, پیش دبستانی, دبستان, حس عدد,
چکیده مقاله :
حس عدد در دهه‌ی اخیر در آموزش ریاضی مورد توجه زیادی قرار گرفته و برای کسب مهارت‌های پیشرفته‌تر در ریاضی مورد نیاز است. با توجه به اهمیت حس عدد در آموزش ریاضی مدرسه‌ای و به خصوص در سال‌های پیش از دبستان و دبستان، شناخت شیوه‌های اندازه‌گیری و سنجش این مهارت مهم است. پژوهش حاضر با هدف معرفی آزمون‌های مورد استفاده‌ی پژوهشگران و شناسایی نقاط قوت و ضعف آزمون‌ها با روش مرور نقادانه نگاشته شده است. پس از جست‌وجو در پایگاه های اسکوپوس، وب آف ساینس و پایگاه‌های داخلی اطلاعات علمی جهاد دانشگاهی و نورمگز در بازه زمانی 2012 تا 2022، 75 مطالعه با کلید واژه‌ی حس عدد بازیابی شد. از این تعداد 22 مطالعه طبق ملاک مرتبط بودن با سنجش حس عدد دانش‌آموزان پیش‌دبستانی و دبستانی انتخاب شدند. معیار خروج شامل مقاله‌های مروری، مقاله‌های مربوط به گروه سنی بالای 12 سال و گروه سنی کمتر از 5 سال و مقاله‌های تحلیل محتوای کتاب‌های درسی بود. با بررسی آزمون‌های مورد استفاده در مطالعات منتخب، 6 آزمون شناسایی و با استفاده از نشانگرهای تعیین شده، مورد تحلیل قرار گرفت. نتایج نشان داد همه‌ی آزمون‌های سنجش حس عدد به مؤلفه‌‌های شمارش، تشخیص اعداد، مقایسه اعداد و عملیات روی اعداد پرداخته‌اند. با توجه به نتایج، پیشنهادهایی در راستای طراحی یک آزمون بومی جهت سنجش حس عدد ارائه شد.
In the last decades, number sense has received a lot of attention in math education as it is necessary to acquire more advanced math skills. Knowing how to measure and evaluate number sense is important because it plays a crucial role in teaching mathematics at schools, particularly in pre-school and elementary grades. The present study was written to introduce the tests used by researchers and identify their strengths and weaknesses with a critical review methodology. Searching related documents in” Scopus”, “Web of Science” “Scientific Information Database” and “Noormags” from 2012 to 2022, 75 documents were retrieved with the key word ‘number sense’. Twenty-two of these documents were chosen based on their relevance to assessing the number sense of preschool and elementary school students. The exclusion criteria included review articles, articles related to the age group above 12 years of age as well as the age group below 5 years of age, and articles analyzing the content of textbooks. By examining the tests used in the selected studies, 6 tests were identified and analyzed using the determined indicators. The results showed that all the number sense tests dealt with the components of counting components, number recognition, number comparison, and operations on numbers. Based on the findings some suggestions were made for designing a native test to measure number sense.
پاکزاد، رضا و علاءالدینی، فرشید (1395). سوء استفاده و سوء برداشت از ضریب آلفای کرونباخ به عنوان شاخصی برای ثبات درونی ابزار سنجش. مجله تخصصی اپیدمیولوژی ایران, 12(4)، 64-71.
پوشنه، کامبیز و نیکنام، صدف (1398). اثربخشی برنامه آموزش حس عدد بر بهبود مهارت‌های عددی و پیشرفت تحصیلی ریاضی دانش‌آموزان دیرآموز پایه اول ابتدایی. روانشناسی افراد استثنایی، 9(36)، 55-70.
زارع‌پور، فاطمه؛ قاسمی، مسعود؛ شریعت باقری، محدمهدی و درتاج، فریبرز (1400). اثربخشی آموزش ریاضی بر حس عدد و حافظه فعال دیداری-فضایی کودکان دختر با مشکلات ریاضی. نشریه پرستاری کودکان و نوزادان، 9(1)، 42-46.
Akkaya, R. (2016). An Investigation into the Number Sense Performance of Secondary School Students in Turkey. Journal of Education and Training Studies, 4(2): 113-123.
Artut, P. D., & Er, Z. (2022, February). Investigation of number sense strategies used by 5th grade gifted students in Turkey. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Feb 2022, BozenBolzano, Italy
Baroody, A. J., Eiland, M., & Thompson, B. (2009). Fostering at-risk preschoolers' number sense. Early Education and Development, 20(1): 80-128.
Barth, H., La Mont, K., Lipton, J., Dehaene, S., Kanwisher, N., & Spelke, E. (2006). Non-symbolic arithmetic in adults and young children. Cognition, 98(3): 199-222.
Bliss, S. (2006). Test of early mathematics ability–Third edition. Journal of psychoeducational Assessment, 24(1): 85-98.
Bütüner, S. Ö. (2018). Comparing the use of number sense strategies based on student achievement levels. International Journal of Mathematical Education in Science and Technology, 49(6): 824-855.
Chinn, S. J., & Ashcroft, J. R. (1993). Mathematics for dyslexics. London: WhulT Publishers Ltd.
Connolly, A. J. (1988). KeyMath Revised: A Diagnostic Inventory of Essential Mathematics: Manual, Forms A and B. American Guidance Service.
Dehaene, S. (2011). The number sense: How the mind creates mathematics: OUP USA.
Devlin, K. (2017). All the mathematical methods I learned in my university math degree became obsolete in my lifetime. Retrieved January 25, 2019, from HUFFPOST: https://www. huffpost.com/entry/all-the-mathematical-methods-i-learned-in-my-university_b_58693ef9e4b014e7c72ee248
Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37: 21-29.
Gardner, H. (1983). Frames of mind: The theory of multiple intelligence. New York: Basic Books Inc
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4): 293-304.
Ghazali, M., Mohamed, R., & Mustafa, Z. (2021). A Systematic Review on the Definition of Children's Number Sense in the Primary School Years. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), 1-12 Article 1968.
Gurganus, S. (2004). Promote number sense. Intervention in School and Clinic, 40(1): 55-56.
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the" Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. Developmental psychology, 44(5): 1457–1465
Harling, P., & Roberts, T. (1988). Primary mathematics schemes. London: Hodder and Stoughton.
Jordan, N. C., Glutting, J., & Ramineni, C. (2008). A number sense assessment tool for identifying children at risk for mathematical difficulties. In Mathematical Difficulties (pp. 45-58): Elsevier.
Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and individual differences, 20(2): 82-88.
Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. School Psychology Review, 39(2): 181-195.
Locuniak, M. N., & Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41(5): 451-459
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
Pakzad, R., & Alaeddini F. (2017). Misuse and misinterpretation of Cronbach's alpha coefficient as an indicator of the internal consistency of the measuring instrument. Iranian specialized journal of epidemiology, 12(4): 64-71[In Persian].
Parsons, S., & Bynner, J. (2005). Does numeracy matter more? London: National Research and Development Centre for Adult Literacy and Numeracy.
Principles, N. (2000). standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics. In: Inc.
poushneh, K., & niknam, S. (2020). The Effectiveness of Number Sense Teaching Program on Number Sense Ability and Math Achievement of Slow Learner Students. Psychology of Exceptional Individuals, 9(36): 55-70 [In Persian].
Şengül, S., & Gülbağcı, D. (2014). The strategies of mathematics teachers when solving number sense problems. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 5(1): 73-88.
Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences, 110(45): 18116-18120.
Tunali, S. D. (2022). A test for identification of math talent: developing a three-tier number sense test. Journal of Gifted Education and Creativity, 9(3): 285-301.
UNESCO. (1977). New trends in mathematics teaching (Second Impressions). Volume In. France.
Wang, J. J., Halberda, J., & Feigenson, L. (2017). Approximate number sense correlates with math performance in gifted adolescents. Act a Psychologica, 176, 78-84. DOI: 10.1016/j.actpsy.2017.03.014
Whitfield, P. (1987). Assessment and evaluation. M. Preston (Ed). Mathematics in Primary Education. London: The Falmer Press
Yang, D. C. (2007). Investigating the strategies used by preservice teachers in Taiwan when responding to number sense questions. School Science and Mathematics, 107(7): 293-301.
Yang, D. C., M. N. Li, & C. I. Lin. (2008). A Study of the Performance of 5th Graders in Number Sense and Its Relationship to Achievement in Mathematics. International Journal of Science and Mathematics Education. 6(4): 789–807.
Yang, D. C. (2019). Development of a three-tier number sense test for fifth-grade students. Educational Studies in Mathematics, 101(3): 405-424.
Yang, D. C., & Lin, Y. C. (2015). Assessing 10- to 11-year-old children’s performance and misconceptions in number sense using a four-tier diagnostic test. Educational Research, 57(4): 368–388.
Yang, D. C., & Tsai, Y. F. (2010). Promoting sixth graders' number sense and learning attitudes via technology-based environment. Journal of Educational Technology & Society, 13(4): 112-125.
Yilmaz, Z. (2017). Young children’s number sense development: Age related complexity across cases of three children. International Electronic Journal of Elementary Education, 9(4): 891-902.
Zare, F., ghasemi, M., shariat, M., & dortaj, F. (2022). The effectiveness of mathematics education on numerical sense and visual-spatial working memory of girls with mathematical problems. Journal of Pediatric Nursing, 9(1): 42-46 [In Persian]
_||_پاکزاد، رضا و علاءالدینی، فرشید (1395). سوء استفاده و سوء برداشت از ضریب آلفای کرونباخ به عنوان شاخصی برای ثبات درونی ابزار سنجش. مجله تخصصی اپیدمیولوژی ایران, 12(4)، 64-71.
پوشنه، کامبیز و نیکنام، صدف (1398). اثربخشی برنامه آموزش حس عدد بر بهبود مهارت‌های عددی و پیشرفت تحصیلی ریاضی دانش‌آموزان دیرآموز پایه اول ابتدایی. روانشناسی افراد استثنایی، 9(36)، 55-70.
زارع‌پور، فاطمه؛ قاسمی، مسعود؛ شریعت باقری، محدمهدی و درتاج، فریبرز (1400). اثربخشی آموزش ریاضی بر حس عدد و حافظه فعال دیداری-فضایی کودکان دختر با مشکلات ریاضی. نشریه پرستاری کودکان و نوزادان، 9(1)، 42-46.
Akkaya, R. (2016). An Investigation into the Number Sense Performance of Secondary School Students in Turkey. Journal of Education and Training Studies, 4(2): 113-123.
Artut, P. D., & Er, Z. (2022, February). Investigation of number sense strategies used by 5th grade gifted students in Turkey. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Feb 2022, BozenBolzano, Italy
Baroody, A. J., Eiland, M., & Thompson, B. (2009). Fostering at-risk preschoolers' number sense. Early Education and Development, 20(1): 80-128.
Barth, H., La Mont, K., Lipton, J., Dehaene, S., Kanwisher, N., & Spelke, E. (2006). Non-symbolic arithmetic in adults and young children. Cognition, 98(3): 199-222.
Bliss, S. (2006). Test of early mathematics ability–Third edition. Journal of psychoeducational Assessment, 24(1): 85-98.
Bütüner, S. Ö. (2018). Comparing the use of number sense strategies based on student achievement levels. International Journal of Mathematical Education in Science and Technology, 49(6): 824-855.
Chinn, S. J., & Ashcroft, J. R. (1993). Mathematics for dyslexics. London: WhulT Publishers Ltd.
Connolly, A. J. (1988). KeyMath Revised: A Diagnostic Inventory of Essential Mathematics: Manual, Forms A and B. American Guidance Service.
Dehaene, S. (2011). The number sense: How the mind creates mathematics: OUP USA.
Devlin, K. (2017). All the mathematical methods I learned in my university math degree became obsolete in my lifetime. Retrieved January 25, 2019, from HUFFPOST: https://www. huffpost.com/entry/all-the-mathematical-methods-i-learned-in-my-university_b_58693ef9e4b014e7c72ee248
Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37: 21-29.
Gardner, H. (1983). Frames of mind: The theory of multiple intelligence. New York: Basic Books Inc
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4): 293-304.
Ghazali, M., Mohamed, R., & Mustafa, Z. (2021). A Systematic Review on the Definition of Children's Number Sense in the Primary School Years. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), 1-12 Article 1968.
Gurganus, S. (2004). Promote number sense. Intervention in School and Clinic, 40(1): 55-56.
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the" Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. Developmental psychology, 44(5): 1457–1465
Harling, P., & Roberts, T. (1988). Primary mathematics schemes. London: Hodder and Stoughton.
Jordan, N. C., Glutting, J., & Ramineni, C. (2008). A number sense assessment tool for identifying children at risk for mathematical difficulties. In Mathematical Difficulties (pp. 45-58): Elsevier.
Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and individual differences, 20(2): 82-88.
Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. School Psychology Review, 39(2): 181-195.
Locuniak, M. N., & Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41(5): 451-459
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
Pakzad, R., & Alaeddini F. (2017). Misuse and misinterpretation of Cronbach's alpha coefficient as an indicator of the internal consistency of the measuring instrument. Iranian specialized journal of epidemiology, 12(4): 64-71[In Persian].
Parsons, S., & Bynner, J. (2005). Does numeracy matter more? London: National Research and Development Centre for Adult Literacy and Numeracy.
Principles, N. (2000). standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics. In: Inc.
poushneh, K., & niknam, S. (2020). The Effectiveness of Number Sense Teaching Program on Number Sense Ability and Math Achievement of Slow Learner Students. Psychology of Exceptional Individuals, 9(36): 55-70 [In Persian].
Şengül, S., & Gülbağcı, D. (2014). The strategies of mathematics teachers when solving number sense problems. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 5(1): 73-88.
Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences, 110(45): 18116-18120.
Tunali, S. D. (2022). A test for identification of math talent: developing a three-tier number sense test. Journal of Gifted Education and Creativity, 9(3): 285-301.
UNESCO. (1977). New trends in mathematics teaching (Second Impressions). Volume In. France.
Wang, J. J., Halberda, J., & Feigenson, L. (2017). Approximate number sense correlates with math performance in gifted adolescents. Act a Psychologica, 176, 78-84. DOI: 10.1016/j.actpsy.2017.03.014
Whitfield, P. (1987). Assessment and evaluation. M. Preston (Ed). Mathematics in Primary Education. London: The Falmer Press
Yang, D. C. (2007). Investigating the strategies used by preservice teachers in Taiwan when responding to number sense questions. School Science and Mathematics, 107(7): 293-301.
Yang, D. C., M. N. Li, & C. I. Lin. (2008). A Study of the Performance of 5th Graders in Number Sense and Its Relationship to Achievement in Mathematics. International Journal of Science and Mathematics Education. 6(4): 789–807.
Yang, D. C. (2019). Development of a three-tier number sense test for fifth-grade students. Educational Studies in Mathematics, 101(3): 405-424.
Yang, D. C., & Lin, Y. C. (2015). Assessing 10- to 11-year-old children’s performance and misconceptions in number sense using a four-tier diagnostic test. Educational Research, 57(4): 368–388.
Yang, D. C., & Tsai, Y. F. (2010). Promoting sixth graders' number sense and learning attitudes via technology-based environment. Journal of Educational Technology & Society, 13(4): 112-125.
Yilmaz, Z. (2017). Young children’s number sense development: Age related complexity across cases of three children. International Electronic Journal of Elementary Education, 9(4): 891-902.
Zare, F., ghasemi, M., shariat, M., & dortaj, F. (2022). The effectiveness of mathematics education on numerical sense and visual-spatial working memory of girls with mathematical problems. Journal of Pediatric Nursing, 9(1): 42-46 [In Persian]