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Kavramsal Bilginin Gelişiminin İncelenmesi: Cebirsel Kesirli İfadeleri İçeren Denklemler Bağlamında

Year 2021, Issue: 16, 83 - 103, 15.12.2021
https://doi.org/10.20860/ijoses.967628

Abstract

Bu araştırmanın amacı, cebirsel kesirli ifadeleri içeren denklemlerde katılımcıların kavramsal bilgilerindeki değişimi incelemektir. Bu araştırmada yürütülen öğretim sürecinde katılımcılardan cebirsel kesirli ifadeleri içeren denklemlere sözel problem yazmaları istenerek, kavramsal anlamaya dair bilişsel yapılarının değişimleri izlenmiştir. Bu Araştırmanın modelini “öğretim deneyi”, bunu desteklemek için yapılan “klinik görüşmeler” ve “doküman incelemesi” oluşturmaktadır. Araştırmadan elde edilen veriler içerik analizi yöntemiyle analiz edilmiştir. Araştırma 2015-2016 öğretim yılında Türkiye’de bir ilde iki farklı lisede öğrenim gören 4 dokuzuncu sınıf öğrencisi ile gerçekleştirilmiştir. Elde edilen verilere göre, katılımcılar diğer çalışmalara benzer şekilde önce kesrin anlamını oluşturmuş, ardından sözel problem yazabilmişlerdir. Bu araştırmada yazılan sözel problemlerde en çok kullanılan anlamlar kesrin bölüm, oran ve ölçme anlamları olurken, işlemci ve parça bütün anlamları ise en az kullanılan anlamlar olmuştur. Literatüre gore, nümerik kesirlerle ilgili en çok kullanılan anlam ise bu araştırmanın aksine parça bütün anlamıdır. Kullanılan kesrin anlamlarının, kesrin türü ile ilişkili olduğu belirlenmiştir. Sözel problem yazarken, katılımcıların hatalar yaptığı ve kesrin farklı anlamlarına göre yapılan hataların da farklılık gösterdiği belirlenmiştir. Alanyazında bu sonuç ile ilgili herhangi bir çalışmaya rastlanmamıştır. Bu araştırmanın uygulama süresi ve yöntemi göz önünde bulundurularak farklı kavramlara dair farklı düzeyde katılımcıların kavramsal değişim süreçleri incelenebilir. 

Supporting Institution

Anadolu Üniversitesi BAP Komisyonu

Project Number

1603E099 no.lu proje kapsamında desteklenmiştir.

References

  • Acar, N. (2010). Kesir Çubuklarının İlköğretim 6. Sınıf öğrencilerinin Kesirlerde Toplama ve Çıkarma İşlemlerindeki Başarılarına Etkisi. Yayınlanmış Yüksek Lisans Tezi. Selçuk Üniversitesi, Fen Bilimleri Enstitüsü, KONYA.
  • Alacaci, C. (2012). Öğrencilerin kesirler konusundaki kavram yanılgıları. Bingölbali, E ve Özmantar, M., F. (Edt). İlköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm Önerileri. Ankara: Pegem Akademi
  • Alibali, Martha W., Mitchell J. Nathan, Matthew S. Wolfgram , R. Breckinridge Church, Steven A. Jacobs, Chelsea Johnson Martinez & Eric J. Knuth (2014) How Teachers Link Ideas in Mathematics Instruction Using Speech and Gesture: A Corpus Analysis, Cognition and Instruction, 32:1, 65-100, DOI: 10.1080/07370008.2013.858161
  • Behr, M.J., Lesh, R., Post, T.R., and Silver, E.A. (1983). Rational number concepts. In R. Lesh, and M. Landau (Eds.), Acquisition of mathematics concepts and processes (92–127). New York: Academic Press.
  • Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 296–333). New York: Macmillan.
  • Birgin, O. ve Gürbüz, R.(2009). İlköğretim II. Kademe Öğrencilerinin Rasyonel Sayılar konusundaki İşlemsel ve Kavramsal Bilgi Düzeylerinin İncelenmesi. Eğitim Fakültesi Dergisi, XXII (2), 2009, 529-550
  • Booth, L. R. (1986). Difficulties in algebra. Australian Mathematics Teacher, 42(3), 2–4.
  • Booth, L. R., & Watson, J. (1990). Research for teaching: Learning and teaching algebra. Australian Mathematics Teacher, 46(3), 12–14.
  • Crooks, N. M. & Alibali, M. W. (2014). Defining and measuring conceptual knowledge of mathematics. Developmental Review. doi: 10.1016/j.dr.2014.10.001
  • Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.
  • Işık, C. ve Kar, T. (2012). Matematik dersinde problem kurmaya yönelik öğretmen görüşleri üzerine nitel bir çalışma. Millî Eğitim. Sayı 194/ Bahar/ 2012 (s. 199-215)
  • Kılıç, Ç. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22, 1-10.
  • Kieren, T. E. (1976) On the mathematical, cognitive and instructional foundations of rational numbers. In: Lesh, R. (ed) Number and measurement: papers from a research workshop. Columbus, Ohio: Eric/Smeac, p. 101-144.
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 318–326. http://dx.doi.org/10.1007/BF00311062
  • Kieren, T. E. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. In J. Hiebertand M. Behr (Eds.), Number concepts and operations in the middle grades (162–181). Reston VA: The National Council of Teachers of Mathematics.
  • Kilpatrick, J., Swafford, J. O., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.
  • Lavy, I., & Bershadsky, I. (2003). Problem posing via ‘‘what if not?’’ strategy in solid geometry a case study. Journal of Mathematical Behavior, 22, 369–387.
  • MEB. (2013). Ortaokul matematik dersi öğretim programı. Retrieved March, 15, 2013 from .
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Fractions: Children's strategies and errors: A report of the strategies and error in secondary mathematics Project NFER-Nelson, Windson (1986)
  • National Council of Teachers of Mathematics [NCTM]. (2011). Principles and standards for school mathematics. Reston, Va: National Council of Teachers of Mathematics.
  • Olkun, S., Uçar, Z. T. (2007) İlköğretimde Etkinlik Temelli Matematik Öğretimi (üçüncü baskı),Ankara: Maya Akademi.
  • Öksüz, C. (2004). Children understanding of algebric fraction as quotients. (Unpublished doctoral dissertation). University of Arizona, Arizona
  • Patton, M.Q. (1997). How to use qualitative methods in evaluation. Newbury park, CA: SAGE Publications
  • Pope, L. (1994), Teaching Algebra. Mathematics Education: A Handbook for Teachers. elsington College of Education: New Zealand, 1, 88-99 .
  • Sasman, M. Linchevski, L., Olivier, A. 1997. Reconceptualising school algebra. Internet: http://academic.sun.ac.za/mathed/MALATI/Rational.pdf
  • Saxe, G.,Gearhart, M., and Nasir, N. S. (2001). Enhancing students' understanding of mathematics: A study of three contrasting approaches to Professional support Journal of Mathematics Teacher Education, 4, 55–79.
  • Schoenfeld, A. ve Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher. 81 (6), 420-427.
  • Sheffield, L. J., & Cruikshank, D. E. (2005). Teaching and learning mathematics pre-kindergarten through middle school. Hoboken, N.J.: Wiley Jossey Bass Education
  • Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing, International Journal of Mathematical Education in Science and Technology, 48(2), 163-184
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics. 14(1), 19–28.
  • Skemp, R., R. (1976). Relational Understanding and Instrumental Understanding. Department of Education, University of Warwick (http://static1.squarespace.com/static/53b6662ae4b00ce9a7c30e76/t/5548a95ae4b03cee0387aef9/1430825306203/Mona+Rosseland+12.11.14+Vedlegg.pdf)
  • Skemp, R. R. (1978). Relational and instrumental understanding. Arithmetic Teacher, 26, 9-15.
  • Stacey, K., and MacGregor, M. (1997b). Ideas about symbolism that students bring to algebra. Mathematics Teacher, 90, 110-113.
  • Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404–411.
  • Star, J. R. (2007). Foregrounding procedural knowledge. Journal for Research in Mathematics Education, 38(2), 132–135.
  • Steffe, L. P., and Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essentialelements. In R. Lesh& A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267- 307). Hillsdale, NJ: Erlbaum.
  • Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp.518–525). Melbourne: Mathematics Education Research Group of Australasia. Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem posing. The Australian Mathematics Teacher, 59(2), 32–40.
  • Şengül, S. & Katrancı, Y. (2012). Problem solving and problem posing skills of prospective mathematics teachers about the ‘sets’ subject. Procedia - Social and Behavioral Sciences, 69, 1650 – 1655.
  • Şengül, S ve Öz, C. (2008). İlköğretim 6. Sınıf Kesirler Ünitesinde Çoklu Zekâ KuramınaUygun Öğretimin Öğrenci Tutumuna Etkisi. İlköğretim Online, 7(3), 800-813, 2008. [Online]: http://ilkogretim-online.org.tr
  • Ticha, M., & Hošpesová, A. (2009, Ocak). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Paper presented at Congress of European Research in Mathematics Education (CERME 6), Lyon, France.
  • Toluk, Z.(2001). Eşit paylaşım ortamlarının kesir öğretiminde kullanımı. Kuram ve Uygulamada Eğitim Bilimleri. 1 (1)
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175.
  • Ünlü, M. & Ertekin, E. (2012). Why do pre-service teachers pose multiplication problems instead of division problems in fractions? Procedia - Social and Behavioral Sciences, 46, 490 – 494.
  • Ünlü, M. ve Sarpkaya Aktaş, G. (2017). Ortaokul matematik öğretmeni adaylarının cebirsel ifade ve denklemlere yönelik kurdukları problemlerin incelenmesi. Turkish Journal of Computer and Mathematics Education Vol.8 No.1 (2017), 161-187
  • Vacc, N. N. (1993). Implementing the' Professional standards for teaching mathematics': questioning in the mathematics classroom. Arithmetic Teacher ,41(2), 88-92.
  • Van De Walle, J., A., Karp, K., S. ve Bay-Williams, J., M. (2013). İlkokul ve ortaokul matematiği, gelişimsel bir yaklaşımla (Durmuş, S. çev. Edt.). Nobel Akademik Yayıncılık, ANKARA.
  • Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82, 201-221.
  • Yanık, H.,B. (2015). Rasyonel sayılar. Zembat, İ., Ö., Özmantar, M., F., Bingölbali, E., Şandır, H. ve Delice, A. (Edt.).Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar (sf. 95-110). Ankara: Pegem Akademi
  • Yıldırım, A. ve Şimşek, H. (2005) Sosyal Bilimlerde Nitel Aratırma Yöntemleri. (2. baskı). Ankara: Seçkin yayıncılık
  • Yıldız, A., & Baltacı, S. (2015). İlköğretim matematik öğretmen adaylarının problem kurma etkinlikleri ile olasılığa yönelik bilgilerinin incelenmesi [Researching primary preservice mathematics teachers’ knowledge of probability with problem posing activities]. Ahi Evran University Journal of Kırsehir Education Faculty (KEFAD), 16 (1), 201-213.

Examining the Development of Conceptual Knowledge: In the Context of Equations Containing Algebraic Fractional Expressions

Year 2021, Issue: 16, 83 - 103, 15.12.2021
https://doi.org/10.20860/ijoses.967628

Abstract

The purpose of this research is to examine the change in the conceptual knowledge of the participants in equations containing algebraic fractional expressions. In a teaching process carried out in this research, by asking the participants to write word problems on equations containing algebraic fractional expressions, the changes in the cognitive structures of conceptual understanding were monitored. The model of the research is "teaching experiment", "clinical interviews" and "document review" to support this. The obtained data were analyzed by content analysis method. The research was carried out with 4 ninth grade students studying in two different high schools in a city in Turkey in the 2015-2016 academic year. According to the data obtained, Similar to other studies, the participants first formed the meaning of the fraction and then they were able to write a word problem.In the verbal problems written in this research, the most used meanings were fraction, ratio and measurement, while operator and part whole meanings were the least used meanings.According to the literature, the most used meaning related to numerical fractions is the part and whole meaning, contrary to this research. It was determined that the participants made mistakes while writing a verbal problem and the mistakes made according to the different meanings of the fraction also differed. No study has been found in the literature regarding this result. Considering the implementation period and method of this research, the conceptual change processes of the participants at different levels regarding different concepts can be examined.

Project Number

1603E099 no.lu proje kapsamında desteklenmiştir.

References

  • Acar, N. (2010). Kesir Çubuklarının İlköğretim 6. Sınıf öğrencilerinin Kesirlerde Toplama ve Çıkarma İşlemlerindeki Başarılarına Etkisi. Yayınlanmış Yüksek Lisans Tezi. Selçuk Üniversitesi, Fen Bilimleri Enstitüsü, KONYA.
  • Alacaci, C. (2012). Öğrencilerin kesirler konusundaki kavram yanılgıları. Bingölbali, E ve Özmantar, M., F. (Edt). İlköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm Önerileri. Ankara: Pegem Akademi
  • Alibali, Martha W., Mitchell J. Nathan, Matthew S. Wolfgram , R. Breckinridge Church, Steven A. Jacobs, Chelsea Johnson Martinez & Eric J. Knuth (2014) How Teachers Link Ideas in Mathematics Instruction Using Speech and Gesture: A Corpus Analysis, Cognition and Instruction, 32:1, 65-100, DOI: 10.1080/07370008.2013.858161
  • Behr, M.J., Lesh, R., Post, T.R., and Silver, E.A. (1983). Rational number concepts. In R. Lesh, and M. Landau (Eds.), Acquisition of mathematics concepts and processes (92–127). New York: Academic Press.
  • Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 296–333). New York: Macmillan.
  • Birgin, O. ve Gürbüz, R.(2009). İlköğretim II. Kademe Öğrencilerinin Rasyonel Sayılar konusundaki İşlemsel ve Kavramsal Bilgi Düzeylerinin İncelenmesi. Eğitim Fakültesi Dergisi, XXII (2), 2009, 529-550
  • Booth, L. R. (1986). Difficulties in algebra. Australian Mathematics Teacher, 42(3), 2–4.
  • Booth, L. R., & Watson, J. (1990). Research for teaching: Learning and teaching algebra. Australian Mathematics Teacher, 46(3), 12–14.
  • Crooks, N. M. & Alibali, M. W. (2014). Defining and measuring conceptual knowledge of mathematics. Developmental Review. doi: 10.1016/j.dr.2014.10.001
  • Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.
  • Işık, C. ve Kar, T. (2012). Matematik dersinde problem kurmaya yönelik öğretmen görüşleri üzerine nitel bir çalışma. Millî Eğitim. Sayı 194/ Bahar/ 2012 (s. 199-215)
  • Kılıç, Ç. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22, 1-10.
  • Kieren, T. E. (1976) On the mathematical, cognitive and instructional foundations of rational numbers. In: Lesh, R. (ed) Number and measurement: papers from a research workshop. Columbus, Ohio: Eric/Smeac, p. 101-144.
  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 318–326. http://dx.doi.org/10.1007/BF00311062
  • Kieren, T. E. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. In J. Hiebertand M. Behr (Eds.), Number concepts and operations in the middle grades (162–181). Reston VA: The National Council of Teachers of Mathematics.
  • Kilpatrick, J., Swafford, J. O., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.
  • Lavy, I., & Bershadsky, I. (2003). Problem posing via ‘‘what if not?’’ strategy in solid geometry a case study. Journal of Mathematical Behavior, 22, 369–387.
  • MEB. (2013). Ortaokul matematik dersi öğretim programı. Retrieved March, 15, 2013 from .
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Fractions: Children's strategies and errors: A report of the strategies and error in secondary mathematics Project NFER-Nelson, Windson (1986)
  • National Council of Teachers of Mathematics [NCTM]. (2011). Principles and standards for school mathematics. Reston, Va: National Council of Teachers of Mathematics.
  • Olkun, S., Uçar, Z. T. (2007) İlköğretimde Etkinlik Temelli Matematik Öğretimi (üçüncü baskı),Ankara: Maya Akademi.
  • Öksüz, C. (2004). Children understanding of algebric fraction as quotients. (Unpublished doctoral dissertation). University of Arizona, Arizona
  • Patton, M.Q. (1997). How to use qualitative methods in evaluation. Newbury park, CA: SAGE Publications
  • Pope, L. (1994), Teaching Algebra. Mathematics Education: A Handbook for Teachers. elsington College of Education: New Zealand, 1, 88-99 .
  • Sasman, M. Linchevski, L., Olivier, A. 1997. Reconceptualising school algebra. Internet: http://academic.sun.ac.za/mathed/MALATI/Rational.pdf
  • Saxe, G.,Gearhart, M., and Nasir, N. S. (2001). Enhancing students' understanding of mathematics: A study of three contrasting approaches to Professional support Journal of Mathematics Teacher Education, 4, 55–79.
  • Schoenfeld, A. ve Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher. 81 (6), 420-427.
  • Sheffield, L. J., & Cruikshank, D. E. (2005). Teaching and learning mathematics pre-kindergarten through middle school. Hoboken, N.J.: Wiley Jossey Bass Education
  • Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing, International Journal of Mathematical Education in Science and Technology, 48(2), 163-184
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics. 14(1), 19–28.
  • Skemp, R., R. (1976). Relational Understanding and Instrumental Understanding. Department of Education, University of Warwick (http://static1.squarespace.com/static/53b6662ae4b00ce9a7c30e76/t/5548a95ae4b03cee0387aef9/1430825306203/Mona+Rosseland+12.11.14+Vedlegg.pdf)
  • Skemp, R. R. (1978). Relational and instrumental understanding. Arithmetic Teacher, 26, 9-15.
  • Stacey, K., and MacGregor, M. (1997b). Ideas about symbolism that students bring to algebra. Mathematics Teacher, 90, 110-113.
  • Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404–411.
  • Star, J. R. (2007). Foregrounding procedural knowledge. Journal for Research in Mathematics Education, 38(2), 132–135.
  • Steffe, L. P., and Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essentialelements. In R. Lesh& A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267- 307). Hillsdale, NJ: Erlbaum.
  • Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp.518–525). Melbourne: Mathematics Education Research Group of Australasia. Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem posing. The Australian Mathematics Teacher, 59(2), 32–40.
  • Şengül, S. & Katrancı, Y. (2012). Problem solving and problem posing skills of prospective mathematics teachers about the ‘sets’ subject. Procedia - Social and Behavioral Sciences, 69, 1650 – 1655.
  • Şengül, S ve Öz, C. (2008). İlköğretim 6. Sınıf Kesirler Ünitesinde Çoklu Zekâ KuramınaUygun Öğretimin Öğrenci Tutumuna Etkisi. İlköğretim Online, 7(3), 800-813, 2008. [Online]: http://ilkogretim-online.org.tr
  • Ticha, M., & Hošpesová, A. (2009, Ocak). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Paper presented at Congress of European Research in Mathematics Education (CERME 6), Lyon, France.
  • Toluk, Z.(2001). Eşit paylaşım ortamlarının kesir öğretiminde kullanımı. Kuram ve Uygulamada Eğitim Bilimleri. 1 (1)
  • Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175.
  • Ünlü, M. & Ertekin, E. (2012). Why do pre-service teachers pose multiplication problems instead of division problems in fractions? Procedia - Social and Behavioral Sciences, 46, 490 – 494.
  • Ünlü, M. ve Sarpkaya Aktaş, G. (2017). Ortaokul matematik öğretmeni adaylarının cebirsel ifade ve denklemlere yönelik kurdukları problemlerin incelenmesi. Turkish Journal of Computer and Mathematics Education Vol.8 No.1 (2017), 161-187
  • Vacc, N. N. (1993). Implementing the' Professional standards for teaching mathematics': questioning in the mathematics classroom. Arithmetic Teacher ,41(2), 88-92.
  • Van De Walle, J., A., Karp, K., S. ve Bay-Williams, J., M. (2013). İlkokul ve ortaokul matematiği, gelişimsel bir yaklaşımla (Durmuş, S. çev. Edt.). Nobel Akademik Yayıncılık, ANKARA.
  • Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82, 201-221.
  • Yanık, H.,B. (2015). Rasyonel sayılar. Zembat, İ., Ö., Özmantar, M., F., Bingölbali, E., Şandır, H. ve Delice, A. (Edt.).Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar (sf. 95-110). Ankara: Pegem Akademi
  • Yıldırım, A. ve Şimşek, H. (2005) Sosyal Bilimlerde Nitel Aratırma Yöntemleri. (2. baskı). Ankara: Seçkin yayıncılık
  • Yıldız, A., & Baltacı, S. (2015). İlköğretim matematik öğretmen adaylarının problem kurma etkinlikleri ile olasılığa yönelik bilgilerinin incelenmesi [Researching primary preservice mathematics teachers’ knowledge of probability with problem posing activities]. Ahi Evran University Journal of Kırsehir Education Faculty (KEFAD), 16 (1), 201-213.
There are 50 citations in total.

Details

Primary Language Turkish
Journal Section Research Articles
Authors

Mehtap Taştepe 0000-0002-4535-3606

H. Bahadır Yanık 0000-0001-7769-2306

Project Number 1603E099 no.lu proje kapsamında desteklenmiştir.
Publication Date December 15, 2021
Submission Date July 8, 2021
Acceptance Date October 18, 2021
Published in Issue Year 2021 Issue: 16

Cite

APA Taştepe, M., & Yanık, H. B. (2021). Kavramsal Bilginin Gelişiminin İncelenmesi: Cebirsel Kesirli İfadeleri İçeren Denklemler Bağlamında. Uluslararası Sosyal Ve Eğitim Bilimleri Dergisi(16), 83-103. https://doi.org/10.20860/ijoses.967628

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INDEX COPERNİCUS [ICI], Eurasian Scientific Journal Index [ESJI], ISAM [Makaleler Veri Tabanı], SOBIAD, Scilit, İdeal Online
tarafından dizinlenmekte.

TÜBİTAK/ULAKBİM(TR) SBVT tarafından izlenmektedir.