The Analysis of the Relation between Eight-Grade Students’ Estimation Performance in Triangles with Their Teaching Style Expectations and Sources of Motivation
Year 2014,
Volume: 1 Issue: 1, 44 - 64, 01.06.2014
Bülent Altunkaya
,
Cahit Aytekin
,
Bekir Kürşat Doruk
,
Bilal Özçakır
Abstract
In
this study, eight-grade students’ estimation achievements in triangles were
analysed according to motivation types and knowledge type expectations. Three
hundred and thirty-seven students from three different elementary schools
attended in this study. In order to determine the students’ estimation
performances, an estimation test in triangles (ETT) was developed. At the end
of the study, it was indicated that the estimation performances of the students
in triangles related with high level intrinsic motivation and conceptual
knowledge expectation. It was also indicated that the estimation performances
of the students who have extrinsic motivation source were lower. Moreover it
was pointed out that the students expecting procedural knowledge from their
teachers had low level of estimation performance in triangles. This study shows
that estimation skills in triangles, one of the subjects of geometry, are related
with some important variables like motivation types and conceptual knowledge.
There are some important questions that should be answered by future studies
like ‘How can students’ estimation skills in geometry be developed? ‘How can it
be integrated into curriculum? What are the possible strategies students apply
and which factors are they related to?’
Supporting Institution
Ahi Evran University
Project Number
PYO-EGF.4001.13.003
References
- Adams, T.L. and Harrel, G. (2010). A Study of Estimation by Professionals at Work. Journal of Mathematics & Culture,November, 5 (2)
- Akman, H. (2011). İçsel ve Dışsal Motivasyon Unsurlarına İlişkin Türk Telekomünikasyon A.Ş.’de Çalışanlar Üzerinde Bir Araştırma [A research on the impacts on the engineers and them technicians working for Türk Telekominikasyon A.Ş. of internal and external factor of motivation]. Süleyman Demirel Üniversitesi Sosyal Bilimler Enstitüsü İşletme Anabilim Dalı Yüksek Lisans Tezi
- Argon, R., & Ertürk, R. (2013). İlköğretim okulu öğretmenlerinin içsel motivasyonları ve örgütsel kimliğe yönelik algıları[Intrinsic Motivations of Primary School Teachers and Their Perceptions of Organizational Identity].Kuram ve Uygulamada Eğitim Yönetimi [Educational Administration: Theory and Practice], 19(2), 159-179.
- Aytekin, C. (2012). İlköğretim ikinci kademe öğrencilerinin kesirlerde tahmin becerilerinin incelenmesi [Investigation of middle school students’ estimation ability with fractions]. Yayımlanmamış Yüksek Lisans Tezi, Bolu: Abant İzzet Baysal Üniversitesi Eğitim Bilimleri Enstitüsü.
- Bal, A.P. (2008). Yeni İlköğretim Matematik Öğretim Programının Öğretmen Görüşleri Açısından Değerlendirilmesi[The Evaluation of new mathematics curriculum in term of teacher perpectives]. Ç.Ü. Sosyal Bilimler Enstitüsü Dergisi, Cilt 17, Sayı 1, s.53-68
- Bana, J.& Dolma,P.(2004). The relationship between the estimation and computation abilities of year 7 students. [20.11.2010] http://www.merga.net.au/documents/RP52004.pdf
- Berger, P. L., & Luckmann, T. (1996). The Social Construction of Reality. New York: Anchor.
- Bestgen, B. J., Reys, R. E., Rybolt, J. F. ve Wyatt, J. W. (1980). Effectiveness of systematic instruction on attitudes and computational estimation skills of preservice elementary teachers. Journal for Research in Mathematics Education, 11, 124-135.
- Biggs, J. (1993). What do inventories of students'ʹ learning processes really measure? A theoretical review and clarification. British Journal of Educational Psychology, 63(3‑19).
- Bright, G.W. (1979). Measuring experienced teachers’ linear estimation skills at two levels of abstraction. School Science and Mathematics, 79, 161-64.
- Bulut, İ. (2006) Yeni İlköğretim Birinci Kademe Programlarının Uygulamadaki EtkililiğininDeğerlendirilmesi [An evaluation of the effectiveness of the new primary school curricula in practice, Unpublished Dissertation], Fırat Üniversitesi, Sosyal Bilimler Enstitüsü, Eğitim Bilimleri Anabilim Dalı, Elazığ
- Bulut, M. (2007). Curriculum reform in Turkey: A case of primary school mathematics curriculum. Eurasia Journal of Mathematics, Science & Technology Education, 3(3), 203-212.
- Byrnes, J. P., & Wasik, B. A. (1991). Role of Conceptual knowledge in Mathematical Procedural Learnig. Developmental Psychology, 27(5), 777‑786.
- Carpenter, T. P. (1986). Conceptual Knowledge as a Foundation for Procedural Knowledge. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics. Hillsdale, NJ: Erlbaum, 113-132.
- Case, R. ve Okamoto, Y. (1996). The role of conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development, 61, 1-2.
- Case, R. ve Sowder, J.T. (1990). The development of computational estimation: a neo-piagetion analysis. Cognition and Instruction,7, 79–104.
- Cobb, P. (1988). The Tension Between Theories of Learning and Instruction in Mathematics Education. Educational Psychologist, 23(2), 87‑103.
- Covington, M. V. and Dray E. (2002). The Developmental Course of Achievement Motivation: A Need Based Approach. Development of achievement motivation. Academic press.
- Covington, M. V. (1999). Caring about learning: The nature and nurturing of subject matter appreciation. Educational Psychologist, 34(2), 127-136
- Covington, M. V. and Omelich, C.L. (1984). Controversies or consistencies? A reply to Brown and Weiner. Journal of Educational Psychology, 76, 159-168.
- Davis, R. B. (1992). Understanding ʺUnderstanding". Journal of Mathematical Behavior, 11, 225‑241.
- Deci, E. L., & Ryan, R. M. (2000). The "What" and "Why" of Goal Pursuits: Human needs and the Self-Determination of Behavior. Psychological Inquiry, 11(4), 227-268.
- Deci, E. L., Vallerand, R. I., Pelletier, L. G., & Ryan, R. M. (1991). Motivation and education: The self-determination perspective. Educational Psychologist, 26(3 & 4), 325-346.
- Deci, E., & Ryan, R. (1985).Intrinsic motivation and self-determination in human behavior. New York: Plenum Press.
- Eccles, 1. S., Wigfield, A., Midgley, C, Reuman, D., Maclver, D., & Feldlaufer, H. (1993). Negative effects of traditional middle schools on students' motivation. The Elementary School journal. 93(5), 553-574.
- Entwistle, N., & Tait, H. (1990). Approaches to learning, evaluations of teaching, and preferences for contrasting academic environments. Higher Education, 19, 169‑194.
- ERG.(2005). Yeni Öğretim Programını İnceleme ve Değerlendirme Raporu, online source, [http://www.erg.sabanciuniv.edu/docs/mufredat_raporu.doc] Date: 22.05.2006.
- Evans, J., & Wedege, T. (2004). Motivation and resistance to learning mathematics in a lifelong perspective. The 10th International Congress on Mathematical Education, [http://www.icme10.dk/], TSG 6, Copenhagen, Denmark.
- Forrester, Michael A.(1990). Exploring estimation in young children.Educational Psychology, 4(10).
- Gearhart, M., Saxe, G. B., Fall, R., Schlackman, J., Nasir, N., Ching, C. C., Bennett, T. R., Rhine, S., & Sloan, T. (1999). Opportunities to learn fractions in elementary mathematics classrooms. Journal for Research in Mathematics Education, 30, 286-315.
- Gottfried, A. E. (1982). Relationships between academic intrinsic motivation and anxiety in children and adolescents. Journal of School Psychology, 20, 205-215.
- Grolnick, W. S., & Ryan, R. M. (1987). Autonomy in children's learning: An experimental and individual difference investigation. Journal of Personality & Social Psychology, 52(5), 890-898
- Haapasalo, L. (1993). Systematic Constructivism in Mathematical Concept Building. In P. Kupari & L. Haapasalo (Eds.), Constructivist and Curricular Issues in the School Mathematics Education. Mathematics Education Research in Finland. Yearbook 1992‑1993. University of Jyväskylä. Institute for Educational Research. Publication Series B, Theory and Practice 82. University of Jyväskylä & The Finnish Association of Mathematics and Science Education Research, 9‑22.
- Hanson, S.A. ve Hogan P.T., (2000). Computational estimation skill of college students. Journal for Research in Mathematics Education, 4(31), 483-499.
- Harter, S., &Connell, I. P. (1984). A comparison of alternative models of the relationships between academic achievement and children's perceptions of competence, control and motivational orientation. In I. Nicholls (Ed.), The development of achievement-related cognitions and behaviors. Greenwich, CT: lAI Press.
- Herzberg, F., Mausner, B., & Snyderman, B. (1959). Motivation to Work. New York: John Wiley.
- Hiebert, J. (1981). Cognitive development and learning linear measurement. Journal for Research in Mathematics Education, 12(3), 197–211.
- Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.
- Järvelä, J., & Haapasalo, L. (2005). Three Types of Orientations by Learning Basic Routines in ICT. Paper presented at the Learning and Instruction on Multiple Context and Settings III. Proceedings of the Fifth Joensuu Symposium on Learning and Instruction. , Joensuu.
- Joram, E., Gabriele, A. J.,Bertheau,M.,Gelman, R.&Subrahmanyam, K. (2005). Children's use of the reference point strategy for measurement estimation. Journal for Research in Mathematics Education, 36(1),4-23.
- Joram, E., Subrahmanyam, K. ve Gelman, R. (1998). Measurement Estimation: Learning to Map the Route from Number to Quantity and Back. Review of Educational Research, Vol. 68, No. 4 (Winter, 1998), pp. 413-449.
- Kadijevich, D., & Haapasalo, L. (2001). Linking procedural and conceptual mathematical knowledge through CAL. Journal of Computer Assisted Learning, 17(2), 156‑165.
- Kızılçaoğlu, A. (2006). Eğitim Fakültelerinde Yeniden Yapılandırma Sürecine İlişkin Eleştiriler ve Öneriler [Critics and suggestions on redevelopment processes of colleges of education]. Balıkesir Üniversitesi, Sosyal Bilimler Enstitüsü Dergisi, 8(14), 132-140.
- Krapp, A. (1999). Interest, motivation and learning: An educational psychological perspective. European journal of Psychology of Education, 14, 23-40
- Lauritzen, Pal (2012). Conceptual and Procedural Knowledge of Mathematical Functions. Publications of the University of Eastern Finland.
- Lemaire,P., Lecacheur,M. ve Farioli, F. (2000). Children's strategy use in computational estimation. Canadian Journal of Experimental Psychology, 2 (54), 141-148.
- Leutzinger, Rathmell ve Urbatsch (1986). Developing estimation skills in the primary grades. In H.L. Schoen ve M.J. Zweng (Eds.) Estimation and mental computation. Yearbook 82-92. N.C.T.M. Reston, VA.
- Levin, J. A. (1981). Estimation techniques for arithmetic: Everyday math and mathematics instruction. Education Studies in Mathematics, 12, 421-434.
- Levine,D.J. (1982). Strategy, Use, and Estimation Ability of College Students, Journal for Research in Mathematics Education 13, 350–359.
- Ma, L. (1999). Knowing and Teaching Elementary Mathematics Teachersʹ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Erlbaum.
- Maciejewski, W., Mgombelo, J. and Savard, A. (2011). Meaningful procedural knowldge in mathematics learning. CMESG/GCEDM Proceedings 2011. Working Group Report
- Markovits, Z. and Herskovits, R. (1993). Visual estimation of discrete quantities. ZDM. 93/4, 137-140.
- Markovitz, Z. (1987). Estimation Reseacrh and Curriculum development. Thesis submitted to the scientific council of the wiezmann Institute of Science Rehovat, Israel.
- Marton, F., & Säljö, R. (1976). On qualitative differences in learning: I. Outcome and process. British Journal of Educational Psychology, 46(1), 4-11.
- McLaughin, J. (1981). Development of children’s ability to judge relative numerosity. Journal of Experimental Child Psychology, 31, 103-114.
- MoNE (1998). İlköğretim Okulu Matematik Dersi Öğretim Programı 6-7-8. Sınıflar [6-8 Grades elementary mathematics curriculum]. İstanbul. Milli Eğitim Basımevi.
- MoNE (2009). 6-8.Sınıflar İlköğretim Matematik Öğretim Programı [6-8 Grades elementary mathematics curriculum].Ankara
- MoNE (2013). Ortaokul matematik dersi öğretim program [Middle school mathematics curriculum in Turkey]. Ankara
- MoNE, (2012). 12 Yıllık zorunlu eğitime yönelik uygulamalar [Practices for 12 years compulsory education in Turkey]. Genelge [Circular Letter]. Milli Eğitim Bakanlığı Özel Kalem Müdürlüğü.
- National Education Statistics (2013). Milli Eğitim Örgün Eğitim İstatistikleri [Statistics for Turkey Ministry of National Education] . Resmi İstatistik Programı Yayınları.
- National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
- National Council of Teachers of Mathematics (NCTM) (1996). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
- National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics.Reston, VA: NCTM.
- O’Daffer, P. (1979). A case and techniques for estimation: Estimation experiences in elementary school mathematics – Essential, not extra! Arithmetic Teacher, 26, 46-51.
- Olkun, S. ve Toluk Uçar, Z. (2006) .İlköğretimde Matematik Öğretimine Çağdaş Yaklaşımlar [Contemporary Approaches in Elementary Mathematics Education], Ankara:Ekinoks Yayıncılık.
- Pajera, J.L. (2001). Estimation de candidades discretas por alumnos de Magisteria (Memoria de Tercer Ciclo). Estimation of discrete quantities by preservice teachers (Third Cycle Report). Mathematics Didactics Department, University of Granada.
- Piaget, J.L. and Szeminska, A. (1964). Genesis del numero en el nino, Guedalupe, Buenos Aires.
- Reys, R,E. ve Bestgen, B,J. (1981). Teaching and assessing computational Estimation skills. The Elementary School Journal, 2(82), 116-127.
- Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2009). Helping children learn mathematics (9th ed.). Danvars: John Wiley & Sons.
- Reys,Barbara J. , Reys Robert E. ve Penafiel, Alfinio Flores. (1991). Estimation performance and strategy use of mexican 5th and 8th grade student sample.Educational Studies in Mathematics, 22(4). 353-375.
- Rubenstein, N.R.(1985). Computational Estimation and Related Mathematical Skills, Journal for Research in Mathematics Education, 16(2),106–119
- Ryan, R. M., & Deci, E. L. (2000). Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions. Contemporary Educational Psychology, 25, 54-67.
- Schoenfeld, A. H. (1982). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: a Project of the National Council of Teachers of Mathematics. New York: Macmillan, 334‑370.
- Schoenfeld, A. H. (1990). A source book for college mathematics teaching. Washington DC: Mathematical Association of America.
- Segovia, I. (1997). Estimación de cantidades discretas. Estudio de variables y procesos. Granada: Comares.
- Segovia, I. ve Castro,E. (2009), Computational and measurement estimation; curriculum foundations and research carried out at the University of Granada. Electronic Journal of Research in Educational Psyhology, 17(7),499-536.
- Siegel, A. W., Goldsmith, L. T., ve Madson, C. R. (1982). Skill in estimation problems of extent and numerosit. Journal for Research in Mathematics Education, 3(13), 211-232.
- Sowder, J., ve Wheeler, M. (1989). The development of concepts and strategies usedin computational estimation. Journal for Research in Mathematics Education, 20, 130-146.
- Sriraman, B. ve Knott, L. (2009). The Mathematics of Estimation: Possibilities for Interdisciplinary Pedagogy and Social Consciousness. Interchange, Vol. 40/2, 205–223.
- Tekinkır, D. (2008). İlköğretim 6-8.Sınıf Öğrencilerinin Matematik Alanındaki Tahmin Stratejilerini Belirleme Ve Tahmin Becerisi İle Matematik Başarısı Arasındaki İlişki [To determine the estimate strategies in maths field for the primary school studens of 6th-8th grades and the relation between the estimate ability and success for maths]. Yayımlanmamıış Yüksek Lisans Tezi, İzmir: Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü.
- Van de Walle, J. A., Karp, K. S., ve Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Allyn & Bacon.
- Volkova, Tanya N. (2005). Characterizing Middle School Students Thinking İn Estimation. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 289-296. Melbourne: PME.
- Wæge, Kjersti (2009). Relations between students' motivation for learning mathematics and a mathematical teaching approach. Nordic Research in Mathematics Education.
- Wedege, T., & Evans, J. (2006). Adults' resistance to learning in school versus adults' competences in work: The case of mathematics. Adults learning mathematics, 1(2), 28-43.
- Workman, J.E. ve Ahn, I. (2011). Linear Measurement and Linear Measurement Estimation Skills in Apparel Design. Clothing & Textiles Research Journal 29(2) 150-164.
- Yates, S. M. (2000). Student optimism, pessimism, motivation and achievement in mathematics: A longitudinal study. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 297-304). Japan: Hiroshima University.
Year 2014,
Volume: 1 Issue: 1, 44 - 64, 01.06.2014
Bülent Altunkaya
,
Cahit Aytekin
,
Bekir Kürşat Doruk
,
Bilal Özçakır
Project Number
PYO-EGF.4001.13.003
References
- Adams, T.L. and Harrel, G. (2010). A Study of Estimation by Professionals at Work. Journal of Mathematics & Culture,November, 5 (2)
- Akman, H. (2011). İçsel ve Dışsal Motivasyon Unsurlarına İlişkin Türk Telekomünikasyon A.Ş.’de Çalışanlar Üzerinde Bir Araştırma [A research on the impacts on the engineers and them technicians working for Türk Telekominikasyon A.Ş. of internal and external factor of motivation]. Süleyman Demirel Üniversitesi Sosyal Bilimler Enstitüsü İşletme Anabilim Dalı Yüksek Lisans Tezi
- Argon, R., & Ertürk, R. (2013). İlköğretim okulu öğretmenlerinin içsel motivasyonları ve örgütsel kimliğe yönelik algıları[Intrinsic Motivations of Primary School Teachers and Their Perceptions of Organizational Identity].Kuram ve Uygulamada Eğitim Yönetimi [Educational Administration: Theory and Practice], 19(2), 159-179.
- Aytekin, C. (2012). İlköğretim ikinci kademe öğrencilerinin kesirlerde tahmin becerilerinin incelenmesi [Investigation of middle school students’ estimation ability with fractions]. Yayımlanmamış Yüksek Lisans Tezi, Bolu: Abant İzzet Baysal Üniversitesi Eğitim Bilimleri Enstitüsü.
- Bal, A.P. (2008). Yeni İlköğretim Matematik Öğretim Programının Öğretmen Görüşleri Açısından Değerlendirilmesi[The Evaluation of new mathematics curriculum in term of teacher perpectives]. Ç.Ü. Sosyal Bilimler Enstitüsü Dergisi, Cilt 17, Sayı 1, s.53-68
- Bana, J.& Dolma,P.(2004). The relationship between the estimation and computation abilities of year 7 students. [20.11.2010] http://www.merga.net.au/documents/RP52004.pdf
- Berger, P. L., & Luckmann, T. (1996). The Social Construction of Reality. New York: Anchor.
- Bestgen, B. J., Reys, R. E., Rybolt, J. F. ve Wyatt, J. W. (1980). Effectiveness of systematic instruction on attitudes and computational estimation skills of preservice elementary teachers. Journal for Research in Mathematics Education, 11, 124-135.
- Biggs, J. (1993). What do inventories of students'ʹ learning processes really measure? A theoretical review and clarification. British Journal of Educational Psychology, 63(3‑19).
- Bright, G.W. (1979). Measuring experienced teachers’ linear estimation skills at two levels of abstraction. School Science and Mathematics, 79, 161-64.
- Bulut, İ. (2006) Yeni İlköğretim Birinci Kademe Programlarının Uygulamadaki EtkililiğininDeğerlendirilmesi [An evaluation of the effectiveness of the new primary school curricula in practice, Unpublished Dissertation], Fırat Üniversitesi, Sosyal Bilimler Enstitüsü, Eğitim Bilimleri Anabilim Dalı, Elazığ
- Bulut, M. (2007). Curriculum reform in Turkey: A case of primary school mathematics curriculum. Eurasia Journal of Mathematics, Science & Technology Education, 3(3), 203-212.
- Byrnes, J. P., & Wasik, B. A. (1991). Role of Conceptual knowledge in Mathematical Procedural Learnig. Developmental Psychology, 27(5), 777‑786.
- Carpenter, T. P. (1986). Conceptual Knowledge as a Foundation for Procedural Knowledge. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics. Hillsdale, NJ: Erlbaum, 113-132.
- Case, R. ve Okamoto, Y. (1996). The role of conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development, 61, 1-2.
- Case, R. ve Sowder, J.T. (1990). The development of computational estimation: a neo-piagetion analysis. Cognition and Instruction,7, 79–104.
- Cobb, P. (1988). The Tension Between Theories of Learning and Instruction in Mathematics Education. Educational Psychologist, 23(2), 87‑103.
- Covington, M. V. and Dray E. (2002). The Developmental Course of Achievement Motivation: A Need Based Approach. Development of achievement motivation. Academic press.
- Covington, M. V. (1999). Caring about learning: The nature and nurturing of subject matter appreciation. Educational Psychologist, 34(2), 127-136
- Covington, M. V. and Omelich, C.L. (1984). Controversies or consistencies? A reply to Brown and Weiner. Journal of Educational Psychology, 76, 159-168.
- Davis, R. B. (1992). Understanding ʺUnderstanding". Journal of Mathematical Behavior, 11, 225‑241.
- Deci, E. L., & Ryan, R. M. (2000). The "What" and "Why" of Goal Pursuits: Human needs and the Self-Determination of Behavior. Psychological Inquiry, 11(4), 227-268.
- Deci, E. L., Vallerand, R. I., Pelletier, L. G., & Ryan, R. M. (1991). Motivation and education: The self-determination perspective. Educational Psychologist, 26(3 & 4), 325-346.
- Deci, E., & Ryan, R. (1985).Intrinsic motivation and self-determination in human behavior. New York: Plenum Press.
- Eccles, 1. S., Wigfield, A., Midgley, C, Reuman, D., Maclver, D., & Feldlaufer, H. (1993). Negative effects of traditional middle schools on students' motivation. The Elementary School journal. 93(5), 553-574.
- Entwistle, N., & Tait, H. (1990). Approaches to learning, evaluations of teaching, and preferences for contrasting academic environments. Higher Education, 19, 169‑194.
- ERG.(2005). Yeni Öğretim Programını İnceleme ve Değerlendirme Raporu, online source, [http://www.erg.sabanciuniv.edu/docs/mufredat_raporu.doc] Date: 22.05.2006.
- Evans, J., & Wedege, T. (2004). Motivation and resistance to learning mathematics in a lifelong perspective. The 10th International Congress on Mathematical Education, [http://www.icme10.dk/], TSG 6, Copenhagen, Denmark.
- Forrester, Michael A.(1990). Exploring estimation in young children.Educational Psychology, 4(10).
- Gearhart, M., Saxe, G. B., Fall, R., Schlackman, J., Nasir, N., Ching, C. C., Bennett, T. R., Rhine, S., & Sloan, T. (1999). Opportunities to learn fractions in elementary mathematics classrooms. Journal for Research in Mathematics Education, 30, 286-315.
- Gottfried, A. E. (1982). Relationships between academic intrinsic motivation and anxiety in children and adolescents. Journal of School Psychology, 20, 205-215.
- Grolnick, W. S., & Ryan, R. M. (1987). Autonomy in children's learning: An experimental and individual difference investigation. Journal of Personality & Social Psychology, 52(5), 890-898
- Haapasalo, L. (1993). Systematic Constructivism in Mathematical Concept Building. In P. Kupari & L. Haapasalo (Eds.), Constructivist and Curricular Issues in the School Mathematics Education. Mathematics Education Research in Finland. Yearbook 1992‑1993. University of Jyväskylä. Institute for Educational Research. Publication Series B, Theory and Practice 82. University of Jyväskylä & The Finnish Association of Mathematics and Science Education Research, 9‑22.
- Hanson, S.A. ve Hogan P.T., (2000). Computational estimation skill of college students. Journal for Research in Mathematics Education, 4(31), 483-499.
- Harter, S., &Connell, I. P. (1984). A comparison of alternative models of the relationships between academic achievement and children's perceptions of competence, control and motivational orientation. In I. Nicholls (Ed.), The development of achievement-related cognitions and behaviors. Greenwich, CT: lAI Press.
- Herzberg, F., Mausner, B., & Snyderman, B. (1959). Motivation to Work. New York: John Wiley.
- Hiebert, J. (1981). Cognitive development and learning linear measurement. Journal for Research in Mathematics Education, 12(3), 197–211.
- Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.
- Järvelä, J., & Haapasalo, L. (2005). Three Types of Orientations by Learning Basic Routines in ICT. Paper presented at the Learning and Instruction on Multiple Context and Settings III. Proceedings of the Fifth Joensuu Symposium on Learning and Instruction. , Joensuu.
- Joram, E., Gabriele, A. J.,Bertheau,M.,Gelman, R.&Subrahmanyam, K. (2005). Children's use of the reference point strategy for measurement estimation. Journal for Research in Mathematics Education, 36(1),4-23.
- Joram, E., Subrahmanyam, K. ve Gelman, R. (1998). Measurement Estimation: Learning to Map the Route from Number to Quantity and Back. Review of Educational Research, Vol. 68, No. 4 (Winter, 1998), pp. 413-449.
- Kadijevich, D., & Haapasalo, L. (2001). Linking procedural and conceptual mathematical knowledge through CAL. Journal of Computer Assisted Learning, 17(2), 156‑165.
- Kızılçaoğlu, A. (2006). Eğitim Fakültelerinde Yeniden Yapılandırma Sürecine İlişkin Eleştiriler ve Öneriler [Critics and suggestions on redevelopment processes of colleges of education]. Balıkesir Üniversitesi, Sosyal Bilimler Enstitüsü Dergisi, 8(14), 132-140.
- Krapp, A. (1999). Interest, motivation and learning: An educational psychological perspective. European journal of Psychology of Education, 14, 23-40
- Lauritzen, Pal (2012). Conceptual and Procedural Knowledge of Mathematical Functions. Publications of the University of Eastern Finland.
- Lemaire,P., Lecacheur,M. ve Farioli, F. (2000). Children's strategy use in computational estimation. Canadian Journal of Experimental Psychology, 2 (54), 141-148.
- Leutzinger, Rathmell ve Urbatsch (1986). Developing estimation skills in the primary grades. In H.L. Schoen ve M.J. Zweng (Eds.) Estimation and mental computation. Yearbook 82-92. N.C.T.M. Reston, VA.
- Levin, J. A. (1981). Estimation techniques for arithmetic: Everyday math and mathematics instruction. Education Studies in Mathematics, 12, 421-434.
- Levine,D.J. (1982). Strategy, Use, and Estimation Ability of College Students, Journal for Research in Mathematics Education 13, 350–359.
- Ma, L. (1999). Knowing and Teaching Elementary Mathematics Teachersʹ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Erlbaum.
- Maciejewski, W., Mgombelo, J. and Savard, A. (2011). Meaningful procedural knowldge in mathematics learning. CMESG/GCEDM Proceedings 2011. Working Group Report
- Markovits, Z. and Herskovits, R. (1993). Visual estimation of discrete quantities. ZDM. 93/4, 137-140.
- Markovitz, Z. (1987). Estimation Reseacrh and Curriculum development. Thesis submitted to the scientific council of the wiezmann Institute of Science Rehovat, Israel.
- Marton, F., & Säljö, R. (1976). On qualitative differences in learning: I. Outcome and process. British Journal of Educational Psychology, 46(1), 4-11.
- McLaughin, J. (1981). Development of children’s ability to judge relative numerosity. Journal of Experimental Child Psychology, 31, 103-114.
- MoNE (1998). İlköğretim Okulu Matematik Dersi Öğretim Programı 6-7-8. Sınıflar [6-8 Grades elementary mathematics curriculum]. İstanbul. Milli Eğitim Basımevi.
- MoNE (2009). 6-8.Sınıflar İlköğretim Matematik Öğretim Programı [6-8 Grades elementary mathematics curriculum].Ankara
- MoNE (2013). Ortaokul matematik dersi öğretim program [Middle school mathematics curriculum in Turkey]. Ankara
- MoNE, (2012). 12 Yıllık zorunlu eğitime yönelik uygulamalar [Practices for 12 years compulsory education in Turkey]. Genelge [Circular Letter]. Milli Eğitim Bakanlığı Özel Kalem Müdürlüğü.
- National Education Statistics (2013). Milli Eğitim Örgün Eğitim İstatistikleri [Statistics for Turkey Ministry of National Education] . Resmi İstatistik Programı Yayınları.
- National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
- National Council of Teachers of Mathematics (NCTM) (1996). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
- National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics.Reston, VA: NCTM.
- O’Daffer, P. (1979). A case and techniques for estimation: Estimation experiences in elementary school mathematics – Essential, not extra! Arithmetic Teacher, 26, 46-51.
- Olkun, S. ve Toluk Uçar, Z. (2006) .İlköğretimde Matematik Öğretimine Çağdaş Yaklaşımlar [Contemporary Approaches in Elementary Mathematics Education], Ankara:Ekinoks Yayıncılık.
- Pajera, J.L. (2001). Estimation de candidades discretas por alumnos de Magisteria (Memoria de Tercer Ciclo). Estimation of discrete quantities by preservice teachers (Third Cycle Report). Mathematics Didactics Department, University of Granada.
- Piaget, J.L. and Szeminska, A. (1964). Genesis del numero en el nino, Guedalupe, Buenos Aires.
- Reys, R,E. ve Bestgen, B,J. (1981). Teaching and assessing computational Estimation skills. The Elementary School Journal, 2(82), 116-127.
- Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2009). Helping children learn mathematics (9th ed.). Danvars: John Wiley & Sons.
- Reys,Barbara J. , Reys Robert E. ve Penafiel, Alfinio Flores. (1991). Estimation performance and strategy use of mexican 5th and 8th grade student sample.Educational Studies in Mathematics, 22(4). 353-375.
- Rubenstein, N.R.(1985). Computational Estimation and Related Mathematical Skills, Journal for Research in Mathematics Education, 16(2),106–119
- Ryan, R. M., & Deci, E. L. (2000). Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions. Contemporary Educational Psychology, 25, 54-67.
- Schoenfeld, A. H. (1982). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: a Project of the National Council of Teachers of Mathematics. New York: Macmillan, 334‑370.
- Schoenfeld, A. H. (1990). A source book for college mathematics teaching. Washington DC: Mathematical Association of America.
- Segovia, I. (1997). Estimación de cantidades discretas. Estudio de variables y procesos. Granada: Comares.
- Segovia, I. ve Castro,E. (2009), Computational and measurement estimation; curriculum foundations and research carried out at the University of Granada. Electronic Journal of Research in Educational Psyhology, 17(7),499-536.
- Siegel, A. W., Goldsmith, L. T., ve Madson, C. R. (1982). Skill in estimation problems of extent and numerosit. Journal for Research in Mathematics Education, 3(13), 211-232.
- Sowder, J., ve Wheeler, M. (1989). The development of concepts and strategies usedin computational estimation. Journal for Research in Mathematics Education, 20, 130-146.
- Sriraman, B. ve Knott, L. (2009). The Mathematics of Estimation: Possibilities for Interdisciplinary Pedagogy and Social Consciousness. Interchange, Vol. 40/2, 205–223.
- Tekinkır, D. (2008). İlköğretim 6-8.Sınıf Öğrencilerinin Matematik Alanındaki Tahmin Stratejilerini Belirleme Ve Tahmin Becerisi İle Matematik Başarısı Arasındaki İlişki [To determine the estimate strategies in maths field for the primary school studens of 6th-8th grades and the relation between the estimate ability and success for maths]. Yayımlanmamıış Yüksek Lisans Tezi, İzmir: Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü.
- Van de Walle, J. A., Karp, K. S., ve Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Allyn & Bacon.
- Volkova, Tanya N. (2005). Characterizing Middle School Students Thinking İn Estimation. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 289-296. Melbourne: PME.
- Wæge, Kjersti (2009). Relations between students' motivation for learning mathematics and a mathematical teaching approach. Nordic Research in Mathematics Education.
- Wedege, T., & Evans, J. (2006). Adults' resistance to learning in school versus adults' competences in work: The case of mathematics. Adults learning mathematics, 1(2), 28-43.
- Workman, J.E. ve Ahn, I. (2011). Linear Measurement and Linear Measurement Estimation Skills in Apparel Design. Clothing & Textiles Research Journal 29(2) 150-164.
- Yates, S. M. (2000). Student optimism, pessimism, motivation and achievement in mathematics: A longitudinal study. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 297-304). Japan: Hiroshima University.