تحليل أداء معلمي الرياضيات وفق مجالات التفكير الجبري في ضوء معرفة بيداغوجيا محتوى الجبر
الكلمات المفتاحية:
مجالات التفكير الجبري، معرفة بيداغوجيا محتوى الجبر، معلمة رياضيات المرحلة الأساسية
الملخص
هدفت الدراسة إلى تحليل أداء معلمات رياضيات المرحلة الأساسية ضمن تطبيق برنامج تدريبي وفق معرفة بيداغوجيا محتوى الجبر بهدف تحسين الأداء وفق مجالات التفكير الجبري لدى معلمات الرياضيات، تم إعداد دليل البرنامج التدريبي وأدوات الدراسة، والتأكد من صدقها وثباتها، تم اختيار عينة متيسرة من مدارس قصبة جرش، تكونت من (36) معلمة رياضيات مقسمة إلى مجموعتين: واحدة تجريبية تكونت من (18) معلمة خضعوا للتدريب وفق معرفة بيداغوجيا محتوى الجبر، والأخرى ضابطة مكونة من (18) معلمة لم يخضعوا للتدريب. أظهرت النتائج وجود فروق ذات دلالة إحصائية في اختبار التفكير الجبري بين أفراد المجموعتين الضابطة والتجريبية لصالح المجموعة التجريبية التي تم تدريبها، كما اقترحت مواقف تعليمية ملائمة لطبيعة المحتوى الرياضي الجبري تساعد المعلم في تحسين الأداء التدريسي داخل الفصول الدراسية.
المراجع
1. خصاونة، أمل والبركات، علي. (2007(. المعرفة الرياضية والمعرفة البيداغوجية في الرياضيات لدى الطلبة/ المعلمين. المجلة الأردنية في العلوم التربوية. 3(3)، 287-300
2. عثمان، شذا محمد. (2020). التّفكير الجبري المبكر لدى معلمي المرحلة الأساسية وتلامذتهم. (رسالة دكتوراة غير منشورة)، جامعة اليرموك، اربد، الأردن.
3. عمر، العالم بن عبد القادر. (2015). الأسس التربوية لاستراتيجية النمذجة الجبرية في حل المشكلات في الرياضيات. مجلة كلية التربية الأساسية للعلوم التربوية والإنسانية.24، 15-35
4. المركز الوطني لتطوير المناهج. (2021). الإطار العام والخاص للرياضيات ومعاييرها ومؤشرات أدائها من مرحلة رياض الأطفال حتى الصف الثاني عشر. عمان. الأردن.
5. موسى، عدنان والجبر، شاكر. (2019). واقع المعرفة البيداغوجية عند معلمي الرياضيات للصف التاسع الأساسي المتعلقة بوحدة تحليل المقادير الجبرية. مجلة جامعة القدس المفتوحة للأبحاث والدراسات التربوية والنفسية. 11(29)، 44-55
6. وزارة التربية والتعليم. (2019). ميثاق مهنة التعليم (الجزء الثالث) -المعايير التخصصية لمعلم الرياضيات. إدارة الإشراف والتدريب التربوي. عمان. الأردن.
7. Aliustaoğlu, F. Tuna, A. (2022). Analysis of the Pedagogical Content Knowledge Development of Prospective Teachers in the Lesson Plan Development Process: 4MAT Model, International Journal of Progressive Education.18(1),298-321
8. Aminah, N. Wahyuni, I. (2019). The ability of pedagogic content knowledge (PCK) of mathematics teacher candidate based on multiple intelligent. Journal of Physics: Conference Series. 1280(4), 1-6 https://iopscience.iop.org/article/10.1088/1742-6596/1280/4/042050
9. Ball, D, Thames, M & Phelps, G. (2008). Content Knowledge for Teaching "What Makes It Special". Journal of Teacher Education. 59(5), 389-407
10. Black, J. (2009) "Content Knowledge and Pedagogical Content Knowledge of Algebra Teachers and Changes in Both Types of Knowledge as a Result of Professional Development," Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators. 3(1), 3 https://digitalcommons.georgiasouthern.edu/gamte-proceedings/vol3/iss1/3
11. Bos, B, Lee, K. (2014). Mathematical content, pedagogy, and technology: what it can mean to practicing teachers. https://www.researchgate.net/publication/268207329
12. Carraher, D. Schliemann, A. (2018). Cultivating Early Algebraic Reasoning. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- 12- year-olds. The Global Evolution of an Emerging Field of Research and Practice. ICME-13 Monographs. Chaim, Switzerland: Springer International Publishing, 107-138.
13. Geraniou, E, Mavrikis, M. (2015). Building Bridges to Algebra Through a Constructivist Learning Environment. CONSTUCTIVIST FOUNDATIONS. 10(3). 321-330 https://discovery.ucl.ac.uk/id/eprint/1475782
14. Glassmeyer, D., & Edwards, B. (2016). How middle grades teachers think about algebraic reasoning. Mathematics Teachers Education and Development, 18(2),92-106
15. Guler, M, Celik, D. (2021). The Effect of an Elective Algebra Teaching Course on Perspective Mathematics Teachers Pedagogical Content Knowledge. International Electronic Journal of Mathematics Education.16(2),1-12 https://doi.org/10.29333/iejme/10902
16. Hernon, C. (2009). Teacher Exploration of Instructional Strategies to Promote Algebraic Thinking. University of Nevada, Las Vegas. Thesis & Dissertations. http://dx.doi.org/10.25669/zs7u-hksp
17. Hill, H, Schilling, S, & Ball, D. (2004). Developing Measures of Teachers' Mathematics Knowledge for Teaching. The Elementary School Journal, 105(1), 11–30 https://doi.org/10.1086/428763
18. Hill, H. Ball, D. & Schilling, S. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education, 39, 372-400
19. Hodgen, J. Oldenburg, R. & Strømskag, H. (2018). Algebraic thinking. In book: Developing research in mathematics education: Twenty years of communication, cooperation and collaboration in Europe, Routledge,3 ,32–45
20. Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades, 5-17. New York: Lawrence Erlbaum Associates.
21. Khasawneh, Amal and Barakat, Ali. (2007). Mathematical knowledge and pedagogical knowledge in mathematics among students/teachers. Jordanian Journal of Educational Sciences. 3(3), 287-300
22. Kaye, S, Helen, C, Margaret, K. (2004). The Future of the Teaching and Learning of Algebra, The 12th ICMI Study,8, 329–346, https://doi.org/10.1007/1-4020-8131-6_13
23. Kieran, C. (2004). Algebraic Thinking in the Early Grades: What Is It. The Mathematics Educator. 8(1), 139-151
24. Krauss, S & Brunner, M & Kunter, M & Baumert, J & Blum, W & Neubrand, M & Jordan, A. (2008). Pedagogical Content Knowledge and Content Knowledge of Secondary Mathematics Teachers. Journal of Educational Psychology. 100(3). 716-725
25. Magiera, M, van den Kieboom, L, & Moyer, J. (2017). K-8 Pre-service Teachers Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions. Mathematics, Statistics and Computer Science Faculty Research and Publications.19(2), 25-50
26. Mason, J. Graham, A. & Johnston. S. (2005) Wilder Developing Thinking in Algebra. The Open University in association with Paul Chapman Publishing
27. Mastuti, A. G. (2023). Investigating Pedagogical Content Knowledge and Decision Making on Algebraic Tasks. JRPM (Journal Review Pembelajaran Matematika), 8(1), 1-17
28. Mastuti, A. G., & Prayitno, L. L. (2023). Exploring high school teacher’s design of rich algebra tasks. Journal Elemen, 9(1), 1-14. https://doi.org/10.29408/jel.v9i1.5851
29. McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D. & Senk, S. L. (2012). Knowledge of algebra for teaching: a framework of knowledge and practices. Journal for Research in Mathematics Education, 43 (5), 584–615.
30. Ministry of Education. (2019). Charter of the Teaching Profession (Part III) - Specialized Standards for Mathematics Teacher. Department of Educational Supervision and Training. Oman. Jordan.
31. McAuliffe, S, Lubben, F. (2013). Perspective on pre-service teacher Knowledge for teaching early algebra. Perspectives in Education. 31(3), 155-169.
32. Murtafiah, W, Lukitasari, M. (2019). DEVELOPING PEDAGOGICAL CONTENT KNOWLEDGE OF MATHEMATICS PRE-SERVICE TEACHER THROUGH MICROTEACHING LESSON STUDY. Journal Pendidikan Matematika, 13(2), 201-218
33. Musa, Adnan and al-Jabr, Shaker. (2019). The reality of pedagogical knowledge among mathematics teachers for the ninth grade related to the unit of analysis of algebraic expressions. Journal of Al-Quds Open University for Educational and Psychological Research and Studies. 11(29), 44-55
34. National Center for Curriculum Development. (2021). The general and specific framework of mathematics, its standards and performance indicators from kindergarten to twelfth grade. Oman. Jordan.
35. National Research Council (NCTM). (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC. The National academic press,133-134
36. Omar, the scholar ibn Abd al-Qadir. (2015). Educational foundations of algebraic modeling strategy in problem solving in mathematics. Journal of the Faculty of Basic Education for Educational Sciences and Humanities.24, 15-35
37. Osei, W. & Agyei, D. (2023). Teaching knowledge and difficulties of In-field and Out-of-field Junior High School mathematics teachers in algebra. Cogent Education,10, 1-25 https://doi.org/10.1080/2331186X.2023.2232240
38. Othman, Shaza Mohammed. (2020). Early algebraic thinking among primary school teachers and their students. (Unpublished PhD thesis), Yarmouk University, Irbid, Jordan.
39. Ribeiro, A, Ponte, J. (2019). Professional Learning Opportunities in a Practice- Based Teacher Education Programme about the Concept of Function. Acta Scientiae, Canoas. 21(2), 49- 74
40. Shulman, L. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher.15(2). 4-14. http://www.jstor.org/stable/1175860
41. Sibgatullin, I, Korzhuev, A, Khairullina, E, Sadykova, A, Baturina, R, Chhauzova, V. (2021). A systematic Review on Algebraic Thinking in Education. (EURASIA) Journal of Mathematics Science and Technology Education.18(1),1-15 https://doi.org/10.29333/ejmste/11486
42. Steinweg. A. (2017). Key ideas as guiding principles to support algebraic thinking in German primary schools. Tenth Congress of the European Society for Research in Mathematics Education CERME ,10. 512-519 https://hal.science/hal-01914648
43. Tsafe, A. (2013). Teacher pedagogical knowledge in mathematics: a tool for addressing learning problems. Scientific Journal of Pure and Applied Sciences, 2(1), 1-7
44. Turnuklu, E. Yesildere, S. (2007). THE PEDAGOGICAL CONTENT KNOWLEDGE IN MATHEMATICS: PRE-SERVICE PRIMARY MATHEMATICS TEACHERS’ PERSPECTIVES IN TURKEY. IUMPST: The Journal, Vol. 1, 1-13
45. Windsor, W. (2010). Algebraic Thinking: A Problem-Solving Approach. Mathematics Education Research Group of Australasia, 665-672
2. عثمان، شذا محمد. (2020). التّفكير الجبري المبكر لدى معلمي المرحلة الأساسية وتلامذتهم. (رسالة دكتوراة غير منشورة)، جامعة اليرموك، اربد، الأردن.
3. عمر، العالم بن عبد القادر. (2015). الأسس التربوية لاستراتيجية النمذجة الجبرية في حل المشكلات في الرياضيات. مجلة كلية التربية الأساسية للعلوم التربوية والإنسانية.24، 15-35
4. المركز الوطني لتطوير المناهج. (2021). الإطار العام والخاص للرياضيات ومعاييرها ومؤشرات أدائها من مرحلة رياض الأطفال حتى الصف الثاني عشر. عمان. الأردن.
5. موسى، عدنان والجبر، شاكر. (2019). واقع المعرفة البيداغوجية عند معلمي الرياضيات للصف التاسع الأساسي المتعلقة بوحدة تحليل المقادير الجبرية. مجلة جامعة القدس المفتوحة للأبحاث والدراسات التربوية والنفسية. 11(29)، 44-55
6. وزارة التربية والتعليم. (2019). ميثاق مهنة التعليم (الجزء الثالث) -المعايير التخصصية لمعلم الرياضيات. إدارة الإشراف والتدريب التربوي. عمان. الأردن.
7. Aliustaoğlu, F. Tuna, A. (2022). Analysis of the Pedagogical Content Knowledge Development of Prospective Teachers in the Lesson Plan Development Process: 4MAT Model, International Journal of Progressive Education.18(1),298-321
8. Aminah, N. Wahyuni, I. (2019). The ability of pedagogic content knowledge (PCK) of mathematics teacher candidate based on multiple intelligent. Journal of Physics: Conference Series. 1280(4), 1-6 https://iopscience.iop.org/article/10.1088/1742-6596/1280/4/042050
9. Ball, D, Thames, M & Phelps, G. (2008). Content Knowledge for Teaching "What Makes It Special". Journal of Teacher Education. 59(5), 389-407
10. Black, J. (2009) "Content Knowledge and Pedagogical Content Knowledge of Algebra Teachers and Changes in Both Types of Knowledge as a Result of Professional Development," Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators. 3(1), 3 https://digitalcommons.georgiasouthern.edu/gamte-proceedings/vol3/iss1/3
11. Bos, B, Lee, K. (2014). Mathematical content, pedagogy, and technology: what it can mean to practicing teachers. https://www.researchgate.net/publication/268207329
12. Carraher, D. Schliemann, A. (2018). Cultivating Early Algebraic Reasoning. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- 12- year-olds. The Global Evolution of an Emerging Field of Research and Practice. ICME-13 Monographs. Chaim, Switzerland: Springer International Publishing, 107-138.
13. Geraniou, E, Mavrikis, M. (2015). Building Bridges to Algebra Through a Constructivist Learning Environment. CONSTUCTIVIST FOUNDATIONS. 10(3). 321-330 https://discovery.ucl.ac.uk/id/eprint/1475782
14. Glassmeyer, D., & Edwards, B. (2016). How middle grades teachers think about algebraic reasoning. Mathematics Teachers Education and Development, 18(2),92-106
15. Guler, M, Celik, D. (2021). The Effect of an Elective Algebra Teaching Course on Perspective Mathematics Teachers Pedagogical Content Knowledge. International Electronic Journal of Mathematics Education.16(2),1-12 https://doi.org/10.29333/iejme/10902
16. Hernon, C. (2009). Teacher Exploration of Instructional Strategies to Promote Algebraic Thinking. University of Nevada, Las Vegas. Thesis & Dissertations. http://dx.doi.org/10.25669/zs7u-hksp
17. Hill, H, Schilling, S, & Ball, D. (2004). Developing Measures of Teachers' Mathematics Knowledge for Teaching. The Elementary School Journal, 105(1), 11–30 https://doi.org/10.1086/428763
18. Hill, H. Ball, D. & Schilling, S. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education, 39, 372-400
19. Hodgen, J. Oldenburg, R. & Strømskag, H. (2018). Algebraic thinking. In book: Developing research in mathematics education: Twenty years of communication, cooperation and collaboration in Europe, Routledge,3 ,32–45
20. Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades, 5-17. New York: Lawrence Erlbaum Associates.
21. Khasawneh, Amal and Barakat, Ali. (2007). Mathematical knowledge and pedagogical knowledge in mathematics among students/teachers. Jordanian Journal of Educational Sciences. 3(3), 287-300
22. Kaye, S, Helen, C, Margaret, K. (2004). The Future of the Teaching and Learning of Algebra, The 12th ICMI Study,8, 329–346, https://doi.org/10.1007/1-4020-8131-6_13
23. Kieran, C. (2004). Algebraic Thinking in the Early Grades: What Is It. The Mathematics Educator. 8(1), 139-151
24. Krauss, S & Brunner, M & Kunter, M & Baumert, J & Blum, W & Neubrand, M & Jordan, A. (2008). Pedagogical Content Knowledge and Content Knowledge of Secondary Mathematics Teachers. Journal of Educational Psychology. 100(3). 716-725
25. Magiera, M, van den Kieboom, L, & Moyer, J. (2017). K-8 Pre-service Teachers Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions. Mathematics, Statistics and Computer Science Faculty Research and Publications.19(2), 25-50
26. Mason, J. Graham, A. & Johnston. S. (2005) Wilder Developing Thinking in Algebra. The Open University in association with Paul Chapman Publishing
27. Mastuti, A. G. (2023). Investigating Pedagogical Content Knowledge and Decision Making on Algebraic Tasks. JRPM (Journal Review Pembelajaran Matematika), 8(1), 1-17
28. Mastuti, A. G., & Prayitno, L. L. (2023). Exploring high school teacher’s design of rich algebra tasks. Journal Elemen, 9(1), 1-14. https://doi.org/10.29408/jel.v9i1.5851
29. McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D. & Senk, S. L. (2012). Knowledge of algebra for teaching: a framework of knowledge and practices. Journal for Research in Mathematics Education, 43 (5), 584–615.
30. Ministry of Education. (2019). Charter of the Teaching Profession (Part III) - Specialized Standards for Mathematics Teacher. Department of Educational Supervision and Training. Oman. Jordan.
31. McAuliffe, S, Lubben, F. (2013). Perspective on pre-service teacher Knowledge for teaching early algebra. Perspectives in Education. 31(3), 155-169.
32. Murtafiah, W, Lukitasari, M. (2019). DEVELOPING PEDAGOGICAL CONTENT KNOWLEDGE OF MATHEMATICS PRE-SERVICE TEACHER THROUGH MICROTEACHING LESSON STUDY. Journal Pendidikan Matematika, 13(2), 201-218
33. Musa, Adnan and al-Jabr, Shaker. (2019). The reality of pedagogical knowledge among mathematics teachers for the ninth grade related to the unit of analysis of algebraic expressions. Journal of Al-Quds Open University for Educational and Psychological Research and Studies. 11(29), 44-55
34. National Center for Curriculum Development. (2021). The general and specific framework of mathematics, its standards and performance indicators from kindergarten to twelfth grade. Oman. Jordan.
35. National Research Council (NCTM). (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC. The National academic press,133-134
36. Omar, the scholar ibn Abd al-Qadir. (2015). Educational foundations of algebraic modeling strategy in problem solving in mathematics. Journal of the Faculty of Basic Education for Educational Sciences and Humanities.24, 15-35
37. Osei, W. & Agyei, D. (2023). Teaching knowledge and difficulties of In-field and Out-of-field Junior High School mathematics teachers in algebra. Cogent Education,10, 1-25 https://doi.org/10.1080/2331186X.2023.2232240
38. Othman, Shaza Mohammed. (2020). Early algebraic thinking among primary school teachers and their students. (Unpublished PhD thesis), Yarmouk University, Irbid, Jordan.
39. Ribeiro, A, Ponte, J. (2019). Professional Learning Opportunities in a Practice- Based Teacher Education Programme about the Concept of Function. Acta Scientiae, Canoas. 21(2), 49- 74
40. Shulman, L. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher.15(2). 4-14. http://www.jstor.org/stable/1175860
41. Sibgatullin, I, Korzhuev, A, Khairullina, E, Sadykova, A, Baturina, R, Chhauzova, V. (2021). A systematic Review on Algebraic Thinking in Education. (EURASIA) Journal of Mathematics Science and Technology Education.18(1),1-15 https://doi.org/10.29333/ejmste/11486
42. Steinweg. A. (2017). Key ideas as guiding principles to support algebraic thinking in German primary schools. Tenth Congress of the European Society for Research in Mathematics Education CERME ,10. 512-519 https://hal.science/hal-01914648
43. Tsafe, A. (2013). Teacher pedagogical knowledge in mathematics: a tool for addressing learning problems. Scientific Journal of Pure and Applied Sciences, 2(1), 1-7
44. Turnuklu, E. Yesildere, S. (2007). THE PEDAGOGICAL CONTENT KNOWLEDGE IN MATHEMATICS: PRE-SERVICE PRIMARY MATHEMATICS TEACHERS’ PERSPECTIVES IN TURKEY. IUMPST: The Journal, Vol. 1, 1-13
45. Windsor, W. (2010). Algebraic Thinking: A Problem-Solving Approach. Mathematics Education Research Group of Australasia, 665-672
منشور
2024-12-10
كيفية الاقتباس
أ.د. علي محمد الزعبي, & د. نبيله أحمد عتوم. (2024). تحليل أداء معلمي الرياضيات وفق مجالات التفكير الجبري في ضوء معرفة بيداغوجيا محتوى الجبر . Journal of Educational and Human Sciences, (41), 185-206. https://doi.org/10.33193/JEAHS.41.2024.572
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