IMPLEMENTATION OF NEW PEDAGOGIES IN ONTARIO CANADA MATHEMATICS TEACHING, 1950 TO 2024

Jeff Irvine

Abstract


This paper examines the implementation of a new curriculum and new pedagogies in mathematics education in Ontario between 1950 and 2024. This was a particularly important period for mathematics education, as reform mathematics based on a constructivist paradigm replaced the traditional transmission pedagogy of the behaviorist era. This radical departure from tradition clashed with the personal perceptual fields of many mathematics teachers, which impeded the successful implementation of newer, research-affirmed strategies. The paper examines historical pedagogical changes from 1950 to date and makes recommendations to improve the implementation of new pedagogies in mathematics education going forward.

 

Article visualizations:

Hit counter


Keywords


curriculum, pedagogy, Ontario, reform mathematics

Full Text:

PDF

References


Alper, L., Fendel, D., Fraser, S., & Resek. D. (1996). Problem-based mathematics—not just for the college bound. Educational Leadership, 53(8), 18–21. https://ascd.org/el/exemplary-curriculums

Arthur, L., Beecher, B., Death, E., Dockett, S., & Farmer, S. (2018). Programming and planning in early childhood settings (7th ed.). Cengage.

Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 30(3), 14–17, 20–22, 43–46. http://hdl.handle.net/2027.42/65072

Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554

Barnett, S. M., & Ceci, S. J. (2002). When and where do we apply what we learn? A taxonomy for far transfer. Psychological Bulletin, 128(4), 612–637. https://doi.org/10.1037/0033-2909.128.4.612

Baron, L. (2015). “True to myself”: Transforming secondary mathematics teachers’ beliefs and practices. International Journal of Education in Mathematics, Science and Technology, 3(3), 193–218. http://doi.org/10.18404/ijemst.30350

Blum, W., & Ferri, R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.

Bobis, J., Russo, J., Downton, A., Feng, M., Livy, S., McCormick, M., & Sullivan, P. (2021). Instructional moves that increase chances of engaging all students in learning mathematics. Mathematics, 2001(9), Article 582. https://doi.org/10.3390/math9060582

Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., & Palmberg, B. (2014). Developing mathematical competence: From the intended to the enacted curriculum. Journal of Mathematical Behavior, 33, 72–87. https://doi.org/10.1016/j.jmathb.2013.10.001

Bonotto, C. (2010). Engaging students in mathematical modeling and problem posing activities. Journal of Mathematical Modelling and Application, 1(3), 18–32.

Borko, H., Peeressini, D., Romagnano, L., Knuth, E., Willis-Yorker, C., Wooley, C., Hovermill, J., & Masarik, K. (2000). Teacher education does matter: A simulative view of learning to teach secondary mathematics. Educational Psychology, 35(3), 193–206. http://doi.org/10.1207/S15326985EP3503_5

Brown, C., Stein, M., & Forman, E. (1996). Assisting teachers and students to reform the mathematics classroom. Educational Studies in Mathematics, 31, 63–93. https://doi.org/10.1007/BF00143927

Burton, L. (2003, April 20). The “formal,” the “planned,” and the “learned” curriculum in an elementary education methods course for mathematics: Perspectives on course content [Paper presentation]. Second annual meeting of the American Association for the Advancement of Curriculum Studies, Chicago, IL, United States. https://eric.ed.gov/?q=hear&pg=167&id=ED476073

Butterfield, E. C., & Nelson, G. D. (1991). Promoting positive transfer of different types. Cognition and Instruction, 8(1), 69–102. https://doi.org/10.1207/s1532690xci0801_3

Campbell, C., & Cabrera, A. (2014). Making the mark: Are grades and deep learning related? Research in Higher Education, 55, 494–507. http://doi.org/10.1007/s11162-013-9323-6

Clarkson, P. (2013, January 31). A paradox? Students’ mathematical well-being [Poster presentation]. Mathematics Educational Research Unit seminar series, Ottawa, ON, Canada.

Collie, R. (2020). Social and emotional competence: Advancing understanding of what, for whom, and when. Educational Psychology, 40(6), 663–665. https://doi.org/10.1080/01443410.2020.1775936

Combs, A. (1999). Being and becoming: A field approach to psychology. Springer.

Corry, L. (1997). The origins of eternal truth in modern mathematics: Hilbert to Bourbaki and_beyond. Science in Context, 10(2), 253–296. https://doi.org/10.1017/S0269889700002659

Cotič, M., & Zuljan, M. V. (2009). Problem‐based instruction in mathematics and its impact on the cognitive results of the students and on affective‐motivational aspects. Educational Studies, 35(3), 297–310. https://doi.org/10.1080/03055690802648085

Council of Chief State School Officers. (2000). Using data on enacted curriculum in mathematics and science: Sample results from a study of classroom practices and subject content. https://curriculumanalysis.org/Reference/DECStudy2000.pdf

Deng, Z. (2018). Pedagogical content knowledge reconceived: Bringing curriculum thinking into the conversation on teachers’ content knowledge. Teaching and Teacher Education, 72, 155–164. https://doi.org/10.1016/j.tate.2017.11.021

Dewey, J. (1916). Democracy and education: An introduction to the philosophy of education. Macmillan. Retrieved from https://nsee.memberclicks.net/assets/docs/KnowledgeCenter/BuildingExpEduc/BooksReports/10.%20democracy%20and%20education%20by%20dewey.pdf

Doerr, H. M., & English, L. D. (2006). Middle grade teachers’ learning through students’ engagement with modeling tasks. Journal of Mathematics Teacher Education, 9(1), 5–32. https://doi.org/10.1007/s10857-006-9004-x

Drake, C., & Sherin, M. G. (2006). Practicing change: Curriculum adaptation and teacher narrative in the context of mathematics education reform. Curriculum Inquiry, 36(2), 153–187. http://doi.org/10.1111/j.1467-873X.2006.00351.x

Eccles, J., & Wigfield, A. (2024). The development, testing, and refinement of Eccles, Wigfield, and colleagues situated expectancy-value model of achievement, performance, and choice. Educational Psychology Review, 36, Article 51. https://doi.org/10.1007/s10648-024-09888-9

Elliott, J. W., Thevenin, M. K., & Bigelow, B. F. (2017). Promoting CM student success: Establishing an academic performance benchmark given construction-education self-efficacy, motivation and planned behavior. International Journal of Construction Education and Research, 13(4), 284–298. https://doi.org/10.1080/15578771.2016.1249316

Fernandez-Rivas, M., & Espada-Mateos, M. (2019). The knowledge, continuing education and use of teaching styles in Physical Education teachers. Journal of Human Sport and Exercise, 14(1), 99–111. http://doi.org/10.14198/jhse.2019.141.08

Gamoran Sherin, M., & Drake, C. (2009). Curriculum strategy framework: Investigating patterns in teachers’ use of a reform-based mathematics curriculum. Journal of Curriculum Studies, 41(4), 467–500. https://doi.org/10.1080/00220270802696115

Gravemeijer, K., & Rampal, A. (2015). Mathematics curriculum development. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 549–555). Springer. http://doi.org/10.1007/978-3-319-12688-3_57

Grouws, D., Tarr, J., Chavez, O., Sewars, R., Soria, V., & Taylan, R. (2013). Curriculum and implementation effects on high school students’ mathematics learning from curricula representing subject-specific and integrated content organizations. Journal for Research in Mathematics Education, 44(2), 416–463. https://doi.org/10.5951/jresematheduc.44.2.0416

Haimes, D. (1996). Destreaming in Grade 9: Teachers’ strategies and sources of ideas. OAME Gazette, 35(2), 24–27. https://www.oame.on.ca/main/files/gazettefiles/Gz60i3.pdf

Harvard Balanced Assessment Project. (2003). Balanced assessment: Transition & middle school tasks. Teachers’ College Press. Retrieved from https://hgse.balancedassessment.org/

Hattie, J. (2009). Visible learning. Routledge. Retrieved from https://inspirasifoundation.org/wp-content/uploads/2020/05/John-Hattie-Visible-Learning_-A-synthesis-of-over-800-meta-analyses-relating-to-achievement-2008.pdf

Herbel-Eisenmann, B., Lubienski, S.., & Id-Deen, L. (2006). Reconsidering the study of mathematics instructional practices: The importance of curricular context in understanding local and global teacher change. Journal of Mathematics Teacher Education, 9, 313–345. https://doi.org/10.1007/s10857-006-9012-x

Hess, K. K. (2004, August). Applying Webb’s depth-of-knowledge (DOK) levels in reading. NCIEA. https://www.veronaschools.org/cms/lib/NJ01001379/Centricity/Domain/17/DOKreading_KH08.pdf

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(4), 372–400. http://doi.org/10.5951/jresematheduc.39.4.0372

Irvine, J. (2015a). Enacting Glasser’s (1998) choice theory in a Grade 3 classroom: A case study. Journal of Case Studies in Education, 7, Article 4, 1–14. https://eric.ed.gov/?id=EJ1060625

Irvine, J. (2015b). Problem solving as motivation in mathematics: Just in time teaching. Journal of Mathematical Sciences, 2, 106–117.

Irvine, J. (2017). Problem posing in consumer mathematics classes: Not just for future mathematicians. The Mathematics Enthusiast, 14(1), 387–412. https://doi.org/10.54870/1551-3440.1404

Irvine, J. (2018). A focus on student understanding: George Pólya’s problem solving heuristic. OAME Gazette, 56(4), 36–38.

Irvine, J. (2019a). Conjecture, predict, and the power of What If? OAME Gazette, 57(3), 34–36.

Irvine, J. (2019b). Constructivism in secondary math education: A teacher’s experience. The Variable, 4(2), 27–32.

Irvine, J. (2019c). Strategies for enhancing mathematics learning for students who are kinesthetic learners. OAME Gazette, 57(4), 41–44.

Irvine, J. (2020). The new social-emotional strand in elementary mathematics—Part 1. Ontario Mathematics Gazette, 59(2), 34–44.

Irvine, J. (2021a). Blast from the past: The common curriculum and destreamed math. Ontario Mathematics Gazette, 59(4), 9–12.

Irvine, J. (2021b). Blast from the past: The rise and fall of the hand-held calculator in mathematics education. Ontario Mathematics Gazette, 60(2), 7–9.

Irvine, J. (2021c). The new social-emotional strand in elementary mathematics—-Part 2. Ontario Mathematics Gazette, 59(3), 10–15.

Irvine, J. (2022). Blast from the past: (New)2—The new new math. Ontario Mathematics Gazette, 61(1), 10–14.

Irvine, J. (2023). Blast from the past: The mathematical processes. Ontario Mathematics Gazette, 61(3), 6–9.

Irvine, J., & Telford, W. (2015). Mathematics coaching and the coaching cycle: The Math GAINS project. Journal of Case Studies in Education, 7, Article 1, 1–16.

Irvine, J., Telford, W., Anusic, V., & Alves, P. (2016). A straightforward model eliciting activity (MEA) and the power of What If? questions in supporting students’ higher-order thinking. Journal of Mathematical Sciences, 3(1), 7–22.

Irvine, J., Telford, W., Alves, P., & Cloutier, A. (2023). Teaching mathematics during COVID-19: Lessons learned and best practices. Journal of Instructional Pedagogies, 30, Article 2, 1–34. Retrieved from https://www.researchgate.net/publication/376409659_Teaching_mathematics_during_COVID-19_Lessons_learned_and_best_practices

Johnson, D., & Johnson, R. (1994). Cooperative learning in the classroom. ASCD. Retrieved from https://eric.ed.gov/?id=ED379263

Kilpatrick, J., Swafford, J., & Findell, B. (Eds). (2011). Adding it up (2nd ed.). National Research Council.

Kind, V. (2009). Pedagogical content knowledge in science education: Potential and perspectives for progress. Studies in Science Education, 45(2), 169–204. https://doi.org/10.1080/03057260903142285

Kristensen-Irvine, K. (1996). A teacher’s working document for implementing the common curriculum. Peel District School Board.

Kurz, A., Elliott, S., Webby, J., & Smithson, J. (2010). Alignment of the intended, planned, enacted curriculum in general and special education and its relation to student achievement. The Journal of Special Education, 44(3), 131–145. https://doi.org/10.1177/0022466909341196

Lee, J. (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. Journal of Mathematics Teacher Education, 15, 429–452. https://doi.org/10.1007/s10857-012-9220-5

Lesh, R., & Caylor, B. (2007). Introduction to the special issue: Modeling as application versus modeling as a way to create mathematics. International Journal for Mathematics Learning, 12, 173–194. http://doi.org/10.1007/s10758-007-9121-3

Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2–3), 157–189. https://doi.org/10.1080/10986065.2003.9679998

Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2–3), 109–129. http://doi.org/10.1207/S15327833MTL0502&3_01

Linares, S., Krainer, K., & Brown, L. (2018). Mathematics teachers and curricula. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed.). Springer. https://doi.org/10.1007/978-3-319-77487-9_111-5

Lortie, D. (2002). Schoolteacher: A sociological study (2nd ed.). University of Chicago Press. Retrieved from https://press.uchicago.edu/ucp/books/book/chicago/S/bo3645184.html

Loughran, J., Berry, A., & Mulhall, P. (2006). Understanding and developing science teachers’ pedagogical content knowledge. Sense. Retrieved from https://link.springer.com/book/10.1007/978-94-6091-821-6

Mayer, R. E., & Wittrock, M. C. (1996). Problem-solving transfer. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 47–62). Macmillan.

Meader, E. (1995, April 11). Teacher-made reform: Influences shaping curriculum in a high school mathematics department [Paper presentation]. Annual meeting of the American Educational Research Association, San Francisco, CA, United States.

Middleton, J., & Spanias, P. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for Research in Mathematics Education, 30(1), 65–88. https://doi.org/10.2307/749630

Milic, N., Masic, S., Milin-Lazovic, J., Raskovic, G., Beaumaris, Z., Slavic, M., & Stanisavljevic, D. (2016). The importance of medical students’ attitudes regarding cognitive competence for teaching applied statistics: Multi-site study and meta-analysis. PLOS ONE, 11(10). https://doi.org/10.1371/journal.pone.0164439

Mintzberg, H. (1989). Mintzberg on management. Free Press. Retrieved from https://books.google.ro/books/about/Mintzberg_on_Management.html?id=9XOXVxN1GMsC&redir_esc=y

Moyer, J., Robison, V. & Cai, J. (2018). Attitudes of high-school students taught using traditional and reform mathematics curricula in middle school: A retrospective analysis. Educational Studies in Mathematics, 98(1), 115–134. https://doi.org/10.1007/s10649-018-9809-4

Mueller, S. (2019). An historical examination of the secondary mathematics curriculum in Ontario through two lenses: Curriculum policy documents and reflections of leaders in the field [Master’s thesis, Queen’s University]. QSpace. https://qspace.library.queensu.ca/items/24940861-c1eb-48e2-a3da-43c60b4c5002

National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations for school mathematics of the 1980s. https://www.nctm.org/flipbooks/standards/agendaforaction/html5/index.html

Nurlelah, S., Hendriana, H., Fitrianna, A., & Fitriana, A. Y. (2023). The implementation of scientific approach to increase mathematical problem solving ability on junior high school students. Journal of Innovative Mathematics Learning, 6(3), 178–185. https://doi.org/10.22460/jiml.v6i3.17580

OECD. (2023). PISA 2022 results (Volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en

OECD. (2024). Education GPS: United States—Overview of the education system (EAG 2023). https://gpseducation.oecd.org/CountryProfile?primaryCountry=USA&treshold=10&topic=EO

Ontario Department of Education. (1950). Intermediate division, Grades VII, VIII, IX, X. King’s Printer for Ontario.

Ontario Department of Education. (1951). Intermediate division, Grades 7, 8, 9, 10: Outlines of courses for experimental use. King’s Printer for Ontario.

Ontario Department of Education. (1961). Mathematics: Senior division, Grades 11,12 and 13. Queen’s Printer for Ontario.

Ontario Department of Education. (1964). Mathematics: Intermediate division, Grades 7, 8, 9 and 10. Queen’s Printer for Ontario.

Ontario Department of Education. (1968). Living and learning: The report of the Provincial Committee on Aims and Objectives of Education in the Schools of Ontario. Newton.

Ontario Ministry of Education. (1972). Mathematics intermediate and senior division. Queen’s Printer for Ontario.

Ontario Ministry of Education. (1980). Mathematics curriculum guideline for the Intermediate division. Queen’s Printer for Ontario.

Ontario Ministry of Education. (1985). Curriculum guideline: Mathematics: Intermediate and senior divisions. Queen’s Printer for Ontario.

Ontario Ministry of Education. (1995a). Provincial standards, mathematics, Grades 1 to 9. Queen’s Printer for Ontario.

Ontario Ministry of Education. (1995b). The common curriculum. Policies and outcomes, Grades 19. Queen’s Printer for Ontario.

Ontario Ministry of Education. (1999). Mathematics: The Ontario curriculum, Grades 9 and 10. Queen’s Printer for Ontario.

Ontario Ministry of Education. (2000). Mathematics: The Ontario Curriculum, Grades 11 and 12. Queen’s Printer for Ontario.

Ontario Ministry of Education. (2005). The Ontario curriculum, Grades 9 and 10: Mathematics (Revised). Queen’s Printer for Ontario.

Ontario Ministry of Education. (2007). The Ontario curriculum, Grades 11 and 12: Mathematics (Revised). Queen’s Printer for Ontario.

Ontario Ministry of Education. (2010). Growing success: Assessment, evaluation and reporting in Ontario's schools: Covering Grades 1 to 12. Queen’s Printer for Ontario.

Ontario Ministry of Education. (2020a). High-impact instructional practices in mathematics. https://tinyurl.com/2w37nw4r

Ontario Ministry of Education. (2020b). The Ontario curriculum, mathematics. https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics

Ontario Ministry of Education. (2021). The Ontario curriculum, mathematics MTH1W Grade 9. https://www.dcp.edu.gov.on.ca/en/curriculum/secondary-mathematics/courses/mth1w

O’Shea, T. (2003). The Canadian mathematics curriculum from new math to the NCTM standards. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 843–896). National Council of Teachers of Mathematics.

Osta, I., Oteiza, F., Sullivan, P., & Volmink, J. (2023). Case studies in agents and processes of mathematics curriculum development and reform. In Y. Shimizu & R. Vithal (Eds.), Mathematics curriculum reforms around the world (pp 401–430). Springer. https://doi.org/10.1007/978-3-031-13548-4_26

Pang, X., & Rogers, W. T. (2014). Comparative examination of the influence of selected factors on achievement in Grade 9 academic and applied mathematics courses in English-language schools in Ontario. EQAO.

Pearce, J., Mann, M., Jones, C., van Buschbach, S., Olff, M., & Bisson, J. (2012). The most effective way of delivering a train-the-trainers program: A systematic review. Journal of Continuing Education in the Health Professions, 32(3), 215–226. https://doi.org/10.1002/chp.21148

Perrell, A., Erdie, J., & Kasay, T. (2017). What motivates students to learn? Applications to all classroom levels. Journal of Asian Economic Policy Review, 3(1), 73–80. https://journals.charlotte.edu/jaepr/article/view/658

Polya, G. (1957). How to solve it: A new aspect of mathematical method. Doubleday. Retrieved from https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pdf

Popkewitz, T. (1988). Institutional issues in the study of school mathematics curriculum research. Educational Studies in Mathematics, 19, 221–249. https://doi.org/10.1007/BF00751234

Puentedura, R. (2006). Transformation, technology, and education. Hippasus. http://hippasus.com/resources/tte/

Radwanski, G. (1987). Ontario study of the relevance of education, and the issue of dropouts. Ontario Ministry of Education.

Rampal, A., Usiskin, Z., Buchter, A., Hodgen, J., & Osta, I. (2017). Topic study group no. 37: Mathematics curriculum development. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education: ICME-13 monographs (pp. 555–559). Springer. https://doi.org/10.1007/978-3-319-62597-3_64

Remillard, J. (1999). Curriculum materials in mathematics education reform: A framework for examining teachers’ curriculum development. Curriculum Inquiry, 29(3), 315–342. https://doi.org/10.1111/0362-6784.00130

Remillard, J. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246. http://doi.org/10.3102/00346543075002211

Remillard, J., & Bryans, M. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics, 35(5), 352–388. http://doi.org/10.2307/30034820

Reys, B., & Reys, R. (2011). Curriculum as a vehicle for reform in U. S. mathematics education. Quadrante, 20(1), 191–121. https://doi.org/10.48489/quadrante.22857

Rogers, E. (2003). Diffusion of innovations (5th ed.). Simon & Schuster.

Ross, S. (2008). Motivation correlates of academic achievement: Exploring how motivation influences academic achievement in the PISA 2003 dataset [Doctoral dissertation, University of Victoria]. DSpace. https://dspace.library.uvic.ca/handle/1828/3209

Ruiz, A., Niss, M., Artigue, M., Cao, Y., & Reston, E. (2023). A first exploration to understand mathematics curricula implementation: Results, limitations, and successes. In Y. Shimizu & R. Vital (Eds.), Mathematics curriculum reforms around the world (pp. 231–260). Springer. https://doi.org/10.1007/978-3-031-13548-4_16

Schön, D. (1983). The reflective practitioner. Basic Books.

Scott, C. (2015). Designing mathematics curriculum using crowdsourcing as a professional development model. Journal of Education Theory and Practice, 15(2), 11–18. http://www.na-businesspress.com/JHETP/ScottC_Web15_2_.pdf

Seagall, A. (2004). Revisiting pedagogical content knowledge: The pedagogy of content/the content of pedagogy. Teaching and Teacher Education, 20, 489–504. https://doi.org/10.1016/j.tate.2004.04.006

Seitz, P. (2017). Curriculum alignment among the intended, enacted and assessed curriculum for Grade 9 mathematics. Journal of the Canadian Association for Curriculum Studies, 15(1), 72–94. https://doi.org/10.25071/1916-4467.40286

Sherin, M. G., & Drake, C. (2009). Curriculum strategy framework: Investigating patterns in teachers' use of a reform-based elementary mathematics curriculum. Journal of Curriculum Studies, 41(4), 467–500. https://doi.org/10.1080/00220270802696115

Shernoff, D., Csikszentmihalyi, M., Schneider, B., & Shernoff, E. (2003). Student engagement in high school classrooms from the perspective of flow theory. School Psychology Quarterly, 18(2), 158–176. https://doi.org/10.1521/scpq.18.2.158.21860

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.2307/1175860

Smith, J., III, & Star, J. (2007). Expanding the notion of impact of K-12 standards-based mathematics and reform calculus programs. Journal for Research in Mathematics Education, 38(1), 3–34. https://doi.org/10.2307/30034926

Spyker, G., & Malone, J. (1993). Curriculum reform: Difficulties experienced by teachers in implementing a new statewide mathematics curriculum (ED373970). ERIC. https://eric.ed.gov/?id=ED373970

Steinmayr, R., & Spinath, B. (2009). The importance of motivation as a predictor of school achievement. Learning and Individual Differences, 19(1), 80–90. https://doi.org/10.1016/j.lindif.2008.05.004

Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32–40.

Stoyanova, E. (2005). Problem-posing strategies used by years 8 & 9 students. Australian Mathematics Teacher, 61(3), 6–11. https://files.eric.ed.gov/fulltext/EJ743563.pdf

Suurtamm, C., & Graves, B. (2007). Curriculum implementation in intermediate mathematics: Research report. University of Ottawa. https://tinyurl.com/3zt9pp7p

Tarr, J., Chavez, O., Reys, R., & Reys, B. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students’ opportunity to learn. School Science and Mathematics, 106(4), 191–201. https://doi.org/10.1111/j.1949-8594.2006.tb18075.x

Taylor, G., Jungert, T., Mageau, G., Schattke, K., Dedic, H., Rosenfield, S., & Koestner, R. (2014). A self-determination theory approach predicting school achievement over time: The unique role of intrinsic motivation. Contemporary Educational Psychology, 39(4), 342–358. https://doi.org/10.1016/j.cedpsych.2014.08.002

Temur, O. (2012). Analysis of prospective classroom teachers’ teaching of mathematical modeling and problem solving. Eurasia Journal of Mathematics, Science & Technology, 8(2), 83–93. https://doi.org/10.12973/eurasia.2012.822a

Tsafe, A. (2014). Mathematics curriculum: The philosophy behind content alteration. International Journal of Physical and Social Sciences, 4(2), 221–228. https://www.ijmra.us/project%20doc/2014/IJPSS_FEBRUARY2014/IJMRA-4888.pdf

Tyminski, A., Ledford, S., & Hembree, D. (2010). What was really accomplished today? Mathematics content specialists observe a class for prospective K–8 teachers. Montana Mathematics Enthusiast, 7(1), 75–91. https://doi.org/10.54870/1551-3440.1176

Vygotsky, L. (1978). Mind in society: The development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman (Eds.). Harvard University Press.

Wein, C., & Dudley-Marling, C. (1998). Limited vision: the Ontario curriculum and outcomes-based learning. Canadian Journal of Education, 23(4), 405–420. Retrieved from https://www.jstor.org/stable/1585755

Weiner, J. (1994). Assessment. OAME Gazette, 33(2), 25–32.

Wilson, M., & Goldenberg, M. (1998). Some conceptions are difficult to change: One middle school mathematics teacher’s struggle. Journal of Mathematics Teacher Education, 1(3), 269–293. Retrieved from https://eric.ed.gov/?id=EJ584593

Yarber, L., Brownson, C., Jacob, R., Baker, E., Jones, E., Baumann, C., Despande, A., Gillespie, K., Scharff, D., & Brownson, R. (2015). Evaluating a train-the-trainer approach for improving capacity for evidence-based decision making in public health. BMC Health Services Research, 15, Article 547. https://doi.org/10.1186/s12913-015-1224-2

Zeng, Y., Yang, W., & Bautista, A. (2023). Teaching programming and computational thinking in early childhood education: A case study of content knowledge and pedagogical knowledge. Frontiers in Psychology, 14, Article 1252718. https://doi.org/10.3389/fpsyg.2023.1252718




DOI: http://dx.doi.org/10.46827/ejes.v12i2.5803

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Jeff Irvine

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2015-2026. European Journal of Education Studies (ISSN 2501 - 1111) is a registered trademark of Open Access Publishing Group. All rights reserved.


This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).