A Framework for Content Sequencing from Junior to Senior Mathematics Curriculum

Musarurwa David Chinofunga; Philemon Chigeza; Subhashni Taylor

doi:10.29333/ejmste/11930

Full Text (PDF)

Musarurwa David Chinofunga ¹ ^* , Philemon Chigeza ¹ , Subhashni Taylor ¹

More Detail

¹ College of Arts, Society and Education, James Cook University, AUSTRALIA^* Corresponding Author

Abstract

This paper argues for effective sequencing of mathematics content to aid transition from junior (Year 7 to Year 10) to senior mathematics (Year 11 to Year 12) curriculum in Queensland, Australia and provides a tool for sequencing the mathematics content. Planning templates and samples are available to schools; however, it is imperative for teachers to understand the processes that underpin planning. This paper provides a step-by-step systematic sequencing of mathematics concepts. The premise is that depending on the level of assumed prior knowledge and skills students recall and apply, teachers can start teaching from any level. The study draws from constructivism to develop a planning tool that can be adapted to all mathematics subjects and levels, help identify conceptual relationships and skills from lower to upper levels and provide students with the opportunity to build their mathematical knowledge.

Keywords

collaborative planning
mathematics content sequencing
functions and graphs
secondary school mathematics
content break down
concepts

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 18, Issue 4, April 2022, Article No: em2100

https://doi.org/10.29333/ejmste/11930

Publication date: 27 Mar 2022

Article Views: 3365

Article Downloads: 1461

Open Access Disclosures References How to cite this article

Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Achmetli, K., Achmetli, K., Schukajlow, S., Schukajlow, S., Rakoczy, K., & Rakoczy, K. (2019). Multiple solutions for real-world problems, experience of competence and students’ procedural and conceptual knowledge. International Journal of Science and Mathematics Education, 17(8), 1605-1625. https://doi.org/10.1007/s10763-018-9936-5
AITSL. (2014). National professional standards for teachers. Australian Institute for Teaching and School Leadership. https://www.aitsl.edu.au/docs/default-source/national-policy-framework/australian-professional-standards-for-teachers.pdf?sfvrsn=5800f33c_74
Australian Academy of Science. (2015). Desktop review of mathematics school education. Department of Education. https://www.dese.gov.au/australian-curriculum/resources/desktop-review-mathematics-school-education-pedagogical-approaches-and-learning-resources-june-2015
Australian Association of Mathematics Teachers [AAMT]. (2006). Standards for excellence in teaching mathematics in Australian schools. https://aamt.edu.au/wp-content/uploads/2020/10/Standard-of-Excellence.pdf
Australian Curriculum, & Assessment and Reporting Authority [ACARA]. (2018a). Foundation to Year 10 curriculum: Mathematics: Structure. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/structure/
Australian Curriculum, & Assessment and Reporting Authority [ACARA]. (2018b). Shaping of the Australian curriculum: Mathematics. https://docs.acara.edu.au/resources/Australian_Curriculum_-_Maths.pdf
Ben-Hur, M. (2006). Concept-rich mathematics instruction building a strong foundation for reasoning and problem solving. Association for Supervision and Curriculum Development.
Bieda, K. N., Lane, J., Evert, K., Hu, S., Opperman, A., & Ellefson, N. (2020). A large-scale study of how districts’ curriculum policies and practices shape teachers’ mathematics lesson planning. Journal of Curriculum Studies, 52(6), 770-799. https://doi.org/10.1080/00220272.2020.1754921
Brosvic, G. M., & Epstein, M. L. (2007). Enhancing learning in the introductory course. The Psychological Record, 57(3), 391-408. https://doi.org/10.1007/BF03395584
Bruner, J. S. (1977). The process of education. Harvard University Press.
Clarke, D. J., Clarke, D. M., & Sullivan, P. (2012). How do mathematics teachers decide what to teach? Australian Primary Mathematics Classroom, 17(3), 9-12.
Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344-377. https://doi.org/10.1016/j.dr.2014.10.001
Darling-Hammond, L., & Richardson, N. (2009). Teacher learning: What matters. Educational Leadership, 66(5), 46-53.
Darling-Hammond, L., Wei, R. C., & Orphanos, S. (2009). Professional learning in the learning profession: A status report on teacher development in the United States and abroad. National Staff Development Council.
Davidson, A. (2019). Ingredients for planning student-centred learning in mathematics. Australian Primary Mathematics Classroom, 24(3), 8-14.
Demski, D., & Racherbäumer, K. (2017). What data do practitioners use and why? Evidence from Germany comparing schools in different contexts. Nordic Journal of Studies in Educational Policy, 1(3), 82-94. https://doi.org/10.1080/20020317.2017.1320934
DoE. (2020). State schools improvement strategy 2021-2025. Department of Education. https://education.qld.gov.au/curriculums/Documents/state-schools-strategy.docx
DoE. (2021a). Curriculum, assessment and reporting framework. Department of Education. https://education.qld.gov.au/curriculums/Documents/p-12-curriculum-assessment-reporting-framework.pdf
DoE. (2021b). Working together: Supporting students, staff and leaders in Queensland’s rural and remote schools. Department of Education. https://schoolreviews.education.qld.gov.au/res/Documents/eib-working-together-spotlight-paper.pdf
Ervin, L., Carter, B., & Robinson, P. (2013). Curriculum mapping: Not as straightforward as it sounds. Journal of Vocational Education & Training, 65(3), 309-318. https://doi.org/10.1080/13636820.2013.819559
Evans, M., Lipson, K., Wallace, D., & Greenwood, D. (2018). Cambridge senior mathematics for Queensland. Cambridge University Press.
Fernandez, C., & Cannon, J. (2005). What Japanese and U.S. teachers think about when constructing mathematics lessons: A preliminary investigation. The Elementary School Journal, 105(5), 481-498. https://doi.org/10.1086/431886
Garbett, D. (2011). Constructivism deconstructed in science teacher education. Australian Journal of Teacher Education, 36(6), 36-49. https://doi.org/10.14221/ajte.2011v36n6.5
Garet, M. S., Porter, A. C., Desimone, L., Birman, B., & Yoon, K. (2001). What makes professional development effective? Analysis of a national sample of teachers. American Educational Research Journal, 38, 915-945. https://doi.org/10.3102/00028312038004915
Gilbert, M., & Gilbert, B. (2013). Connecting teacher learning to curriculum. In A. M. Lindmeier, & A. Heinze (Eds.), Mathematics learning across the life span (pp. 337-344). PME.
González, M. J., Gómez, P., & Pinzón, A. (2020). Characterising lesson planning: A case study with mathematics teachers. Teaching Education (Columbia, S.C.), 31(3), 260-278. https://doi.org/10.1080/10476210.2018.1539071
Grundén, H. (2020). Planning in mathematics teaching–a varied, emotional process influenced by others. LUMAT: International Journal on Math, Science and Technology Education, 8(1), 67-88. https://doi.org/10.31129/LUMAT.8.1.1326
Gurupur, V. P., Pankaj Jain, G., & Rudraraju, R. (2015). Evaluating student learning using concept maps and Markov chains. Expert Systems with Applications, 42(7), 3306-3314. https://doi.org/10.1016/j.eswa.2014.12.016
Hailikari, T. K., & Nevgi, A. (2010). How to diagnose at-risk students in chemistry: The case of prior knowledge assessment. International Journal of Science Education, 32(15), 2079-2095. https://doi.org/10.1080/09500690903369654
Harden, R. M. (1999). What is a spiral curriculum? Medical Teacher, 21(2), 141-143. https://doi.org/10.1080/01421599979752
Harden, R. M. (2001). AMEE guide No. 21: Curriculum mapping: A tool for transparent and authentic teaching and learning. Medical Teacher, 23(2), 123-137. https://doi.org/10.1080/01421590120036547
Harmon, J. M., Hedrick, W. B., & Wood, K. D. (2005). Research on vocabulary instruction in the content areas: Implications for struggling readers. Reading & Writing Quarterly, 21(3), 261-280. https://doi.org/10.1080/10573560590949377
Hornby, A. S., Ashby, M., & Wehmeier, S. (2000). Oxford advanced learner’s dictionary of current English. Oxford University Press.
Ioanna, V. (2002). What is the value of graphical displays in learning? Educational Psychology Review, 14(3), 261-312. https://doi.org/10.1023/A:1016064429161
John, D., Katherine, A. R., Elizabeth, J. M., Mitchell, J. N., & Daniel, T. W. (2013). Improving students’ learning with effective learning techniques: Promising directions from cognitive and educational psychology. Psychological Science in the Public Interest, 14(1), 4-58. https://doi.org/10.1177/1529100612453266
Kafyulilo, A. C. (2013). Professional development through teacher collaboration: An approach to enhance teaching and learning in science and mathematics in Tanzania. Africa Education Review: Teacher Education and Technology, 10(4), 671-688. https://doi.org/10.1080/18146627.2013.853560
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academies Press.
Konuk, N. (2018). Mathematics teacher educators’ roles, talks, and knowledge in collaborative planning practice: Opportunities for professional development [PhD dissertation, Penn State University]. ProQuest Dissertations Publishing.
Koppang, A. (2004). Curriculum mapping: Building collaboration and communication. Intervention in School and Clinic, 39(3), 154-161. https://doi.org/10.1177/10534512040390030401
Levin, P. F., & Suhayda, R. (2018). Transitioning to the DNP: Ensuring integrity of the curriculum through curriculum mapping. Nurse Educator, 43(3), 112-114. https://doi.org/10.1097/NNE.0000000000000431
Li, H., Zhu, J., Zhang, J., Zong, C., & He, X. (2020). Keywords-guided abstractive sentence summarization. In Proceedings of the 34^th AAAI Conference on Artificial Intelligence (pp. 8196-8203). https://doi.org/10.1609/aaai.v34i05.6333
Li, Y., Chen, X., & Kulm, G. (2009). Mathematics teachers’ practices and thinking in lesson plan development: A case of teaching fraction division. ZDM, 41(6), 717-731. https://doi.org/10.1007/s11858-009-0174-8
Lowrie, T., Logan, T., & Patahuddin, S. (2018). A learning design for developing mathematics understanding: The ELPSA framework. Australian Mathematics Teacher, 74(4), 26-31.
Lynch, C. M. (2017). Collaborative planning for elementary mathematics methods course in a third space: The role of expertise in a community of practice [PhD dissertation, Penn State University]. ProQuest Dissertations Publishing.
McTighe, J., & Willis, J. (2019). Upgrade your teaching: understanding by design meets neuroscience. ASCD.
Munthe, E., & Conway, P. F. (2017). Evolution of research on teachers’ planning: Implications for teacher education. In D. J. Clandinin, & J. Husu (Eds.), SAGE handbook of research on teacher education (pp. 836-849). https://doi.org/10.4135/9781526402042.n48
National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all.
National Council of Teachers of Mathematics (NCTM). (2018). Catalyzing change in high school mathematics: Initiating critical conversations.
Newton, K. J., Lange, K., & Booth, J. L. (2020). Mathematical flexibility: Aspects of a continuum and the role of prior knowledge. The Journal of Experimental Education, 88(4), 503-515. https://doi.org/10.1080/00220973.2019.1586629
Novak, J. D. (2010). Learning, creating, and using knowledge: Concept maps as facilitative tools in schools and corporations. Routledge. https://doi.org/10.20368/1971-8829/441
O’Neill, G., Donnelly, R., & Fitzmaurice, M. (2014). Supporting programme teams to develop sequencing in higher education curricula. The International Journal for Academic Development, 19(4), 268-280. https://doi.org/10.1080/1360144X.2013.867266
Peterson, M., Delgado, C., Tang, K.-S., Bordas, C., & Norville, K. (2021). A taxonomy of cognitive image functions for science curriculum materials: identifying and creating ‘performative’ visual displays. International Journal of Science Education, 43(2), 314-343. https://doi.org/10.1080/09500693.2020.1868609
QCAA. (2013). Advice for developing and sequencing units of work. Queensland Curriculum and Assessment Authority. https://www.qcaa.qld.edu.au/downloads/senior/snr_tech_studies_13_res_dev_units.docx
QCAA. (2014). Mathematics senior subjects. Queensland Curriculum and Assessment Authority. www.qcaa.qld.edu.au/senior/subjects/mathematics
QCAA. (2018). Mathematical methods. General senior syllabus. Queensland Curriculum and Assessment Authority. https://www.qcaa.qld.edu.au/downloads/senior-qce/syllabuses/snr_maths_methods_19_syll.pdf
QCAA. (2019). Planning for teaching, learning and assessment. Queensland Curriculum and Assessment Authority. https://www.qcaa.qld.edu.au/downloads/aciq/general-resources/teaching/ac_plan_teach_learn_assess.pdf
Queensland Teachers’ Union. (2020). Basic guide to: General conditions of service. https://www.qtu.asn.au/application/files/8015/9556/2335/Basic_Guide_General_working_conditions_Jul2020.pdf
Reina, L, J., (2018). Route-finding: Developing curricular knowledge and impacting practice through a collaborative curriculum mapping process. https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=8445&context=etd
Reys, R. E., Rogers, A., Bennett, S., Cooke, A., Robson, K., Ewing, B., & West, J. (2020). Helping children learn mathematics. Wiley.
Rittle-Johnson, B. (2017). Developing mathematics knowledge. Child Development Perspectives, 11(3), 184-190. https://doi.org/10.1111/cdep.12229
Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561-574. https://doi.org/10.1037/0022-0663.99.3.561
Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587-597. https://doi.org/10.1007/s10648-015-9302-x
Roche, A., Clarke, D. M., Clarke, D. J., & Sullivan, P. (2014). Primary teachers’ written unit plans in mathematics and their perceptions of essential elements of these. Mathematics Education Research Journal, 26(4), 853-870. https://doi.org/10.1007/s13394-014-0130-y
Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47(6), 1525-1538. https://doi.org/10.1037/a0024997
Schuhl, S. (2020). Mathematics unit planning in a PLC at work. Grades 3-5. Solution Tree Press.
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. https://doi.org/10.2307/749205
Smith, G. (2007). Place‐based education: Breaking through the constraining regularities of public school. Environmental Education Research, 13(2), 189-207. https://doi.org/10.1080/13504620701285180
Stoll, C., Giddings, G., & Marzano, R. J. (2012). Re-awakening the learner: Creating learner-centric, standards-driven schools. R&L Education.
Sullivan, P., Clarke, D. J., Clarke, D. M., Farrell, L., & Gerrard, J. (2013). Processes and priorities in planning mathematics teaching. Mathematics Education Research Journal, 25(4), 457-480. https://doi.org/10.1007/s13394-012-0066-z
Sullivan, P., Clarke, D. M., Albright, J., Clarke, D. J., Farrell, L., Freebody, P., Gerrard, J., & Michels, D. (2012). Teachers’ planning processes: Seeking insights from Australian teachers. Australian Primary Mathematics Classroom, 17(3), 4-8.
Superfine, A. C. (2008). Planning for mathematics instruction: A model of experienced teachers’ planning process in the context of a reform mathematics curriculum. The Mathematics Educator, 18(2), 11-22.
Swan, M., (2006). Collaborative learning in mathematics: A challenge to our beliefs and practices. NIACE.
Tricoglus, G. (2000). Teacher planning in the development of collaborative cultures. Education 3-13, 28(1), 22-28. https://doi.org/10.1080/03004270085200051
Usha, K. (2010). Collaborative planning for a unit on the quadratic formula. The Mathematics Teacher, 103(9), 669-674.
Vashe, A., Devi, V., Rao, R., & Abraham, R. R. (2020). Curriculum mapping of dental physiology curriculum: The path towards outcome‐based education. European Journal of Dental Education, 24(3), 518-525. https://doi.org/10.1111/eje.12531
Voogt, J. M., Pieters, J. M., & Handelzalts, A. (2016). Teacher collaboration in curriculum design teams: effects, mechanisms, and conditions. Educational Research and Evaluation, 22(3-4), 121-140. https://doi.org/10.1080/13803611.2016.1247725
Wilson, J., Mandich, A., & Magalhães, L. (2016). Concept mapping: A dynamic, individualized and qualitative method for eliciting meaning. Qualitative Health Research, 26(8), 1151-1161. https://doi.org/10.1177/1049732315616623
Wong, N., Lam, C. & Wong, K.P. (2001). Students’ view of mathematics learning: A cross-sectional survey in Hong Kong. Educational Journal, 29(2), 37-59.

How to cite this article

APA

Chinofunga, M. D., Chigeza, P., & Taylor, S. (2022). A Framework for Content Sequencing from Junior to Senior Mathematics Curriculum. Eurasia Journal of Mathematics, Science and Technology Education, 18(4), em2100. https://doi.org/10.29333/ejmste/11930

Vancouver

Chinofunga MD, Chigeza P, Taylor S. A Framework for Content Sequencing from Junior to Senior Mathematics Curriculum. EURASIA J Math Sci Tech Ed. 2022;18(4):em2100. https://doi.org/10.29333/ejmste/11930

AMA

Chinofunga MD, Chigeza P, Taylor S. A Framework for Content Sequencing from Junior to Senior Mathematics Curriculum. EURASIA J Math Sci Tech Ed. 2022;18(4), em2100. https://doi.org/10.29333/ejmste/11930

Chicago

Chinofunga, Musarurwa David, Philemon Chigeza, and Subhashni Taylor. "A Framework for Content Sequencing from Junior to Senior Mathematics Curriculum". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 4 (2022): em2100. https://doi.org/10.29333/ejmste/11930

Harvard

Chinofunga, M. D., Chigeza, P., and Taylor, S. (2022). A Framework for Content Sequencing from Junior to Senior Mathematics Curriculum. Eurasia Journal of Mathematics, Science and Technology Education, 18(4), em2100. https://doi.org/10.29333/ejmste/11930

MLA

Chinofunga, Musarurwa David et al. "A Framework for Content Sequencing from Junior to Senior Mathematics Curriculum". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 4, 2022, em2100. https://doi.org/10.29333/ejmste/11930