In a range of meaningful contexts: 25 years of struggle for meaning in mathematics teaching

Authors

DOI:

https://doi.org/10.26686/nzaroe.v23i0.5283

Keywords:

Mathematics education, word problems, contexts, problem-solving, assessment

Abstract

 

The use of meaningful contexts has been a given in New Zealand’s mathematics curricula for the last 25 years. They hold a privileged position, but there has been little examination of why they are given this position either nationally or internationally, even though there is solid evidence that the use of contexts and word problems in mathematics is not without implications for equitable access to mathematics, student learning, and assessment of learning. So what are the affordances and constraints of taking the meaningful context approach to mathematics? What has been the impact of taking this approach on student achievement and learning? These are important questions given The New Zealand Curriculum is ten years old and a curriculum review is looming. These questions are being raised to start an essential debate for mathematics education in New Zealand, one that needs to take place prior to any curriculum review so an informed decision on the place and nature of meaningful contexts in future mathematics curricula can be made.

Downloads

Download data is not yet available.

Author Biography

Michael Drake

Michael Drake is a senior lecturer in the mathematics education team at Victoria University of Wellington’s Faculty of Education. He lectures in the primary and secondary pre-service programmes. His research interests relate to developing students’ understanding of mathematics and how affect influences learning, teacher professional development, and pre-service teacher education. He is currently involved in research into the learning of basic facts, linear scales of the kind found in measurement and graphing, and ambitious mathematics teaching.

References

Averill, R., Anderson, D., & Drake, M. (2015). Developing culturally responsive teaching through professional noticing within teacher educator modelling. Mathematics Teacher Education and Development, 17(2), 64–83.

Baranes, R., Perry, M., & Stigler, J. (1989). Activation of real-world knowledge in the solution of word problems. Cognition and Instruction, 6(4), 287–318. https://doi.org/10.1207/s1532690xci0604_1 DOI: https://doi.org/10.1207/s1532690xci0604_1

Barwell, R. (2011). Word problems: Connecting language, mathematics and life. In What works? Research into practice: Research monograph number 34. Ontario: Literacy and Numeracy Secretariat.

Bishton, S. (1998). Interpretation and clarification of “what is a problem”. Wellington: NZQA.

Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more “real”? For the Learning of Mathematics, 13(2), 12–17.

Boaler, J. (1994). When do girls prefer football to fashion? An analysis of female underachievement in relation to ‘realistic’ mathematic contexts. British Education Research Journal, 20(5), 551–564. https://doi.org/10.1080/0141192940200504 DOI: https://doi.org/10.1080/0141192940200504

Boaler, J. (2008). The elephant in the classroom: Helping children learn and love maths. London: Souvenir Press.

Boaler, J. (2015a). Anyone can learn to high levels. Retrieved from https://www.youcubed.org/think-it-up/anyone-can-learn-to-high-levels

Boaler, J. (2015b). When you believe in yourself your brain operates differently. Retrieved from https://www.youcubed.org/think-it-up/believe-brain-operates-differently

Boaler, J. (2015c). Parents’ beliefs about math change their children’s achievement. Retrieved from https://www.youcubed.org/think-it-up/parents-beliefs-math-change-childrens-achievement

Boaler, J. (2017). The way we are teaching math is holding women back. Retrieved from http://motto.time.com/4717463/jo-boaler-women-stem-ivanka-trump-betsy-devos

Boonen, A., de Koning, B., Jolles, J., & van der Schoot, M. (2016). Word problem solving in contemporary math education: A plea for reading comprehension skills training. Frontiers in Psychology, 7, 191. https://doi.org/10.3389/fpsyg.2016.00191 DOI: https://doi.org/10.3389/fpsyg.2016.00191

Boonen, A., van der Schoot, M., van Wesel, F., de Vries, M., & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38, 271–279. https://doi.org/10.1016/j.cedpsych.2013.05.001 DOI: https://doi.org/10.1016/j.cedpsych.2013.05.001

Carbonneau, K., Marley, S., & Selig, J. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084 DOI: https://doi.org/10.1037/a0031084

Carpenter, T., & Moser, J. (1983). Acquisition of addition and subtraction concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 7–44). New York: Academic Press.

Carpenter, T., Fennema, E., & Franke, M. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20. https://doi.org/10.1086/461846 DOI: https://doi.org/10.1086/461846

Carraher, T., Carraher, D., & Schliemann, A. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21–29. https://doi.org/10.1111/j.2044-835X.1985.tb00951.x DOI: https://doi.org/10.1111/j.2044-835X.1985.tb00951.x

Caygill, R., & Kirkham, S. (2008). Mathematics: Trends in year 5 mathematics achievement 1994 to 2006: New Zealand results from three cycles of the Trends in International Mathematics and Science Study (TIMSS). Wellington: Comparative Education Research Unit, Research Division, MOE.

Caygill, R., Hanlar, V., & Singh, S. (2016). TIMSS 2015/5 key findings: Mathematics year 9. Wellington: Comparative Education Research Unit, Analysis and Research Group, MOE.

Caygill, R., Singh, S., & Hanlar, V. (2016). TIMSS 2015/5 key findings: Mathematics year 5. Wellington: Comparative Education Research Unit, Analysis and Research Group, MOE.

Cobb, P. (2007). Forewords. In G. Anthony, & M. Walshaw (Eds.), Effective pedagogy in mathematics/pāngarau (pp. vii–x). Wellington: Ministry of Education.

Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23(1), 2–33. https://doi.org/10.2307/749161 DOI: https://doi.org/10.5951/jresematheduc.23.1.0002

Cockcroft, W. (1982). Mathematics counts. London: DES/HMSO.

Cooper, B., & Dunne, M. (2000). Assessing children’s mathematical knowledge: Social class, sex and problem solving. Buckingham, UK: Open University Press.

Cooper, B., & Harries, T. (2009). Realistic contexts, mathematics assessment, and social class. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 93–110). Rotterdam: Sense. DOI: https://doi.org/10.1163/9789087909383_007

De Corte, E., Vershaffel, L., & Greer, B. (2000). Connecting mathematics problem solving to the real world. In Proceedings of the International Conference on Mathematics Education into the 21st Century: Mathematics for living (pp. 66–73).

Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers’ metacognitive and heuristic approaches to word problem solving: Analysis and impact on students’ beliefs and performance. ZDM Mathematics Education, 42, 205–218. https://doi.org/10.1007/s11858-009-0221-5 DOI: https://doi.org/10.1007/s11858-009-0221-5

Donaldson, M. (1978). Children's minds. London: Fontana.

Earle, D. (2009). Skills, qualifications and wages: An analysis from the Adult Literacy and Life Skills survey. Wellington: Tertiary Sector Performance Analysis and Reporting, Strategy and System Performance, Ministry of Education.

Earle, D. (2011). Literacy and numeracy at work: Skills, education and job tasks. Wellington: Tertiary Sector Performance Analysis and Reporting, Strategy and System Performance, Ministry of Education.

Education and Science Committee (2015). Managing national assessment review survey, 2014. (Education and Science Committee 2014/15 financial review, questions attachment 3, vol. 1.) Retrieved from https://www.parliament.nz/resource/en-nz/51sces_evi_00dbsch_anr_66383_1_a488336/0d92975e12f03932beb79bb73726fcd2d00216f2

Fairweather, J. (2008). Linking evidence and promising practices in science, technology, engineering, and mathematics (STEM) undergraduate education. Board of Science Education, National Research Council, The National Academies, Washington, DC.

Flockton, L., Crooks, T., Smith, J., & Smith, L. (2006). Mathematics assessment results, 2005. Dunedin: Educational Assessment Research Unit, University of Otago.

Foley, A., Herts, J., Borgonovi, F., Guerriero, S., Levine, S., & Beilock, S. (2017). The math-anxiety performance link: A global phenomenon. Current Directions in Psychological Science, 26(1), 52–57. https://doi.org/10.1177/0963721416672463 DOI: https://doi.org/10.1177/0963721416672463

Fuson, K. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). New York: Macmillan. DOI: https://doi.org/10.1108/978-1-60752-874-620251016

Garden, R. (Ed.). (1996). Mathematics performance of New Zealand form 2 and form 3 students. Wellington: Ministry of Education.

Gerofsky, S. (1996). Communication: Simulation, reality, and mathematical word problems. For the Learning of Mathematics, 16(2), 36-45.

Good, R. (1972). Science, mathematics, and perceptual skills at the elementary school level: An interdisciplinary approach to learning based on manipulative materials. The Journal of Teacher Education, 23(4), 471–475. https://doi.org/10.1177/002248717202300415 DOI: https://doi.org/10.1177/002248717202300415

Greer, B., Verschaffel, L., Van Dooren W., & Mukhopadhyay, S. (2009). Introduction. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. xi–xxvii). Rotterdam: Sense. DOI: https://doi.org/10.1163/9789087909383

Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, 33–46. https://doi.org/10.2307/749455 DOI: https://doi.org/10.5951/jresematheduc.21.1.0033

Hendery, S. (2016). Teachers and NCEA students outraged over difficult Level 1 MCAT algebra exam. Retrieved from http://www.stuff.co.nz/national/education/84391247/Teachers-and-NCEA-students-outraged-over-difficult-Level-1-MCAT-algebra-exam

Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York: Macmillan. DOI: https://doi.org/10.1108/978-1-60752-874-620251006

Higgins, J. (2005). Equipment-in-use in the Numeracy Development Project: Its importance to the introduction of mathematical ideas. In Findings from the New Zealand Numeracy Development Project 2004 (pp. 89–96). Wellington: Ministry of Education.

Hill, S., & Edwards, F. (1991). Language and learning in secondary schools: Mathematics. Wellington: Learning Media.

Hodgen, J., & Wiliam, D. (2006). Mathematics inside the black box: Assessment for learning in the mathematics classroom. London: GL Assessment.

Hoogland, K., Pepin, B., Bakker, A., de Koning, J., & Gravemeijer, K. (2016). Representing contextual mathematics problems in descriptive or depictive form: Design of an instrument and validation of its uses. Studies in Educational Evaluation, 50, 22–32. https://doi.org/10.1016/j.stueduc.2016.06.005 DOI: https://doi.org/10.1016/j.stueduc.2016.06.005

Jolly, J. (2009). Historical perspectives: The National Defense Education Act, current STEM initiative, and the gifted. Gifted Child Today, 32(2), 50–53. https://doi.org./10.4219/gct-2009-873 DOI: https://doi.org/10.4219/gct-2009-873

Kempert, S., Saalbach, H., & Hardy, I. (2011). Cognitive benefits and costs of bilingualism in elementary school students: The case of mathematical word problems. Journal of Educational Psychology, 103(3), 547–561. https://doi.org./10.1037/a0023619 DOI: https://doi.org/10.1037/a0023619

Lamon, S. (1996). The development of unitizing: Its role in children’s partitioning strategies. Journal for Research in Mathematics Education, 27(2), 170–193. https://doi.org./10.2307/749599 DOI: https://doi.org/10.5951/jresematheduc.27.2.0170

Lave, J. (1992). Word problems: A microcosm of theories of learning. In P. Light & G. Butterworth (Eds.), Contexts and cognition: Ways of learning and knowing (pp. 74–92). New York: Harvester Wheatsheaf.

Lawes, E. (2009). Literacy and life skills for Pasifika adults: Results from the Adult Literacy and Life Skills (ALL) survey. Wellington: Comparative Education Research Unit, Research Division, Ministry of Education.

Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude towards mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 28(1), 26–47. https://doi.org./10.2307/749662 DOI: https://doi.org/10.2307/749662

Mack, N. (1993). Learning rational numbers with understanding: The case of informal knowledge. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 85–106). Hillsdale, NJ: Lawrence Erlbaum.

Martino, P., & Zan, R. (2010). ‘Me and maths’: Towards a narrative of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13, 27–48. https://doi.org/10.1007/s10857-009-9134-z DOI: https://doi.org/10.1007/s10857-009-9134-z

Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10–32. https://doi.org./10.1007/BF03217543 DOI: https://doi.org/10.1007/BF03217543

May, S., Cowles, S., & Lamy, M. (2013). PISA 2012: New Zealand summary report. Wellington: Comparative Education Research Unit, Research Division, Ministry of Education.

May, S., Flockton, J., & Kirkham, S. (2016). PISA 2015. New Zealand summary report. Wellington: Ministry of Education.

McLeod, D. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: McMillan. DOI: https://doi.org/10.1108/978-1-60752-874-620251028

Meyer, M., Dekker, T., & Querelle, N. (2001). Innovations in curriculum: Contexts in mathematics curricula. Mathematics Teaching in the Middle School, 6(9), 2001. DOI: https://doi.org/10.5951/MTMS.6.9.0522

Ministry of Education. (1992). Mathematics in the New Zealand curriculum. Wellington: Learning Media.

Ministry of Education. (1993). The New Zealand curriculum framework. Wellington: Learning Media.

Ministry of Education. (2004). Learning for tomorrow’s world: Programme for International Student Assessment (PISA) 2003: New Zealand summary report. Wellington: Author.

Ministry of Education. (2005). Book 1: The number framework. Wellington: Author.

Ministry of Education. (2007a). The New Zealand curriculum. Wellington: Learning Media.

Ministry of Education. (2007b). The Adult Literacy and Life Skills (ALL) Survey: Headline results and background. Wellington: Author.

Ministry of Education. (2009). Mathematics standards for years 1-8. Wellington: Learning Media.

Ministry of Education. (2015). NMSSA Report 4: Mathematics and Statistics 2013. Dunedin: Educational Assessment Research Unit & New Zealand Council for Educational Research: University of Otago.

Ministry of Education. (2016). E-ASTTLE practice test. Retrieved from https://e-asttle.education.govt.nz/StudentWeb/practice-test-subject.faces

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Nyabanyaba, T. (1999). Whither relevance? Mathematics teachers’ discussion of the use of ‘real-life’ contexts in school mathematics. For the Learning of Mathematics, 19(3), 10–14.

New Zealand Council for Educational Research. (2016a). Assessment resource banks. Retrieved from https://arbs.nzcer.org.nz

New Zealand Council for Educational Research. (2016b). PAT: Mathematics. Retrieved from http://www.nzcer.org.nz/tests/pat-mathematics?cPath=31_424_427

NZmaths. (2016). Gloss forms. Retrieved from https://nzmaths.co.nz/gloss-forms

New Zealand Qualifications Authority. (2015a). MCAT exemplar (91027). Retrieved from http://www.nzqa.govt.nz/assets/qualifications-and-standards/qualifications/ncea/NCEA-subject-resources/Mathematics/MCAT-exemplar-2015.pdf

New Zealand Qualifications Authority. (2015b). Level 1 mathematics and statistics CAT, 2015: 91027 Apply algebraic procedures in solving problems. Day 1: Tuesday. Retrieved from https://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2015/91027-cat-A-2015.pdf

New Zealand Qualifications Authority. (2017a). Clarification workshop slide show for 91027 and 91028. Retrieved from https://www.nzqa.govt.nz/ncea/subjects/mathematics/levels/

New Zealand Qualifications Authority. (2017b). Achievement standard AS91027: Apply algebraic procedures in solving problems. Retrieved from https://www.nzqa.govt.nz/nqfdocs/ncea-resource/achievements/2017/as91027.pdf

OECD. (2013a). PISA 2012 Assessment and analytical framework. Paris: PISA, OECD.

OECD (2013b). PISA 2012 results: Ready to learn: Students’ engagement, drive and self-beliefs (Vol III). Paris: Author.

OECD. (2016). PISA 2015 Results excellence and equity in education volume 1. Paris: Author. DOI: https://doi.org/10.1787/9789264266490-en

Parsons, S., & Bynner, J. (2005). Does numeracy matter anymore? London: National Research and Development Centre for Adult Literacy and Numeracy.

Patterson, R. (2015). Un(ac)countable why millions on maths returned little. Wellington: The New Zealand Initiative.

Piaget, J. (1953). How children form mathematical concepts. Scientific American, 189(5), 74–79. https://doi.org/10.1038/scientificamerican1153-74 DOI: https://doi.org/10.1038/scientificamerican1153-74

Piaget, J. (1968). The construction of reality in the child. London: Routledge & Kegan Paul.

Pintrich, P., & de Groot, E. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of Educational Psychology, 82, 33–40. https://doi.org./10.1037/0022-0663.82.1.33 DOI: https://doi.org/10.1037/0022-0663.82.1.33

Pirie, S., & Martin, L. (1997). The equation, the whole equation and nothing but the equation! One approach to the teaching of linear equations. Educational Studies in Mathematics, 34(2), 159–181. https://doi.org./10.1023/A:1003051829991 DOI: https://doi.org/10.1023/A:1003051829991

Radio New Zealand. (2016). NZ scores drop but rankings rise in international test. Retrieved from http://www.radionz.co.nz/news/national/319783/nz-scores-drop-but-rankings-rise-in-international-test

Satherley P., & Lawes, E. (2007). The Adult Literacy and Life Skills (ALL) survey: An introduction. Wellington: Comparative Education Research Unit, Research Division, Ministry of Education.

Satherley P., & Lawes, E. (2009a). The Adult Literacy and Life Skills (ALLs) survey: Numeracy skills in New Zealand and Australia. Wellington: Comparative Education Research Unit, Research Division, Ministry of Education.

Satherley, P., & Lawes, E. (2009b). Literacy and life skills for Māori adults: Results from the Adult Literacy and Life Skills (ALL) survey. Wellington: Comparative Education Research Unit, Research Division, Ministry of Education.

Satherley P., Lawes, E., & Sok, S. (2008). The Adult Literacy and Life Skills (ALLs) survey: Overview and international comparisons. Wellington: Comparative Education Research Unit, Research Division, Ministry of Education.

Schagen, I., & Lawes, E. (2009). Well-being and education level. Wellington: Comparative Education Research Unit, Research Division, Ministry of Education.

Schoenfeld, A. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, 23(2), 145–166. https://doi.org/10.1207/s15326985ep2302_5 DOI: https://doi.org/10.1207/s15326985ep2302_5

Schoenfeld, A. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. Voss, D. Perkins, & J. Segal (Eds.), Informal reasoning and education (pp. 311–343). Hillsdale, NJ: Lawrence Erlbaum.

Sowell, E. (1989). Effects of manipulatives materials on classroom instruction. Journal for Research in Mathematics Education, 20(5), 498–505. https://doi.org./10.2307/749423 DOI: https://doi.org/10.5951/jresematheduc.20.5.0498

Steffe, L. (1988). Children’s construction of number sequences and multiplying schemes. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 119–140). Reston, VA: National Council of Teachers of Mathematics. DOI: https://doi.org/10.4324/9781003726777-8

Steffe, L., Cobb, P., & von Glasersfeld, E. (1988). Construction of arithmetical meanings and strategies. New York: Springer. DOI: https://doi.org/10.1007/978-1-4612-3844-7

Sullivan, P. (2010, August). Learning about selecting classroom tasks and structuring mathematics lessons from students. Paper presented at the ACER Research Conference 2010, Teaching mathematics: Make it count: What research tells us about effective mathematics teaching and learning (pp. 53–55), Crown Conference Centre, Melbourne.

Sullivan, P. (2011). Australian education review. Teaching mathematics: Using research-informed strategies. Camberwell, Victoria: ACER.

Sullivan, P., Mornane, A., Prain, V., Campbell, C., Deed, C., Drane, S. … Smith, C. (2009). Junior secondary students’ perceptions of influences on their engagement with schooling. Australian Journal of Education, 53(2), 176–191. https://doi.org./10.1177/000494410905300206 DOI: https://doi.org/10.1177/000494410905300206

Sullivan, P., Zevenbergen, R., & Mousley, J. (2003). The contexts pf mathematics tasks and the context of the classroom: Are we including all students? Mathematics Education Research Journal, 15(2), 107–121. https://doi.org./10.1007/BF03217373 DOI: https://doi.org/10.1007/BF03217373

Swan, P., & Marshall, L. (2010). Revisiting mathematics manipulative materials. Australian Primary Mathematics Classroom, 15(2), 13–19.

Swetz, F. (2009). Word problems: Footprints from the history of mathematics. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 73–91). Rotterdam: Sense. DOI: https://doi.org/10.1163/9789087909383_006

Tertiary Education Commission. (2009). Strengthening literacy and numeracy: Theoretical framework. Retrieved from https://hagleyace.files.wordpress.com/2010/03/theoretical-framework-2009.pdf

Treffers, A., & Beishuizen, M. (1999). Realistic mathematics education in the Netherlands. In I. Thompson (Ed.), Issues in teaching numeracy in primary schools (pp. 27–38). Berkshire, UK: Open University.

Van de Walle, J., Karp, K., & Bay-Williams, J. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). New Jersey: Pearson.

Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–9.

Verschaffel, L., Depaepe, F., & Van Dooren, W. (2014). Word problems in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 641–645). Dordrecht, The Netherlands: Springer Science and Business Media. DOI: https://doi.org/10.1007/978-94-007-4978-8_163

Vygotsky, L. (1978). Mind in society: Development of higher psychological processes. Cambridge, MA: Harvard University Press.

Watson, A. (2004). Red herrings: Post-14 ‘best’ mathematical teaching and curricula. British Journal of Educational Studies, 52(4), 359–376. https://doi.org./10.1111/j.1467-8527.2004.00273.x DOI: https://doi.org/10.1111/j.1467-8527.2004.00273.x

Wiest, L. (2001). The role of fantasy contexts in word problems. Mathematics Education Research Journal, 13(20), 74–90. doi.org/10.1007/BF03217100 DOI: https://doi.org/10.1007/BF03217100

Wijaya, A., van den Heuvel-Panhuizen, M., Doormana, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), Article 8. DOI: https://doi.org/10.54870/1551-3440.1317

Wright, R. (1998). An overview of a research-based framework for assessment and teaching early number. In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching mathematics in new times: Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 701–708). Brisbane: MERGA.

Wright, R., & Gould, P. (2000). Reviewing literature relevant to a systemic early numeracy initiative: Bases of CMIT. In J. Bana & A. Chapman (Eds.), Mathematics education beyond 2000: Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 56–63). Freemantle: MERGA.

Downloads

Published

2018-12-30