Articles (peer-reviewed)
Inglis, M., Foster, C., Lortie-Forgues, H., & Stokoe, E. (2024). British education research and its quality: An analysis of Research Excellence Framework submissions. British Educational Research Journal, 50(5), 2495–2518. http://doi.org/10.1002/berj.4040
Foster, C., & Trundley, R. (2024). Adapting lesson study for early years practitioners. International Journal for Lesson and Learning Studies, 13(3), 225–231. https://doi.org/10.1108/IJLLS-07-2024-184
Foster, C., & Renie, P. (2024). Changes in students’ confidence calibration across a sequence of low-stakes confidence assessments. Asian Journal for Mathematics Education, XX(X), X–X. https://doi.org/10.1177/27527263241298968
Kinnear, G., Hood, G., Lardet, E., Sheard, C., & Foster, C. (2024). Lecturers' use of questions in undergraduate mathematics lectures. Journal of Mathematical Behavior, 76, 101190. https://doi.org/10.1016/j.jmathb.2024.101190
Foster, C., Woollacott, B., Francome, T., Shore, C., Peters, C., & Morley, H. (2024). Challenges in applying principles from cognitive science to the design of a school mathematics curriculum. The Curriculum Journal, 35(1), 489–513. https://doi.org/10.1002/curj.249
Foster, C., Francome, T., Shore, C., Hewitt, D., & Sangwin, C. (2024). Priority of operations: Necessary or arbitrary? For the Learning of Mathematics, 44(2), 24–26.
Foster, C. (2024). Methodological pragmatism in educational research: From qualitative-quantitative to exploratory-confirmatory distinctions. International Journal of Research and Method in Education, 47(1), 4–19. https://doi.org/10.1080/1743727X.2023.2210063
Kinnear, G., Jones, I., Sangwin, C., Alarfaj, M., Davies, B., Fearn, S., Foster, C., Heck, A., Henderson, K., Hunt, T., Iannone, P., Kontorovich, I., Larson, N., Lowe, T., Meyer, J. C., O’Shea, A., Rowlett, P., Sikurajapathi, I., & Wong, T. (2024). A collaboratively-derived research agenda for e-assessment in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 10(2), 201–231. https://doi.org/10.1007/s40753-022-00189-6
Foster, C. (2024). $\int_0^\pi \sin^2 \theta \, d\theta$ from a shear-like transformation of a circle. Mathematical Gazette, 108(573), 541–542. https://doi.org/10.1017/mag.2024.132
Foster, C. (2024). Editorial: The peer review process. International Journal of Mathematical Education in Science and Technology, 55(1), 1–3. https://doi.org/10.1080/0020739X.2023.2293601
Foster, C. (2023). Problem solving in the mathematics curriculum: From domain-general strategies to domain-specific tactics. The Curriculum Journal, 34(4), 594–612. https://doi.org/10.1002/curj.213
Foster, C. (2023). A quotient effect size for educational interventions. International Journal of Research and Method in Education, 46(5), 528–537. https://doi.org/10.1080/1743727X.2023.2182877
Calleja, J., Foster, C., & Hodgen, J. (2023). Teachers’ structuring of mathematical inquiry lessons: Shifting from ‘task-first’ to ‘scaffolded inquiry’. Research in Mathematics Education. Advance online publication. https://doi.org/10.1080/14794802.2023.2176915
Hodgen, J., Foster, C., Brown, M., & Martin, D. (2023). Low-attaining secondary school mathematics students’ perspectives on recommended teaching strategies. International Journal of Science and Mathematics Education, 22(X), 1325–1343. https://doi.org/10.1007/s10763-023-10420-8
Foster, C. (2023). Less is more: Improving by removing. Mathematical Gazette, 107(570), 386–398. https://doi.org/10.1017/mag.2023.90
Baldry, F., Mann, J., Horsman, R., Koiwa, D., & Foster, C. (2023). The use of carefully-planned board-work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson. Journal of Mathematics Teacher Education, 26(2), 129–153. https://doi.org/10.1007/s10857-021-09511-6
Foster, C. (2023). Editorial. International Journal of Mathematical Education in Science and Technology, 54(1), 1–3. https://doi.org/10.1080/0020739X.2023.2153962
Foster, C. (2022). Using coherent representations of number in the school mathematics curriculum. For the Learning of Mathematics, 42(3), 21–27.
Foster, C., Woodhead, S., Barton, C., & Clark-Wilson, A. (2022). School students’ confidence when answering diagnostic questions online. Educational Studies in Mathematics, 109, 491–521. https://doi.org/10.1007/s10649-021-10084-7
Foster, C. (2022). Implementing confidence assessment in low-stakes, formative mathematics assessments. International Journal of Science and Mathematics Education, 20(7), 1411–1429. https://doi.org/10.1007/s10763-021-10207-9
Foster, C., Barichello, L., Bustang, B., Najjuma, R., & Saralar-Aras, İ (2022). Decolonizing educational design for school mathematics. For the Learning of Mathematics, 42(2), 9–14.
Foster, C., Burkhardt, H., & Schoenfeld, A. (2022). Crisis-ready educational design: The case of mathematics. The Curriculum Journal, 33(4), 519–535. https://doi.org/10.1002/curj.159
Jones, I., Foster, C., & Hunter, J. (2022). Comparing examination standards without graded candidate scripts. European Journal of Mathematics and Science Education, 3(2), 79–90. https://doi.org/10.12973/ejmse.3.2.79
Hodgen, J., Foster, C., & Brown, M. (2022). Low attainment in mathematics: An analysis of 60 years of policy discourse in England. The Curriculum Journal, 33(1), 5–24. https://doi.org/10.1002/curj.128
Foster, C. (2022). Editorial. International Journal of Mathematical Education in Science and Technology, 53(1), 1–3. https://doi.org/10.1080/0020739X.2022.2030990
Foster, C., Francome, T., Hewitt, D., & Shore, C. (2021). Principles for the design of a fully-resourced, coherent, research-informed school mathematics curriculum. Journal of Curriculum Studies, 53(5), 621–641. https://doi.org/10.1080/00220272.2021.1902569
Calleja, J., Foster, C., & Hodgen, J. (2021). Integrating ‘just-in-time’ learning in the design of mathematics professional development. Mathematics Teacher Education and Development, 23(2), 79–101. https://mted.merga.net.au/index.php/mted/article/view/599
Foster, C. (2021). Editorial. International Journal of Mathematical Education in Science and Technology, 52(1), 1–2. https://doi.org/10.1080/0020739X.2021.1861701
Marks, R., Foster, C., Barclay, N., Barnes, A., & Treacy, P. (2021). A comparative synthesis of UK mathematics education research: What are we talking about and do we align with international discourse? Research in Mathematics Education, 23(1), 39–62. https://doi.org/10.1080/14794802.2020.1725612
Seino, T., & Foster, C. (2020). Analysis of the final comments provided by a knowledgeable other in Lesson Study. Journal of Mathematics Teacher Education, 24(5), 507–528. https://doi.org/10.1007/s10857-020-09468-y
Foster, C. (2020). Editorial. International Journal of Mathematical Education in Science and Technology, 51(1), 1–2. https://doi.org/10.1080/0020739X.2020.1700609
Foster, C., & Inglis, M. (2019). Mathematics teacher professional journals: What topics appear and how has this changed over time? International Journal of Science and Mathematics Education, 17(8), 1627–1648. https://doi.org/10.1007/s10763-018-9937-4
Foster, C. (2019). Editorial. International Journal of Mathematical Education in Science and Technology, 50(1), 1–2. https://doi.org/10.1080/0020739X.2019.1573786
Inglis, M., & Foster, C. (2018). Five decades of mathematics education research. Journal for Research in Mathematics Education, 49(4), 462–500. https://doi.org/10.5951/jresematheduc.49.4.0462
Foster, C. (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97(2), 121–141. https://doi.org/10.1007/s10649-017-9788-x
Foster, C., & Inglis, M. (2017). Teachers’ appraisals of adjectives relating to mathematics tasks. Educational Studies in Mathematics, 95(3), 283–301. https://doi.org/10.1007/s10649-017-9750-y
Foster, C. (2016). Confidence and competence with mathematical procedures. Educational Studies in Mathematics, 91(2), 271–288. https://doi.org/10.1007/s10649-015-9660-9
Wake, G., Swan, M., & Foster, C. (2016). Professional learning through the collaborative design of problem-solving lessons. Journal of Mathematics Teacher Education, 19(2), 243–260. https://doi.org/10.1007/s10857-015-9332-9
Foster, C., & De Villiers, M. (2016). The definition of the scalar product: An analysis and critique of a classroom episode. International Journal of Mathematical Education in Science and Technology, 47(5), 750–761. https://doi.org/10.1080/0020739X.2015.1117148
Foster, C. (2016). Proof without words: Integer right triangle hypotenuses without Pythagoras. The College Mathematics Journal, 47(2), 101. https://doi.org/10.4169/college.math.j.47.2.101
Foster, C., & Martin, D. (2016). Two-dice horse race. Teaching Statistics, 38(3), 98–101. https://doi.org/10.1111/test.12108 (Spreadsheet resource xlsm)
Foster, C. (2015). Closed but provocative questions: Curves enclosing unit area. International Journal of Mathematical Education in Science and Technology, 46(5), 776–783. https://doi.org/10.1080/0020739X.2014.992989
Foster, C. (2015). Exploiting unexpected situations in the mathematics classroom. International Journal of Science and Mathematics Education, 13(5), 1065–1088. https://doi.org/10.1007/s10763-014-9515-3
Foster, C. (2015). The convergent–divergent model: An opportunity for teacher–learner development through principled task design. Educational Designer, 2(8). http://www.educationaldesigner.org/ed/volume2/issue8/article28/index.htm
Foster, C. (2015). Expression polygons. Mathematics Teacher, 109(1), 62–65. https://doi.org/10.5951/mathteacher.109.1.0062 (Resource sheet doc)
Foster, C. (2014). Minimal interventions in the teaching of mathematics. European Journal of Science and Mathematics Education, 2(3), 147–154. https://doi.org/10.30935/scimath/9407
Foster, C. (2014). Confidence trick: The interpretation of confidence intervals. Canadian Journal of Science, Mathematics, and Technology Education, 14(1), 23–34. https://doi.org/10.1080/14926156.2014.874615
Foster, C. (2014). Equal volumes of revolution. Mathematical Gazette, 98(543), 504–507. https://doi.org/10.1017/S0025557200008287
Foster, C. (2014). Getting goose bumps about teaching evolution. Primary Science, 131, 5–7.
Foster, C. (2013). Resisting reductionism in mathematics pedagogy. The Curriculum Journal, 24(4), 563–585. https://doi.org/10.1080/09585176.2013.828630
Foster, C. (2013). Mathematical études: Embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematical Education in Science and Technology, 44(5), 765–774. https://doi.org/10.1080/0020739X.2013.770089
Foster, C. (2013). Problems with generalising: Pythagoras in n dimensions. Australian Senior Mathematics Journal, 27(1), 8–11.
Foster, C. (2012). Creationism as a misconception: Socio-cognitive conflict in the teaching of evolution. International Journal of Science Education, 34(14), 2171–2180. https://doi.org/10.1080/09500693.2012.692102
Foster, C. (2012). How to manipulate test scores. The College Mathematics Journal, 43(2), 121–122. https://doi.org/10.4169/college.math.j.43.2.121
Foster, C. (2012). Working without a safety net. The Australian Mathematics Teacher, 68(2), 25–29.
Foster, C. (2012). The probability distribution for a biased spinner. Teaching Statistics, 34(1), 41–43. https://doi.org/10.1111/j.1467-9639.2011.00481.x
Foster, C. (2012). Quadratic doublets. Mathematical Gazette, 96(536), 264–266. https://doi.org/10.1017/S0025557200004514
Foster, C. (2012). Squares within squares. Mathematical Gazette, 96(536), 328–331. https://doi.org/10.1017/S002555720000468X
Foster, C. (2012). Symmetrical cubics. Mathematical Gazette, 96(536), 109–112. https://doi.org/10.1017/S0025557200004071
Foster, C. (2012). Orthogonal mappings. Mathematical Gazette, 96(536), 112–115. https://doi.org/10.1017/S0025557200004083
Foster, C. (2012). Taking a short cut through Pascal’s triangle. Mathematical Gazette, 96(536), 142–145. https://doi.org/10.1017/S0025557200004198
Foster, C. (2012). When is a parabola not a parabola? Mathematics Teacher, 105(7), 486–487.
Foster, C. (2011). Student-generated questions in mathematics teaching. Mathematics Teacher, 105(1), 26–31. https://doi.org/10.5951/mathteacher.105.1.0026
Foster, C. (2011). A slippery slope: Resolving cognitive conflict in mechanics. Teaching Mathematics and its Applications, 30(4), 216–221. https://doi.org/10.1093/teamat/hrr015
Foster, C. (2011). Peripheral mathematical knowledge. For the Learning of Mathematics, 31(3), 24–26.
Foster, C. (2011). Productive ambiguity in the learning of mathematics. For the Learning of Mathematics, 31(2), 3–7.
Foster, C. (2011). The significance of a square-root rule. The American Statistician, 65(4), 222. https://doi.org/10.1198/tas.2011.11160
Foster, C. (2011). A comment on Schnell and Mendoza. Mathematical Gazette, 95(533), 357. https://doi.org/10.1017/S0025557200003284
Foster, C. (2010). A fortuitous value. Mathematical Gazette, 94(530), 335. https://doi.org/10.1017/S0025557200006719
Foster, C. (2009). Isometric graphs. Mathematical Gazette, 93(527), 289–292. https://doi.org/10.1017/S0025557200184840
Foster, C. (2009). Knowing your limitations. Teaching Statistics, 31(2), 59–60. https://doi.org/10.1111/j.1467-9639.2009.00349.x
Foster, C. (2008). Avoiding Pythagoras. Mathematical Gazette, 92(523), 110–111. https://doi.org/10.1017/S0025557200182683
Book chapters
Hodgen, J., & Foster, C. (2024). What’s so hard about algebra? In J. Berry, & C. Pritchard (Eds), Learning mathematics: What the experts say (pp. 159–161). Mathematical Association.
Foster, C. (2021). Checking for understanding. In E. Southall (Ed.), If I only tell you one thing (pp. 3–9). Mathematical Association.
Baldry, F., & Foster, C. (2019). Lesson study partnerships in initial teacher education. In P. Wood, D. Larssen, W. Cajkler, & N. Helgevold (Eds), Lesson Study in Initial Teacher Education: A critical perspective (pp. 147–160). Emerald Group Publishing. https://doi.org/10.1108/978-1-78756-797-920191011
Baldry, F., & Foster, C. (2019). Lesson study in mathematics Initial Teacher Education in England. In R. Huang, A. Takahashi, & P. da Ponte (Eds), Theory and Practice of Lesson Study in Mathematics: An international perspective (pp. 577–594). Springer. https://doi.org/10.1007%2F978-3-030-04031-4_28
Swan, M., & Foster, C. (2018). Formative assessment lessons. In D. R. Thompson, M. Burton, A. Cusi, & D. Wright (Eds), Classroom assessment in mathematics: Perspectives from around the globe (pp. 11–24). Springer. https://doi.org/10.1007/978-3-319-73748-5_2
Foster, C. (2018). A picture is worth a thousand exercises. In A. Watson (Ed.), Variation in Mathematics Teaching and Learning: A collection of writing from ATM: Mathematics Teaching (pp. 29–30). Association of Teachers of Mathematics. https://www.atm.org.uk/Shop/Variation-in-mathematics-A-collection-of-writings-from-ATM-Mathematics-Teaching/REA027
Book reviews (peer-reviewed)
Foster, C. (2017). [Review of the book Validity in educational and psychological assessment, by P. E. Newton & S. D. Shaw]. Research in Mathematics Education, 19(2), 108–111. https://doi.org/10.1080/14794802.2017.1318086
Foster, C. (2014). [Review of the book How to study for a mathematics degree, by L. Alcock]. Mathematical Gazette, 98(542), 377–378. https://doi.org/10.1017/S0025557200001625
Foster, C. (2013). [Review of the book Teaching with tasks for effective mathematics learning, by P. Sullivan, D. Clarke & B. Clarke]. Research in Mathematics Education, 15(3), 309–313. https://doi.org/10.1080/14794802.2013.830357
Conference proceedings (peer-reviewed)
Barmby, P., Foster, C., Jones, I., Kelly, J., & Milinkovic, J. (2023). Using a comparative judgement approach to assess the problem-solving skills of primary school pupils. Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education (IGPME) (p. 1-229). Haifa, Israel, July 16-21, 2023.
Barmby, P., Jones, I., Foster, C., & Milinkovic, J. (2021). Using a comparative judgement approach to assess the problem-solving skills of primary school pupils. Proceedings of the 29th Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE) (pp. 9-13). Port Elizabeth, South Africa, January 12-15, 2021.
Wake, G., Foster, C., & Nishimura, K. (2020). Lesson study: A case of expansive learning. Proceedings of the 25th International Commission on Mathematical Instruction. University of Lisbon, Lisbon, Portugal, February 4–7, 2020. Lisbon: ICMI.
Swan, M., & Foster, C. (2016). Formative assessment lessons for concept development and problem solving. Proceedings of the 13th International Congress on Mathematical Education. University of Hamburg, Germany: ICME.
Kent, G., & Foster, C. (2016). Re-conceptualising conceptual understanding in mathematics. In K. Krainer, & N. Vondrová (Eds), Proceedings of the Ninth Congress of European Research in Mathematics Education (CERME9): Thematic Working Group 17 (pp. 2656–2661). Charles University, Prague, Czech Republic: CERME.
Wake, G., Foster, C., & Swan, M. (2016). Understanding issues in teaching mathematical modelling: lessons from lesson study. In K. Krainer, & N. Vondrová (Eds), Proceedings of the Ninth Congress of European Research in Mathematics Education (CERME9): Thematic Working Group 6 (pp. 937–943). Charles University, Prague, Czech Republic: CERME.
Foster, C., Wake, G., & Swan, M. (2014). Mathematical knowledge for teaching problem solving: Lessons from lesson study. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, Vol. 3, pp. 97–104. Vancouver, Canada: PME.
Wake, G., Foster, C., & Swan, M. (2014). Understanding issues in mathematical problem solving and modelling: Lessons from lesson study. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, Vol. 6, p. 259. Vancouver, Canada: PME.
Foster, C. (2014). “Can’t you just tell us the rule?” Teaching procedures relationally. In S. Pope (Ed.), Proceedings of the 8th British Congress of Mathematics Education, Vol. 34, No. 2 (pp. 151–158). University of Nottingham.
Wake, G., Foster, C., & Swan, M. (2014). Teacher knowledge for modelling and problem solving. In S. Pope (Ed.), Proceedings of the 8th British Congress of Mathematics Education, Vol. 34, No. 2 (pp. 335–342). University of Nottingham.
Wake, G., Foster, C., & Swan, M. (2013). A theoretical lens on lesson study: Professional learning across boundaries. In A.M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 369–376). Kiel, Germany: PME.
Reports
Marks, R., Barclay, N., Barnes, A., Allen, B., Foster, C., & Hodgen, J. (2023). The prevalence and use of textbooks and curriculum resources in primary mathematics. Nuffield Foundation. https://cris.brighton.ac.uk/ws/portalfiles/portal/40340288/The_Prevalence_and_Use_of_Textbooks_and_Curriculum_Resources_Final_Report_120623.pdf
Foster, C. (2022). Learning times tables through systematic connections. https://www.foster77.co.uk/Learning%20Times%20Tables%20Through%20Systematic%20Connections.pdf
Foster, C. (2022). Mathematics curriculum resourcing in England: What might the future hold? Research on global trends in mathematics and mathematics textbooks: Bulletin of the Textbook Research Center, August, pp. 198–202. Tokyo, Japan. https://textbook-rc.or.jp/wp-content/uploads/2022/09/80160bf7b38e4d1fd6ab6aa113f8bd3e.pdf
Wake, G., Foster, C., & Hatakenaka, S. (2020). Developing a sustainable and scalable model for the professional learning of mathematics teachers: Final report of the LeMaPS (Lessons for Mathematical Problem Solving) Project. University of Nottingham. https://www.nottingham.ac.uk/research/groups/crme/documents/lemaps-report.pdf
Hodgen, J., Barclay, N., Foster, C., Gilmore, C., Marks, R., & Simms, V. (2020). Early Years and Key Stage 1 Mathematics Teaching: Evidence Review. Education Endowment Foundation. https://educationendowmentfoundation.org.uk/public/files/Early_Years_and_Key_Stage_1_Mathematics_Teaching_Evidence_Review.pdf
Education Endowment Foundation (2020). Improving Mathematics in The Early Years and Key Stage One: Guidance Report. Education Endowment Foundation. https://educationendowmentfoundation.org.uk/public/files/Publications/Maths/EEF_Maths_EY_KS1_Guidance_Report.pdf
Hodgen, J., Coe, R., Foster, C., Brown, M., Higgins, S., & Küchemann, D. (2020). Low attainment in mathematics: An investigation focusing on Year 9 students in England. University College London Institute of Education. https://discovery.ucl.ac.uk/id/eprint/10091720/
Hodgen, J., Coe, R., Foster, C., Brown, M., Higgins, S., & Küchemann, D. (2020). Low attainment in mathematics: An investigation focusing on Year 9 students in England: Technical Report. University College London Institute of Education. https://discovery.ucl.ac.uk/id/eprint/10099162/
Education Endowment Foundation (2017). Improving Mathematics in Key Stages Two and Three: Guidance Report. Education Endowment Foundation. https://educationendowmentfoundation.org.uk/education-evidence/guidance-reports/maths-ks-2-3
Hodgen, J., Foster, C., Marks, R., & Brown, M. (2018). Evidence for Review of Mathematics Teaching: Improving Mathematics in Key Stages Two and Three. Education Endowment Foundation. https://educationendowmentfoundation.org.uk/education-evidence/evidence-reviews/mathematics-in-key-stages-2-and-3
Media and engagement
Foster, C. (2024, May 8). Using principles from cognitive science to design a school mathematics curriculum [Blog post]. https://www.bera.ac.uk/blog/using-principles-from-cognitive-science-to-design-a-school-mathematics-curriculum
Foster, C. (2024, March 22). The Launch of the LUMEN Curriculum [Blog post]. https://blog.lboro.ac.uk/cmc/2024/03/22/the-launch-of-the-lumen-curriculum/
Foster, C. (2024, February 28). Understanding how the brain works can transform how school students learn maths. The Conversation. https://theconversation.com/understanding-how-the-brain-works-can-transform-how-school-students-learn-maths-223941
Foster, C. & Francome, T. (2023). Teaching Dilemma 1: If they probably won’t know, should I ask anyway? Loughborough University Mathematics Education Network.
Foster, C. (2023, June 29). The teaching of problem solving in the school mathematics curriculum [Blog post]. https://www.bera.ac.uk/blog/the-teaching-of-problem-solving-in-the-school-mathematics-curriculum/
Foster, C. (2023, June 13). Teaching mathematical problem solving in the school curriculum [Blog post]. https://blog.lboro.ac.uk/cmc/2023/06/13/teaching-mathematical-problem-solving-in-the-school-curriculum//
BAGs to Learn Podcast by Ben Gordon (2021, December 2). Episode 4 – Colin Foster – Problem Solving in the mathematics curriculum [Audio podcast]. https://anchor.fm/ben-gordon83/episodes/Episode-4---Colin-Foster---Problem-Solving-in-the-mathematics-curriculum-e1b5ic3
Mr Barton Maths Podcast (2021, June 21). Writing a maths curriculum with Colin Foster [Audio podcast]. http://www.mrbartonmaths.com/blog/research-in-action-16-writing-a-maths-curriculum-with-colin-foster/
Foster, C., Francome, T., Hewitt, D., & Shore, C. (2021, May 18). Designing a fully-resourced, research-informed school mathematics curriculum [Blog post]. https://blog.lboro.ac.uk/cmc/2021/05/18/designing-a-fully-resourced-research-informed-school-mathematics-curriculum/
Foster, C. (2021, March 31). Developing fluency with procedures without using traditional exercises [Video]. YouTube. https://https://www.youtube.com/watch?v=OSrnbf9YyO0
Foster, C. & Burkhardt, H. (2020, September 2). UK Parliament: Education Committee: The impact of COVID-19 on education and children’s services: CIE0382 [Evidence submission]. London, UK: HMSO. https://committees.parliament.uk/writtenevidence/9074/default/
AssocTeachersMaths. (2020, July 13). Armchair Responses to Classroom Events - with Colin Foster [Video]. YouTube. https://youtu.be/L0ovhillL0c
Foster, C. (2019, October 8). Moving Forward with Formative Assessment [Blog post]. https://www.lboro.ac.uk/services/lumen/resources/lumen-blog/formative-assessment-blog-post/
Mr Barton Maths Podcast (2018, July 17). Slice of Advice: What did you learn this year? [Audio podcast]. http://www.mrbartonmaths.com/blog/slice-of-advice-what-did-you-learn-this-year/
Foster, C. (2018, June 15). Creative approaches to practising mathematical procedures [Blog post]. http://maths4maryams.org/mathed/wp-content/uploads/2018/06/Wikiletters-4.pdf (English) or https://maths4maryams.org/mathed/wp-content/uploads/2018/08/Foster-WikiLetter.pdf (Farsi).
Foster, C. (2018, March 23). Interview by BBC Breakfast, BBC1 [Television broadcast]. London: British Broadcasting Corporation.
Foster, C. (2018, March 23). Interview by Newsday, BBC World Service [Radio broadcast]. London: British Broadcasting Corporation.
Foster, C. (2018, March 23). Interview by Newsroom, BBC World Service [Radio broadcast]. London: British Broadcasting Corporation.
Mr Barton Maths Podcast (2017, November 26). Colin Foster: Mathematical Etudes, Confidence and Questioning [Audio podcast]. http://www.mrbartonmaths.com/blog/colin-foster-mathematical-etudes-confidence-and-questioning/
Inglis, M., & Foster, C. (2017, June 9). How do teachers describe mathematics tasks? [Blog post]. http://www.bsrlm.org.uk/teachers-describe-mathematics-tasks/
Blog
Foster, C. (2023, March 30). Teaching specific tactics for problem solving [Blog post]. https://blog.foster77.co.uk/2023/03/teaching-specific-strategies-for.html
Foster, C. (2023, March 16). Crocodiles and inequality signs [Blog post]. https://blog.foster77.co.uk/2023/03/crocodiles-and-inequality-signs.html
Foster, C. (2023, March 2). Are probabilities and inequalities approximate? [Blog post]. https://blog.foster77.co.uk/2023/03/are-probabilities-and-inequalities.html
Foster, C. (2023, February 16). Don't forget the units? [Blog post]. https://blog.foster77.co.uk/2023/02/dont-forget-units.html
Foster, C. (2023, February 2). Non-expository video clips [Blog post]. https://blog.foster77.co.uk/2023/02/non-expository-video-clips.html
Foster, C. (2023, January 19). Is zero really a number? [Blog post]. https://blog.foster77.co.uk/2023/01/is-zero-really-number.html
Foster, C. (2023, January 5). Proportionality [Blog post]. https://blog.foster77.co.uk/2023/01/proportionality.html
Foster, C. (2022, December 22). Mixing the dimensions in models of number [Blog post]. https://blog.foster77.co.uk/2022/12/mixing-dimensions-in-models-of-number.html
Foster, C. (2022, December 8). Dividing into thirds [Blog post]. https://blog.foster77.co.uk/2022/12/dividing-into-thirds.html
Foster, C. (2022, November 24). Fractions as factors [Blog post]. https://blog.foster77.co.uk/2022/10/fractions-as-factors.html
Foster, C. (2022, November 10). Is area more difficult than volume? [Blog post]. https://blog.foster77.co.uk/2022/11/is-area-more-difficult-than-volume.html
Foster, C. (2022, October 27). Butterfly effects when adapting tasks [Blog post]. https://blog.foster77.co.uk/2022/10/butterfly-effects-when-adapting-tasks.html
Foster, C. (2022, October 13). How open should a question be? [Blog post]. https://blog.foster77.co.uk/2022/10/how-open-should-question-be.html
Foster, C. (2022, September 29). Tasks that can't fail [Blog post]. https://blog.foster77.co.uk/2022/09/tasks-that-cant-fail.html
Foster, C. (2022, September 15). Always simplify your answer [Blog post]. https://blog.foster77.co.uk/2022/09/always-simplify-your-answer.html
Foster, C. (2022, September 1). Interactive introductions [Blog post]. https://blog.foster77.co.uk/2022/09/interactive-introductions.html
Foster, C. (2022, August 18). The Differentiator [Blog post]. https://blog.foster77.co.uk/2022/08/the-differentiator.html
Foster, C. (2022, August 4). Misremembering Goldbach's conjecture [Blog post]. https://blog.foster77.co.uk/2022/08/misremembering-goldbachs-conjecture.html
Foster, C. (2022, July 21). Making rounding interesting [Blog post]. https://blog.foster77.co.uk/2022/07/making-rounding-interesting.html
Foster, C. (2022, July 7). A football on the roof [Blog post]. https://blog.foster77.co.uk/2022/07/a-football-on-roof.html
Foster, C. (2022, June 23). Lines of not-very-good fit [Blog post]. https://blog.foster77.co.uk/2022/06/lines-of-not-very-good-fit.html
Foster, C. (2022, June 9). Motivation for measurement [Blog post]. https://blog.foster77.co.uk/2022/06/motivation-for-measurement.html
Foster, C. (2022, May 26). Are two cars better than one? [Blog post]. https://blog.foster77.co.uk/2022/05/are-two-cars-better-than-one.html
Foster, C. (2022, May 12). Learning times tables efficiently [Blog post]. https://blog.foster77.co.uk/2022/05/learning-times-tables-efficiently.html
Foster, C. (2022, April 28). Tangible contexts for mathematics [Blog post]. https://blog.foster77.co.uk/2022/04/tangible-contexts-for-mathematics.html
Foster, C. (2022, April 14). Intro-ducing and outro-ducing methods [Blog post]. https://blog.foster77.co.uk/2022/04/intro-ducing-and-outro-ducing-methods.html
Professional articles
Foster, C. (2024). Questions pupils ask: Is infinity a number? Mathematics in School, XX(X), XX–XX.
Moeller, K., O’Brien, D., & Foster, C. (2024). Which way should your number line go? Primary Mathematics, XX(X), XX–XX.
Foster, C. (2024). Being flexible about division. Primary Mathematics, XX(X), XX–XX.
Foster, C. (2024). Rationalising all kinds of denominators. Mathematics in School, XX(X), XX–XX.
Foster, C. (2024). Venn diagrams for probability. Teach Secondary, XX(X), XX.
Foster, C. (2024). Lower and upper bounds. Teach Secondary, XX(X), XX.
Foster, C. (2024). Repeating explanations. Teach Secondary, XX(X), XX.
Foster, C. (2024). Embrace your flaws. Teach Secondary, 13(8), 56–57.
Foster, C. (2024). Bar charts versus pie charts. Teach Secondary, 13(8), 10.
Foster, C. (2024). Questions pupils ask: Why aren't square roots additive? Mathematics in School, 53(5), 29–31.
Foster, C. (2024). Terminal digits and prime numbers. Mathematics in School, 53(5), 8–9.
Foster, C. (2024). Having fun being wrong. Mathematics Teaching, 293, 23.
Foster, C. (2024). Know your limits. Teach Secondary, 13(7), 34–35.
Foster, C. (2024). Adding and subtracting numbers in standard form. Teach Secondary, 13(7), 21.
Foster, C. (2024). Speed calculations. Teach Secondary, 13(6), 55.
Foster, C. (2024). When good is better than perfect. Teach Secondary, 13(5), 22–23.
Foster, C. (2024). Mixed numbers when combining fractions. Teach Secondary, 13(5), 55.
Foster, C. (2024). Inequality signs turning round. Teach Secondary, 13(4), 21.
Foster, C. (2024). Go below the surface. Teach Secondary, 13(4), 68–69.
Foster, C., Francome, T., & Shore, C. (2024). Trigonometry without SOHCAHTOA. Mathematics in School, 53(3), 8–11.
Foster, C. (2024). Expanding pairs of brackets. Teach Secondary, 13(3), 21.
Foster, C. (2024). Failing to see both sides. Mathematics Teaching, 290, 10–11.
Foster, C. (2024). The power of framing. Teach Secondary, 13(2), 52–53.
Foster, C. (2024). Trigonometry in right-angled triangles. Teach Secondary, 13(2), 21.
Foster, C. (2024). Minimalist approaches to teaching trigonometry. Mathematics in School, 53(2), 20–24.
Foster, C. (2024). In favour of the Euclidean Algorithm. Mathematics in School, 53(1), 24–26.
Foster, C. (2024). More than a feeling. Teach Secondary, 13(1), 70–71.
Foster, C. (2024). The quadratic formula. Teach Secondary, 13(1), 21. (Resource sheet pdf)
Foster, C. (2023). Improving educational design by comparing alternatives. Mathematics Teaching, 289, 14–18.
Foster, C. (2023). Unconvincing proofs: The sum of a geometric sequence. Scottish Mathematical Council Journal, 53, 62–64.
Foster, C. (2023). Perpendicular gradients. Teach Secondary, 12(8), 11.
Shore, C., Francome, T., & Foster, C. (2023). The sheer delight of shearing. Mathematics in School, 52(4), 32–34.
Foster, C. (2023). Subtractive solutions. Teach Secondary, 12(7), 46–47.
Foster, C. (2023). Finding the Nth term. Teach Secondary, 12(7), 11.
Foster, C. (2023). Schools of thought. Teach Secondary, 12(6), 42–43.
Foster, C. (2023). Recurring decimals. Teach Secondary, 12(6), 13.
Foster, C. (2023). Less is more: Improving by removing. Mathematics Teaching, 287, 7–14.
Foster, C. (2023). Emotional preparation. Teach Secondary, 12(4), 44–45.
Foster, C. (2023). Perimeters of sectors. Teach Secondary, 12(4), 13.
Foster, C. (2023). Questions pupils ask: Why do we divide by $n – 1$? Mathematics in School, 52(3), 20–22.
Foster, C. (2023). Simultaneous equations. Teach Secondary, 12(3), 13.
Foster, C. (2023). Easy when you know how. Teach Secondary, 12(3), 38–39.
Foster, C. (2023). Abolish degrees! Mathematics in School, 52(2), 21–23.
Foster, C. (2023). Equilateral triangles within a regular hexagon. Symmetry Plus, 80, 4.
Foster, C. (2023). Area and volume scale factors. Teach Secondary, 12(2), 13.
Foster, C. (2022). Writing articles for professional publications. MA News - The Mathematical Association Newsletter, 180, 1–6.
Foster, C. (2023). Is there any place for rote learning in mathematics? Mathematics Teaching, 285, 20–22.
Foster, C. (2023). Learning isn't linear. Teach Secondary, 12(1), 50–51.
Foster, C. (2023). Significant figures. Teach Secondary, 12(1), 13.
Foster, C. (2022). Unconvincing proofs: The harmonic series. Scottish Mathematical Council Journal, 52, 76–78.
Foster, C. (2022). Converting recurring decimals to fractions. Scottish Mathematical Council Journal, 52, 68–70.
Foster, C. (2022). Compass constructions are not methods. Scottish Mathematical Council Journal, 52, 54–58.
Foster, C. (2022). Factor puzzles. Symmetry Plus, 79, 4–5.
Foster, C. (2022). Leading professional development sessions. MA News - The Mathematical Association Newsletter, 179, 1–4.
Foster, C. (2022). Originality is overrated. Teach Secondary, 11(8), 30–31.
Foster, C. (2022). Completing the square. Teach Secondary, 11(8), 13. (Resource sheet pdf)
Foster, C. (2022). Making sense of proof by contradiction. Mathematics in School, 51(5), 32–35. (Reprinted from Scottish Mathematical Council Journal: Original article published 2021)
Foster, C. (2022). The floor and ceiling functions. Mathematics in School, 51(5), 30–31.
Foster, C. (2022). Thinking hard about easy content: Odd and even functions. Mathematics in School, 51(5), 28–29.
Foster, C., Francome, T., Hewitt, D., & Shore, C. (2022). What is a fraction? Mathematics in School, 51(5), 25–27.
Foster, C. (2022). Are words sometimes better than formulae? Mathematics in School, 51(5), 12–14.
Foster, C. (2022). Connecting things up coherently. Mathematics in School, 51(5), 8–11.
Foster, C. (2022). The directionality of the equals sign. Mathematics in School, 51(5), 6–7.
Foster, C. (2022). Starting with completing the square. Mathematics in School, 51(5), 2–5.
Foster, C. (2022). Is it wrong to want to be liked? Teach Secondary, 11(7), 48–49.
Foster, C. (2022). Adding surds. Teach Secondary, 11(7), 13.
Foster, C., & Francome, T. (2022). Diagrams not drawn accurately. Mathematics in School, 51(4), 20–22.
Foster, C. (2022). Crossing out. Mathematics in School, 51(4), 6–7.
Foster, C. (2022). Home truths. Teach Secondary, 11(6), 32–33.
Foster, C. (2022). A clear account of events. Teach Secondary, 11(6), 13. (Resource sheet pdf)
Foster, C. (2022). A journey from pupil to researcher. MA News - The Mathematical Association Newsletter, 178, 1–4.
Foster, C. (2022). The trouble with groupwork. Teach Secondary, 11(5), 70–71.
Foster, C. (2022). Dividing fractions. Teach Secondary, 11(5), 13.
Foster, C. (2022). The usual suspects? Teach Secondary, 11(4), 62–63.
Foster, C. (2022). Pythagoras's Theorem. Teach Secondary, 11(4), 13. (Resource sheet pdf)
Francome, T., & Foster, C. (2022). Plenary - or just ponder? Mathematics Teaching, 281, 19–21.
Foster, C. (2022). Choosing the best proofs. Mathematics in School, 51(3), 2–7.
Foster, C. (2022). Must feedback always be constructive? Teach Secondary, 11(3), 40–41.
Foster, C. (2022). Factors and multiples. Teach Secondary, 11(3), 13.
Foster, C. (2022). Meet the next MA President - Colin Foster. MA News - The Mathematical Association Newsletter, 177, 6.
Foster, C. (2022). Exterior angles. Teach Secondary, 11(2), 13. (Resource sheet pdf)
Foster, C. (2022). Methods that are just mental clutter. Mathematics in School, 51(2), 20–22.
Foster, C. (2022). Getting multiplication the right way round. Mathematics in School, 51(2), 16–17.
Foster, C. (2022). Listening is slow, reading is fast. Teach Secondary, 11(1), 72–73.
Foster, C. (2022). What is an angle? Teach Secondary, 11(1), 13.
Foster, C. (2022). Giving everything a twist. Mathematics in School, 51(1), 24–25.
Foster, C. (2021). Making sense of proof by contradiction. Scottish Mathematical Council Journal, 51, 74–77.
Foster, C. (2021). Identity crisis. Scottish Mathematical Council Journal, 51, 36–37.
Foster, C. (2021). Multiplying makes things bigger. Teach Secondary, 10(8), 13.
Foster, C. (2021). Assuming the worst is often for the best. Teach Secondary, 10(7), 23.
Foster, C. (2021). Symmetry. Teach Secondary, 10(7), 13.
Foster, C. (2021). Area and perimeter. Teach Secondary, 10(6), 13.
Foster, C. (2021). First things first. Teach Secondary, 10(6), 82–83. https://www.teachwire.net/news/your-early-career-teachers-shouldnt-be-planning-lessons
Foster, C. (2021). Questions pupils ask: What are 'like terms'? Mathematics in School, 50(4), 20–21.
Foster, C. (2021). Problem solving and prior knowledge. Mathematics in School, 50(4), 6–8.
Foster, C. (2021). "But I'm no good...". Teach Secondary, 10(5), 58–59.
Foster, C. (2021). Understanding indices. Teach Secondary, 10(5), 11.
Foster, C. (2021). Adding fractions. Teach Secondary, 10(4), 11.
Foster, C. (2021). Trapezium artist: Some thoughts on the formula for the area of a trapezium. Mathematics in School, 50(3), 4–5. (Reprinted: Original article published 2004)
Foster, C. (2021). Quotative and partitive models of division. Mathematics in School, 50(3), 24–25.
Foster, C. (2021). What's in a name? Teach Secondary, 10(3), 11.
Foster, C. (2021). Percentage change. Teach Secondary, 10(2), 11.
Foster, C. (2021). On hating formula triangles. Mathematics in School, 50(1), 31–32.
Foster, C. (2021). In a spin. Teach Secondary, 10(1), 11.
Foster, C. (2020). Half of the sum of the others. Scottish Mathematical Council Journal, 50, 47–48.
Foster, C. (2020). Tailoring the examples to the method. Scottish Mathematical Council Journal, 50, 34–35.
Foster, C. (2020). Number snakes. Teach Secondary, 9(8), 70–71.
Foster, C. (2020). Questions pupils ask: Differentiating inverse trigonometric functions. Mathematics in School, 49(5), 10–12.
Foster, C. (2020). Combining square numbers. Teach Secondary, 9(7), 94–95.
Foster, C. (2020). A slice of the pie. Teach Secondary, 9(6), 102–103.
Foster, C., & Ollerton, M. (2020). Mathematical white lies. Mathematics Teaching, 272, 24–25.
Foster, C. (2020). Revisiting 'Four 4s'. Mathematics in School, 49(3), 22–23.
Foster, C. (2020). Trusting in patterns. Mathematics in School, 49(3), 17–19.
Foster, C. (2020). Counting out. Teach Secondary, 9(3), 70–71. (Spreadsheet resource xlsx)
Foster, C. (2020). Twice as hot? Mathematics in School, 49(2), 28–29.
Foster, C., & Baldry, F. (2020). Blink, and it's gone! Mathematics Teaching, 270, 12–13.
Foster, C. (2020). The tethered goat. Teach Secondary, 9(2), 90–91.
Foster, C. (2020). Stop planning lessons! Teach Secondary, 9(1), 80–81.
Foster, C. (2020). Statistical puzzler. Teach Secondary, 9(1), 84–85.
Foster, C. (2019). Alternative vouchers. Teach Secondary, 8(8), 90–91. (Resource sheet pdf)
Seino, T., & Foster, C. (2019). Why the details matter: Learning from Japanese Kyouzai kenkyuu. Mathematics in School, 48(5), 2–8.
Foster, C. (2019). What's your style, sir? Teach Secondary, 8(7), 22–23.
Foster, C. (2019). Sine language. Teach Secondary, 8(7), 92–93.
Foster, C. (2019). Questions pupils ask: What counts as a random number? Mathematics in School, 48(4), 30–31.
Foster, C. (2019). Spider on a cuboid. Teach Secondary, 8(6), 116–117.
Foster, C. (2019). Doing it with understanding. Mathematics Teaching, 267, 8–10.
Foster, C. (2019). Spotting sequences. Teach Secondary, 8(5), 94–95.
Foster, C. (2019). Trapezia acts. Teach Secondary, 8(4), 82–83.
Foster, C. (2019). Armchair responses. Mathematics in School, 48(3), 26–27.
Foster, C. (2019). Box plots. Teach Secondary, 8(3), 102–103. (Resource sheet pdf) (Spreadsheet resource xlsx)
Foster, C. (2019). The fundamental problem with teaching problem solving. Mathematics Teaching, 265, 8–10.
Foster, C. (2019). Missing the point. Teach Secondary, 8(2), 86–87. (Resource sheet pdf)
Foster, C. (2019). Questions pupils ask: Why can’t it be distance plus time? Mathematics in School, 48(1), 15–17.
Foster, C. (2019). Knowing the unknowns. Teach Secondary, 8(1), 86–87.
Foster, C. (2018). Almost zero. Teach Secondary, 7(8), 84–85.
Foster, C. (2018). The converse of Pythagoras' Theorem. Mathematics in School, 47(5), 40–42.
Hodgen, J., & Foster, C. (2018). What’s so hard about algebra? Mathematics in School, 47(5), 6–7.
Foster, C. (2018). Robot rendezvous. Teach Secondary, 7(7), 86–87.
Foster, C. (2018). Stop the clock! Symmetry Plus, 67, 18. (For answers, click here.)
Foster, C. (2018). Take your seat. Symmetry Plus, 67, 6.
Foster, C. (2018). Two spinners. Teach Secondary, 7(6), 114–115.
Foster, C. (2018). Questions pupils ask: What is the formula for factorial? Mathematics in School, 47(4), 40–41.
Hodgen, J., & Foster, C. (2018). Calculators - friend or foe? Mathematics Teaching, 262, 18.
Foster, C. (2018). Beat the calculator. Teach Secondary, 7(5), 86–87.
Foster, C. (2018). Questions pupils ask: Is calculus exact? Mathematics in School, 47(3), 36–38.
Foster, C. (2018). Boxing clever. Teach Secondary, 7(4), 84–85.
Foster, C. (2018). [Review of the book Practising Mathematics, by T. Francome & D. Hewitt]. Mathematics Teaching, 261, 48.
Foster, C. (2018). Surviving in the desert. Teach Secondary, 7(3), 88–89. (Resource sheet pdf)
Foster, C. (2018). [Review of the book Mathematics Rebooted, by L. Alcock]. Mathematics in School, 47(2), 57–58.
Foster, C. (2018). Proportionality with Malcolm. Mathematics in School, 47(2), 34–35.
Foster, C. (2018). Editorial: Special issue. Mathematics in School, 47(2), 1.
Foster, C., Hodgen, J., & Küchemann, D. (2018). Defining a rhombus. Mathematics Teaching, 260, 31.
Foster, C., & Inglis, M. (2018). How do you describe mathematics tasks? Mathematics Teaching, 260, 18–20.
Foster, C. (2018). Five triangles. Teach Secondary, 7(2), 30–31. (Resource sheet pdf)
Foster, C. (2018). Questions pupils ask: Is i irrational? Mathematics in School, 47(1), 31–33.
Foster, C. (2017). Trigonometry without tears. Teach Secondary, 7(1), 30–31. (Resource sheet pdf)
Foster, C. (2017). Get your bearings. Teach Secondary, 6(8), 32–33. (Resource sheet pdf and solution sheet pdf)
Foster, C. (2017). The guessing game. Teach Secondary, 6(8), 85.
Foster, C. (2017). Questions pupils ask: What is the net for a parallelepiped? Mathematics in School, 46(5), 38–39.
Foster, C., & Martin, D. (2017). Playing with dice. Mathematics in School, 46(5), 26–27.
Foster, C. (2017). Just four numbers. Teach Secondary, 6(7), 36–37.
Foster, C. (2017). Buying coffee. Symmetry Plus, 64, 19.
Foster, C. (2017). Questions pupils ask: Can I just move the decimal point? Mathematics in School, 46(4), 39.
Foster, C. (2017). Always up to? Mathematics in School, 46(4), 30–31.
Foster, C. (2017). A fitting challenge. Teach Secondary, 6(6), 48–49. (Full lesson plan)
Foster, C. (2017). Making quadratics. Teach Secondary, 6(5), 31. (Full lesson plan [pdf] and resource sheet pdf)
Foster, C. (2017). Mathematical etudes. NRICH article available at: https://nrich.maths.org/13206
Foster, C. (2017). Pink paint. Teach Secondary, 6(4), 32. (Full lesson plan [pdf])
Foster, C. (2017). Reaching the 100th square. Mathematics in School, 46(3), 32–34.
Foster, C. (2017). Counting zeroes. Symmetry Plus, 63, 18.
Foster, C. (2017). Hit ten! Teach Secondary, 6(3), 37. (Full lesson plan [pdf] and resource sheet pdf)
Foster, C. (2017). Newspaper pages. Teach Secondary, 6(2), 36–38.
Foster, C. (2017). Inferring sample size. Mathematics in School, 46(2), 32–33.
Foster, C. (2017). Surprise, surprise! Teach Secondary, 6(1), 42–44.
Foster, C. (2017). Carrying your provisions. Mathematics in School, 46(1), 30.
Foster, C. (2016). Mind your head! Teach Secondary, 5(8), 30–32.
Foster, C. (2016). Family negotiations. Mathematics in School, 45(5), 10–11.
Foster, C. (2016). Sports centre. Teach Secondary, 5(7), 29–31. (Resource sheets: bar charts pdf; main task sheets: pdf)
Foster, C. (2016). Clock watching. Symmetry Plus, 61, 7.
Foster, C. (2016). Rolls of the dice. Teach Secondary, 5(6), 43–45. (Spreadsheet resource xlsx)
Foster, C. (2016). Making products. Teach Secondary, 5(5), 31–33.
Foster, C. (2016). Abdul and Bella. Symmetry Plus, 60, 4.
Foster, C. (2016). Hopping along. Teach Secondary, 5(4), 31–33. (Resource sheet pdf)
Foster, C. (2016). Questions pupils ask: Why isn’t 1 a prime number? Mathematics in School, 45(3), 12–13.
Foster, C. (2016). Confidence and ‘negative’ marking. Mathematics Teaching, 251, 11–13.
Foster, C. (2016). All square. Teach Secondary, 5(3), 33–35.
Foster, C. (2016). Thirty factors. Mathematics in School, 45(2),25–27.
Foster, C. (2016). The simple life. Teach Secondary, 5(2), 31–33. (Resource sheet pdf; NRICH version: https://nrich.maths.org/13207)
Foster, C. (2016). Sums of pairs. Symmetry Plus, 59, 14–16.
Foster, C. (2016). Painting a wall. Teach Secondary, 5(1), 29–31. (Resource sheet pdf, docx)
Foster, C. (2015). Plus-minus graphs. Scottish Mathematical Council Journal, 44, 52–53.
Foster, C. (2015). Where does the third come from? Scottish Mathematical Council Journal, 44, 59–62.
Foster, C. (2015). Clock watching. Teach Secondary, 4(8), 31–32. (Spreadsheet resource xls)
Foster, C. (2015). Questions pupils ask: Where does the third come from? Mathematics in School, 44(5), 13–16. (Resource sheet pdf)
Foster, C. (2015). Symmetry combinations. Teach Secondary, 4(7), 43–45. (Resource sheet pdf)
Foster, C. (2015). Observing other subjects. Mathematics Teaching, 248, 21.
Foster, C. (2015). The meaning of the mean. Teach Secondary, 4(6), 37–39. (Resource sheet pdf)
Foster, C., Ollerton, M., & Watson, A. (2015). Knowing and not knowing how a task for use in a mathematics classroom might develop. Mathematics Teaching, 247, 5–8.
Foster, C. (2015). The shortest way. Teach Secondary, 4(5), 33–35. (Resource sheet pdf)
Foster, C. (2015). Shaping up. Teach Secondary, 4(4), 33–35. (Resource sheet pdf)
Foster, C. (2015). Crossing lines. Teach Secondary, 4(3), 31–33.
Foster, C. (2015). Prime suspects. Teach Secondary, 4(2), 41–43. (Resource sheet pdf and completed sheet pdf)
Foster, C. (2015). Repeated rotations. Teach Secondary, 4(1), 35–37. (Resource sheet pdf and Geogebra files ggb, ggb)
Foster, C. (2015). Questions pupils ask: Doubly positive. Mathematics in School, 44(2), 34–35.
Foster, C. (2015). Fitting shapes inside shapes: Closed but provocative questions. Mathematics in School, 44(2), 12–14.
Foster, C. (2014). The power of puzzles. Teach Secondary, 3(8), 34–35. (Resource sheet pdf)
Foster, C. (2014). What’s the deal? Teach Secondary, 3(7), 34–35. (Resource sheet pdf)
Foster, C. (2014). Teaching to the test – a parable. Mathematics Teaching, 242, 33.
Foster, C. (2014). Sweet solutions. Teach Secondary, 3(6), 46–47.
Griffiths, J., & Foster, C. (2014). “Bath mat” versus “bar mat”. Mathematics Teaching, 241, 18–21.
Foster, C. (2014). Sum fractions. Teach Secondary, 3(5), 48–49. (NRICH version: https://nrich.maths.org/13205)
Foster, C. (2014). Angle chasing. Teach Secondary, 3(4), 40–41. (Resource sheets pdf)
Foster, C. (2014). Mathematical fluency without drill and practice. Mathematics Teaching, 240, 5–7.
Foster, C. (2014). Being inclusive. Mathematics in School, 43(3), 12–13.
Foster, C. (2014). Going with the flow. Teach Secondary, 3(3), 43–45. (Resource sheet pdf)
Foster, C. (2014). Questions pupils ask: Why isn’t pi a whole number? Mathematics in School, 43(2), 37–38.
Foster, C. (2014). Simultaneous inequalities. Mathematics in School, 43(2), 34–35.
Foster, C. (2014). Arithmagons. Teach Secondary, 3(2), 57–59.
Foster, C. (2014). Being mean about the mean. Mathematics in School, 43(1), 32–33.
Foster, C. (2013). Staying on the page. Teach Secondary, 3(1), 57–59. (Resource sheet pdf)
Foster, C. (2013). Cancelling out. Teach Secondary, 2(8), 47–49. (Resource sheet pdf, doc)
Foster, C. (2013). Coining queries. Teach Secondary, 2(7), 25–27.
Foster, C. (2013). Plenty of lolly. Teach Secondary, 2(6), 49–51.
Foster, C. (2013). Growing shapes. Teach Secondary, 2(5), 30–32.
Foster, C. (2013). Rich pickings. Teach Secondary, 2(4), 32–34.
Foster, C. (2013). Non-linear inequalities. Mathematics in School, 42(3), 31–33.
Foster, C. (2013). Precise perimeters. Teach Secondary, 2(3), 30–32.
Foster, C. (2013). A 3-sided story. Teach Secondary, 2(2), 32–34.
Foster, C. (2013). Unequal reasoning. Mathematics in School, 42(1), 19–21.
Foster, C. (2013). Treat creationism as a misconception. Science Education Review, 11(3), 54–55.
Back, J., Foster, C., Tomalin, J., Mason, J., Swan, M., & Watson, A. (2013). Tasks and their place in mathematics teaching and learning – part 2. Mathematics Teaching, 232, 6–8.
Foster, C. (2013). Connected quadratics. Teach Secondary, 2(1), 46–48.
Foster, C. (2012). Connected expressions. Mathematics in School, 41(5), 32–33.
Foster, C. (2012). Straight to the point. Learning and Teaching Mathematics, 13, 6–10.
Foster, C. (2012). Shape up. Teach Secondary, 1(5), 24–26.
Back, J., Foster, C., Tomalin, J., Mason, J., Swan, M., & Watson, A. (2012). Tasks and their place in mathematics teaching and learning – part 1. Mathematics Teaching, 231, 33–37.
Foster, C. (2012). The what factor? Teach Secondary, 1(4), 56–58.
Foster, C. (2012). Triangular roots. Mathematical Spectrum, 45(1), 8–9.
Foster, C. (2012). What’s the point? Teach Secondary, 1(3), 39–41.
Foster, C. (2012). Questions pupils ask: a straight question. Mathematics in School, 41(4), 31–34.
Foster, C. (2012). Parking problem. Mathematics Teaching, 229, 47–48.
Foster, C. (2012). Changing the subject. Teach Secondary, 1(2), 33–35.
Foster, C. (2012). HCF and LCM – Beyond procedures. Mathematics in School, 41(3), 30–32.
Foster, C. (2012). Trigonometry without right angles. Mathematical Spectrum, 44(3), 98–101.
Foster, C. (2012). Odd and even fractions. Mathematical Spectrum, 44(2), 69–72.
Foster, C. (2012). A day at the c-side: Introducing Pythagoras’ theorem. Teach Secondary, 1(1), 30–33.
Foster, C. (2012). Plus–minus graphs. Mathematics in School, 41(2), 32–33.
Foster, C. (2011). Sandbox: Rooting for you. Math Horizons, 19(2), 30. https://doi.org/10.4169/mathhorizons.19.2.30
Foster, C. (2011). A picture is worth a thousand exercises. Mathematics Teaching, 224, 10–11. (Extra material)
Foster, C. (2011). Straight dice. Symmetry Plus, 45(2), 9–10.
Foster, C. (2011). Small is beautiful after all. Mathematics Teaching, 222, 38–39.
Foster, C. (2011). Marking time. Mathematics Teaching, 222, 3–6.
Foster, C. (2011). Clock problem: 469. The New York State Mathematics Teachers’ Journal, 61(2), 92.
Foster, C. (2011). Table settings. Symmetry Plus, 44(1), 6–7.
Foster, C. (2011). Questions pupils ask: odd questions pupils ask. Mathematics in School, 40(1), 34–35.
Foster, C. (2010). A formula for a square root. Mathematics Teaching, 220, 6.
Foster, C. (2009, March 12). Consistency – it’s a foolish obsession. SecEd, p. 6.
Foster, C. (2009). Reflections on editing MT 2005–2008. Mathematics Teaching, 212, 3.
Foster, C. (2008). Connected codes. Journal of Recreational Mathematics, 37(2), 119–121.
Foster, C. (2008, November 28). String along. Times Educational Supplement – Magazine, p. 30.
Foster, C. (2008, November 21). Dead good. Times Educational Supplement – Magazine, p. 30.
Foster, C. (2008, November 7). Add some fun. Times Educational Supplement – Magazine, p. 31.
Foster, C. (2008). Questions pupils ask: how many detentions will I get? Mathematics in School, 37(5), 26–27.
Foster, C. (2008, October 31). Anyone for consistency? Times Educational Supplement – Magazine, p. 62.
Foster, C. (2008, October 24). Who is missing? Times Educational Supplement – Magazine, p. 36.
Foster, C. (2008, September 26). Exam boards should stick to examining. Times Educational Supplement, p. 45.
Foster, C. (2008, September 5). Ready to shake on it. Times Educational Supplement, p. 34.
Foster, C. (2008, August 8). Element of surprise keeps learning alive. Times Educational Supplement, p. 21.
Foster, C. (2008, July 18). Touching story. Times Educational Supplement – Magazine, p. 30.
Foster, C. (2008). Making twelve. Journal of Recreational Mathematics, 37(1), 74.
Foster, C. (2008, June 6). Name your price. Times Educational Supplement – Magazine, p. 34.
Foster, C. (2008, May 23). If the answer is instant, the question is pointless. Times Educational Supplement, p. 33.
Foster, C. (2008). Higher priorities. Mathematics in School, 37(3), 17.
Foster, C. (2008). Leaping around. Mathematics Teaching, 208, 48.
Foster, C. (2008, March 13). All my own work? SecEd, 7. https://doi.org/10.12968/sece.2008.3.1120
Foster, C. (2008, March 7). You’re having a graph. Times Educational Supplement – Magazine, pp. 58–59.
Foster, C. (2008, January 25). In the area. Times Educational Supplement – Magazine, p. 52.
Foster, C. (2008, January 18). Beware the rise of helicopter teachers. Times Educational Supplement, p. 29.
Foster, C. (2007). Twenty–one forever! Journal of Recreational Mathematics, 36(3), 194–195.
Foster, C. (2007, December 14). Counting cubes. Times Educational Supplement – Magazine, p. 45.
Foster, C. (2007, November 8). Getting your bearings. SecEd, 12. https://doi.org/10.12968/sece.2007.5.902
Foster, C. (2007). Questions pupils ask: impossibility. Mathematics in School, 36(5), 13.
Foster, C. (2007, November 16). Solving the X factor. Times Educational Supplement – Magazine, pp. 48–49.
Foster, C. (2007, October 12). Stage fright does not equal lack of involvement. Times Educational Supplement, p. 29.
Foster, C. (2007, September 28). Pencils make a point. Times Educational Supplement – Magazine, pp. 48–49.
Foster, C. (2007, September 21). Start making money. Times Educational Supplement – Magazine, p. 52.
Foster, C. (2007). The Warwick dials. Symmetry Plus, 34(3), 4.
Foster, C., & Williams, H. (2007). Mathematics is a spectator sport. Mathematics Teaching, 204, 40–41.
Foster, C. (2007). Line multiplication. Mathematics Teaching, 203, 29.
Foster, C. (2007, May 24). Make maths sparkle. SecEd, 12. https://doi.org/10.12968/sece.2007.5.902
Foster, C. (2007, May 18). Pushing the limits. Times Educational Supplement – Magazine, p. 50.
Foster, C. (2007). A degree of confusion. Symmetry Plus, 33(2), 7.
Foster, C. (2007). Triangles and parabolas – The hard part! Symmetry Plus, 33(2), 3.
Foster, C. (2007, May 11). Economies of scale. Times Educational Supplement – Magazine, p. 54.
Foster, C. (2007, May 11). There’s a positive side to negative marking. Times Educational Supplement, p. 27.
Foster, C. (2007). Mathematical behaviour. Mathematics Teaching, 202, 12–13.
Foster, C. (2007). As easy as 1, 2, 3, ...? Mathematics Today, 43(2), 76.
Foster, C. (2007, March 2). Petrol–pump learning won't fuel thinking skills. Times Educational Supplement, p. 27.
Foster, C. (2007). Right–angled triangles and parabolas. Symmetry Plus, 32(1), 10–11.
Foster, C. (2007). Stop interrupting! Equals, 13(1), 10–11.
Foster, C. (2007). Questions pupils ask: introducing ... Maths–man! Mathematics in School, 36(1), 15.
Foster, C. (2007, January 5). Model lessons put spontaneity in a straitjacket. Times Educational Supplement, p. 27.
Foster, C. (2006, November 24). To infinity and beyond. Times Educational Supplement – Magazine, p. 54.
Foster, C. (2006). A different pictorial way of looking at simultaneous equations. Mathematics in School, 35(5), 20–21.
Foster, C. (2006, November 17). Targets miss the point. Times Educational Supplement, p. 27.
Foster, C. (2006). Emily’s discovery. Mathematics Teaching, 199, 30–31.
Foster, C. (2006). Anamorphic art. Mathematics Teaching, 199, 24–25.
Foster, C. (2006). Questions pupils ask: asking questions. Mathematics in School, 35(4), 24.
Foster, C. (2006, September 14). Pointless compasses? SecEd, 13. https://doi.org/10.12968/sece.2006.9.705
Foster, C. (2006). ’Wordsworth’ puzzle. Mathematics Teaching, 196, 48.
Foster, C. (2006). Tessellations in Word. Mathematics Teaching, 196, 24–25.
Foster, C. (2006). ’2006’ puzzle. Mathematics Teaching, 195, 48.
Foster, C. (2006). My accidental parabola. Mathematics Teaching, 195, 33.
Foster, C. (2006, January 20). How do we get them going? Times Educational Supplement: Friday.
Foster, C. (2006). Preparing the lesson or preparing the teacher? Report: Association of Teachers and Lecturers, January, 11.
Foster, C. (2006). Webwatch. Mathematics Teaching, 194, 47.
Foster, C. (2006). Getting confused. Mathematics Teaching, 194, 18.
Foster, C. (2005). Reflections. Mathematics Teaching, 192, 2.
Foster, C. (2005). What we did in our Easter holiday! Mathematics Today, 41(3), 71–72.
Foster, C., Galligan, L., Mackrell, K., Mason, J., Melville, A., Piggott, J., & Watson, A. (2005). Freedom and constraint. Mathematics Teaching, 191, 37–39.
Foster, C. (2005). Another look at revision. Mathematics Teaching, 191, 6–7.
Foster, C. (2005). Slippery slopes. Mathematics in School, 34(3), 33–34.
Foster, C. (2005). Golden opportunities for creativity. Mathematics Teaching, 190, 26–27.
Foster, C. (2004). Differences over differences methods: Pros and cons of different ways of finding the nth term of a sequence of numbers. Mathematics in School, 33(5), 24–25.
Foster, C. (2004). Trapezium artist: Some thoughts on the formula for the area of a trapezium. Mathematics in School, 33(5), 6–7.
Foster, C. (2004). Y8 area lesson. Mathematics Teaching, 188, 31.
Foster, C. (2004). The nth term. Mathematics Teaching, 188, 30–31.
Foster, C. (2003, March 14). Mean difference. Times Educational Supplement: Teacher, p. 5.
With thanks to the Association of Teachers of Mathematics and the Mathematical Association for permission to post the pdf versions of my articles above.
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