**Articles (peer-reviewed)**

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*. Advance online publication. 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), XX–XX.

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

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*. Advance online publication. 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. (2024). $\int_0^\pi \sin^2 \theta \, d\theta = \frac{\pi}{2}$ from a shear-like transformation of a circle. *Mathematical Gazette*. Advance online publication. https://doi.org/XXX

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

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. (2022). A collaboratively-derived research agenda for e-assessment in undergraduate mathematics. *International Journal of Research in Undergraduate Mathematics Education*. Advance online publication. https://doi.org/10.1007/s40753-022-00189-6

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)* (pp. XX-XX). 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 8 ^{th} British Congress of
Mathematics Education, *Vol. 34, No. 2

Wake, G., Foster, C., & Swan, M.
(2014). Teacher
knowledge for modelling and problem solving. In S. Pope
(Ed.), *Proceedings of the 8 ^{th} British Congress of Mathematics
Education, *Vol. 34, No. 2

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, 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). Terminal digits and prime numbers. *Mathematics in School*, *53*(X), XX–XX.

Foster, C. (2024). Mixed numbers. *Teach Secondary*, *XX*(X), XX.

Foster, C. (2024). Inequality signs turning round. *Teach Secondary*, *XX*(X), XX.

Foster, C. (2024). One step back, two steps forwards. *Teach Secondary*, *XX*(X), XX.

Foster, C., Francome, T., & Shore, C. (2024). Trigonometry without SOHCAHTOA. *Mathematics in School*, *53*(3), XX–XX.

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 *N*th 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 *n*th
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 *n*th 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.*

**Books**

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© Colin Foster 2024