**Academic
articles (peer-reviewed)**

Hodgen, J., Foster, C., & Brown, M. (2021). Low attainment in mathematics: An analysis of 60 years of policy discourse in England. *Curriculum Journal*. Advance online publication. https://doi.org/10.1002/curj.128

Foster, C., Woodhead, S., Barton, C., & Clark-Wilson, A. (2021). School students’ confidence when answering diagnostic questions online. *Educational
Studies in Mathematics.* Advance online publication. https://doi.org/10.1007/s10649-021-10084-7

Foster, C. (2021). Implementing confidence assessment in low-stakes, formative mathematics assessments. *International Journal of Science and Mathematics Education.* Advance online publication. https://doi.org/10.1007/s10763-021-10207-9

Baldry, F., Mann, J., Horsman, R., Koiwa, D., & Foster, C. (2021). 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.* Advance online publication. https://doi.org/10.1007/s10857-021-09511-6

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.

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.
(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).

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.
(2013). Resisting
reductionism in mathematics pedagogy. *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.
(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.
(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.

**Book
chapters**

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). Bingley, UK: 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). Cham, Switzerland: 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). Cham, Switzerland: 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). Derby, UK: Association of Teachers of Mathematics.

**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., 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**

Foster, C. (2022). Mathematics curriculum resourcing in England: What might the future hold? *Bulletin of the Textbook Research Center*, June. Tokyo, Japan.

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*. Nottingham: 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*. London: 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*. London: 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*. London: 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*. London: 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*. London: 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*. London: Education Endowment Foundation. https://educationendowmentfoundation.org.uk/education-evidence/evidence-reviews/mathematics-in-key-stages-2-and-3

**Media and engagement**

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/

**Professional
articles (peer-reviewed)**

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). Expression
polygons. *Mathematics Teacher, 109*(1), 62–65. https://doi.org/10.5951/mathteacher.109.1.0062 (Resource sheet doc)

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). Problems
with generalising: Pythagoras in *n* dimensions. *Australian Senior
Mathematics Journal, 27*(1), 8–11.

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). 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

**Other
articles**

Francome, T. & Foster, C. (2022). Plenary - or just ponder? *Mathematics Teaching*,

Foster, C. (2022). Choosing the best proofs. *Mathematics in School*,

Foster, C. & Francome, T. (2022). Diagrams not accurately drawn. *Mathematics in School*,

Foster, C. (2022). Methods that are just mental clutter. *Mathematics in School*,

Foster, C. (2022). The directionality of the equals sign. *Mathematics in School*,

Foster, C. (2022). Crossing out. *Mathematics in School*,

Foster, C. (2022). Getting multiplication the right way round. *Mathematics in School*,

Foster, C. (2022). Should feedback always be constructive? *Teach Secondary*, *X*(X), XX.

Foster, C. (2022). Listening is slow, reading is fast. *Teach Secondary*, *X*(X), XX.

Foster, C. (2022). Exterior angles. *Teach Secondary*, *11*(2), XX.

Foster, C. (2022). What is an angle? *Teach Secondary*, *11*(1), XX.

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*, XX–XX.

Foster, C. (2021). Identity crisis. *Scottish Mathematical Council Journal, 51*, XX–XX.

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**

For details of my books, click here.

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© Colin Foster 2021