## Position/Status

- Professor of Education
- Professorial Fellow of Hughes Hall

## E-mail Address

kr18@cam.ac.uk

## Phone

+44 (0)1223 767600

## Qualifications

- BA [Hons], MA (Oxford) Mathematics
- PGCertEd (Moray House) Secondary Mathematics Teaching
- DipEd (Edinburgh) Education and Psychology
- PhD (Stirling) Education
- MA (Cambridge)

## Membership of Professional Bodies/Associations

- Academy of Social Sciences (Fellow)
- American Educational Research Association
- British Educational Research Association
- British Society for Research into Learning Mathematics (former Chair)
- European Society for Research in Mathematics Education

## Profile

Kenneth Ruthven taught in schools in Scotland and England before joining the Faculty. His teaching and research focus on curriculum, pedagogy and assessment, especially in mathematics, and particularly in the light of technological change. His research and development projects have been carried out with support from agencies including the Economic and Social Research Council, the Nuffield Foundation, the (former) Qualifications and Curriculum Authority, and the (former) National Council for Educational Technology. Information about recent projects and publications can be found below.

Ken(neth) is former Editor-in-Chief (and a current Advisory Editor) of the international research journal, *Educational Studies in Mathematics*; and recent Chair of the British Society for Research into Learning Mathematics (remaining an Advisory Editor of its journal, *Research in Mathematics Education*). He serves as Chair of Trustees of the (UK) curriculum development charity, the *School Mathematics Project*; and has a longstanding association with the (US) curriculum development project, *Core-Plus Mathematics,* as a member of its Advisory Board.

Within the Faculty (and its predecessor Department), he has served as Deputy Head (1997/2002 and 2004/2007), Dean/Director of Research (2003/2007 and 2011/2014), Coordinator of Graduate Studies (1994/1997), and Coordinator of Initial Teacher Education (1990/1993). He has also acted as Chair of Science, Technology & Mathematics Education (2007/2011) and Chair of the Faculty Board of Education (2006/2007 and 2011).

## Academic Groups/Areas

## Course Involvement

- PGCE Secondary Mathematics Teaching
- MPhil/MEd Educational Research
- MPhil/MEd Mathematics Education
- PhD/EdD

## Research Topics

- Curriculum, pedagogy and assessment; particularly in relation to mathematics.
- Design and improvement of mathematics, informatics and science teaching.
- Development of teacher expertise; particularly in relation to subject teaching and technology use.
- Educational use of new (and old) technologies; particularly in school mathematics.

## Recently completed funded research projects

**Effecting Principled Improvement in STEM Education [ epiSTEMe]**

Project funded by the UK Economic and Social Research Council as part of its Targeted Research Inititative on Science and Mathematics Education, from August 2008 to January 2013. With Christine Howe, Neil Mercer, Keith Taber and Riikka Hofmann, and Stefanie Luthman, Paula Guardia and Fran Riga.

**Innovations in Mathematics Education [InnoMathEd]**

Research-based professional development project funded by the EC Directorate General for Education, from December 2008 to November 2010. Led by Volker Ulm with participating groups from 8 European countries. With Zsolt Lavicza.

**Mathematical Knowledge in Teaching [MKiT]**

Seminar series and subsequent publication supported by the Nuffield Foundation from November 2006 to October 2010. With Tim Rowland and further colleagues from Cambridge and beyond. Final report on seminar series.

Edited collection now available in the Springer Mathematics Education Library.

## Associated researchers

**Doctoral students (current)**

Melise Camargo: *Surveying mathematics teachers' knowledge of formative assessment: a study of teachers in the Federal District of Brazil.*

Claire Kennedy: *How do students learn about distant places? A critical analysis of how students' perceptions of Ghana change over a unit of work.*

Aisling Brown:* A design-based research study into the conceptualisation and support of critical reading in post-16 physics using digital adaptations of scientific articles.*

**Doctoral students (recent)**

Gulay Bozkurt (2016): *Teaching with technology: a multiple-case study of secondary teachers’ practices of GeoGebra use in mathematics teaching. *

Fiona Jackson (2014): *Implementation infidelity or aligned adaptation? Exploring tutors' interpretations and enactments of *Catch Up Numeracy,* a primary mathematics intervention. *

Pamela Black (2013): *School students' everyday and school science understanding of genetics and inheritance, in the context of health and disease. *(ESRC studentship)

Wai Yi Feng (2009): *Developing a framework for understanding mathematics enrichment in the UK.* (ESRC studentship)

Liz Taylor (2009): *The negotiation of distant place: learning about Japan at Key Stage 3.*

Riikka Hofmann (2008): *Ownership in learning: A sociocultural perspective on pupil engagement, collaboration and agency in the classroom*. (Gates scholarship)

## Most recent conference presentations

*Constructing dynamic geometry: The interpretative flexibility of mathematical software in teaching practice. * Invited lecture, quadrennial International Congress on Mathematical Education of the International Commission on Mathematical Instruction (ICME-13), Hamburg, July 2016. Lecture paper.

*Digital computational tools in school mathematics: ecological, epistemological and existential challenges.* Plenary lecture, biennial meeting of the Swedish Society for Research in Mathematics Education (MADIF-10), Karlstad, January 2016. Lecture paper.

## Most recent publications

**Ruthven, K., Mercer, N., Taber, K., Guardia, P., Hofmann, R., Ilie, S., Luthman, S., & Riga, F. **(2016 online). A research-informed dialogic-teaching approach to early secondary-school mathematics and science: the pedagogical design and field trial of the *epiSTEMe* intervention. *Research Papers in Education. *Open access

** Bozkurt, G., & Ruthven, K. **(2016 online). Classroom-based professional expertise: a mathematics teacher’s practice with technology. *Educational Studies in Mathematics.* Open access

**Ruthven, K., & Hofmann, R. **(2016). A case study of epistemic order in mathematics classroom dialogue. *PNA (Pensamiento Numérico y Algebráico)* Special Issue on Language and Mathematics 11(1), 5-33. Open access ** Ruthven, K. **(2016). The re-sourcing movement in mathematics teaching: some European initiatives. In M. Bates & Z. Usiskin (Eds.) *Digital Curricula in School Mathematics * (pp. 75-86). Charlotte NC: Information Age Publishing.

** Ruthven, K. **(2016). The contribution of university training schools to developing research-informed professional knowledge in teaching: ideas from the Cambridge Faculty of Education. In P. Gronn & J. Biddulph (Eds.) *University Challenge: Cambridge’s Primary School for the Nation* (pp. 161-177). Cambridge: Cambridge University Press.

**Arcavi, A., Boero, P., Kilpatrick, J., Radford, L., Dreyfus, T., & Ruthven, K. **(2016). Didactique goes travelling: its actual and potential articulations with other traditions of research on the learning and teaching of mathematics. In B. Hodgson, A. Kuzniak & J.-B. Lagrange (Eds.) *The Didactics of Mathematics: Approaches and Issues * (pp. 15-41). New York: Springer.

** Taber, K. S., Ruthven, K., Mercer, N., Riga, F., Luthman, S., & Hofmann, R. **(2016). Developing teaching with an explicit focus on scientific thinking. *School Science Review*, 97(361), 75-84. Offprint.

## Publications (selected material grouped by topic)

#### Improvement of mathematics and science teaching

**Ruthven, K., Mercer, N., Taber, K., Guardia, P., Hofmann, R., Ilie, S., Luthman, S., & Riga, F. **(2016 online). A research-informed dialogic-teaching approach to early secondary-school mathematics and science: the pedagogical design and field trial of the *epiSTEMe* intervention. *Research Papers in Education. *Open access

** Ruthven, K.** (2015). Numeracy in, across and beyond the school curriculum. In D. Wyse, L. Hayward & J. Pandya (Eds.) *The SAGE Handbook of Curriculum, Pedagogy and Assessment* (pp. 638-654). London: Sage. ** Howe, C., Luthman, S., Ruthven, K., Mercer, N., Hofmann, R., Ilie, S., & Guardia, P. ** (2015). Rational number and proportional reasoning in early secondary school: towards principled improvement in mathematics. *Research in Mathematics Education*, 17(1), 38-56.

** Ruthven, K. **(2014). Characteristics and impact of the Further Mathematics Knowledge Networks: analysis of an English professional development initiative on the teaching of advanced mathematics. *Teaching Mathematics and its Applications,* 33(3), 137-149.

**Ruthven, K. & Hofmann, R.** (2013). Chance by design: devising an introductory probability module for implementation at scale in English early-secondary education. *ZDM – The International Journal on Mathematics Education,* Special Issue on *Classroom-based interventions in mathematics education,* 45(3), 409-423. Preprint

**Ruthven, K. **(2011). Using international study series and meta-analytic research syntheses to scope pedagogical development aimed at improving student attitude and achievement in school mathematics and science. *International Journal of Science and Mathematics Education *9(2), 419-458. Preprint

**Reiss, M. & Ruthven, K. **(Eds.) (2011). Enhancing the participation, engagement and achievement of young people in science and mathematics education. Special Issue of *International Journal of Science and Mathematics Education *9(2).

**Design research**

**Ruthven, K.** (2015). Taking design to task: a critical appreciation. In A. Watson & M. Ohtani (Eds.) *Task Design In Mathematics Education* (pp. 311-32). Heidelberg: Springer.

**Ruthven, K. & Hofmann, R.** (2013). Chance by design: devising an introductory probability module for implementation at scale in English early-secondary education. *ZDM – The International Journal on Mathematics Education,* Special Issue on *Classroom-based interventions in mathematics education,* 45(3), 409-423. Preprint

**Ruthven, K. **(2013). From design-based research to re-sourcing ‘in the wild’: reflections on studies of the co-evolution of mathematics teaching resources and practices. *ZDM – The International Journal on Mathematics Education,* Special Issue on Re-Sourcing Teacher Work and Interaction: New Perspectives on Resource Design, Use and Teacher Collaboration, 45(7), 1071-1079.

**Ruthven, K., Laborde, C., Leach, J., & Tiberghien, A.** (2009). Design tools in didactical research: Instrumenting the epistemological and cognitive aspects of the design of teaching sequences. *Educational Researcher* 38(5), 329-342. Offprint

**Classroom dialogue in mathematics**

**Ruthven, K., Mercer, N., Taber, K., Guardia, P., Hofmann, R., Ilie, S., Luthman, S., & Riga, F. **(2016 online). A research-informed dialogic-teaching approach to early secondary-school mathematics and science: the pedagogical design and field trial of the *epiSTEMe* intervention. *Research Papers in Education. *Open access

**Ruthven, K., & Hofmann, R. **(2016). A case study of epistemic order in mathematics classroom dialogue. *PNA (Pensamiento Numérico y Algebráico)* Special Issue on Language and Mathematics 11(1), 5-33. Open access

**Ruthven, K., Hofmann, R., & Mercer, N.** (2011). A dialogic approach to plenary problem synthesis. In B. Ubuz (Ed.). *Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, *Vol. 4, pp. 81-88. Ankara, Turkey: PME. Offprint

#### Resources in mathematics teaching

** Ruthven, K. **(2016). The re-sourcing movement in mathematics teaching: some European initiatives. In M. Bates & Z. Usiskin (Eds.) *Digital Curricula in School Mathematics * (pp. 75-86). Charlotte NC: Information Age Publishing.

** Ruthven, K. **(2013). From design-based research to re-sourcing ‘in the wild’: reflections on studies of the co-evolution of mathematics teaching resources and practices. *ZDM – The International Journal on Mathematics Education, Special Issue on Re-Sourcing Teacher Work and Interaction: New Perspectives on Resource Design, Use and Teacher Collaboration,* 45(7), 1071-1079.

** Ruthven, K. **(2013). Métamorphose des ressources et des métiers de l'enseignement : un bilan anglais. In *Cultures numériques, éducation aux médias et à l’information * (pp. 92-95). Paris: Centre National de Documentation Pédagogique.Chapter preprint

#### Education and training of mathematics teachers

** Ruthven, K. **(2014). Characteristics and impact of the Further Mathematics Knowledge Networks: analysis of an English professional development initiative on the teaching of advanced mathematics. *Teaching Mathematics and its Applications,* 33(3), 137-149.

**Ruthven, K. ** (2011). Conceptualising mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), *Mathematical Knowledge in Teaching* (pp. 83-96). Springer: New York. Preprint

**Rowland. T. & Ruthven, K. **(Eds.) (2011). *Mathematical Knowledge in Teaching*. Springer: New York.

**Ruthven, K. **(2010). Summing up mathematics teacher education. *Educational Studies in Mathematics* 73(1), 87–97. (Essay review). Preprint

**Ruthven, K.** (2001). Mathematics teaching, teacher education and educational research: Developing 'practical theorising' in initial teacher education. In F.-L. Lin & T. Cooney (Eds.) *Making Sense of Mathematics Teacher Education* (pp. 165-183). Dordrecht: Kluwer.

#### Technology use and integration in secondary-school mathematics teaching

** Bozkurt, G., & Ruthven, K. **(2016 online). Classroom-based professional expertise: a mathematics teacher’s practice with technology. *Educational Studies in Mathematics.* Open access

**Ruthven, K. **(2014). Frameworks for analysing the expertise that underpins successful integration of digital technologies into everyday teaching practice. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.) *The Mathematics Teacher in the Digital Era* (pp. 373-393), New York: Springer. Preprint

**Ruthven, K. **(2012). The didactical tetrahedron as a heuristic for analysing the incorporation of digital technologies into classroom practice in support of investigative approaches to teaching mathematics. *ZDM: The International Journal on Mathematics Education, *Special Issue on *New perspectives on the didactic triangle,* 44(2), 627-640. Preprint

**Ruthven, K. **(2011). Constituting digital tools and materials as classroom resources: The example of dynamic geometry. In G. Gueudet, B. Pepin & L. Trouche (Eds.), *From Text to ‘Lived’ Resources: Mathematics Curriculum Materials and Teacher Development.* New York: Springer. Preprint

**Ruthven, K, & Lavicza, Z. **(2011). Didactical conceptualization of dynamic mathematical approaches: example analysis from the Innomathed program.* International Electronic Journal of Mathematics Education,* 6(2), 89-110. Offprint

**Ruthven, K.** (2009). Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics. *Education & Didactique* 3(1), 131-152. Offprint Preprint

**Ruthven, K., Deaney, R., & Hennessy, S.** (2009). Using graphing software to teach about algebraic forms: A study of technology-supported practice in secondary-school mathematics. *Educational Studies in Mathematics* 71(3), 279-297. Preprint

**Ruthven, K., Hennessy, S., & Deaney, R**. (2008). Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice. *Computers and Education* 51(1), 297-317 Preprint

**Ruthven, K.** (2008). The interpretative flexibility, instrumental evolution and institutional adoption of mathematical software in educational practice: The examples of computer algebra and dynamic geometry. *Journal of Educational Computing Research* 39(4), 379-394. Preprint

**Ruthven, K.** (2008). Mathematical technologies as a vehicle for intuition and experiment: A foundational theme of the International Commission on Mathematical Instruction, and a continuing preoccupation. *International Journal for the History of Mathematics Education* 3(2), 91-102. Preprint

**Guin, D., Ruthven, K., & Trouche, L.** (Eds.) (2005). *The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument* (Springer, New York).

**Ruthven, K.** (2003/2004). *Linking algebraic and geometric reasoning with dynamic geometry software.* Reports to the Qualifications and Curriculum Authority. Phase 1; Phase 2 (with **Oldknow, A., Taylor, R., & others**).

**Ruthven, K.** (2002). Instrumenting mathematical activity: Reflections on key studies of the educational use of computer algebra systems. *International Journal of Computers for Mathematical Learning* 7(3), 275-291. Preprint

**Ruthven, K., & Hennessy, S**. (2002). A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning. *Educational Studies in Mathematics* 49(1), 47-88. JSTOR link. Preprint

#### Technology use and integration in secondary-school science teaching

**Ong, E. T., & Ruthven, K.** (2010). The distinctiveness and effectiveness of science teaching in the Malaysian 'Smart School'. *Research in Science and Technological Education* 28(1), 25-41. Preprint

**Hennessy, S., Deaney, R., Ruthven, K., & Winterbottom, M**. (2007). Pedagogical strategies for using the interactive whiteboard to foster learner participation in school science. *Learning, Media and Technology* 32(3), 283-301. Preprint

**Hennessy, S., Wishart, J., Whitelock, D., Deaney, R., Brawn, R., la Velle, L., McFarlane, A., Ruthven, K. & Winterbottom, M**. (2007). Pedagogical approaches for technology-integrated science teaching. *Computers and Education* 48(1), 137-152. Preprint

**Ong, E.T., & Ruthven, K.** (2007). ICT practices in Malaysian Smart and mainstream schools. *Malaysian Journal of Educational Technology* 7(1), 47-58.

**Deaney, R., Hennessy, S., & Ruthven, K.** (2006). Teachers' strategies for making effective use of datalogging in secondary science lessons. *School Science Review* 88 (323), 103-110. Offprint

**Hennessy, S., Deaney, R., & Ruthven, K**. (2006). Situated pedagogy for integrating use of multimedia simulation into secondary science teaching. *International Journal of Science Education* 28(7), 701-732.

**Technology use and integration in teaching across the secondary-school curriculum**

**Ruthven, K. **(2014). Frameworks for analysing the expertise that underpins successful integration of digital technologies into everyday teaching practice. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.) *The Mathematics Teacher in the Digital Era* (pp. 373-393). New York: Springer Preprint

**Ruthven, K.** (2009). Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics. *Education & Didactique* 3(1), 131-152. Offprint Preprint

**Deaney, R., Ruthven, K., & Hennessy, S.** (2006). Teachers' developing 'practical theories' of the contribution of information and communication technologies to subject teaching and learning: An analysis of cases from English secondary schools. *British Educational Research Journal* 32(3), 459-480. Preprint

**Ruthven, K., Hennessy, S., & Deaney, R.** (2005). Incorporating Internet resources into classroom practice: Pedagogical perspectives and strategies of secondary-school subject teachers. *Computers and Education* 44(1), 1-34. Preprint

**Hennessy, S., Deaney, R., & Ruthven, K.** (2005). Emerging teacher strategies for mediating technology-integrated instructional conversations: A socio-cultural perspective. *The Curriculum Journal* 16(3), 265-292.

**Hennessy, S., Ruthven, K., & Brindley, S.** (2005). Teacher perspectives on integrating ICT into subject teaching: Commitment, constraints, caution and change. *Journal of Curriculum Studies* 37(2), 155-192. Preprint

**Ruthven, K., Hennessy, S., & Brindley, S.** (2004). Teacher representations of the successful use of computer-based tools and resources in secondary-school English, Mathematics and Science. *Teaching and Teacher Education* 20(3), 259-275. Preprint

**Deaney, R., Ruthven, K., & Hennessy, S.** (2003). Pupil perspectives on the contribution of information and communication technology to teaching and learning in the secondary school. *Research Papers in Education* 18(2), 141-165. Preprint

**Calculator use and integration in primary-school mathematics teaching**

**Ruthven, K.** (2009). Towards a calculator-aware mathematics curriculum. *Mediterranean Journal for Research in Mathematics Education* 8(1), 111-124. Preprint

**Ruthven, K.** (2001). Towards a new numeracy: The English experience of a 'calculator-aware' number curriculum. In J. Anghileri (Ed.) *Principles and Practice in Arithmetic Teaching* (pp. 165-188). Buckingham: Open University Press.

**Ruthven, K.** (1999). The pedagogy of calculator use. In I. Thompson (Ed.) *Issues in Teaching Numeracy in Primary Schools* (pp. 195-206) Buckingham: Open University Press.

**Ruthven, K.** (1998). The use of mental, written and calculator strategies of numerical computation by upper-primary pupils within a 'calculator-aware' number curriculum. *British Educational Research Journal* 24(1), 21-42. JSTOR link

**Ruthven, K., Rousham, L., & Chaplin, D.** (1997). The long-term influence of a 'calculator-aware' number curriculum on pupils' mathematical attainments and attitudes in the primary phase. *Research Papers in Education* 12(3), 249-282.

**Ruthven, K., & Chaplin, D.** (1997). The calculator as a cognitive tool: Upper-primary pupils tackling a realistic number problem. *International Journal of Computers for Mathematical Learning* 2(2), 93-124.

**Linking research, policy and practice in mathematics education**

**Ruthven, K. & Goodchild, S. **(2015). Knowledge creation through dialogic interaction between the practices of teaching and researching. In L. English & D. Kirshner (Eds.) *Handbook of International Research in Mathematics Education*, Third Edition (pp. 523-539). London: Routledge.

**Ruthven, K.** (2008). Reflexivity, effectiveness, and the interaction of researcher and practitioner worlds: A reflection on Bishop's "Research, Effectiveness, and the Practitioners' World" in the light of a quarter-century of systemic improvement effort in English mathematics education. In P. Clarkson & N. Presmeg (Eds.) *Critical Issues in Mathematics Education: Major Contributions of Alan Bishop*. New York: Springer. Preprint

**Ruthven, K. , & Goodchild, S.** (2008). Linking researching with teaching: Towards synergy of scholarly and craft knowledge [revised and extended version]. In L. English (Ed.) *Handbook of International Research in Mathematics Education*, Second Edition (pp. 561-588). Routledge: New York.

**Ruthven, K.** (2005). Towards a normal science of mathematics education? In M. H. G. Hoffmann, J. Lenhard, & F. Seeger (Eds.) *Activity and Sign – Grounding Mathematics Education.* (pp. 153-158). New York: Springer Preprint

**Ruthven, K.** (2005). Improving the development and warranting of good practice in teaching. *Cambridge Journal of Education* 35(3), 407-426.

**Ruthven, K.** (2002). Linking researching with teaching: Towards synergy of scholarly and craft knowledge. In L. English (Ed.) *Handbook of International Research in Mathematics Education* (pp. 581-598). Mahwah NJ: Lawrence Erlbaum. Preprint

**Ruthven, K.** (1999). Reconstructing professional judgement in mathematics education: From good practice to warranted practice. In C. Hoyles, C. Morgan & G. Woodhouse (Eds.) *Rethinking the Mathematics Curriculum* (pp. 203-216). London: Falmer.

#### Theory and method in mathematics education research

** Arcavi, A., Boero, P., Kilpatrick, J., Radford, L., Dreyfus, T., & Ruthven, K. **(2016). Didactique goes travelling: its actual and potential articulations with other traditions of research on the learning and teaching of mathematics. In B. Hodgson, A. Kuzniak & J.-B. Lagrange (Eds.) *The Didactics of Mathematics: Approaches and Issues * (pp. 15-41). New York: Springer

** Ruthven, K. ** (2014). From networked theories to modular tools? In A. Bikner-Ahsbahs & S. Prediger (Eds.) *Networking of Theories as a Research Practice in Mathematics Education * (pp. 267-279). New York: Springer.

** Ruthven, K. ** (2014). Some methodological reflections on studies of mathematical affect. In B. Pepin & B. Roesken-Winter (Eds.) *From beliefs to dynamic affect systems in mathematics education * (pp. 383-393). Heidelberg: Springer.

**Earlier highlights**

**Ruthven, K.** (1996). Calculators in the mathematics curriculum: The scope of personal computational technology. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds.) *International Handbook of Mathematics Education *(pp. 435-468). Dordrecht: Kluwer.

**Ruthven, K.** (1995). Pupils' views of number work and calculators. *Educational Research* 37(3), 229-37.

**Ruthven, K.** (1995). Beyond common sense: Reconceptualizing National Curriculum assessment. *The Curriculum Journal* 6(1), 5-28.

**Ruthven, K.** (1994). Better judgement: Rethinking assessment in mathematics education. *Educational Studies in Mathematics* 27(4), 433-450. JSTOR link

**Ruthven, K. & Coe, R.** (1994). A structural analysis of students' epistemic views. *Educational Studies in Mathematics* 27(1), 101-109. JSTOR link

**Coe, R. & Ruthven, K.** (1994). Proof practices and constructs of advanced mathematics students. *British Educational Research Journal* 20(1), 41-53. JSTOR link

**Ruthven, K.** (1990). The influence of graphic calculator use on translation from graphic to symbolic forms. *Educational Studies in Mathematics* 21(5), 431-450. JSTOR link

**Ruthven, K.** (1989). An exploratory approach to advanced mathematics. *Educational Studies in Mathematics* 20(4), 449-467. JSTOR link

**Ruthven, K.** (1987). Ability stereotyping in mathematics. *Educational Studies in Mathematics* 18(3), 243-253. JSTOR link