Calidad del apoyo para el aprendizaje de las matemáticas en la transición a la Universidad.


  • Maria Pampaka The University of Manchester
  • Graeme Hutcheson The University of Manchester
  • Julian Williams The University of Manchester


Palabras clave:

Educación superior, Transiciones, Educación matemática, Educación científico-tecnológica y matemática, Enseñanza y aprendizaje de calidad, Medida, Modelo de Rasch


Este artículo muestra el desarrollo y la validación de un instrumento de medida de las percepciones de los estudiantes de secundaria acerca de, la calidad y la eficacia del apoyo para el aprendizaje de las matemáticas, en el proceso de transición a la educación superior. Para ello, se ha llevado a cabo un análisis cuantitativo de los datos obtenidos mediante un estudio de encuesta que, tomando algunos modelos de predicción, ha conjugado otros datos derivados de entrevistas. La validación de constructo de la medida se ha realizado mediante el RSM (Rating Scale Model) de Rasch. Los resultados incluyen estadísticos de ajuste y de categorías, así como la jerarquización del constructo con algunos extractos de los datos de las entrevistas. El artículo finaliza aportando las principales implicaciones educativas que se derivan de este proceso, mostrando ejemplos de cómo esta medida puede ser utilizada para obtener resultados prácticos importantes sobre el apoyo en el aprendizaje de las matemáticas en los procesos de transición educativa.




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Biografía del autor/a

Maria Pampaka, The University of Manchester

Maria is currently holding a joint position, as a Lecturer and research fellow, at the Institute of Education and the Social Statistics group, at the University of Manchester. Her role involves leading an ESRC funded project in mathematics education (, and delivering courses in advanced quantitative methods. Her research expertise spreads along the spectrum of educational studies, focussing in teachers’ knowledge and practices and students’ attitudes and progress in their educational trajectories. She is particularly interested in the association between teaching practices and students’ learning outcomes. Methodologically, her expertise and interests lie within evaluation and measurement, and advanced quantitative methods, including complex survey design, longitudinal data analysis, and missing data and imputation techniques.

Graeme Hutcheson, The University of Manchester

Graeme’s teaching and research interests are broadly in the area of methodology and data analysis. His PhD was a study into the acquisition of complex syntax in children and since then he has worked on a number of projects from a wide range of research areas including the conversational behaviour of children, interviewing techniques used on child witnesses, alcohol use in the workplace, the application of knowledge-based expert systems, the application of generalized linear models in predictive modelling, multi-level analysis of data related to Inclusion and Pupil achievement, an assessment of the Early Support Project (DfES) and a project investigating mathematically demanding F and HE programmes.

Julian Williams, The University of Manchester

Julian Williams is Professor of Mathematics Education at The University of Manchester, where he led a series of ESRC-funded “Transmaths” ( research projects that investigated mathematics education in the post-compulsory transitions from school to university. He has a longstanding interest in curriculum, pedagogy and assessment in mathematics and across STEM, in mathematical modelling, and in links with vocational and outside-school mathematics. This work has led to interests in social theory and the political economy of education.


Agresti, A. (1996). An Introduction to Categorical Data Analysis. London: John Wiley &

Sons, Inc.

Alcock, L., Attridge, N., Kenny, S., & Inglis, M. (2014). Achievement and behaviour in undergraduate mathematics: personality is a better predictor than gender. Research in Mathematics Education, 16(1), 1-17.

Andrich, D. (1999). Rating Scale Model. In G. N. Masters & J. P. Keeves (Eds.), Advances in Measurement in Educational Research and Assessment (pp. 110 - 121). Oxford: Pergamon.

Baeten, M., Struyven, K., & Dochy, F. (2013). Student-centred teaching methods: Can they optimise students’ approaches to learning in professional higher education? Studies in Educational Evaluation, 39(1), 14-22.

Ball, S., Davies, J., David, M., & Raey, D. (2002). ‘Classification’ and ‘Judgement’: social class and the ‘cognitive structures’ of choice of Higher Education. British Journal of Sociology of Education, 23(1), 51-72.

Bell, N. J., Wieling, E., & Watson, W. (2007). Narrative processes of identity construction: Micro indicators of developmental patterns following transition to university. Identity, 7(1), 1-26.

Biggs, J., Kember, D., & Leung, Y. P. (2001). The revised two-factor Study Process Questionnaire: R-SPQ-2F. British Journal of Educational Psychology, 71, 133-149.

Black, L., Williams, J., Hernandez-Martinez, P., Davis, P., Pampaka, M., & Wake, G. (2010). Developing a ‘leading identity’: the relationship between students’ mathematical identities and their career and higher education aspirations. Educational Studies in Mathematics, 73(1), 55-72.

Boaler, J. (1999). Participation, knowledge and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40(3), 259-281.

Boaler, J., & Greeno, J. (2000). Identity, Agency and Knowing in Mathematics Worlds. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning. Westport: Ablex Publishing.

Bodycott, P. (1997). A model for supporting student learning and development at the tertiary level. Innovations in Education and Teaching International, 34(3), 219-225.

Bond, T. G., & Fox, C. M. (2001). Applying the Rasch Model: Fundamental Measurement in the Human Sciences. NJ: Lawrence Erlbaum Associates Inc.

Cassidy, C., & Trew, K. (2004). Identity change in Northern Ireland: A longitudinal study of students’ transition to University. Journal of Social Issues, 60(3), 523-540.

Chaisanit, S., Trangansri, A., & Meeanan, L. (2012). The development of online interactive whiteboard for supporting collaboration learning. Research Journal of Applied Sciences, Engineering and Technology, 4(16), 2660-2665.

Chamorro-Premuzic, T., Furnham, A., & Lewis, M. (2007). Personality and approaches to learning predict preference for different teaching methods. Learning and Individual Differences, 17(3), 241-250.

Cook, A., & Leckey, J. (1999). Do Expectations Meet Reality? A survey of changes in first-year student opinion. Journal of Further and Higher Education, 23(2), 157 - 171.

D’Agostino, J. V., & Bonner, S. M. (2009). High School Exit Exam Scores and University Performance. Educational Assessment, 14, 25-37.

Han, H., Nelson, E., & Wetter, N. (2014). Medical students’ online learning technology needs. Clinical Teacher, 11(1), 15-19.

Harley, D., Winn, S., Pemberton, S., & Wilcox, P. (2007). Using texting to support students’ transition to university. Innovations in Education and Teaching International, 44(3), 229-241.

Harnisch, H., & Taylor-Murison, L. (2012). Transition and technology - Evaluation of blended learning delivered by university staff to 6th form students. British Journal of Educational Technology, 43(3), 398-410.

Heirdsfield, A., Walker, S., & Walsh, K. (2005). Developing peer mentoring support for TAFE students entering 1st -year university early childhood studies. Journal of Early Childhood Teacher Education, 26(4), 423-436.

Hoffman, J. P. (2004). Generalized Linear Models: An Applied Approach: Pearson Education.

Hourigan, M., & O’Donoghue, J. (2007). Mathematical under-preparedness: the influence of the pre-tertiary mathematics experience on students’ ability to make a successful transition to tertiary level mathematics courses in Ireland. International Journal of Mathematical Education in Science and Technology, 38(4), 461-476.

Howie, P., & Bagnall, R. (2012). A critique of the deep and surface approaches to learning model. Teaching in Higher Education, 18(4), 389-400.

Hoyles, C., Newman, K., & Noss, R. (2001). Changing patterns of transition from school to university mathematics. International Journal of Mathematical Education in Science and Technology, 32(6), 829-845.

Hutcheson, G., Pampaka, M., & Williams, J. S. (2011). Enrolment, achievement and retention on ‘traditional’ and ‘use of mathematics’ AS courses. Research in Mathematics Education, 13(2),147-168.

Hutcheson, G., & Sofroniou, N. (1999). The Multivariate Social Scientist. Introductory Statistics Using Generalized Linear Models. London: Sage.

Jackson, L. M., Pancer, S. M., Pratt, M. W., & Hunsberger, B. E. (2000). Great expectations: The relation between expectancies and adjustment during the transition to university. Journal of Applied Social Psychology, 30(10), 2100-2125.

Karantzas, G. C., Avery, M. R., Macfarlane, S., Mussap, A., Tooley, G., Hazelwood, Z., & Fitness, J. (2013). Enhancing critical analysis and problem-solving skills in undergraduate psychology: An evaluation of a collaborative learning and problem-based learning approach. Australian Journal of Psychology, 65(1), 38-45.

Linacre, J. M. (2002). Optimizing Rating Scale Category Effectiveness Journal of Applied Measurement, 3(1), 85-106.

Linacre, J. M. (2014). Winsteps® Rasch measurement computer program. Beaverton, Oregon:

Lopez, W. A. (1996). Communication Validity and Rating Scales. Rasch Measurement Transactions, 10 (1), 482-483.

Lowe, H., & Cook, A. (2003). “Mind the Gap: Are students prepared for higher education?”. Journal of Further and Higher Education, 27(1), 53-76.

Loyens, S. M. M., Gijbels, D., Coertjens, L., & Côté, D. J. (2013). Students’ approaches to learning in problem-based learning: Taking into account professional behavior in the tutorial groups, self-study time, and different assessment aspects. Studies in Educational Evaluation, 39(1), 23-32.

Messick, S. (1989). Validity. In R. L. Linn (Ed.), Educational Measurement (Third ed., pp. 13-103). USA: American Council of Education and the Oryx Press.

Pampaka, M., Kleanthous, I., Hutcheson, G. D., & Wake, G. (2011). Measuring mathematics self-efficacy as a learning outcome. Research in Mathematics Education, 13(2), 169-190.

Pampaka, M., Pepin, B., & Sikko, S. A. (forthcoming). Supporting or alienating students during their transition to Higher Education: mathematically relevant trajectories in two educational contexts. International Journal of Educational Research (Special Issue, on Alienation from Mathematics)


Pampaka, M., Williams, J., & Hutchenson, G. (2012). Measuring students’ transition into university and its association with learning outcomes. British Educational Research Journal, 38(6), 1041-1071.

Pampaka, M., & Williams, J. S. (2010). Measuring Mathematics Self Efficacy of students at the beginning of their Higher Education Studies. Paper presented at the Proceedings of the British Congress for Mathematics Education (BCME) (pp. 159-166), Manchester.

Pampaka, M., Williams, J. S., Hutchenson, G., Black, L., Davis , P., Hernandez-Martines, P., & Wake, G. (2013). Measuring Alternative Learning Outcomes: Dispositions to Study in Higher Education. Journal of Applied Measurement, 14(2), 197-218.

Pampaka, M., Williams, J. S., Hutcheson, G., Wake, G., Black, L., Davis, P., & Hernandez - Martinez, P. (2012). The association between mathematics pedagogy and learners’ dispositions for university study. British Educational Research Journal, 38(3), 473-496.

Pancer, S. M., Hunsberger, B., Pratt, M. W., & Alisat, S. (2000). Cognitive complexity of expectations and adjustment to university in the first year. Journal of Adolescent Research, 15(1), 38-55.

Peat, M., Dalziel, J., & Grant, A. M. (2000). Enhancing the transition to university by facilitating social and study networks: Results of a one-day workshop. Innovations in Education and Teaching International, 37(4), 293-303.

Scanlon, L., Rowling, L., & Weber, Z. (2007). ‘You don’t have like an identity you are just lost in a crowd’: Forming a Student Identity in the First-year Transition to University. Journal of Youth Studies, 10(2), 223-241.

Schworm, S., & Gruber, H. (2012). E-Learning in universities: Supporting help-seeking processes by instructional prompts. British Journal of Educational Technology, 43(2), 272-281.

Shah, C., & Burke, G. (1999). An Undergraduate Student Flow Model: Australian Higher Education. Higher Education, 37(4), 359-375.

Smyth, L., Mavor, K. I., Platow, M. J., Grace, D. M., & Reynolds, K. J. (2013). Discipline social identification, study norms and learning approach in university students. Educational Psychology, 1-21.

Thissen, D., Steinberg, L., & Wainer, H. (1993). Detection of Differential Item Functioning Using the Parameters of Item Response Models. In P. W. Holland & H. Wainer (Eds.), Differential Item Functioning (pp. 67-114). London Lawrence Erlbaum Associates, Publishers.

Tormey, R. (2013). The centre cannot hold: untangling two different trajectories of the ‘approaches to learning’ framework. Teaching in Higher Education, 19(1), 1-12.

Weiner-Levy, N. (2008). Universities as a meeting point with new academic knowledge, society and culture: Cognitive and emotional transitions during higher education. Cambridge Journal of Education, 38(4), 497-512.

Weisberg, S. (1985). Applied Linear Regression (second edition): John Wiley & Sons.

Williams, J. S. (2012). Use and exchange value in mathematics education: contemporary CHAT meets Bourdieu’s sociology. Educational Studies in Mathematics, 80(1-2), 147-168.

Williams, J. S., Black, L., Hernandez-Martinez, P., Davis, P., Pampaka, M., & Wake, G. (2009). Repertoires of aspiration, narratives of identity, and cultural models of mathematics in practice. In M. César & K. Kumpulainen (Eds.), Social Interactions in Multicultural Settings (pp. 39-69). Rotterdam: Sense. Publishers.

Wingate, U. (2007). A Framework for Transition: Supporting ‘Learning to Learn’ in Higher Education. Higher Education Quarterly, 61(3), 391-405.

Wolfe, E. W., & Smith Jr., E. V. (2007a). Instrument Development Tools and Activities for Measure Validation Using Rasch Models: Part I - Instrument Development Tools. Journal of Applied Measurement, 8(1), 97-123.

Wolfe, E. W., & Smith Jr., E. V. (2007b). Instrument Development Tools and Activities for Measure Validation Using Rasch Models: Part II - Validation Activities. Journal of Applied Measurement, 8(2), 204-234.

Wright, B. D. (1999). Rasch Measurement Models. In G. N. Masters & J. P. Keeves (Eds.), Advances in Measurement in Educational Research and Assessment (pp. 268-281). Oxford: Pergamon.

Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.

Wright, B. D., & Mok, M. (2000). Rasch Models Overview. Journal of Applied Measurement, 1(1), 83-106