Where learning starts? A framework for thinking about lectures in university mathematics

Lectures have been widely criticized as a method of teaching, but remain a standard component of most university mathematics courses. Does this necessarily harm students' education? This critical review contends that many arguments against lecturing are misconceived, at least when applied to mathematics. The effectiveness of lectures in carrying out various functions is discussed with reference to some recent educational research. There is evidence that lectures can be effective in communicating information, modelling reasoning and motivating students. Therefore, when supported appropriately by other activities, lectures provide an effective component of a mathematical education.

[1]  B. Charlton,et al.  Lectures are such an effective teaching method because they exploit evolved human psychology to improve learning. , 2006, Medical hypotheses.

[2]  Elizabeth Tindle,et al.  Transition to higher education , 1999 .

[3]  Renata Retkute.  Exploring Technology-Based Continuous Assessment via Electronic Voting Systems in Mathematics and Statistics , 2009 .

[4]  Mj Cook,et al.  Developing and Evaluating a Novel Technique for Recording and Asynchronous Delivery of Lectures , 2001 .

[5]  D. Hounsell.  The Experience of Learning: Implications for Teaching and Studying in Higher Education , 1997 .

[6]  Paul R. Halmos,et al.  I Want to be a Mathematician , 1985 .

[7]  R. Neumann.  Disciplinary Differences and University Teaching , 2001 .

[8]  The effectiveness of school-type classes compared to the traditional lecture/tutorial method for teaching quantitative methods to business students , 1996 .

[9]  Martyn Cooper.  Making Mathematics Teaching Inclusive — Access for Disabled Students to Symbolic Languages in Electronic Media , 2006 .

[10]  Donald R. Chalice,et al.  HOW TO TEACH A CLASS BY THE MODIFIED MOORE METHOD , 1995 .

[11]  C. Shaw.  Attitudes of engineering students to mathematics a comparison across universities , 1999 .

[12]  Samuel O. King,et al.  'Pretty Lights' and Maths! Increasing student engagement and enhancing learning through the use of electronic voting systems , 2009, Comput. Educ..

[13]  R. Felder,et al.  Understanding Student Differences , 2005 .

[14]  Tony Becher.  The significance of disciplinary differences , 1994 .

[15]  Margaret I. Brown,et al.  Increasing interactivity in lectures using an electronic voting system , 2004, J. Comput. Assist. Learn..

[16]  María S. Pérez-Hernández,et al.  Are web self-assessment tools useful for training? , 2005, IEEE Transactions on Education.

[17]  D. Nicol,et al.  Formative assessment and self‐regulated learning: a model and seven principles of good feedback practice , 2006 .

[18]  Chris Good.  Teaching by the Moore Method , 2006 .

[19]  G. Boulton‐Lewis.  Teaching for quality learning at university , 2008 .

[20]  K. Patricia Cross,et al.  Classroom Assessment Techniques , 1993 .

[21]  L. Brinckerhoff,et al.  Making the Transition to Higher Education , 1996, Journal of learning disabilities.

[22]  Suellen Shay,et al.  Beyond social constructivist perspectives on assessment: the centring of knowledge , 2008 .

[23]  Perry D. Klein,et al.  Rethinking the multiplicity of cognitive resources and curricular representations: Alternatives to 'learning styles' and 'multiple intelligences' , 2003 .

[24]  S. Derry,et al.  Learning from Examples: Instructional Principles from the Worked Examples Research , 2000 .

[25]  John Mason,et al.  Mathematics Teaching Practice: Guide for University and College Lecturers , 2002 .

[26]  Yvette Solomon,et al.  Not belonging? What makes a functional learner identity in undergraduate mathematics? , 2007 .

[27]  S. Mann,et al.  Boredom in the lecture theatre: An investigation into the contributors, moderators and outcomes of boredom amongst university students , 2009 .

[28]  G. Lueddeke,et al.  Professionalising Teaching Practice in Higher Education: A study of disciplinary variation and 'teaching-scholarship' , 2003 .

[29]  W. Cox.  What Sort of Pedagogic Theory do we need for Teaching Mathematics in Higher Education , 2006 .

[30]  R. Moreno.  When worked examples don't work: Is cognitive load theory at an Impasse?☆ , 2006 .

[32]  D. Bligh.  What's the Use of Lectures? , 1971 .

[33]  Cornelia S. Große,et al.  How Fading Worked Solution Steps Works – A Cognitive Load Perspective , 2004 .

[34]  C. W. Tate.  Solve it. , 2005, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[35]  D. Nicol,et al.  Peer Instruction versus Class-wide Discussion in Large Classes: A comparison of two interaction methods in the wired classroom , 2003 .

[36]  J. Sweller.  The worked example effect and human cognition , 2006 .

[37]  John Mason.  Mathematics teaching practice , 2002 .

[38]  M. Reisslein,et al.  Toward a Fundamental Understanding of Worked Example Instruction: Impact of Means-Ends Practice, Backward/Forward Fading, and Adaptivity , 2006, Proceedings. Frontiers in Education. 36th Annual Conference.

[39]  Vivien Hodgson,et al.  Lectures and the experience of relevance , 1997 .

[40]  J. Sweller,et al.  The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra , 1985 .

[41]  C. Penney.  Modality effects and the structure of short-term verbal memory , 1989, Memory & cognition.

[42]  Paul Ginns.  Meta-Analysis of the Modality Effect. , 2005 .

[43]  Derek Holton,et al.  Developing active learners , 2003 .

[44]  Robert Burn.  The genesis of mathematical structures , 2003 .

[45]  Tony Becher,et al.  Teaching and Learning in their Disciplinary Contexts: A conceptual analysis , 2002 .

[46]  Fred Paas,et al.  Effects of studying sequences of process-oriented and product-oriented worked examples on troubleshooting transfer efficiency , 2008 .

[47]  Lara Alcock,et al.  Ideas from mathematics education: an introduction for mathematicians , 2009 .

[48]  Steve E. Jones,et al.  Reflections on the lecture: outmoded medium or instrument of inspiration? , 2007 .

[49]  Paul R. Halmos,et al.  I Want to Be A Mathematician: An Automathography , 1986 .

[50]  A. Sfard.  On Two Metaphors for Learning and the Dangers of Choosing Just One , 1998 .

[51]  Sue Cowley,et al.  Getting the Buggers to Behave , 2001 .

[52]  Anthony Croft,et al.  A modern and interactive approach to learning engineering mathematics , 2001, Br. J. Educ. Technol..