Teaching and Learning Research Papers Post 2001

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MacBean J, Graham E and Sangwin C (2004), Group Work in Mathematics: A Survey of Students' Experiences and Attitudes, Teaching Mathematics and its Applications, Vol. 23, 49-68.
This study investigates students’ experiences of group work at both school and at university, along with their current attitudes towards group work, in mathematics. Three groups of students from differing universities were involved, and data was gathered using a questionnaire and semi-structured interviews. Results revealed some significant differences between the universities in the students’ experiences of, and attitudes towards, group work. Overall their attitudes were positive, but mainly utilitarian, and the most common form of group work they experienced was of an informal nature. No difference was found in their school experience of group work.

E Graham (2002), AS Mathematics : The Results of a Survey of Schools and Colleges, Teaching Mathematics and its Applications, Vol. 21, No. 1, 11-28. ISSN 0268-3679
There has been considerable debate about the problems associated with the new Advanced Subsidiary (AS) award introduced in 2000. There have been problems with examination arrangements, but there have also been concerns about the very high failure rate for AS mathematics, and the difficulty that teachers have faced in covering the content required in the time available. A survey of schools and colleges was carried out. This confirmed that teachers view the content of the specifications as being too much and that the examinations were inaccessible to many students. The paper also reports on entry patterns, the changes that teachers would like to see to the current system, progression to A2 and the benefits/disadvantages of the system as perceived by teachers.

J. MacBean, E. Graham and C. Sangwin, 2001, Group Work Reluctance in Maths Education, MSOR Connections, Vol. 1, No. 3, 24-25.
This provides an interim report on a research project to investigate undergraduate students views of the use of group work as part of their studies. The project aims to identify student views and to make recommendations on the use of group work.

Judith MacBean, Ted Graham and Chris Sangwin, 2001, Guidelines for Introducing Group Work in Undergraduate Mathematics, published by the LTSN Maths, Stats & OR Network.
These guidelines result from a research study that was undertaken by three differing higher education institutions in the UK. First year undergraduate students were surveyed and interviewed to find the extent to which students worked in groups and their attitudes to this.

 
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Berry J. and Sharp J., 2002, The Use of Technology in Developing Mathematical Modelling Skills
Proceedings of the International Teachers Teaching with Technology Conference, Calgary, Canada, 2002, CDRom
Much has been said about the importance of mathematics in the school and college curriculum and much has been written about what should be included in the curriculum for the beginning of the twenty first century. Often there is a tension between the school curriculum and the perceived needs of college and university mathematicians. Too often the mathematics curriculum at all levels is seen as a ‘body of knowledge’ which needs to be delivered in order to provide an ‘acceptable graduate in mathematics’. In this era of powerful software on hand-held and computer technologies we need to review the procedures and rules that have been the central focus of the mathematics curriculum for over one hundred years. That is not to say that we do not need some of the traditional skills so that students can make effective use of the technology. However there are important generic skills that mathematics provides, and to the employer of our graduates these skills are often more important than the actual mathematics that they have learnt. In this paper we explore the use of graphic calculators in developing mathematical modelling skills.

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Sahlberg P. and Berry J., 2003, Small Group Learning in Mathematics: Teachers’ and pupils’ ideas about groupwork in school. Finnish Educational Research Association, Volume 13, ISBN 952-5401-12-XS; ISSN 1458-1094, Turku Finland
The style of teaching and learning mathematics and the type of tasks used affect the conceptions, attitudes and views of mathematics held by teachers and pupils. Our purpose in this research study is to investigate the occurrence of small group learning and the methods of co-operative learning in school mathematics in Finland and in England. Furthermore, we wish to draw more educators’ and researchers’ attention to the role of these methods of learning and to the importance of task design in implementing them into school mathematics.

We conclude that small group learning is not common in the teaching and learning of mathematics and that the tasks used in school mathematics determine the teaching and learning styles and these are not conducive to the methods of contemporary co-operative learning.

Sahlberg P. and Berry J., 2002, One and One is Sometimes Three in Small Group Mathematics Learning, Asia Pacific Journal of Education, Vol 22 No 1, pp 83 - 94
In recent years, Mathematics teaching has been confronted by demands for higher standards and better pupil achievement in several parts of the world. Researchers have suggested a shift from teacher-centred instruction towards more active participatory learning methods as one way to improve the quality of the learning process. The tension between whole class teaching versus small group learning in Mathematics has been particularly apparent in many education systems. This article analyses the development of Mathematics teaching by asking whether small group learning is an effective arrangement in teaching school Mathematics. We conclude that although there is no unanimity about the effects of small group learning on student achievement in school Mathematics, it seems that it produces at least equal academic outcomes among all students compared to more traditional methods of instruction. Working in pairs is a particularly effective form of learning Mathematics and that small groups are beneficial for developing mathematical problem-solving skills. We also conclude that the present educational policies and increased quality assurance structures in many countries conflict, or are not consistent with scientific-professional thinking and research on the teaching of mathematics.

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Berry J.and Nyman M., Small Group Assessment Methods in Mathematics, The International Journal of Mathematics Education in Science and Technology, Vol 33 No 5, pp 641-649, 2002
Assessment of students’ attainment in courses is often driven by the method of instruction. When mathematics is taught in the traditional style of lectures on theory coordinated with homework on standard problems, the testing is often oriented to reproducing the skills demonstrated by the instructor. If a more collaborative teaching method is used, how does one assess the students’ acquisition of problem-solving and mathematical thinking skills. In this paper we discuss a team-oriented formal testing method used in a mathematical modelling course taught during the Alma College intensive spring term.

Sahlberg P. and Berry J., 2002, Matematiikan oppiminen pienryhmissä (Small Group Learning in Mathematics) in eds. Sahlberg, P. and Sharan, S. Yhteis-toiminnallisen oppimisen käsikirja (Handbook of Co-operative Learning Methods) Chapter 2.1, pp 176-198, WSOY: Helsinki, Finland. ISBN 951-0-25962-4

Nyman M. and Berry J., 2002, Developing Transferable Skills in Undergraduate Mathematics Students through Mathematical Modelling, Journal of Teaching Mathematics and Its Applications, 21 No 1, 29-46, 2002, ISSN 0268-3679
Undergraduate mathematics students should possess certain transferable skills upon completion of a degree. The Mathematical Association of America’s recently published CUPM Discussion Papers about Mathematics and the Mathematical Sciences in 2010: What Should Students Know and the NCTM’s Principles and Standards for School Mathematics both suggest the importance of transferable skills for success in student’s later careers. These skills and a strategy for developing them via an intensive short course on mathematical modelling are discussed. Student reactions and comments on the course are included. The evaluation suggests that this course on mathematical modelling developed modelling as well as generic skills through the teaching, learning and assessment style.

 
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Picker, S.H. (2005). Mathematical Reasoning Using Bipartite Graphs and Graph Colouring. Mathematics in School, 34(1).