Study-Unit Description

Study-Unit Description


TITLE Inquiry and Assessment in the Mathematics Classroom

LEVEL 05 - Postgraduate Modular Diploma or Degree Course


DEPARTMENT Mathematics and Science Education

DESCRIPTION This study-unit comprises two main components that are related primarily to inquiry and assessment in the mathematics classroom.

(a) With regard to inquiry, this study-unit explores how taking an investigative approach can be an effective way to teach mathematics. The study-unit will (i) present the theoretical foundations of ‘investigations’ as a teaching and learning tool; and (ii) explore how investigations can be integrated within the mathematics curriculum.

The theoretical part will focus on the social constructivist perspective of teaching and learning mathematics through investigations.

The practical part will focus on:
- Integrating investigative tasks within planning a scheme of work.
- Exploring the ‘new’ roles of the teacher in presenting students with investigative tasks, assisting and assessing students’ work.
- Design tasks that provide inquiry-based learning opportunities for students.
- Involving students in small-group activities that allow for collaborative work in planning, discussing, arguing about and presenting their mathematics.
- Establishing a classroom culture that supports an investigative approach.

(b) With regards to assessment, the main focus of this study-unit is to explore ‘classroom assessment’ from an ‘Assessment for Learning’ (AfL) perspective. The study-unit, which lays down the theoretical framework of AfL, will include:

- The traditional and alternative paradigms of assessment (with particular reference to the links between teaching & learning theories and assessment).
- Classroom assessment as incorporating all forms of assessment taking place within the classroom walls (e.g., formative, summative, teacher assessment, self-assessment, etc).
- Professional dimension of assessment to be favoured over the managerial one.
- Assessment for learning (AfL) which is primarily concerned with formative assessment that benefits the present students.
- The 10 AfL principles.
- The 'classroom assessment cycle' of planning, gathering information, interpreting evidence, and using results.

Study-Unit Aims:

The aims of the study-unit are as follows:
(a) With regard to inquiry, it seeks to provide the theoretical background of an investigative mathematics classroom. Moreover, it seeks to support students in understanding how the social constructivist perspective to teaching and learning mathematics through investigations can be translated into actual classroom practices.
(b) With regard to assessment, it seeks to explore educational assessment and classroom assessment, to then present the theoretical framework of Assessment for Learning (AfL) and how this theory complements the classroom assessment cycle.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:

(a) With regards to inquiry:
- describe the features, purposes, roles and benefits of adopting an investigative approach.
- explain what constitutes an investigative task and be able to apply this knowledge to real classroom situations.
- recognise that assessment within the classroom is an on-going process that takes into consideration how pupils actually transform the task presented into their own mathematical activity.
- illustrate how an inquiry approach can be applied effectively in spite of numerous constraint teachers face (e.g., time constraints in covering the syllabus, examinations).

(b) With regards to assessment:
- describe the various forms of assessment present within classroom practice (e.g., teacher assessment, self- and peer assessment, formative assessment, summative assessment, ect.).
- explain why it is important that formative assessment guides and prevails within the classroom.
- list the 10 Assessment for Learning principles and how these can be applied to real classroom situations.
- discuss the cyclic nature of classroom assessment.

2. Skills:

By the end of the study-unit the student will be able to:

(a) With regards to inquiry:
- design and plan tasks that engage students in investigating mathematics.
- integrate investigative tasks within the mathematics curriculum.
- implement a variety of active learning instructional practices where pupils plan, discuss and present their mathematics.
- employ pupils in inquiry learning through cooperative work.
- assess pupils' investigative work.
- create a classroom culture as a ‘community of investigators’.

(b) With regards to assessment:
- list the limitations of an assessment system that is dominated by examinations.
- analyse tasks in relation to the likelihood that they will be used in the classroom.
- demonstrate how the Assessment for Learning principles can be transferred into activities, both within and outside the classroom, that support the learning process.
- plan and evaluate classroom assessment according to the canons of the 'classroom assessment cycle'.

Main Text/s and any supplementary readings:

Main Texts:

- Ponte, J.P. (2001) Investigating mathematics and learning to teach mathematics. In F.L. Lin & T.J. Cooney (eds.) Making Sense of Mathematics Teacher Education. Dordrecht: Kluwer.
- Clarke, S. (2008) Active Learning through Formative Assessment. London: Hodder Education.
- Assessment Reform Group (ARG) (2002). Assessment for learning: 10 principles [Leaflet].
- Assessment Reform Group (ARG) (1999). Assessment for learning: beyond the black box. Cambridge: School of Education, University of Cambridge.
- Blandchard, J. (2009) Teaching, Learning & Assessment. Maidenhead: Open University Press.

Supplementary Readings:

- Doerr, H.M. (2006) Examining the tasks of teaching when using students’ mathematical thinking. Educational Studies in Mathematics, 62(1), 3-24.
- Greenes, C. (1996) Investigations: vehicles for learning and doing mathematics. Journal of Education, 178(2), 35-49.
- Goos, M., Dole, S., & Makar, K. (2007) Supporting an investigative approach to teaching secondary school mathematics: a professional development model. In J.
- Watson & K. Beswick (eds.) Essential Research, Essential Practice: Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, 1. Tasmania: MERGA.
- Goos, M, Galbraith, P., & Renshaw, P. (2004) Establishing a community of practice in a secondary mathematics classroom. In B. Allen & S. Johnston-Wilder (eds.) Mathematics Education: Exploring the Culture of Learning. London: Routledge/Falmer.
- Jaworski, B. (2002) Social constructivism in mathematics learning and teaching. In L. Haggarty (ed.) Teaching Mathematics in Secondary Schools. London: Routledge/Falmer.
- Norton, S., McRobbie, C., & Cooper, T. (2002) Teachers’ responses to an investigative mathematics syllabus: their goals and practices. Mathematics Education Research Journal, 14(1), 37-59.
- Van Reeuwijk, M., & Wijers, M. (2004) Investigations as thought-revealing assessment problems. In T.A. Romberg (ed.) Standards-Based Mathematics Assessment in Middle School: Rethinking classroom practice. New York: Teachers College Press.
- Walshaw, M., & Anthony, G. (2008) The teacher’s role in classroom discourse: a review of recent research in mathematics classrooms. Review of Educational Research, 78(3), 516-551.
- Buhagiar, M.A. (2006) The classroom assessment cycle within the alternative
assessment paradigm: exploring the role of the teacher. Journal of Maltese Education Research, 4(2), pp. 17-36.
- Gardner, J. (ed.) (2006) Assessment and Learning. Los Angeles: SAGE.
- Buhagiar, M.A. (2007) Classroom assessment within the alternative assessment paradigm: revisiting the territory. The Curriculum Journal, 18(1), 39-56.
- Buhagiar, M.A. (2004) ‘How appropriate is this task for my class?’ Exploring teachers’ classroom decision-making processes as they waver between ‘practical’ and ‘ideal’ positions. Mediterranean Journal of Educational Studies, 9(2), 83-108.

ADDITIONAL NOTES Pre-requisite Qualifications: 70 ECTS at Undergraduate level or higher in Mathematics

STUDY-UNIT TYPE Lectures, Seminars and Placement

Assessment Component/s Assessment Due Resit Availability Weighting
Fieldwork See note below Yes 10%
Reflective Diary See note below Yes 20%
Report See note below Yes 30%
Assignment See note below Yes 40%
Note: Assessment due will vary according to the study-unit availability.

LECTURER/S Michael Buhagiar
James Calleja

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2020/1. It may be subject to change in subsequent years.