Undergraduate Course: Problem solving and enquiry in primary school mathematics (EDUA10152)
Course Outline
School  Moray House School of Education 
College  College of Humanities and Social Science 
Credit level (Normal year taken)  SCQF Level 10 (Year 4 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  Enabling children to solve mathematical problems is seen as an important goal of mathematics education. This course aims to introduce students to different approaches to problem solving and investigation in primary schools. It will draw on international perspectives and practices, as well as considering the context of the Scottish curriculum. Students will be expected to engage critically with both relevant mathematics education literature and curriculum policies. An essential element of this will be considering the ways in which problem solving and investigation develop children's abilities to think and reason mathematically. Practical coursework and paired microteaching will focus on developing students' ability to work with learners in solving problems, carrying out investigations, and problematising the learning of mathematics. The use of pairs will facilitate peer learning through collaborative preparation and observation. Students will also develop the ability to analyse and evaluate the difficulty and appropriateness of problems and investigations for different ages and stages of learning, and to construct new contexts, problems and investigations. 
Course description 
Not entered

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Information for Visiting Students
Prerequisites  None 
Course Delivery Information

Academic year 2014/15, Available to all students (SV1)

Quota: 25 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Supervised Practical/Workshop/Studio Hours 27,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
169 )

Assessment (Further Info) 
Written Exam
0 %,
Coursework
100 %,
Practical Exam
0 %

Additional Information (Assessment) 
1. An annotated portfolio of problems, contexts and investigations. (25%)
2. 3000 word written assignment (75%)
Assessment criteria:
Annotated portfolio:
Students will be encouraged to specialise in their portfolio, e.g. relating it to one stage of primary school or to a particular mathematical strand such as Shape.
The portfolio will be assessed on the extent to which it
1. identifies problems, contexts and/or investigations appropriate to the specialism of the portfolio;
2. demonstrates an analytic and evaluative approach to annotating the chosen problems, contexts and/or investigations;
3. identifies relevant questions or prompts to support learners in tackling the problems and/or investigations;
4. demonstrates a good standard of structure and style in its presentation.
Written assignment:
The assignment will be assessed on the extent to which it
1. responds relevantly to the question set;
2. demonstrates knowledge and understanding of theoretical perspectives on mathematical problem solving and investigation;
3. reflects critically on the application of theory to learning and teaching contexts, drawing on experience and relevant literature to support reflection;
4. demonstrates a coherent structure and uses written language and conventions of academic referencing accurately.

Feedback 
Not entered 
No Exam Information 
Learning Outcomes
On completion of this course, the student will be able to:
 Students will demonstrate knowledge and understanding of theories and practices in mathematical problem solving and investigation.
 Students will demonstrate the ability to analyse and evaluate features of problems and investigations which contribute to developing children's mathematical thinking.
 Students will develop the ability to adapt existing mathematical problems, investigations and contexts, and to construct new ones.
 Students will demonstrate skills in leading a group in mathematical investigation or problem solving, from initial presentation, through support and probing questions, to discussion of final solution(s).
 Students will adopt a collaborative, enquirybased approach to their own professional development.

Reading List
Askew, M. (2003). Word problems: Cinderellas or wicked witches? Enhancing primary mathematics teaching. I. Thompson. Maidenhead, Open University Press: 7885.
Barwell, R. (2005). "Working on arithmetic word problems when English is an additional language." British Educational Research Journal 31(3): 329348.
Boaler, J. (2011?). "How complex instruction led to high and equitable achievement: the case of Railside School." Retrieved 29/6/2011, from http://nrich.maths.org/content/id/7011/nrich%20paper.pdf.
Burkhardt, H. and A. Bell (2007). "Problem solving in the United Kingdom." Zeitschrift für Didaktik der Mathematik 39: 395403.
Burton, L. (1984). Thinking things through. Hemel Hempstead, Simon and Schuster.
Cai, J. (2003). What research tells us about teaching mathematics through problem solving. Research and issues in teaching mathematics through problem solving. F. Lester. Reston, VA, National Council of Teachers of Mathematics.
Chapman, O. (1997). "Metaphors in the teaching of mathematical problem solving." Educational Studies in Mathematics 32: 201  228.
Cuoco, A., E. Goldenberg, et al. (1997). "Habits of mind: an organizing principle for mathematics curriculum." Journal of mathematical behavior 15(4): 375402.
Elbers, E. (2003). "Classroom interaction as reflection: learning and teaching mathemtics in a community of inquiry." Educational Studies in Mathematics 54(1): 77 99.
Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. Mathematics teaching: The state of the art. P. Ernest. London, Falmer Press: 249253.
Flessner, R. (2009). "Working toward a third space in the teaching of elementary mathematics." Educational Action Research 17(3): 425446.
Freudenthal, H. (1968). "Why to teach mathematics so as to be useful." Educational Studies in Mathematics 1(1/2): 38.
Gooding, S. (2009). "Children's difficulties with mathematical word problems." Informal Proceedings of the British Society for Research into Learning Mathematics 29(3): 3136.
Halmos, P. (1980). "The heart of mathematics." The American Mathematical Monthly 87(7): 519524.
Jones, L. (2003). The problem with problem solving. Enhancing primary mathematics teaching. I. Thompson. Maidenhead, Open University Press: 8698.
Kilpatrick, J. (1975). Coping with word problems: observations of V.D. Petrova's class. Developing mathematical thinking. A. Floyd. London, AddisonWesley: 186192.
Macnab, D. (1999). "Mathematics education in Scottish schools: an uncertain vision?" Scottish Educational Review 31(1): 1020.
Mason, J., L. Burton, et al. (1982). Thinking mathematically. London, AddisonWesley.
Moffett, P. (2009). Dutch principles. Mathematics Teaching. 215: 1819.
Ollerton, M. (2010). Using problem solving approaches to learn mathematics. Issues in teaching numeracy in primary schools. I. Thompson. Maidenhead, Open University Press: 8496.
Polya, G. (1957). How to solve it. New York, Doubleday Anchor.
Polya, G. (1981). Mathematical discovery. New York, John Wiley and Sons.
Rogers, J. (2004). "Autonomy and mathematical problemsolving: the early years." Education 313 32(3): 2431.
Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sensemaking in mathematics. Handbook for Research on Mathematics Teaching and Learning. D. Grouws. New York, MacMillan: 334 370.
Scottish Executive (2007). Building the Curriculum 2: active learning in the early years. Edinburgh, Scottish Executive.
Scottish Government (2009). Curriculum for Excellence: Mathematics Principles and Practice, Learning and Teaching Scotland.
Scottish Government (2010). Building the curriculum 2  active learning: a guide to developing professional practice. Edinburgh, Scottish Government.
Toom, A. (1999). "Communications." For the learning of mathematics 19(1): 3638.
Van den HeuvelPanhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute Cdrom for ICME9. Utrecht, Freudenthal Institute.
Verschaffel, L. (2000). Realworld knowledge and the modeling of school word problems. The ninth international congress on mathematical education. H. e. a. Fujita. Makuhari Japan, Kluwer.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  mathematics, primary education 
Contacts
Course organiser  Mrs Susan Mclarty
Tel: (0131 6)51 6044
Email: susan.mclarty@ed.ac.uk 
Course secretary  Miss Jenna Mcculloch
Tel: (0131 6)51 6012
Email: Jenna.McCulloch@ed.ac.uk 

