• Algebra
• Arithmetic
• Calculus
• Counting
• Functions and Graphs
• Geometry
• Matrices
• Mechanics
• Mensuration
• Probability
• Statistics
• Sets
• Trigometry
• Vectors
• Problem solving (including the model method)

 

Module Structure

Compulsory Lectures (8 × 1 hr) Topics to be included: Aims & objectives of mathematics education; mathematics curriculum in Singapore; learning theories in mathematics; mathematics pedagogical content knowledge; mathematical sense making; classroom teaching; technology in mathematics education; lesson planning; and an introduction to assessment.

Optional Lectures (3 × 1 hr) Designed to cover the content taught I A-levels, they are intended for students who have mathematics as their CS1 subject. However, they are open to any interested student.

Tutorials (32 × 2 hr) The teaching and learning of various mathematics topics, for example, Arithmetic, Algebra, Functions and Graphs, Mensuration, Geometry, Trigonometry, Statistics and Problem Solving (including the model method). The emphasis will be on both developing a deep understanding of the mathematical concepts in the topics and knowing how these topics fit into the curriculum structure; and, learning how this content can be effectively taught. Included in this discussion of pedagogy will be a variety of other issues that relate to classroom teaching: Lesson planning; learning difficulties; innovative teaching approaches; motivation techniques and management of instruction. Hands-on computer laboratory sessions will also be incorporated where appropriate.

 

Assessment Guidelines

The assessment for this module is intended to provide trainees with the opportunity to investigate possible ways to teach various mathematical topics, to develop the ability to use and evaluate the worth of a variety of instructional materials and to practice many of the skills required of a classroom teacher.

I. Craft Skills and Knowledge for Teaching Mathematics (45%)

Trainee teachers will learn the craft skills and knowledge that would help them succeed in the classroom. These are:

• Pedagogical Content Knowledge (PCK)
• Teaching and learning tools – ICT, worksheets, investigative projects
• Mathematical sense making – problem solving, applications, history

The assessment will take the form of 4 assignments:

I.1 Problem-solving assignment (10%)

Students will be assessed on their ability to demonstrate their understanding and knowledge of various problem solving heuristics and how they can be used in a secondary classroom. The emphasis will be consistent with the approach taken by individual tutors who will provide further details.

I.2 In-class tests (15%)

Students will be assessed on their application of the mathematics PCK learnt during this course. This assessment will consist of 3 in-class closed-book tests of 30 minutes each. The topics covered will be consistent with the emphases of individual tutors who will provide further details.

I.3 Design of worksheet (10%)

Students will be required to design a worksheet to be used by school students. The worksheet may but need not be ICT-based. The requirements of the assessment will be consistent with the emphases of individual tutors who will provide further details.

I.4 Use of ICT software (10%)

Students will be assessed on their knowledge of and ability to use a variety of ICT tools in their teaching. This assessment may consist of a single assignment, or several smaller ones that test specific skills. The requirements of the assessment will be consistent with the tools introduced by individual tutors who will provide further details.

 

II. Professional attitude, punctuality, attendance and participation in class (10%)

 

III. Group Presentation (20%) – starting about the 6 th or 7 th week of semester

1. Students will work in groups (of about 4) for this presentation
2. Each group will be ‘assigned’ a task on the teaching of a secondary school mathematics topic. The topic provides the scope but you do not have to cover everything included under the topic.
3. The group should meet to go through the entire cycle of sourcing for relevant materials from library and internet, selecting key ideas within the scope of the topic and planning the final presentation.
4. Each group is allocated 40 minutes.
5. The purpose of the presentation is to demonstrate the use of the materials and ideas that have been sourced and selected. The demonstration may take the following forms:
• A preamble of the materials, what you intend to do and why you are doing it. At this stage, consider your classmates as peers. This is followed by carrying out lesson segments (in one or more ‘classroom lessons’) to teach these ideas in class. In this case, you are to assume that you are teaching a class in school and that your NIE classmates are school students .
• A more detailed description of the materials and ideas that have been sourced, making clear how they are to be used in class.

The first type of demonstration has the advantage that all will really appreciate the material when it is actually used in a teaching setting. The second type of presentation has the advantage that you can cover more materials in your presentation. You may also have some parts of the presentation using the first form and some parts using the second form.

1. Each member of the group must present. The order of appearance is left to the group but the transition from one teacher to the next should be smooth.
2. The choice of the media of presentation is left entirely to the group. Use the media that the group considers most suited to what you intend to teach to a class in school. Provide worksheets if deemed necessary.
3. Both group and individual performances will be assessed. The assessment criteria are:

• Delivery & communication
• Relevance & suitability
• Level of class interest
• Group co-operation

1. The presentations will be carried out during tutorials/workshops around weeks 7 or 8. The schedule will be arranged by the tutors.

Group Presentation Tasks

• Mensuration – 2-D figures and 3-D solids
• Triangles, quadrilaterals and polygons
• Motion Geometry and tessellations for NT students
• Congruency
• Similarity
• Circle Properties
• Trigonometry
• Probability
• Statistics

 

Possible references (in red-spot or reference section)

Geometry

• Bennett, D. (2002). Exploring Geometry with The Geometer's Sketchpad. Key Curriculum Press, CA. (QA461 Ben)
• Britton, J. (1992). Teaching Tessellating Art. Palo Alto, CA: Dale Seymour Publications. (QA166.8 Bri)
• Britton, J. (2000). Symmetry and Tessellations. Palo Alto, CA: Dale Seymour Publications. (QA166.8 Bri)
• Burnett, J. (2001). Geo Paperpolygons: Exploring 2D Shapes through Paper Folding. Narangba, Qld.: Prime Education. (QA459 Bur)
• Frank, S. (1977). Was Pythagoras Chinese? University Park: Pennsylvania University Press. (QA27.C5 Swe)
• Gerver, R. et al (1998). South-Western Geometry: An Integrated Approach. Cincinnati: South-Western Educational Pub. (QA461 Sou)
• Jacobs, H.R. (2003). Geometry: Seeing, Doing, Understanding. New York: W. H. Freeman and Co. (QA453 Jac)
• Lindquist, M. M. & Shulte, A. P. (ed). (1987). Learning and Teaching Geometry, K-12. 1987 Yearbook. NCTM. (QA1 Nat)
• Lumpkin, B. (1997). Geometry Activities from Many Cultures. Walch Pub. (QA461 Lum)
• N. Z. EQUALS Network. (1990). Towards Better Trigonometry Teaching. Latitude Publications. (QA531 Tow)
• O’Daffer, P. G. & Phares, G. (1992). Geometry: An Investigative Approach. Reading, Mass.: Addison-Wesley. (QA445 Oda)
• Picciotto, H. (1999). Geometry Labs. Key Curriculum Press. (QA 461 Pic).
• Posamentier, A. S. (2000). Making Geometry Come Alive. Thousand Oaks, CA: Corwin Press, Inc. (QA459 Pos)
• Pugalee, D.K. & Friel, S. N. (2002). Navigating through Geometry in Grades 6-8. (with CD) Reston, VA: National Council of Teachers of Mathematics. (QA461 Nav)
• Serra, M. (1997). Discovering Geometry: An Inductive Approach. Emeryville, CA: Key Curriculum Press. (QA461 Ser)
• Serra, M. (2003). Discovering Geometry: An Investigative Approach. Emeryville, CA: Key Curriculum Press. (QA461 Dis)
• Seymour, D. & Britton, J. (1989). Introduction to Tessellations. Palo Alto, CA: Dale Seymour Publications. (QA166.8 Sey)
• Usiskin, Z. (2002). Geometry (Teacher’s Edition). Glenview III: Prentice Hall. (QA445 Geo)

Probability & Statistics

• Baker, D. (1989). Facts and Figures: A practical approach to statistics. Cheltenham, England: Stanley Thornes (Publishers) Ltd.
• Bright, G. W. (2003). Navigating through Data Analysis in Grades 6-8. Reston, VA: NCTM.
• Bright, G. W. (2003). Navigating through Probability in Grades 6-8. Reston, VA: NCTM. (QA276.18 Nav)
• Burrill, G., Franklin C. A., Godbold, L. & Young, L. J. (2003). Navigating through Data Analysis in Grades 9-12. Reston, VA: NCTM. (QA276.18 Nav)
• Graham, A. T. (1987). Statistical Investigations in the Secondary School. Cambridge: Cambridge University Press. (QA276 Gra)
• Lappan, G., Fey, J.T., Fitzgerald, W.M., Friel, S.N. & Phillips, E.D. (2002). Samples and Populations (Teacher Guide). Glenview: Prentice Hall. (QA135.5 Sam)
• Lappan, G., Fey, J.T., Fitzgerald, W.M., Friel, S.N. & Phillips, E.D. (2002). How Likely Is It? (Teacher Guide). Glenview: Prentice Hall. (QA135.5 Sam)
• Lovell, R. E. (1993). Probability Activities for Problem Solving and Skills Reinforcement. Berkeley, CA: Key Curriculum Press. (QA273 Lov)
• Newman, C. M., Obremski, T. E. & Scheaffer, R.L. (1987). Exploring Probability. Dale Seymour Publications. (QA273 New)
• Olson, E. T. (1998). Real-life Math: Probability. Portland, Maine: J. Weston Walch. (QA273.25 Ols)
• Shaughnessy, J. M., Barrett, G., Billstein, R., Kranendonk, H. A. & Peck, R. (2004). Navigating through Probability in Grades 9-12. Reston, VA: NCTM. (QA273.2 Nav)
• Shulte, A. P. & Smart, J.R. (1981). Teaching statistics and probability, National Council of Teachers of Mathematics, Reston. (QA1 Nat)
• The University of North Carolina Mathematics and Science Education Network (1996). Teach-Stat: For Teachers. New York: Dale Seymour Publications. (QA276.18 Tea)
• The Mathematics in Context Development Team. (1998). Dealing with Data (Teacher Guide). Chicago: Encyclopaedia Britannica Educational Corporation. (QA135.5 Dea)
• The Mathematics in Context Development Team. (1998). Take a Chance (Teacher Guide). Chicago: Encyclopaedia Britannica Educational Corporation. (QA135.5 Dea)
• Winters, M. J. & Carlson, R. J. (2000). Probability Simulations. Emeryville, CA: Key Curriculum Press. (QA273.25 Win)

 

Web Resources

1. Euclid’s Elements: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
2. Interactive Mathematics Miscellany and Puzzles: http://www.cut-the-knot.org/index.shtml
3. Manipula Math with Java: http://www.ies.co.jp/math/java/
4. Math Forum: http://mathforum.org/
5. National Library of Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html
6. NCTM Illuminations website: http://illuminations.nctm.org/
7. The Shodor Education Foundation: http://www.shodor.org/interactivate/activities/
8. Peanut software WINSTATS http://math.exeter.edu/rparris/

IV. Individual written report on Lesson Planning (25%)

Due on Monday 30 October, 2006 , 4 p.m.

This report involves the conceptualisation and design of a double period (70 minutes) teaching lesson. You will be assigned a topic by your tutor. Your report should consist of the following components:

A. Table of contents

B. Introduction

• Specify the topic, level, stream and type of pupil.
• Break down the unit in which the lesson is situated and sequence the content for the different lessons. Indicate the number of periods required for the different parts of the unit.
• To support your conceptualization of the lesson, consult books, journals and other resources relevant to the teaching of your lesson. Based on what you have read or found out, write a short summary of teaching approaches, learning activities or common learning difficulties and misconceptions that are specific to your lesson.

C. Development of lesson & evaluation - Detailed lesson plan

• You may choose your own format of the lesson plan but all essential components of a lesson plan must be included.
• Describe tasks and procedures selected and provide a rationale for the choice.
• Describe the teacher’s key moves and pupils’ (intended) actions.
• Include key questions and expected answers.
• Describe the class organisation (whole-class, group, pair or individual).
• Provide all teaching materials (teaching examples, non-examples, worksheets, slides, etc if applicable). In the case of teaching aids, do not submit the actual teaching aids but produce pictures, illustrations or plans how these aids can be made.
• For homework assignments or class practice, provide the actual items and/or worksheets to be used.

Presentation of report

• Your report should be submitted on A4 size papers and page-numbered. Use font size 12 and single spacing. The report should be proof-read and corrected for spelling, punctuation and syntactical errors.
• Your report should not exceed 10 pages in length (excluding the appendices).
• The following information must be indicated on the title page:
• Name of student
• Name of lecturer
• Date of submission
• All ideas, information and quotations taken from books and journals must be appropriately acknowledged in the text itself and the source included in the references.
• Cross-referencing to appendices must be accurate and clear.

• GCE 'N', 'O' and 'A' Levels Mathematics syllabuses
• Graphmatica Original Site
• Geometer's Sketchpad

• OHT on Writing Definitions
• Sample Assignment (Problem Solving)
• ICT Assignment Sample 1
• ICT Assignment Sample 2
• ICT Assignment Sample 3
• Guidelines for writing the Lesson Planning Assignment
• Sample Paper (Maths)
• Sample Paper (A Maths)