Teachers

This workshop will assist primary mathematics teachers to examine the techniques and processes of designing open-ended tasks or problems for their primary students. In this age of accountability, teachers need more and more varied data about their students' mathematical understanding. One way to acquire these data is through the use of assessment tasks that are open-ended. Open-ended tasks have more than one answer and may be solved in a variety of ways. In addition to producing an answer, students must also show their solution process and justify their answer. Open-ended tasks offer opportunities for students to demonstrate their mathematical thinking, reasoning processes, problem-solving and communication skills. As open-ended tasks invite a wider range of solutions and solution methods than closed problems, they can be used to probe deeper understanding of concepts and to promote creative thinking. The workshop will discuss the rationale for introducing open-ended tasks in the classroom, the process of designing open-ended tasks and illustrate some examples of solving open-ended tasks. Teachers will also be given the opportunities to assess samples of students’ open-ended task solutions.

In teaching mathematical problem solving, teachers appear to use one or two strategies of solving a mathematical problem in the classroom. Although some teachers have explicitly advocated students to use varied strategies to solve mathematical problems, students continue to solve a problem using one or two strategies. Research has also indicated that good novice problem solvers were unable to solve problems in more than one way. This session offers insights on how different types of mathematical problems could be solved using varied strategies. Teachers will also learn how to be better problem solvers through the effective use of heuristics and explore strategies for establishing problem-solving environments.

An effective questioning strategy goes beyond finding what has been learned. This workshop will assist mathematics teachers to examine the characteristics of effective questioning. The workshop will discuss the common problems in connection with questioning in the mathematics lessons. Strategies to improve the teachers’ questioning techniques will also be discussed.

Journal writing is incredibly flexible instructional tool that may be used for communication between the student and teacher. Teachers could use journal writing as an alternative assessment in the mathematics classroom. This workshop will present the rationale for workshop will also show to teacher how to carry out journal writing in the primary school mathematics classrooms. Samples of the primary school students’ journals will be illustrated. Scoring rubric for grading journals will be showed.

Learning Objectives

1. To interpret the Primary Mathematics syllabus
2. To set MCQ and SAQ test items
3. To set LAQ test items
4. To vet and modify test items
5. To write a marking scheme
6. To have a hands-on session

The Singapore mathematics assessment framework measures and evaluates what we value in the Singapore mathematics curriculum framework - skills, concepts, processes, metacognition and attitude. This workshop seeks to highlight problem-solving items which go beyond testing skills. Ideas and approaches to prepare primary students to deal with such problem-solving items will be presented. This workshop will also assist primary mathematics teachers to examine the techniques and processes of using assessment items in engaging primary students through mathematical reasoning.

This workshop provides an opportunity for the teachers to learn how to teach less to their students so that they will learn more. It is a call to re-examine the fundamentals of teaching and learning - why we teach, what we teach and how we teach. This workshop also will assist primary mathematics teachers to examine the techniques and processes of conducting activity-based lessons for their primary students. The brain learns best and retains most when the organism is actively involved in exploring physical sites and materials and asking questions to which it actually craves answers. Teachers will also learn how to use manipulative to help students understands mathematics concepts. In this workshop, activities will help the students to link what they have learnt in the mathematics classroom to the real world.

Mathematical games are popular with teachers as alternatives to more traditional forms of repetitive practice, for many parts of the mathematics curriculum, and especially for arithmetical computation. The research literature, as well as popular commercial publishing, supports the idea that mathematical games can fire students’ interest and motivation because students enjoy competition, challenge, and fun. In this workshop, teachers will learn how to specify learning outcomes related to the mathematical games and reinforce their relevance to students. This workshop will present the rationale for integrating mathematical games in the primary school mathematics classrooms. The workshop will also show to teacher how to carry out mathematical games in the primary mathematics lessons. Samples of mathematical games also will be showed, explained and played.

This workshop will assist primary mathematics teachers to examine the techniques and processes of using tangram in teaching mathematical concepts. The tangram is a versatile manipulative that could be used to teach and learn mathematical concepts such as shapes, spatial relationships, fractions, percents, ratio, area, and geometry. This workshop will also present some ideas, activities and strategies that may be suitable for primary students to use tangram in learning mathematical concepts.

In teaching mathematical problem solving, teachers appear to use one or two strategies of solving a mathematical problem in the classroom. Research has also indicated that good novice problem solvers were unable to solve problems in more than one way. This session offers insights on how different types of mathematical problems could be solved using varied strategies. Polya’s four stages of problem solving will be introduced so that teachers and students will have a framework to assist them to solve non-routine problems. Each stage of Polya's model will be discussed in detailed in the workshop so that it could be implemented in the instructional process.

Workshop materials would be provided to each teacher-participant for the above-mentioned workshops.

In this workshop, teachers will learn how to make use of games as a tool for students to learn mathematics and to develop problem-solving skills. It will be a fun-filled hands-on workshop where teachers will also play the games and discover various winning strategies. The games are:

• Game of Fifteen (combination of Magic Square and Tic-tac-toe)
• Maths Warriors
• Game of Nim

Duration: 3 hours
Level: Primary School

Finger Arithmetic is a wonderful technique that uses the memory and fingers to help students reinforce their basic computational and mental mathematics skills. It is excellent for counting drills and can help students with short attention spans. It is easy, fun, accurate and can be faster than using a calculator. Last but not least, it enhances self-esteem and boosts morale of students weak in mathematics.

This workshop aims to help teachers to use the Geometer's Sketchpad (GSP) as a virtual manipulative to explore mathematical concepts and ideas and to use GSP as a visual aid to visualise mathematical objects better. At the end of the workshop, teachers should be able to discover important mathematical concepts and ideas with the help of GSP, enhance their spatial visualization skills, use GSP to construct geometrical figures, develop thinking skills, apply what they have learnt to solve problems and create an end product linked to the Math topic on Geometry.

This workshop will assist primary mathematics teachers to examine the techniques and processes of using mathematical games, mathemagic and competing fun mathematical quizzes in engaging low-achieving primary students in the learning of mathematics. Teachers will learn to use mathematical games, mathemagic and competing fun quizzes to introduce mathematics lessons, to finish mathematics lesson on a ‘high note’ so as to arouse curiosity or to extend the thinking of primary students. This workshop will also present various types of mathematical games, mathemagic and competing fun mathematical quizzes.

This workshop prepares teachers who might be tasked to coach their students in mathematics competitions. The workshop discusses the problem solving heuristics in handling higher order thinking skills.

Pattern gazing is one important aspect of mathematical problem solving. Some problem solving heuristics, e.g. generalisation and making conjectures, and mathematical thinking skills, e.g. inductive reasoning, are especially highlighted here. In this session, teachers are introduced to the skills involved in pattern gazing, in the context of mathematics competition questions.

Students are introduced to arithmetic at a very young age. However, there are many skills and “tricks” in arithmetic which are not very much emphasised in the usual mathematics curriculum. In this workshop, teachers will be introduced to quick ways of arithmetic computation, creative ways of performing the operations, all of which are either based on the usual mathematics curriculum or on algebraic rules. While algebra is not in the primary school mathematics curriculum, many arithmetic rules are based on these results of computation.

Number Theory involves the study of properties of whole numbers. This is a very rich branch of mathematics in which many creative problem solving strategies can be introduced. In part one of Number Theory, teachers will be alerted to some marvellous properties of numbers, and how these can be applied to solve some interesting questions in the mathematics competitions.

In this second part of the Number Theory course, teachers will be introduced to more in-depth properties of numbers: more on number patterns, derivation and application of divisibility tests, principles behind designing interesting number games suitable for the primary school level. All these lead teachers to prepare their students to handle more challenging number theory questions in the mathematics competition.

Making decisions in real life makes use of realistic (non-routine rules). Many of these rules are often not covered in the school mathematics curriculum, not because they are not important, but because they are very situational and “commonsensical”. Usually, a proportion of any mathematics competition questions involve this aspect. In this workshop, teachers will be introduced to some standard algorithms can be used to solve interesting real life problems. Many of these problems occur frequently in some of the mathematics competitions.

Many real life problems involve some sort of optimisation (i.e. finding the “best” possible solutions). This is a continuation of Decision Mathematics I which involves deriving non-routine algorithms. In this workshop, teachers will be introduced to some traditional interesting problems, and how these problems can be used to generate more challenging problems to prepare students for higher order thinking.

Many geometry problems involves finding areas of figures, not by using formulae but by considering areas in proportion using creative means. This is one critical aspect of geometry problems in relation to fractions and proportions which students usually encounter as higher order thinking questions. In this workshop, teachers are introduced to some of these aspects through the use of samples of mathematics competition questions.

In this workshop, teachers will be introduced to more properties of polygons and circles, and how these formulae and results can be used to solve challenging mathematics problems. These formulae can be applied very creatively to solve challenging mathematics problems.

This workshop focuses on the development of lessons to facilitate learning that is consistent with the TSLN philosophy. Teachers would be engaged in samples of such lessons, which are classified in eight categories:

• Lessons to help children construct procedural knowledge
• Lessons to help children construct conceptual knowledge
• Lessons to help children extend knowledge
• Lessons to help children refine knowledge
• Lessons to help children use knowledge
• Lessons to develop creative thinking
• Lessons to develop critical thinking
• Lessons to develop metacognition.

This workshop would help teachers improve important techniques such as worksheet development and appropriate questioning. The purpose of this workshop is to allow teachers to attempt some child-centred lessons. Through teaching child-centred lessons, it is hoped that, in the long run, students in the school would be equipped with sound concepts, skillful processes and good habits of mind when they graduate.

Visualisation is the ability to manipulate three-dimensional objects that are represented in two-dimension without the benefit of the objects. It becomes the focus of the 2007 curriculum where computation is de-emphasized and visualisation is emphasized. In this workshop, teachers will learn several techniques to help students develop the ability in visualisation. Techniques for students in different grade levels will be demonstrated. Remediation for older students who cannot visualize well will also be demonstrated. This workshop will assist primary mathematics teachers to examine the techniques and processes of using activities to enhance students’ spatial visualisation.