Modes of Assessment

Different modes of assessment serve different purposes. Teachers may use them deliberately to focus on the process, progress and product of learning mathematics.

Various assessment activities are required to help teachers collect, judge and interpret information about students’ performance in their development of mathematical knowledge and skills, generic skills, and positive values and attitudes.

Designing appropriate and diversified assessment activities according to the learning targets and students’ learning needs is essential in implementing assessment as learning. Below are some common mathematics assessment activities.

 Class Discussion

In the learning and teaching of mathematics, there are often discussions, asking and answering questions between teachers and students or among students. A discussion in class not only enables teachers to discover what students understand about a particular topic, but also provides opportunities for students to present their views and foster their communication skills.

Teachers could also understand students’ attitudes and abilities in applying thinking skills through class discussions. Assessment criteria for a class discussion may include: Can students explain how they have got the solutions put forward and what strategies they have employed? Do students know how to raise questions? Do students raise questions actively? Constructive feedback from teachers allows students to understand the correctness of their response and achieve an in-depth analysis of the topic. Topics suitable for class discussions include: Why ? Why (x + y)² x² + y² ? How can the height of the school building be estimated? Are the areas of figures with the same perimeter equal? How can a right-angled triangle be constructed by using a straight rule and a pair of compasses? How statistics be applied in real life?

 Classwork and Homework

It is a common practice to assign classwork and homework to help students consolidate their concepts in mathematics and help teachers assess students’

performance. To embrace learner diversity, teachers may consider assigning different classwork to students of different abilities. In assigning homework, it is important for teachers to understand that it is about quality and not quantity.

Moreover, each assignment should be set at a suitable level of difficulty and appropriately related to specific learning objectives. It is inappropriate, for example, to give students an assignment on the drilling of addition and subtraction while the aim is to assess their application of addition and subtraction. Finally, classwork and homework for mathematics should not be confined to routine mathematical problems. There could be open-ended questions, reading assignments, hands-on assignments and preparatory work for class discussions. For example, collecting newspaper cuttings on the use of statistics in daily life for a class discussion on the misuse of statistics;

collecting containers with the volumes in litre written on them for measuring activities in school.

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 Project Work

Project work is a useful activity to assess students’ performance. It is also an effective learning and teaching strategy to promote self-directed learning and enables students to connect their mathematical knowledge, generic skills, values and attitudes. It can also foster students’ critical thinking skills, creativity and problem solving skills. Teachers should note that collaboration and communication skills will be more effectively developed through group projects than individual projects. Teachers may use the following criteria to assess students’ performance in project work:

- comprehension of the project;

- use of strategy and approach;

- coverage, depth and accuracy of content;

- presentation and communication; and

- attitude.

Students’ reflections and peer assessment can be an integral part of the assessment for project work and parents can also contribute their views. Using assessment rubrics is a good practice for self-reflection and peer assessment for achieving self-directed learning. IT may be employed to facilitate assessment of project learning, e.g. submitting students’ project work on schools’ e-platform and sharing of comments.

Typical examples of project work for mathematics include conducting a survey on students’ favourite extra-curricular activities, comparing the heights of boys and girls in the school, investigating the relationship between students’

eyesight and time spent watching TV or using display screen equipment, investigating the story of , designing containers with the optimal use of materials, investigating the application of mathematics in sport, and conducting a statistical survey on students’ time management. Cross-KLA topics or topics on real-life problems can also be assigned for promoting STEM education (refer to Examples 10 and 12 of this Guide for details).

 Exploratory Task and Performance Task

Exploratory tasks and performance tasks are classroom activities that require students to apply various skills to perform mathematical investigations or solve problems in a hands-on way. Through getting students to complete the

tasks in groups, teachers can look at students’ problem solving skills and collaboration skills. The assessment criteria can also include comprehension of the problem, use of strategy and approach, degree of participation and attitude, etc. Typical examples of exploratory tasks and performance task include constructing parallel lines, measuring volumes of irregular objects, geometric constructions by compasses and straightedge (or by dynamic geometry software), constructing special sequences by spreadsheet, making 3-D models of polyhedrons, constructing loci by dynamic geometry software, etc.

 Tests and Examinations

Generally, there are both tests and examinations in schools. Nevertheless, teachers should note the following when setting tests or examination papers.

- The coverage in the paper should be complete and the item format should be diversified.

- Each item should have clear assessment objective(s).

- The levels of difficulty of items should reflect and cater for students’

diverse abilities.

- The number of items in each paper should be reasonable.

- The language used in the paper should be simple, clear and straightforward.

Before setting a test or examination paper, teachers should prepare a specification table with allocation of marks to different learning units/objectives clearly shown. The allocation of marks should reflect the aims and focus of the paper and ensure adequate coverage of topics. The paper should embrace various types of items like explanatory, fill in the blanks, and multiple choice to assess students’ knowledge in various aspects of mathematics. Open-ended questions should also be included to assess students’

critical thinking skills, creativity and communication skills (refer to Examples 2, 5 and 14 of this Guide for details).

The incorporation of peer assessment and self-assessment in various assessment activities is also beneficial as they allow students to learn from peers and understand their own learning. These assessments also direct students to consider the main learning objectives, skills involved and perform self-reflection on the

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learning process and attitude. Learner diversity should also be considered in designing assessment activities. For example, there should be a balance among the number of elementary, intermediate and advanced problems in tests and examinations.

The use of e-assessment may enhance learning and teaching by providing instant feedback to both students and teachers. Students can base on the feedback to perform self-reflections when they are still working on the tasks, while teachers can understand students’ performance when their instruction is still in progress.

e-Assessment can also help adjust the levels of difficulty of assessment items to embrace learner diversity. Besides, students’ work and assessment data can be stored for future analysis.

On the whole, the most appropriate assessment activities for gathering information about students’ performance should be decided according to how the required information will be used and the kind of performance that will provide the information required. No matter which assessment activities are adopted in collecting information about students’ learning, the main purpose of assessment should always be for facilitating and improving students’ learning.