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Flow Chart : Compulsory Part with Module 2 (Algebra and Calculus)

Chapter 5 Assessment

5.4 Internal Assessment

This section presents the guiding principles that can be used as the basis for designing the internal assessment and some common assessment practices for Mathematics for use in schools. Some of these principles are common to both internal and public assessment.

5.4.1 Guiding Principles

Internal assessment practices should be aligned with curriculum planning, teaching progression, student abilities and local school contexts. The information collected will help to motivate, promote and monitor student learning, and will also help teachers to find ways of promoting more effective learning and teaching.

(a) Alignment with the learning objectives

A range of assessment practices should be used to assess the achievement of different learning objectives. These include testing candidates’ ability to: think critically and creatively; conceptualise, investigate and reason mathematically; use mathematics to formulate and solve problems in real-life as well as in mathematical contexts and other disciplines; and communicate with others and express their views clearly and logically in mathematical language. The weighting given to different areas in assessment should be discussed and agreed among teachers. The assessment purposes and criteria should also be made known to students so that they have a full understanding of what is expected of them.

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(b) Catering for the range of student ability

Assessment practices incorporating different levels of difficulty and diverse modes should be used to cater for students with different aptitudes and abilities. This helps to ensure that the more able students are challenged to develop their full potential and the less able ones are encouraged to sustain their interest and succeed in learning.

(c) Tracking progress over time

As internal assessment should not be a one-off exercise, schools are encouraged to use practices that can track learning progress over time (e.g. portfolios). Assessment practices of this kind allow students to set their own incremental targets and manage their own pace of learning, which will have a positive impact on their commitment to learning.

(d) Timely and encouraging feedback

Teachers should provide timely and encouraging feedback through a variety of means, such as constructive verbal comments during classroom activities and written remarks on assignments. Such feedback helps students sustain their momentum in learning, and to identify their strengths and weaknesses.

(e) Making reference to the school’s context

As learning is more meaningful when the content or process is linked to a setting which is familiar to students, schools are encouraged to design some assessment tasks that make reference to the school’s own context (e.g. its location, relationship with the community, and mission).

(f) Making reference to current progress in student learning

Internal assessment tasks should be designed with reference to students’ current progress, as this helps to overcome obstacles that may have a cumulative negative impact on learning. Teachers should be mindful in particular of concepts and skills which form the basis for further development in learning.

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(g) Feedback from peers and from the students themselves

In addition to giving feedback, teachers should also provide opportunities for peer assessment and self-assessment in student learning. The former enables students to learn among themselves, and the latter promotes reflective thinking which is vital for students’ lifelong learning.

(h) Appropriate use of assessment information to provide feedback

Internal assessment provides a rich source of data for providing evidence-based feedback on learning in a formative manner.

5.4.2 Internal Assessment Practices

A range of assessment practices suited to Mathematics, such as tests, examinations, homework assignments, oral questioning, projects and exploratory tasks can be used to promote the attainment of the various learning outcomes. However, teachers should note that these practices should be an integral part of learning and teaching, not “add-on” activities.

Among the most widely used methods for internal assessment are tests, examinations and homework assignments:

Tests can be used for:

• determining what students have mastered and whether they are ready to proceed to the next teaching unit; and

• providing information to teachers so that they can make adjustments in their teaching.

Examinations can be used for:

• deciding whether students have progressed satisfactorily over a school term; and

• providing information about students’ learning to other schools, educational institutions and employers.

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Homework assignments can help:

• students to consolidate concepts in mathematics; and

• teachers to assess the performance of their students.

It is important to ensure that the number of homework assignments given is not excessive and that they are at a suitable level of difficulty and related appropriately to specific objectives. Also, they should not be confined to routine mathematical problems. When marking homework assignments, specific, clear, constructive and supportive comments, and suggestions for improvement, should be given as this helps students to identify their strengths and weaknesses and to know what is required for improvement.

Other possible practices are:

Oral questioning

Oral questioning need not be seen as a test of spoken language only – it can be helpful in other subjects also. It is a flexible approach which allows teachers to discuss matters in depth with able students, to tease out the meaning of obscure statements, and to find out the reasons for conclusions. Teachers are encouraged to try using oral assessment as it can be a valuable supplement to conventional assessment methods.

Projects

A project is any piece of assigned or mutually agreed work from which the constraints of lesson time have been largely removed. Asking students to carry out project work provides them with an opportunity to study a topic of interest in depth. Teachers may wish to draw the following steps in the process to their students’ attention:

• Clarify the areas of interest

• Establish a framework for enquiry

• Find and select resource materials

• Organise data

• Present findings

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Exploratory tasks

Exploratory tasks can be very useful in learning and teaching mathematics as a way of monitoring students’ investigative abilities, higher-order skills and achievements on a continuing basis, and the scores on the tasks can be used to form part of the record of student progress. The use of appropriate tasks which are aligned with learning objectives can help to reduce the pressure of summative assessment; and the results on the tasks can also reflect the effectiveness of teaching and so lead teachers to make reasonable adjustments to their teaching strategies.