Appendix 1
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Mathematical Skills4
Mathematical skills include the ability to perform computations and estimations of numbers in various forms, to describe spatial relationships between objects, to perform measurements, to manage data, to employ logical reasoning for drawing valid conclusions, and to apply mathematical concepts in different contexts.
Key Stage 1 Key Stage 2 Key Stage 3 Key Stage 4
Students will learn to
perform comparison and basic computations of whole numbers
describe shapes, sizes and positions
apply the knowledge of measurement and use appropriate units and tools for measurement
present data by means of and retrieve information from simple charts and graphs
perform simple
deductions with the use of basic logical concepts, such as “and”, “or”, “all”,
“some”, “because”, “if … then” and “contradiction”
apply simple
mathematical knowledge in daily life
Students will learn to
perform computations and simple estimations involving whole numbers, fractions, decimals and percentages, such as estimating expenses
use simple geometric properties, such as symmetry, parallel and perpendicular, to describe shapes, sizes and positions more accurately
apply strategies and formulae in measurement
collect and process data, present data by means of suitable charts and graphs and retrieve information from charts and graphs
perform deductions, such as syllogism and provide counter examples
apply mathematical concepts in daily life
Students will learn to
handle very large or very small numbers and negative numbers with a sense of scale
perform numerical manipulations, such as percentage changes, and perform estimations with appropriate strategies
describe the rules of arrangement of objects or occurrence of events, such as the pattern formed by a set of shapes and the trend of population growth
describe spatial relationships between objects using distance, angle, scale, bearings and gradient
choose appropriate tools and strategies to find
measurements according to the degree of accuracy required by the specific purpose
use different methods for handling (i.e. collecting, organising, analysing and presenting) quantitative information and make reasonable interpretation of the results
estimate risks and chances through the use of elementary probability
perform deductions and verifications, and check their validity
apply various mathematical concepts in authentic situations
Students will learn to
evaluate the appropriateness of tools and strategies for handling quantitative information
use quantitative information for making informed decisions in different contexts
evaluate processes of deductions to avoid committing logical fallacies
apply various
mathematical concepts in different contexts with appropriate strategies and be aware of the need to make adaptations in new situations
4 In the context of generic skills, Mathematical Skills refer to the ability to apply mathematics in different key learning areas and subjects. The concepts and skills of the Mathematics subject to be applied are only those generally applicable to various disciplines.
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Information Technology Skills
Information technology skills are the ability to use IT critically to search, select, analyse, manage and share information. Mastery of IT skills facilitates collaborative learning, problem solving and self-directed learning.
Key Stage 1 Key Stage 2 Key Stage 3 Key Stage 4
Students will learn to
operate computers or mobile devices
input Chinese characters
use e-resources to support learning with the help of teachers
recognise some methods to locate and access information with given search criteria
generate, present, and safely share ideas with IT tools in learning activities
Students will learn to
use a variety of software packages for word-processing, calculation, image-processing and other learning activities
produce multimedia
presentations with simple design
search, select and prudently share information via computer networks and other media
process information and produce user-generated content5 using IT tools
Students will learn to
use appropriate IT tools to facilitate learning
use IT tools and strategies for processing and presenting information
produce multimedia
presentations with appropriate design for different purposes
communicate and collaborate with others via computer networks and other media
verify and evaluate the accuracy and reliability of information
Students will learn to
strengthen capability in IT usage for lifelong learning
analyse and ethically use information from different sources for specific purposes
compare the effectiveness of various ways, including the use of IT tools, to solve a given problem
select and apply appropriate IT tools in different aspects of study, including processing information, generating and communicating original ideas artfully to audience with different backgrounds
5 User-generated content refers to content that is produced and shared by end-users of digital media.
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Critical Thinking Skills
Critical thinking is drawing out meaning from available data or statements, and examining and questioning their accuracy and credibility in order to establish one’s views and evaluate the arguments put forward by oneself and others.
Key Stage 1 Key Stage 2 Key Stage 3 Key Stage 4
Students will learn to
extract, classify and organise information
identify and express main ideas, problems or core issues
understand straightforward cause-and-effect relationships
distinguish between obvious fact and opinion
notice obvious contradictions, seek clarifications and make simple predictions
draw simple but logical conclusions not contradictory to given data and evidence
Students will learn to
make inductions/inferences from sources
cross-reference other sources to determine the reliability of a source
understand the concepts of relevance and irrelevance
distinguish between fact and opinion as well as source and evidence
recognise obvious
inconsistencies, omissions, assumptions, stereotypes and biases
formulate appropriate questions, and make reasonable
predictions and hypotheses
draw logical conclusions based on adequate data and evidence, and make predictions about consequences
Students will learn to
identify the issue at stake
clarify and define key words to guide thinking
compare information from different sources, note contrasts and similarities, and determine its reliability
differentiate between fact, opinion and reasoned judgement
recognise that information providers’ value orientations and ideologies would affect the perspectives or judgement of sources
recognise and challenge stereotypes, emotional factors, propaganda and fallacies
draw and test conclusions as well as hypotheses, identify reasonable alternatives and predict probable consequences
admit their own limitations, shortcomings or errors of the thinking process
Students will learn to
differentiate between real and stated issues, false and accurate representations, and relevant and irrelevant evidence
differentiate between
sophisticated fact, opinion and reasoned judgement
recognise and challenge subtle or fundamental assumptions, permeating value orientations and ideologies
recognise that the selection and deployment of information/facts are affected by personal
perspectives
draw warranted conclusions, predict and assess probable consequences and make
reasoned judgement in reading, writing and speech
apply appropriate thinking skills to evaluate and reflect on their thinking process and suggest ways for improvement
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Creativity
Creativity brings in changes or transformations and is manifested in new ideas, acts or products. It emerges spontaneously or through deliberate processes of divergent and convergent thinking. It involves the integration of general or domain-specific knowledge for a meaningful purpose.
Although the expected achievements of the students in this generic skill cannot be suitably classified according to Key Stages, development of creativity involves the following abilities, dispositions and favourable factors for nurturing creativity.
1. Abilities
Abilities Descriptions
Sensitivity To discern details from observation and quickly respond to stimulus Fluency To generate numerous ideas promptly
Flexibility To adapt varied ideas and to initiate new thoughts for action Originality To produce unusual, novel and unique ideas
Elaboration To expand, refine and embellish ideas
2. Dispositions
Dispositions Descriptions
Curiosity To show interest and desire to find out more
Risk-taking To show courage and determination to deal with uncertainties or ambiguities Imagination To enjoy fantasising and generating new ideas
Complexity To be attracted to intricacies and novelty; to embrace challenges
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3. Favourable Factors for Nurturing Creativity6
Favourable Factors Corresponding actions
Place To foster a supportive environment (open, inviting and accepting atmosphere; resourceful, safe yet stimulating environment)
Person To recognise and accommodate the wide range of attributes and dispositions of students (strengths, weaknesses, learning styles, learning needs, motivation and readiness)
To identify and develop students' potential for creative acts Process To open up alternatives for students to explore personal interest
To provide interesting and stimulating themes conducive to arousing creative acts and satisfying a craving
To expose students to various stages of creating new ideas, acts or products (preparation, incubation, illumination and verification)
To value attempts to present new ideas and encourage further refinements
Product To encourage creative actions and output (ideas, plans, methods, solutions, products, theories)
To value the creative experience and celebrate students’ creative output
To encourage students to persuade others (especially experts in the field) to accept the creative output
6 Mooney, R. L. (1975). A conceptual model for integrating four approaches to the identification of creative talent. In C. W. Taylor & F. Barron (Eds.), Scientific Creativity: Its Recognition and Development (pp. 331-340). New York, NY: Robert E. Krieger.
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Problem Solving Skills
Problem solving involves using various skills to resolve a difficulty. The process includes investigating the problem, synthesising information and generating ideas to determine the best course of action. Students need to adjust and evaluate strategies, as well as consolidate experience for knowledge construction.
Key Stage 1 Key Stage 2 Key Stage 3 Key Stage 4
Students will learn to
develop ideas about the problem and identify related sources of information
identify, under guidance, one or more ways of tackling the problem
choose and implement a solution plan, using support and advice given
follow the given step-by-step methods to check and describe the outcomes
Students will learn to
identify the problem and describe its main features
propose alternative courses of action for solving it
plan and try out the selected option, obtain support and make changes when needed
develop an appropriate method to measure the effectiveness of the solution plan adopted
gain insights from the problem solving process
Students will learn to
explore the problem and identify its main focus
suggest and compare the possible outcomes of each alternative course of action and justify the option selected
execute the planned strategy, monitor the progress and make adjustment when necessary
evaluate against established criteria the quality of outcomes, and review the effectiveness of the problem solving process
formulate personal views, and paraphrase or construct analogies to explain how the problem is solved
Students will learn to
recognise the complexity of the problem and search for
appropriate information required to solve it
formulate feasible strategies to achieve optimal results,
considering both long and short term objectives
modify objectives or strategies and suggest remedial or enhancing measures to cope with circumstantial changes or difficulties
evaluate the overall strategy and outcomes, and anticipate future problems that may be incurred
consolidate experience on problem solving for knowledge construction
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Self-management Skills
Self-management skills comprise essential life skills and desirable personal qualities such as maintaining emotional stability, making decisions and exercising self-discipline. Self-management skills enable students to embrace challenges encountered on a personal or team basis.
The expected achievements of the students in this generic skill are classified according to different levels of mastery.
Elements of
Self-management Skills Beginning --- Developing --- Mastering Students will learn to
Self-worth express positive statements about themselves
identify and apply personal skills, attitudes and values to overcome challenges
uphold, synthesise and renew their own beliefs and values
Goal setting and tracking
set goals to assist their learning and personal development
set and keep track of realistic goals
set, keep track of, and be reflective on and accountable for goals which work towards excellence in life
Decision making make decisions in daily life situations with supporting reasons
list out and evaluate the pros and cons of a suggestion, and make prediction about the
consequences of a decision
consider all factors, such as technical, ethical, resource and community considerations before making a decision
60 Confidence,
resilience and adaptability
develop confidence and resilience in performing simple tasks and appreciate the progress made
demonstrate motivation, confidence, commitment and adaptability when faced with new or difficult situations, and derive satisfaction from
accomplishments and efforts
demonstrate confidence and adaptability in adversities, tolerate ambiguities and appreciate lessons learnt from mistakes
Appropriate expression of emotions
understand, accept and
appropriately express emotions
describe their feelings, such as joy and disappointment and identify factors contributing to these feelings
use appropriate means to contain or release their emotions
Managing resources demonstrate care for personal properties and shared resources
treasure and make good use of time, money and other resources
suggest ways for effective, equitable and ethical use of resources
Keeping promises to others
keep promises and fulfill obligations
assess feasibility before making promises
make determined efforts to keep promises
take responsibility and make up for broken promises obliged by
circumstances Self-discipline exercise self-control against
distractions, and focus on and complete given tasks at hand within a given time
extend self-control in scope and duration over personal impulses through developing positive thinking and self-affirmation
exercise self-control naturally as a habit of mind
Reflective practice review their learning readily to know more about themselves and how they work
form habits of reviewing their learning and identify factors that contribute to or hinder their learning effectiveness
sustain self-improvement by paying attention to and making judicious use of feedback
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Self-learning Skills
Self-learning skills refer to the ability to initiate, plan, carry out, evaluate and adjust learning activities autonomously. Students with advanced self-learning skills can select or design effective strategies for in-depth learning. These skills help students enhance their academic performance and self-efficacy. Self-learning skills form the core part of lifelong learning and help students acquire new knowledge to adapt to the fast changing world.
Key Stage 1 Key Stage 2 Key Stage 3 Key Stage 4
Students will learn to
consciously listen and read to learn, and actively present their learning
concentrate and pay
attention to instructions
identify and retain main ideas
collect information from given sources and organise it into pre-determined categories
try out different means to present ideas and
demonstrate learning
develop simple learning plans to meet short term targets
show interest in enquiring further
Students will learn to
take initiative in the enquiry learning area selected by themselves
actively locate required
information from different media
take initiative in identifying and organising main points from different sources, e.g. note-taking, mind-mapping
decide on the most suitable means to present ideas and demonstrate learning
seek help appropriately when necessary
manage time to complete tasks according to a plan
make use of feedback to reflect on the effectiveness of different learning tactics
Students will learn to
initiate learning activities and apply relevant personal strengths to overcome challenges
set learning plans with stage-wise goals
identify lines of reasoning and possible hidden ideas in sources
function effectively in a group to achieve the learning goals
decide on the most suitable means to manage and present knowledge
adjust the learning strategies to improve learning effectiveness
Students will learn to
initiate challenging learning activities and develop relevant personal
strengths to overcome challenges
plan and set goals for self-initiated enquiries
autonomously select or design more effective learning strategies for in-depth learning
evaluate key ideas, opinions and arguments identified from different sources independently, and synthesise them to construct and develop their own interpretation
evaluate and suggest ways to improve the effectiveness of learning strategies
learn beyond the prescribed
curriculum and apply knowledge in a variety of contexts
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Collaboration Skills
Problem solving, planning and making decisions in a small group require collaboration skills, namely the skills of communication, appreciation, negotiation, making compromises and asserting leadership. Students with these skills will be able to effectively engage in and contribute to tasks involving teamwork.
The expected achievements of the students in this generic skill cannot be suitably classified according to Key Stages.
1. Understanding the nature of group work Students will learn to
recognise the need for teamwork and that the team has a shared responsibility
recognise that individuals as well as the team have to take the consequences for their own actions
2. Desirable dispositions for group work Students will learn to
be open and responsive to others’ ideas; appreciate, encourage and support the ideas and efforts of others
be active in discussing and posing questions to others, as well as in exchanging, asserting, defending and rethinking ideas
recognise and avoid stereotyping; withhold premature judgement until the facts are known
be willing to adjust their own behaviour to fit the dynamics of various groups and situations
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3. Skills for group work Students will learn to
Goal setting select a strategy and plan cooperatively to complete a task in a team
Role taking understand the strengths and weaknesses of members and maximise the potential of the team
clarify and accept various roles and responsibilities of individual members in a team and be willing to follow team rules Synergising liaise with members for views and resources
negotiate and compromise with others
Reflection reflect on and evaluate the strategy used by the group and make necessary adjustments
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Collaborative Problem Solving Skills
Collaborative problem solving skills, an example of integrative use of generic skills, refers to students’ ability to solve problems with synergised efforts through effective division of labour, as well as incorporation of information from multiple sources of knowledge, perspectives and experiences.
Compared to individual problem solving, collaborative problem solving has distinct advantages because it enhances the creativity and quality of solutions through stimulation brought by the ideas of other group members7. In the 21st Century, it is particularly important for people with different perspectives and talents to solve problem as a team with the effective use of communication technology.
The expected achievements of the students in collaborative problem solving skills are classified according to different levels of mastery.
Students will learn to
Beginning Developing Mastering
Collaboration
be ready to act responsively and reach the goals with team members
follow the rules and instructions set for the team work
participate actively in the team and contribute to achievement of the team goals
share other team members’ perspectives on the problem and establish a common understanding
identify and capitalise on the talents and potential of members
be able to work with different people and accept the adjustments to plans or roles in changing situations
treasure working as a team and take
initiative to foster synergy for attaining the team goals
show mutual respect and support when dealing with difficult people and situations
take initiative to propose plans or make adjustments to the plans and roles in changing situations
7 Adapted from OECD 2015 PISA Framework
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Beginning Developing Mastering
Communication
comprehend messages with an open mind and ask questions to identify the problem and team goals
express oneself clearly to team members by verbal and/or non-verbal means
show courage in sharing new or unconventional ideas
ask meaningful questions that clarify the vision, goals and viewpoints for better solutions
respond specifically to queries raised during the problem solving process
enhance mutual understanding through effective means and with a respectful attitude
negotiate for consensus and foster a cooperative atmosphere to resolve conflicts
take the initiative in introducing new resources and exploring further ideas to facilitate the team to progress further
Problem Solving
propose solutions or strategies to solve a problem
complete the task assigned to one’s role in the team
select a problem solving strategy and develop an action plan
execute actions that comply with the planned distribution of roles and make adjustments when necessary
select a problem solving strategy and prepare alternative plans
monitor and evaluate individual and team effectiveness