Ongoing Renewal of the School Curriculum – Focusing, Deepening and Sustaining
Updating the Mathematics Education Key Learning Area Curriculum
(Primary 1 to Secondary 6)
Consultation Brief
Curriculum Development Council
November 2015
Contents
Preamble: Ongoing Renewal of the School Curriculum
- Focusing, Deepening and Sustaining
p.1
1. Why and how is the Mathematics curriculum updated?
p.3
2. What are the major updates?
2.1 Revisiting the curriculum aims
2.2 Updating the curriculum framework 2.3 Pedagogies (including e-learning) 2.4 Assessment
2.5 Curriculum management and planning of learning time
p.6
3. What are the supporting strategies?
3.1 Learning and teaching resources 3.2 Partnerships with key players in the
community
3.3 Professional development of school leaders and teachers
p.25
4. Frequently Asked Questions p.30
Appendices p.33
(black page)
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Preamble
Ongoing Renewal of School Curriculum – Focusing, Deepening and Sustaining
The Learning to Learn curriculum reform that started in 2001 has been promoting curriculum and pedagogical change that fosters learners’ whole-person development and learning to learn capabilities to achieve lifelong learning. Over the past decade or so, much has been achieved in schools through the implementation of the reform.
To mention a few of the achievements, the curriculum reform has brought about a new breed of students who are more proactive and in possession of greater learning agility and stronger transferable skills; the strength of our students’ performance in mathematics, science and reading in Chinese is internationally recognised; teachers have achieved a paradigm shift from teacher-centred classroom practices to learner-centred learning; the assessment culture in schools has changed with greater emphasis placed on assessment for/as learning; and there is increasing collaboration among teachers within and across schools.
Alongside the implementation of the Learning to Learn curriculum reform, there have been a lot of changes and challenges in our society and around the world, such as those observed in economic, scientific, technological and social developments. To maintain Hong Kong’s competitive edge and to prepare our students well for the local and global changes taking place in various fields, it is necessary to enhance the Learning to Learn curriculum reform, to sustain and deepen the accomplishments achieved and to identify new focuses in the curriculum as we move to a new phase of curriculum renewal and updating.
Capitalising on the positive impacts and experience gained, the curriculum renewal (also known as “Learning to Learn 2.0”) being introduced is an enhanced version of the Learning to Learn curriculum reform that started in 2001. It is not an “add-on”
but a continual journey to work smarter and in a more focused manner in promoting Learning to Learn for the next five to ten years. In this new phase of curriculum renewal, the curriculum will remain learner-centred and continue to focus on learning, particularly the improvement of its quality and effectiveness. However, to closely respond to various contextual changes locally and globally, more attention is given to the development of personal attributes expected of our students across KLAs in the coming decade, and focuses such as Reading across the Curriculum (RaC), Information Literacy, as well as Science, Technology, Engineering and Mathematics (STEM) education will be given stronger emphasis with renewed understanding of
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learning goals, generic skills and values and attitudes.
In response to the new phase of curriculum renewal, the Basic Education Curriculum Guide (Primary 1-6) was updated in mid-2014. The corresponding Secondary Education Curriculum Guide and the curriculum guides for the various KLAs are also being updated and will be available for schools’ reference in 2016 upon the completion of consultation. Schools are encouraged to sustain, deepen and focus on areas deemed essential for further improving students’ independent learning capabilities.
This consultation brief presents the major updates related to the Mathematics Education KLA and the key emphases for the ongoing curriculum renewal proposed for schools’ adoption. Examples are also provided to illustrate how these considerations are achieved through this KLA, particularly in the aspects of learning aims/targets/objectives, curriculum planning as well as learning, teaching and assessment. Schools may formulate plans to incorporate these recommended updates and the key emphases for the ongoing curriculum renewal from the 2016/17 school year, taking into consideration the school context, teachers’ readiness and students’ needs. As the recommendations proposed in this Brief have a direct bearing on school-based curriculum development over the next decade and set new directions for future curriculum updating and renewal and chart the way forward for sustaining the existing curriculum reform, we would like to solicit views and feedbacks from stakeholders, in particular the school sector. Comments and suggestions on this consultation brief are welcome and should be sent by 4 Jan 2016 to:
Chief Curriculum Development Officer (Mathematics) Curriculum Development Institute
Education Bureau
4/F Kowloon Government Offices 405 Nathan Road
Yau Ma Tei, Kowloon Fax: 3426 9265
E-mail: ccdoma@edb.gov.hk
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1. Why and how is the Mathematics curriculum updated?
The Mathematics Education Key Learning Area Curriculum Guide (Primary 1 - Secondary 6) (2016) is prepared by the Curriculum Development Council (CDC) Committee on Mathematics Education. It is an updated version of the Mathematics Education Key Learning Area Curriculum Guide (Primary 1 - Secondary 3) (2002) and has been extended to include the three-year senior secondary Mathematics Education.
In response to the changing needs of society, the rapid development of technology, views of stakeholders collected through various engagement activities and events (e.g.
Key Learning Area surveys, New Academic Structure Review, curriculum development visits and focus group interviews), the results of international assessment (e.g. PISA and TIMSS) on the Hong Kong Mathematics education, as well as the direction for ongoing curriculum renewal (also known as Learning to Learn 2.0), the recommendations on Mathematics curriculum provided in the Mathematics Education Key Learning Area Curriculum Guide (Primary 1 - Secondary 3) (2002) are revisited.
Building on the strengths of Hong Kong students in mathematics as revealed from international studies, the Mathematics curriculum has been revisited for renewal to highlight key updated elements, especially STEM1 education. Given that the elements of STEM education are already embedded in individual Key Learning Areas (KLAs) of Science Education, Technology Education and Mathematics Education of the local school curriculum, there is a need to strengthen the coherence and collaboration among KLAs. In this connection, the promotion of STEM education is a key emphasis to further enhance the quality and effectiveness of learning, hence enabling students to become more effective lifelong learners in the 21st century.
The updates of the Mathematics Education KLA Curriculum are in line with the guiding principles for the ongoing renewal of the school curriculum and the updated learning goals of school education. More details are provided in the Overview for Ongoing Renewal of the School Curriculum - Focusing, Deepening and Sustaining.
The updated learning goals of school education, which continue to focus on promoting whole-person development and lifelong learning capabilities, are:
1 STEM is an acronym that refers to the academic disciplines of Science, Technology, Engineering and Mathematics.
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Updated Seven Learning Goals of School Education
1. To be proficient in biliterate and trilingual communication for better study and life;
2. To acquire and construct a broad and solid knowledge base, and to be able to understand contemporary issues that may impact on learners’ daily lives at personal, community, national and global levels;
3. To develop and apply generic skills in an integrative manner, and to become an independent and self-directed learner for future study and work;
4. To be an informed and responsible citizen with a sense of national and global identity, appreciation of positive values and attitudes as well as Chinese culture, and respect for pluralism in society;
5. To use information and information technology ethically, flexibly, and effectively;
6. To understand one’s own interests, aptitudes and abilities, and to develop and reflect upon personal goals with aspirations for further studies and future career;
7. To lead a healthy lifestyle with active participation in physical and aesthetic activities, and be able to appreciate sports and the arts.
[ Please refer to Appendix 1 for the learning goals in primary education as listed in the Basic Education Curriculum Guide – To Sustain, Deepen and Focus on Learning to Learn (Primary 1-6) (2014) ]
With no updates suggested for the curriculum aims and while the content of the Mathematics curriculum is going to be reviewed holistically, the following major areas for updates on curriculum management, pedagogies and assessment are put forth to accommodate students’ learning needs arising from the changing contexts and education trends in the digital age, so as to provide suggestions for the development and implementation of the Mathematics Education KLA Curriculum at the primary and secondary levels for now and in the five to ten years to come.
Enhancing the learning and teaching of the applications of mathematics and strengthening students’ ability to integrate and apply knowledge and skills through STEM education
Highlighting the importance of e-learning for enhancing learning and teaching effectiveness, facilitate self-directed learning and promote Information Literacy (IL)
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Strengthening the development of positive values and attitudes and generic skills in an integrative way through various Mathematics learning activities
Highlighting Language across the Curriculum (LaC) in planning and implementing the school-based Mathematics curriculum. Reading in Mathematics would be promoted to develop students’ understanding on the connection between Mathematics and the real life as well as other disciplines.
Providing suggestions on catering for learner diversity in Mathematics learning, including addressing the needs of students with special educational needs (SEN) and gifted students in the mainstream Mathematics classroom
Developing assessment literacy among teachers and students through extending assessment for learning to assessment as learning and developing students’
self-directed learning skills
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2. What are the Major Updates?
This part of the brief introduces the proposed major development and updates in the Mathematics Education Key Learning Area (KLA) to be elucidated in the Mathematics Education Key Learning Area Curriculum Guide (Primary 1 - Secondary 6) (2016) (hereafter referred to as “KLACG 2016” in this document)
2.1 Revisiting the curriculum aims
The Mathematics curriculum nurtures in students various abilities to think, to communicate and to handle mathematical objects. It helps develop important sense of numbers and space, as well as a positive attitude towards mathematics learning.
These are also set out in the curriculum aims of Mathematics. The curriculum aims of the Mathematics Education KLA, which aligns with the overall learning goals of school education, will remain unchanged in the KLACG 2016. The curriculum aims are as follows.
Curriculum Aims of Mathematics
The overall curriculum aims of the Mathematics Education Key Learning Area are to develop in students:
the ability to think critically and creatively, to conceptualise, inquire and reason mathematically, and to use mathematics to formulate and solve problems in daily life as well as in mathematical contexts and other disciplines;
the ability to communicate with others, express their views clearly and logically in mathematical language;
the ability to manipulate numbers, symbols and other mathematical objects;
number sense, symbol sense, spatial sense, measurement sense and the capacity to appreciate structures and patterns; and
a positive attitude towards mathematics learning and an appreciation of the aesthetic nature and cultural aspect of mathematics.- 7 -
2.2 Updating the curriculum framework
2.2.1 The updated curriculum framework
The updated broad curriculum framework of the Mathematics Education KLA is presented in the diagram on the next page. The core part of the curriculum framework of the Mathematics Education KLA from P1 to S6 continues to be composed of Knowledge2, Generic Skills, and Values and Attitudes3. The considerations for curriculum management, leadership and planning, as well as the effective learning and teaching of Mathematics involve not only the core part, but also the learning needs of students under the contemporary contexts, including the adoption of e-learning, and the development of students’ language abilities and information literacy. The learning of Mathematics also connects with other KLAs/subject disciplines and the main focus is placed on integrating and applying knowledge and skills in STEM education. As before, the implementation of the curriculum needs the effective use of resources and the support from partners.
2.2.2 Holistic review of Mathematics curriculum
Although there will not be proposed updates on curriculum content of the Mathematics curriculum at the levels of Strand, Learning Unit and Learning Objectives in KLACG 2016, updated suggestions on curriculum planning as well as learning and teaching will be given in the KLACG 2016 to enhance students’
ability to integrate and apply knowledge and skills in STEM education and align with the considerations for curriculum planning of the ongoing curriculum renewal. Besides, a holistic review of Mathematics curriculum from P1 to S6 is intended to carry out to further incorporate the considerations for curriculum planning of the ongoing curriculum renewal into the curriculum content, to further improve the learning progression across key stages and to enhance the support to other disciplines, especially other STEM KLAs. The suggested plan of the review has been uploaded to the website of the Mathematics Education KLA (www.edb.gov.hk/cd/maths). Suggested issues to be addressed in the review, e.g. the content of Enrichment Topics of the primary and junior
2 The framework and content of the knowledge part remains unchanged and according to the review recommendations of the New Academic Structure Medium-term Review announced in June 2015, the curriculum framework and content of senior secondary Mathematics is to be kept unchanged for the time being and continues to be reviewed with the finalised decision to be announced by July 2017.
3 The updates of Generic Skills and Values and Attitudes are explain on p.10 and p.11 respectively.
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Diagrammatic Representation of the Mathematics Curriculum Framework
*
**
* In Key Stages 1 and 2, the strands are further divided into “Number”, “Algebra”, “Measures”,
“Shape and Space” and “Data Handling”.
** Module 1 of the Extended Part consists of “Calculus” and “Statistics” and Module 2 consists of
“Algebra” and “Calculus”.
Overall Aims and Learning Targets of Mathematics
Information Literacy Language across the Curriculum (LaC)
Knowledge
organised in strands
KS 1-3*
KS 4 Compulsory Part
KS 4 Extended Part**
Generic Skills
V a lue s a nd A tti tu de s
Number &
Algebra
Measures, Shape &
Space
Data Handling
Number &
Algebra
Measures, Shape &
Space
Data Handling
Algebra Calculus Statistics
Resources & Partnership
Integration and Application (STEM Education)
Curriculum Management, Leadership & Planning
+
Effective Learning, Teaching and Assessment
in response to the needs of students and the contemporary context
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secondary Mathematics curricula, providing better support to the learning and teaching of other KLAs and subjects and strengthening the learning and teaching of Data Handling so as to support students’ development of entrepreneurial spirit, are listed in Appendix 2.
2.2.3 Promoting STEM education
In the local curriculum context, STEM education is promoted through Science Education, Technology Education and Mathematics Education, within and across KLAs. The aim of promoting STEM education in schools is to strengthen the Science, Technology and Mathematics Education to nurture diversified talents in the science and technology fields for enhancing the international competiveness of Hong Kong.
The objectives of promoting STEM education in schools are as follows:
To develop among students a solid knowledge base and to enhance their interests in Science, Technology and Mathematics for further studies and careers in meeting the changes and challenges in the contemporary world
To strengthen students’ ability to integrate and apply knowledge and skills and to nurture students’ creativity, collaboration and problem solving skills, as well as to foster their innovation and entrepreneurial spirit as required in the 21st century
To strengthen the professional capacity of and collaboration among teachers in schools and the partnerships with community stakeholders
To nurture talents and develop experts in STEM areas so as to contribute to the development of Hong Kong and our nation
Through integration and application of knowledge and skills of the KLAs of Science, Technology and Mathematics Education, students would realise that the development of science, technology and mathematics is closely related to the societal environment and that the advancement in science and technology could help improve the quality of life in the contemporary world.
The experiences of integrating and applying knowledge and skills to solve real-life problems and make inventions would help the development of positive values and attitudes among students as part of whole-person development.
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These learning opportunities facilitate their career explorations in STEM fields and the nurturing of entrepreneurial spirit. This would not only enhance students’ interest in STEM areas, but also enable them to prepare for their future studies and careers in the areas and other fields requiring relevant knowledge, skills and attitudes.
More details on STEM education are elaborated in the Overview document on Promotion of STEM education – Unleashing Potential in Innovation
2.2.4 Other key emphases of the ongoing renewal of the school curriculum
2.2.4.1 Refining generic skills
Nine generic skills have been identified as essential for student learning for the 21st century in the school curriculum since 2001. Based on past experience of implementing the reform, as well as dynamic changes in society and recent research, the nine generic skills are grouped in three clusters of related skills, namely “basic skills”, “thinking skills” and “personal and social skills”, for better integrative understanding and application:
Basic Skills Thinking Skills Personal and Social Skills Communication Skills Critical Thinking Skills Self-management Skills
Mathematical Skills a Creativity Self-learning Skills b IT Skills Problem-solving Skills Collaboration Skills Remarks: a Numeracy Skills and b Study Skills were used respectively in Learning to Learn: Life-long Learning and Whole-person Development (2001)
“Numeracy Skills” is renamed to “Mathematical Skills” to reflect a more comprehensive set of skills in various areas such as measurement, logical thinking, describing patterns and data handling for applications in different disciplines. “Study Skills” is replaced by “Self-learning Skills” for nurturing self-directed life-long learners.
The Mathematics Education KLA provides meaningful contexts for the development of generic skills through appropriate learning and teaching activities and specific topics alongside KLA/subject specific skills. Schools should plan Mathematics KLA-related learning and teaching activities in a
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holistic manner whereby the generic/cluster of skills would be suitably and effectively applied and developed. Teachers are encouraged to
embed elements of generic skills in design of school-based learning goals, curriculum, learning activities as well as assessments;
blend naturally the learning elements of generic skills with subject knowledge, values and attitudes;
organise learning activities that require students to apply and reflect on their use of generic skills, such as projects, performance tasks and mini surveying activities; and
create authentic learning environments that bridge students' learning of these generic skills with real world issues.
2.2.4.2 Promoting values education
Values education/cultivation of positive values and attitudes is an integral part of the school curriculum through different components in KLAs/subjects, moral and civic education, cross-curricular learning opportunities and life-wide learning experiences. According to the framework for moral and civic education provided by the Curriculum Development Council in 2008, seven priority values and attitudes, which reflect both Chinese and Western cultures/values and address students’ and societal needs, have been identified as of vital importance for students’ whole-person development. They are “perseverance”,
“respect for others”, “responsibility”, “national identity”, “commitment”,
“integrity”, and “care for others”.
Schools are recommended to implement values education and cultivate positive values and attitudes related to individual, family, society, the country and the world, as well as values in accordance with the mission and contexts of their schools.
Schools should adopt a whole-school approach to curriculum planning that closely connects with the KLA/subjects, and design relevant learning experiences for students to nurture their positive values and attitudes. In Mathematics Education KLA, values education can be carried out through relevant topics and appropriate learning and teaching activities that help students apply and reflect on the priority or relevant values and attitudes (such as “taking
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up challenges”, “open-mindedness”, and “cautiousness”), or introducing different situations in which students are required to understand the issues from different perspectives, analyse them in a rational and objective manner, and adopt positive values and attitudes as the guiding principles to make judgement and decisions.
In planning and implementing the school-based Mathematics curriculum, the Mathematics panel is suggested to include the development of positive values and attitudes by:
providing problems of reasonable level of difficulty to develop students’
positive values such as “taking up challenges” and “persistence”;
assigning open-ended questions to encourage students to be flexible, and to help students realise that there can be more than one way of looking at a problem;
assigning students to carry out short research projects about history of mathematics or the life stories of Chinese mathematicians to nurture students’ humanistic quality; and
adopting inquiry and investigation approach in classroom learning and teaching to encourage construction of knowledge as well as the communication and collaboration between students. Positive values and attitudes, e.g. persistence, can be developed through responding to unexpected situations or situations that do not have an immediate solution.
2.2.4.3 Language across the Curriculum (LaC)
Literacy refers to the ability to read and write effectively to achieve the desired goals or outcomes and develop one’s knowledge and potential. Helping learners master the literacy skills, i.e. reading and writing skills, is central to language learning at school level. It is essential that literacy be also developed in Mathematics which provides the contexts for learners to apply their literacy skills to construct knowledge and to facilitate their development into lifelong learners.
With the rapid development of information technology and the social media, literacy has taken on a new meaning. Students need to be equipped with new literacy skills to process and create multimodal texts in which messages are
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conveyed through different forms. In mathematical reading, students need to handle multimodal reading materials made up of text, diagrams and mathematical symbols and the reading skills applied underpin information processing skills, such as identifying and analysing relationships between elements of multimodal texts.
Therefore, Mathematics teachers are encouraged to collaboration with English and Chinese teachers to help students transfer literacy skills and strategies to the learning of Mathematics and to promote Language across the Curriculum (LaC) for more effective learning of Mathematics.
Reading in Mathematics helps enhance students’ interest in learning Mathematics and develop skills of reading to learn and literacy. The understanding on mathematical knowledge, daily-life applications and cultural aspects of mathematics that students acquire through reading provides students with a more comprehensive conception of mathematics and facilitate students’
learning across the curriculum. Teachers are suggested to:
prepare quality Mathematics reading materials with suitable quantities in classrooms or in the school library and make use of the resources of public libraries;
review and categorise reading materials to fit students of diversified interest and abilities;
help students to connect their learning experiences within the content of Mathematics to the mathematics in daily life, cultural aspects of mathematics and other disciplines; and
design suitable post-reading activities to reinforce students’ development of conceptions of the application of mathematics in different disciplines or the cultural aspects of mathematics.
(Please see Appendix 4 for Example 5 on organising and implementing Mathematics reading schemes.)
2.2.4.4 Strengthening Information Literacy (IL)
Information Literacy is an ability and attitude that would lead to effective and ethical use of information. It aims to help students’ i) identify the need for
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information; ii) locate, evaluate, extract, organise and present information; iii) create new ideas; iv) cope with the dynamics in our information world; and v) use information ethically and refrain from immoral practices such as cyber bullying and infringing intellectual property rights. The Four Key Tasks will provide opportunities for students to develop and apply IL
Student learning requires the use of IL whenever necessary. Mathematics Education KLA has a role to play in developing students’ IL. IL could be developed through the application of the generic skills in the context of handling information in different media in our information world. It involves various knowledge contexts and links with different KLAs, different subjects and STEM education. Infusion of IL in the Mathematics Education KLA would provide authentic contexts for students to apply the skills and better prepare students to live in the modern world as informed and responsible citizens. As an example, learning and teaching of topics on data handling and STEM-related project usually involve data collection, organisation, analysis, interpretation and reporting, which are essential skills related to IL.
2.3 Pedagogies (including e-learning)
2.3.1 Promoting e-learning
Appropriate use of IT for e-learning in Mathematics is suggested to be one of the main focuses in the updating of the Mathematics Education KLA.
e-Learning refers to an open and flexible learning mode involving the use of electronic media, including use of digital resources and communication tools to achieve the target learning objectives. The essence of e-learning is to enhance learning and teaching effectiveness in schools and helps develop students’
necessary qualities (e.g. self-directed learning) for the 21st century. Teachers may develop a repertoire whereby e-learning may help enhance, modify and complement some existing learning and teaching strategies or break new ground in pedagogy. In the context of Mathematics Education, e-learning is suggested to be promoted through:
greater use of IT to allow flexibility for learning inside and outside the classroom and to cater for learner diversity;
effective use of the IT environment (e.g. Wi-Fi infrastructure) to allow
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flexible use of e-resources, IT tools and mobile devices;
effective use of IT tools, such as using different mathematics application software (e.g. graphing tools, virtual 3-D manipulatives and dynamic geometry software) for multiple representations of abstract concepts, to enhance students’ understanding of mathematics concepts;
encouraging students to apply their IT skills for inquiry and investigation (e.g. using computation or graphing tools), presentation, critical thinking, information evaluation and knowledge management;
applying IT to enhance students’ motivation and engage students in interactive and collaborative learning activities; and
effective use of e-learning resources to develop students’ creativity, collaboration and problem-solving skills as well as self-learning skills (e.g.
through the use of immediate feedback from online applets and assessment tools).
(Please see Appendix 4 for Example 4 on effective use of IT for enhancing the learning and teaching of Mathematics.)
2.3.2 Approaches for organising learning activities on STEM education
In respond to the age of technology and innovation, STEM education is considered to be a major focus of updating of the Mathematics Education KLA.
Mathematics teachers are suggested to help students develop knowledge, skills and positive values and attitudes associated with STEM education through:
organising learning activities with themes on application of mathematics, such as project learning, mathematical modeling or problem-based learning to provide contexts for students to integrate and apply their knowledge and skills in STEM related subjects;
creating a learning environment that draws students’ attention to the application of Mathematics in Science and Technology as well as in daily life situations;
encouraging students to engage in mathematics reading on cross-discipline topics, e.g. mathematics and astronomy; and
designing learning activities to encourage students to work out innovative
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solutions to problems or create new ideas or things to enhance their creative capacity.
The Science, Technology and Mathematics Education KLAs and the primary General Studies have an important role in the promotion of STEM education at both the school and classroom level. Schools can strengthen students’ ability to integrate and apply knowledge and skills, as well as develop their positive values and attitudes through:
providing a favourable environment with ample opportunities for students to integrate and apply knowledge and skills of different disciplines during the process of learning
holistic curriculum planning with due consideration being made on providing different scenarios for students to integrate and apply knowledge and skills across disciplines
making use of KLA-based and cross-disciplinary learning activities of different natures, such as project learning, case-based/problem-based learning and mathematical modeling to provide meaningful contexts that are closely geared to the daily life for students to engage themselves in problem solving. The activities may include scientific investigations, “Design &
Make” tasks, etc. that foster the ability to integrate and apply knowledge and skills of different disciplines
encouraging and supporting students to participate in STEM-related competitions and other fun-filled learning activities arranged by different local and overseas organisations wherever appropriate, as well as those regularly organised by local museums and professional bodies
promoting collaboration among teachers at school level in planning and organising cross-disciplinary learning activities
The above suggested at least two approaches that can be adopted by schools when arranging STEM learning activities for students:
Approach One
In this approach, the learning activity is based on a particular topic of a subject of a KLA (Science Education, Technology Education or Mathematics Education). Relevant learning elements are drawn from other KLAs to allow students to integrate and apply the knowledge and skills they have learned.
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For example, in a Mathematics topic about “Integral Indices”, students study the index notation of numbers and numbers expressed in various bases. Related learning elements (e.g.
representing and comparing sizes of cells using scientific notation and the use of binary numbers in computers) from other KLAs, could be incorporated as the learning activity moves on. At the end, students could be assessed for their understanding on the related learning elements and their ability to integrate and apply the knowledge and skills learned.
Approach Two
In this approach, a project learning activity is used to integrate all the related learning elements from Science Education, Technology Education and Mathematics Education KLAs.
Students are given an authentic problem to start with. As the project progresses, students explore the issues, relevant learning elements from different KLAs are brought in by the students themselves, so that they could integrate the knowledge and skills they learned and apply them in a real life context.
A diagrammatic illustration of the two approaches is attached in Appendix 3.
STEM education is also conducive to the development of students’
entrepreneurial spirit. The learning activities associated with STEM education can help develop students’ inquisitiveness to conceive new ideas and the ability to turn ideas into action, as well as nurturing the qualities of taking initiative and responsibilities, taking calculated risks and upholding perseverance. These qualities enable students to meet challenges and make the most of the opportunities ahead. Some of these qualities, such as taking calculated risks and making informed decisions through coat/benefit considerations, involves the application of mathematical knowledge (e.g. probability) and could be nurtured through learning activities in STEM education.
(Please see Appendix 4 for Examples 1 and 2 (Approach One) and Example 3 (Approach Two) on learning activities for STEM education.)
2.3.3 Learning and teaching strategies
With the focuses of STEM education and e-learning, some aspects of the learning and teaching of Mathematics are highlighted in the KLACG 2016 to
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provide teachers with renewed strategies to achieve the aims of the Mathematics curriculum.
It is important to nurture in students an all-round development with balance between their concept acquisition and application of computation algorithm, and between the applications of mathematics and abstract thinking.
Project learning and problem-based tasks are suggested to provide students with opportunities to integrate knowledge across subjects, to apply IT skills and to develop generic skills as well as positive values and attitudes.
Teachers are encouraged to use contemporary examples of application of mathematics to illustrate the use of mathematical knowledge in real life situations, such as the use of graphing skills in scientific investigation and performing error estimation of GPS tracking apps of mobile devices.
Teachers are suggested to strengthen students’ competency in applying mathematical software/application software (such as computer algebra system, dynamic geometry software, statistical tools and graphing tools) to preform problem-based learning or other learning activities.
2.3.4 Catering for learner diversity
Learner diversity remains one of the major concerns in the Mathematics classroom at all levels and suggestions on strategies to cater for learner diversity are enriched in KLACG 2016. Diversity may manifest itself in many ways.
Besides catering for students with different abilities, attention should also be paid to students’ differences in learning styles. Teachers are encouraged, besides continue to take the role of a facilitator in Mathematics lessons, to understand students’ learning characteristics in terms of learning style, cognitive development and pre-requisite knowledge.
Teachers’ attention is drawn to the effective use of learning and teaching resources, including textbook and e-resources, to cater for learner diversity.
Materials of textbooks are used selectively or with adaptation to cater for students’ learning needs and interests. For the more able students, elementary examples and exercises may be skipped; and for the less able students, the more advanced examples, more-demanding questions and enrichment materials may be skipped.
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Hands-on learning activities, which are not replaceable by activities using IT, could be used for visualising concepts and computation process and for motivating students and provoking the understanding of abstract concepts.
Teachers can choose suitable web-based learning materials to enhance students’ motivation and to extend talented students’ learning in their areas of interest, such as in the topic of mathematics and astronomy.
Teachers can also select web-based interactive assessment tools with instant feedback to assist students’ self-directed learning and to cater for students’
different learning pace.
Due consideration should also be given to support students with special education needs (SEN) and gifted students. To maximise the potentials of students talented in Mathematics, teachers are suggested to consider the following in the planning and implementation of the school-based Mathematics Education curriculum:
Allowing flexibility with the curriculum to address differences in the rate, depth and pace of learning
Providing enrichment activities which encourage creativity and original thinking
Encouraging students to pursue independent projects or study based on their interests and abilities
Guiding students to set individual goals and assume ownership of their learning
To accommodate the needs of SEN students in the mainstream Mathematics classroom, teachers could consider the following in the planning and implementation of the school-based Mathematics Education curriculum:
Adapting the learning content
Adopting effective learning and teaching strategies
Using learning and teaching aids and materials
Reinforcing classroom management and instructions
Setting realistic assessment goals/objectives
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2.4 Assessment
Assessment practices of “assessment for learning” have been developing in schools and a future direction for the development of assessment practices is to extend formative assessment from “assessment for learning” to “assessment as learning”.
These will all be highlighted in KLACG 2016.
2.4.1 Highlighting different modes of assessment for different purposes
It is recommended for schools to build on their experience in implementing
“assessment for learning” to further develop students’ habits of mind and skills to monitor and evaluate their own learning. Meaningful learning takes place when students are empowered to take charge of their own learning.
In extending “assessment for learning” to “assessment as learning”, schools could allow greater involvement of students in the learning, teaching and assessment process. Students could be encouraged to set personalised learning goals, formulate plans to attain their learning goals, monitor their own learning performance, and evaluate their learning strategies. In this way, students gradually take ownership and responsibility for their own learning.
Various tools are developed by the Education Bureau to support schools in implementing “assessment for learning” and “assessment as learning”. These include the Basic Competency Assessment (BCA), the Learning Progression Framework (LPF) and Student Assessment Repository (STAR) for Mathematics.
The Basic Competency Assessment (BCA), which has been fully administered at primary three, primary six and secondary three since 2006, is an important assessment for providing schools with data for planning curriculum and designing teaching strategies to enhance the effectiveness of learning and teaching. In the KLACG 2016, schools are encouraged as before to make use of the BCA assessment date for reviewing the school-based curriculum and the effectiveness of the learning and teaching strategies.
The Learning Progression Framework (LPF) provides a common scale and language for teachers to describe students’ performance and progress in Mathematics learning. Schools are encouraged to use the LPF as a tool for
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planning the school-based Mathematics curriculum and assessment. A set of school-based performance descriptors can be developed with the use of the LPF to help students and parents understand students’ performance in assessment tasks. Students can also be engaged in self-reflection and planning for improvement.
The Student Assessment Repository (STAR) is an online assessment bank developed by the Education Bureau to enhance teachers’ assessment literacy and improve students’ learning by means of technology. STAR provides a range of assessment items that cover diversified question types and address the learning outcomes and pointers from the LPF for teachers to check students’ progress or for students to conduct self-directed learning.
STAR can provide online assessment data, such as reports on individual student’s performance and the performance of a whole class, to help schools understand students’ attainment and plan remediation and progression.
2.4.2 Assessment strategies for Mathematics Education KLA
Schools should continue to introduce diversified modes of assessment and flexibly use different types of formative assessment. Other than collecting evidence of student learning through exercises, class discussion, oral presentation and performance task, assessment in the form of exploratory tasks, problem-based tasks and e-assessment can also be considered.
Exploratory tasks and problem-based tasks assess students’ inquiry skills and problem solving skills on unfamiliar problems. When science or technology related topics or topics on the applications of mathematics in daily life are involved, the assessment tasks could also help develop students’ STEM related skills. These tasks challenge students’ integrative application of Mathematics concepts from different strands. Teachers could adjust the level of guidance and assistance provided to suit students of different abilities.
e-Assessment has been a powerful tool for teachers to cater for learner diversity, provide timely feedback and promote “assessment for learning”.
The design of some e-assessment platforms also encourages students to have more active involvement in monitoring their own learning to promote
“assessment as learning”. Teachers are encouraged to make flexible use of e-assessment platforms available at the HKEAA and HKEdCity websites.
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2.4.3 Assessment for STEM-related learning activities
Assessment in relation to STEM-related activities is implemented with a view to strengthening students’ ability of integrating and applying the knowledge and skills from different STEM disciplines and fostering students’
independent/collaborative learning capabilities.
To assess STEM learning activities at school level, formative assessment could be adopted to collect evidence of student learning in both the knowledge and skill domains. During the course when the learning activities are organised, various assessment strategies, such as questioning, discussion, observation, self and peer assessments, and presentation, can be adopted. These assessment strategies allow teachers to provide timely feedback to students, and therefore guide them to monitor and reflect on their own learning. By the end of the learning activities, summative assessment, such as assessing students’ final products or written reports, can be used to provide comprehensive information about what students have acquired.
2.5 Curriculum management and planning of learning time
2.5.1 Holistic Curriculum Planning
During school-based curriculum development for Mathematics, it is essential for schools to conduct holistic planning and strive for providing a balanced Mathematics curriculum that can meet the needs of students. The diagram on the next page shows the major factors to consider during holistic planning of the school-based Mathematics curriculum.
(Please refer to the diagram on the next page)
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Holistic Curriculum Development in Mathematics Education KLA
School vision and mission
Analysis of school context
Students’ interests and abilities, and teachers’ expertise
Curriculum Emphases for
Mathematics Education Curriculum documents:
BECG and SECG Mathematics Education KLA
curriculum documents for
primary and secondary levels
Resources &
Support Learning and teaching resources
Community resources Research &
Development projects Professional development of school leaders and
teachers
Smooth Learning Progression between Key Stages
Holistic
Curriculum Development
Planning, Implementation and Evaluation
Collaboration among teachers (within ME KLA and with other KLAs, e.g. planning STEM education)
A Solid Mathematics Foundation for Students A School-based Mathematics Curriculum with Vertical Continuity and Lateral Coherence
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2.5.2 Planning of learning time
In KLACG 2016, the recommended time allocation for the primary and secondary Mathematics will not be suggested to change. Schools could refer to the respective curriculum document of each key stage for the recommended lesson time and related recommendations. Teachers are encouraged to use the time flexibly to help students attain the learning targets of the curricula, and to broaden students’ learning experiences through various learning activities inside and outside classroom. As general recommendations, the proportion of time allocated for Mathematics at primary, junior secondary and senior secondary levels, as in the current curriculum documents, are as follows:
Primary level: 12 - 15% of total lesson time
Junior secondary level: 12 - 15% of total lesson time
Senior secondary level,
Compulsory Part only: 10 - 12.5% of total lesson time Compulsory Part with a Module: 15% of total lesson time
Schools are also encouraged to use the designated “flexible time” to conduct cross-curricular learning activities, e.g. values education, Reading across the Curriculum and STEM-related activities, to ensure the whole-school curriculum is broad and balanced, in terms of promoting whole-person development. The flexible time for the primary and junior secondary levels is 19% and 8%
respectively in each key stage. As for the senior secondary level, the 10-15%
time allocation is set aside for Other Learning Experiences (OLE). Should schools give due consideration to the overall planning and co-ordination among different KLAs and subjects with flexibility to organise OLE inside and outside the school timetable.
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3. What are the supporting strategies?
In order to facilitate schools to renew their school-based Mathematics curriculum to incorporate the major updates in the Mathematics Education KLA suggested in the Mathematics Education Key Learning Area Curriculum Guide (Primary 1 - Secondary 6) (2016), new, renewed or enriched supports in terms of the followings are provided.
3.1 Learning and teaching resources
Besides traditional learning and teaching resources, e.g. textbooks, models of 3-D figures and resources from school libraries, schools may also use the free learning and teaching resources developed and offered online by the EDB over the years. For easy access of the resources by teachers and students, the EDB has set up a portal at the Hong Kong Education City, namely “EDB One-stop Portal for Learning and Teaching Resources” (www.hkedcity.net/edbosp), for teachers to access the many up-to-date digital resources that have been developed to support the learning and teaching of Mathematics. There are also free resources offered online in the website of Mathematics Education KLA (www.edb.gov.hk/cd/maths).
Resources available from other government departments, non-government organisations, tertiary institutions, professional bodies, etc. could be utilised to facilitate life-wide learning of Mathematics and enrich the learning experiences of students.
3.2 Partnerships with key players in the community
While the Mathematics Education Section of the Curriculum Development Institute, the School-based Curriculum Development Section (primary or secondary) of the Quality Assurance and School-based Support Division, and also the Regional Education Offices offer advices and support schools regularly on various aspects of learning and teaching, it is fairly common nowadays for schools to solicit support from tertiary institutions and professional organisations, through collaborative projects or professional development programmes (PDPs), to strengthen the professional development of their teachers.
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To facilitate the promotion of STEM education, the EDB has been collaborating with various organisations, including the Hong Kong Association for Science and Mathematics Education, the Hong Kong Statistical Society, Hong Kong Science Park, Space Museum, Science Museum, and other relevant government departments such as the Leisure and Cultural Services Department, the Fisheries
& Conservation Department, the Census and Statistics Department, etc. in organising various exhibitions, competitions and other student activities, as well as teacher seminars and workshops. The EDB will continue to strengthen the collaboration with the above organisations to enhance professional development of teachers and strengthen student learning.
3.3 Professional development of school leaders and teachers
The EDB will continue to provide professional development programmes (PDPs) for school leaders and teachers. To support the ongoing curriculum renewal and promptly respond to the feedback from schools on the training needs of teachers, the key focuses of the PDPs are as follows:
(i) Support for teachers to implement the senior secondary curriculum in areas of Understanding and Interpreting the Curriculum, Assessing Student Learning, Learning and Teaching Strategies, and Enriching Knowledge;
(ii) Support for school leaders, middle managers and teachers in curriculum management, leadership and planning;
(iii) Support for teachers on promoting STEM education and value education, enhance learning and teaching strategies, and cater for learner diversity; and (iv) Support for teachers to promote information literacy and conduct
e-learning.
There are specific supports on the major updates in the KLACG 2016 to facilitate schools to develop their school-based Mathematics curricula. They are summarised in the table below.
Major Updates Supporting Strategies
STEM education
Cross-KLA symposium will continue be organised for teachers to understand how to promote STEM education on holistic consideration.
New PDPs for curriculum leaders and teachers on school-based Mathematics curriculum planning as well as
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on learning and teaching of Mathematics for enhancing STEM education and cross-KLA collaboration will be provided. The EDB will also explore further collaborations with tertiary institutions and specialists in organising professional development programmes for teachers.
Schools with good practices will be identified for sharing with other schools in sharing sessions.
An integrative education fair relevant to Science, Technology and Mathematics Education KLAs will be organised to showcase a wide range of student achievements. Through sharing and learning from each other’s work, a cross-disciplinary learning culture will be developed to promote students’ interest and creativity in Science, Technology and Mathematics. This will pave the way for students’ future studies and careers in related areas.
Learning and teaching resources will continue be produced and uploaded to the e-resources platform of learning and teaching for teachers’ reference in the coming school years.
The resources include STEM related cross-disciplinary learning activities and projects, schools’ successful cases, life-wide learning activities and related reference materials.
The EDB will continue enhancing the collaboration among schools, tertiary institutions, professional bodies and related careers to promote their understanding and development of STEM education in related areas. It is hoped that through close partnership, further insights and good practices related to implementation of STEM education would be consolidated and shared among schools
Schools can acquire additional resources to conduct their school-based STEM education programmes and to build communities of practice to enhance knowledge exchange within and across schools through “Professional Development Schools Scheme” and “Quality Education Fund – QEF Thematic Network”.
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e-Learning and Information Literacy
PDPs for primary and secondary teachers on e-learning will continue be provided and renewed to introduce up-to-date e-resources to teachers, equip teachers with the competency to design learning activities using common mathematics application software (apps) and give suggestions on effective and pedagogically sound application of e-resources.
Learning and teaching resources for e-learning in Mathematics will continue be provided through the EDB One-stop Portal for Learning and Teaching Resource (http://www.hkedcity.net/edbosp/).
Examples on the use of mathematics apps for effective learning and teaching will be provided in the KLACG 2016.
Other key emphases of the ongoing
curriculum renewal
Generic skills
PDPs on generic skills will be renewed to introduce the new grouping of the nine generic skills and examples of learning and teaching activities in Mathematics for the integrative application of the skills.
The development of generic skills through learning and teaching activities in Mathematics will be illustrated through examples in the KLACG 2016.
Values education
PDPs on promoting values education will be renewed to provide up-to-date examples on nurturing positive values and attitudes through both routine mathematics exercises as well as specific topics, such as discussion on personal financial management.
PDPs on history of mathematics will continue be organised to enhance teachers’ competency in incorporating cultural elements of mathematics in Mathematics lessons, for provoking students’ humanistic qualities.
The development of positive values and attitudes through learning and teaching activities in Mathematics will be illustrated through examples in the KLACG 2016.
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Language across the Curriculum
PDPs on reading to learn in Mathematics are renewed to promote reading in Mathematics and provide suggestions, good practices and solutions to schools on promoting Mathematics reading
The series of booklets, the “Mathematics Treasure Trove”
series, are published by the Education Bureau to provide Mathematics teachers with references on learning and teaching of Mathematic, enrichment topics as well as the latest development of the application of Mathematics. The booklets can also serve as reading materials for students.
Eighteen booklets have been published and more booklets will be published in the future.
The Mathematics Education Section will continue to organise the Mathematics Book Report Competition for Secondary Schools to enhance students’ interest in Mathematics reading and to develop students’ literacy.
Examples introducing the organising of Mathematics reading programme in schools will be provided in the KLACG 2016.
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4. Frequently Asked Questions
Q 1: What is Learning to Learn 2.0?
A 1: Learning to Learn 2.0 is the curriculum renewal of the Learning to Learn curriculum reform implemented since 2001 in response to the local and global contextual changes in economic, scientific, technological, social and political aspects. With a view to keeping our school education abreast of the times and maintaining the global competitiveness of our students, it is necessary for the Hong Kong school curriculum to embark on the next cycle of updating and renewal, which aims to deepen and sustain the accomplishments and to focus on the possible areas for curriculum planning. Ongoing engagement of stakeholders through multiple channels has been conducted in setting the direction for the ongoing curriculum renewal.
Q 2: Is STEM a new strand in the Mathematics Curriculum?
A 2: STEM is an acronym that refers collectively to the academic disciplines of Science, Technology, Engineering and Mathematics. It is not a new strand in the Mathematics Curriculum.
In the local curriculum context, STEM education is promoted through Science, Technology and Mathematics Education KLAs. The aim of promoting STEM education in schools is to strengthen the Science, Technology and Mathematics Education to nurture diversified talents in the science and technology fields for enhancing the international competiveness of Hong Kong.
STEM-related learning activities bridge across the curricula of the KLAs of Science, Technology and Mathematics Education to enhance students’
interest and innovation, and to develop their ability to integrate and apply knowledge and skills within and across KLAs.
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Q 3: In promoting STEM education, what kinds of support will be provided by the EDB? Will any additional resources be provided to schools?
A 3: Teachers’ professional development and support
The EDB will continue to organise PDPs to enhance teachers’
professional capacity in relation to the promotion of STEM education.
Further to the symposium in July 2015, two events of another symposium cum consultation briefings were organised in early November to enhance teachers’ understanding of STEM education.
In the next three school years, a series of PDPs will be organised for panel heads and teachers, to facilitate teachers in using appropriate strategies to strengthen the ability of students to integrate and apply the knowledge and skills of different disciplines. More seminars and workshops will continue to be organised to enrich teachers with the most up-to-date knowledge on STEM-related fields. At the same time, different platforms will be used to foster sharing of professional knowledge (e.g. through Professional Development Schools Scheme (PDS) of Education Development Fund (EDF), Quality Education Fund (QEF) Thematic Network). Furthermore, opportunities will be provided for teachers to expose themselves to cutting edge development in science and technology fields through exchange with academics/partners in the territory and from the Mainland and overseas.
Programme to nurture students’ capability in STEM fields
The EDB will organise an education fair related to Science, Technology and Mathematics Education in early 2016 to showcase students’ achievements in learning. This event will enhance students’
interest and creativity in science, technology and mathematics, and help them pave the way for future studies and careers in related areas.
Learning and teaching resources
The EDB will continue to develop learning and teaching resources, which are to be uploaded to the EDB One-stop Portal for teachers’
reference. The resources include information about STEM-related learning activities and projects, good practices from schools, information about life-wide learning activities and other related reference materials.
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Using community resources
The EDB will continue to liaise with academic and practitioners who specialise in various science, technology, engineering and mathematics fields, and to explore feasibility of collaborating with tertiary institutions and specialists in organising training programmes and student learning activities.
Other resources
Schools can acquire additional resources from the Professional Development Schools Scheme (PDS) of Education Development Fund (EDF) and Quality Education Fund (QEF) Thematic Network to promote and enhance school-based programmes related to STEM education.
Q 4: Will schools be provided with IT resources or online platforms in support of the learning and teaching of Mathematics?
A 4: One of the actions of the Fourth Strategy on IT Education is to enhance schools’ IT infrastructure. With the enhanced e-environment, teachers can incorporate resources on the Internet and other e-resources to the Mathematics lessons more readily.
Teachers are encouraged to make effective use of IT and e-resources for engaging students in meaningful Mathematics learning activities, e.g. using dynamic geometric software package for presenting geometric properties of figures and using graphing tools to perform investigative activities on graphs of functions.
Opportunities for self-directed learning can also be provided through the adoption of IT. Teachers can select suitable interactive applets or videos on the internet for students’ preparatory activities before the teaching of a topic. Students also can make use of the immediate feedback from online interactive applets to perform enquiry activities.
In the updated Mathematics Education KLA Curriculum Guide, useful e-resources will be suggested for teachers’ reference. Examples of the use of IT for effective learning in Mathematics lessons are also provided.
