The Four Key Tasks

The Four Key Tasks, namely Moral and Civic Education, Reading to Learn, Project Learning and Information Technology for Interactive Learning have been recommended for schools’ implementation of the curriculum reform since 2001.

Over the past decade, schools have been incorporating the Four Key Tasks into their school curriculum to help students develop independent learning capabilities.

In the ongoing curriculum renewal, these tasks are updated as Moral and Civic Education: Towards Values Education, Reading to Learn: Towards Reading across the Curriculum, Project Learning: Towards Integrating and Applying Knowledge and Skills across Disciplines, and Information Technology (IT) for Interactive Learning: Towards Self-directed Learning. The updated key tasks are applicable in the Mathematics Education KLA to enliven learning and teaching, and to help students achieve whole-person development and become self-directed learners.

Moral and Civic Education: Towards Values Education

 The Mathematics Education KLA is an integral part of the school curriculum.

It provides relevant learning experiences, and a conducive learning environment to implement values education and nurture students’ positive values and attitudes from different perspectives.

- Open-ended questions can be incorporated in the learning and teaching of Mathematics to develop students’ respect for others. In tackling mathematical problems which may not have a definite solution, students evaluate not only their own solutions, but also alternative solutions proposed by others. Through discussing or debating on the different solutions proposed by various people, students are led to understand and accept different points of view and have respect for others. This also applies in the context of working out strategies for completing a mathematical project.

- The use of daily life examples in the mathematics classroom may enhance students’ awareness of the importance of mathematics in real-life contexts.

For example, for the learning and teaching of statistics, mathematics teachers could make use of the environmental statistics on air, waste,

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noise and water provided by the Hong Kong Environmental Protection Department for classroom activities. Teachers may use statistical diagrams to illustrate the wastes dumped in landfill to raise students’

awareness of the importance of environmental protection. Students also develop appreciation of role of mathematics in everyday life.

- In project work, students are provided with opportunities to share out the responsibilities among group members and develop a sense of commitment by taking up different roles for completing the group tasks.

Their leadership, social skills and sense of collaboration can also be fostered in authentic contexts.

Reading to Learn: Towards Reading across the Curriculum

 In a knowledge-based society, schools play an essential role to equip students with skills for reading to learn. Schools have, in general, established a reading culture among students at different year levels. With the implementation of a mathematics reading scheme, or systematic provision of mathematics reading materials, students’ interest and knowledge in mathematics is enhanced. At the same time, students are provided with opportunities to apply and consolidate their reading skills and strategies developed in the language lessons.

 Schools are encouraged to build on their achievements in promoting “Reading to Learn” and further motivate students to read texts with themes related to mathematics to broaden their knowledge base and enhance their language competence and ability in handling reading materials made up of not only words, but diagrams, mathematical symbols and multimodal features (i.e.

sounds, images, videos). To strive for improvement and enhancement of

“Reading to Learn” and to promote “Reading across the Curriculum” in the mathematics context, schools could refer to the following suggestions and review the current strategies adopted.

- The effective use of library resources facilitates the promotion of

“Reading to Learn”. Schools could borrow from the public libraries, or purchase for their school library mathematics reading materials that are appropriate to their students’ age, language competence and learning interest.

- Appropriate e-reading materials, including articles from mathematical journals or magazines, could be provided for students to read online for

the development of self-directed learning. Students can have access to these materials by using different devices including mobile phones, tablets and desk-top computers. Reading materials related to the Mathematics lessons can serve as pre-lesson preparation or further studies materials for students.

- Teachers could categorise reading materials with reference to students’

diverse interest and abilities. Reading materials of diversified themes (e.g.

applications of mathematics in daily life, history of mathematics, and stories of famous mathematicians) could help students connect their learning experiences of mathematics with those of other disciplines, mathematics in daily life and the cultural aspects of mathematics.

- Besides reading records, teachers may design suitable post-reading activities for students to share their reading experience. This can also reinforce students’ understanding of the applications of mathematics in different disciplines and the cultural aspects of mathematics. To cater for students’ different learning styles, teacher may allow students to make their presentations in varied ways, such as verbal reports, drawings and role-play.

- Mathematics teachers could collaborate with the English and Chinese teachers to help students transfer their reading skills and strategies learnt in the language lessons to read mathematics books or texts and enhance their reading skills development.

- Mathematics teachers could become role models of their students and share with them book reviews for some recreational mathematics books.

It encourages students to develop reading habits and eventually a good reading culture can be established in the school.

(Please refer to Example 22 of this Guide for suggestions on organising and implementing a mathematics reading scheme.)

Project Learning: Towards Integrating and Applying Knowledge and Skills across Disciplines

 Apart from regular learning and teaching of Mathematics in the classroom, project learning is an effective means to arouse and enrich students’ learning interest in mathematics. It provides an alternative learning experience and is a powerful learning and teaching strategy to promote self-directed, active and

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self-reflective learning. It enables students to incorporate generic skills and values and attitudes in the process of constructing mathematical knowledge.

 The theme of project learning in mathematics can be a specific mathematical topic such as prime numbers or a study on using mathematics to solve a real-life problem that connects mathematics with the real world and other disciplines. Project learning is an effective approach to promoting cross-KLA learning and STEM education (see Section 3.4 and Section 4.3 of this Guide for details). When themes on STEM education are involved, collaboration among KLAs is strongly recommended to help students connect and integrate their learning experiences and outcomes from different disciplines.

 Project learning provides substantial opportunities for students’ development of the nine generic skills. It enhances students’ mathematical skills as charts and graphs are often used in data analysis and data presentation. Other elements of mathematical skills such as performing calculations and describing patterns might also be applied, depending on the themes of project learning. Besides mathematical skills, other generic skills can also be nurtured through project learning. Collaboration skills, self-learning skills and self-management skills are applied when students are required to plan and manage their individual and group work systematically. While creativity, critical thinking skills and problem solving skills are nurtured when students study the project questions, investigate them from different perspectives and explore different approaches to tackle them.

 Some issues only arise in group projects and while handling them, students learnt to listen and respond to alternative ideas and perspectives, respect others, delegate responsibilities and resolve conflicts. Positive values and attitudes are nurtured in these processes.

 In project learning, the roles of teachers change from a knowledge transmitter to a tutor, an advisor and a facilitator. Teachers need to monitor students’

progress and provide continuous support, advice and regular feedback to students to develop their research skills in project learning. Once the students have become more independent in the learning process, teachers can merely act as a facilitator. Well established guideline and clear learning objective can help students conduct their projects effectively. Teacher may use samples of projects done by other students to exemplify the key elements of good projects

and guide students to improve the quality of their projects.

 Examples 3, 9, 12 and 13 of this Guide are provided to illustrate how project learning can be adopted for the learning and teaching of mathematics. Indeed, there are many other topics and types of projects, such as surveys, investigations on applications of mathematics, studies on the history of mathematics or famous mathematics problems, and biographies of mathematicians. The areas of study in project learning should be carefully chosen to suit students’ interests and abilities. The depth of project work can also vary according to students’ abilities. Similarly, different levels of guidance can be provided to cater for students’ abilities, and with reference to the focus, difficulty and nature of the projects. Projects can be done individually or in groups, depending on their nature. Collaboration and communication skills, however, will be more effectively developed in projects carried out in groups. Project work can also be considered as an effective tool for promoting assessment for learning. Some pre-determined criteria could be set to assess the holistic performance of students (see Section 5.2 for details).

Information Technology for Interactive Learning: Towards Self-directed Learning

 The rapid advancement in IT in the past decades has led to its wide application in education. The use of mobile computing devices and application software during lessons has become increasingly popular and made a considerable impact on the learning and teaching of Mathematics. As discussed in Section 3.4, the use of IT in mathematics education is to harness its advantage to enhance student learning. Instead of merely application, IT should be used with effective pedagogies and meaningful learning tasks for enhancing effectiveness in student learning. The pedagogies and technology chosen should fit the characteristics of the topics to be delivered. Schools could refer to the TPACK⁵ framework, which describes the integration of technological knowledge, pedagogical knowledge and content knowledge, for more ideas on the integration of IT with suitable pedagogy for the effective learning of a certain topic.

5 TPACK stands for Technological Pedagogical Content Knowledge. It is a framework that incorporates the kinds of knowledge required by a teacher to develope effective pedagogical practice in a technology enhanced learning environment. More information about TPACK is available at http://www.tpack.org

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 With the launching of ITE4, all classrooms in Hong Kong are Internet-connected to facilitate e-learning. With the help of Wi-Fi network and mobile computing devices, Mathematics lessons are provided with multimedia resources, authentic data, application software packages, communication/sharing platforms and other e-resources for interactive learning and exploratory activities. With the help of application software packages, there could be multiple representations of abstract mathematical concepts to enhance students’ understanding. Moreover, with the increasing use of IT, there is a paradigm shift from a teacher-centered approach to a more interactive student-centered approach to teaching mathematics. During the lessons, students could also make use of the Wi-Fi network to share their ideas with their teachers and classmates.

 Nurturing students to apply IT tools and resources in learning mathematics is important as it also paves ways for students’ self-directed learning. When students are learning mathematical concepts, they can use application software for simulations, analysis and modelling. For example, the dynamic geometry software facilitates the inquiry and investigation in many geometry topics in the Mathematics curriculum. With the help of IT tools, students can easily plot graphs for visualising mathematical relations, propose conjectures and make connections between different areas of mathematics. Appropriate use of IT tools can save students’ effort in routine computation or presentation and create time and space for deeper understanding and thinking. Examples 15 and 19 of this Guide are provided to illustrate how IT can be utilised in the learning and teaching of mathematics.

In many cases, more than one of the updated Four Key Tasks can be connected to achieve a number of learning objectives. For example, a project on investigating the work of ancient mathematicians may require students to use IT skills to search for and evaluate relevant information. Students may also need to read books on the history of mathematics. Past endeavours of ancient mathematicians and collaboration among students during project learning are conducive to the development of perseverance, self-management and other qualities promoted through values education. The updated Four Key Tasks should be flexibly used in the learning and teaching of Mathematics to enhance students’ capabilities for constructing knowledge, to promote the development and applications of generic skills in an integrative manner and to nurture positive values and attitudes.

School may refer to Chapter 3 of the Basic Education Curriculum Guide – To Sustain, Deepen and Focus on Learning to Learn (Primary 1 – 6) (2014) and Booklet 6 of the Secondary Education Curriculum Guide (2017) for more ideas on the implementation of the Four Key Tasks as strategies for deepening, sustaining and focusing on the ongoing renewal of the school curriculum.