PGDE notes
Here are links to some notes for my PGDE Maths classes.
Assessment for Learning (using misconceptions and questioning)
This set of notes talk about resources for classroom teaching with a focus on formative assessment, which is not necessarily in the form of quiz or worksheet. Such resources are useful and important elements of lesson design. They include various types of learning tasks (long or short) that elicit responses from students and associated strategies of sustaining and directing learning activities. This requires good techniques of questioning and awareness of learners’ misconceptions.
We may learn from resources that are new to us, which will probably challenge our common assumptions and inspire our lesson design. On the other hand, we can also revisit familiar materials, such as textbook exercises, homework, exam questions, etc., understanding their potential and limitations, thus finding new ways to better utilise them for learning.
The booklets of Teaching for Mastery, from NCETM, provide different kinds of short examples that can be easily incorporated in classroom teaching. Diagnostic Questions by Craig Barton suggest more examples in a standardised form. They are available for online and offline use, including analysis of students’ responses and discussion about misconceptions. Multiple choice questions from local textbooks or exams can also be adapted in different ways for better use in supporting learning. The e-learning platform Desmos Activities is a powerful tool in many occasions and is recommended here specifically for adaptation of multiple choice questions.
Dylan Wiliam is a very influential scholar in the area of formative assessment. His book, Embedded Formative Assessment, gives many useful examples and practical classroom teaching techniques. Malcolm Swan was a productive educational designer. His work includes packages for classroom teaching and professional development. The are available in the Shell Centre for Mathematics Education, Mathematics Assessment Project and National STEM Centre eLibrary.
This set of notes talk about resources for classroom teaching with a focus on formative assessment, which is not necessarily in the form of quiz or worksheet. Such resources are useful and important elements of lesson design. They include various types of learning tasks (long or short) that elicit responses from students and associated strategies of sustaining and directing learning activities. This requires good techniques of questioning and awareness of learners’ misconceptions.
We may learn from resources that are new to us, which will probably challenge our common assumptions and inspire our lesson design. On the other hand, we can also revisit familiar materials, such as textbook exercises, homework, exam questions, etc., understanding their potential and limitations, thus finding new ways to better utilise them for learning.
The booklets of Teaching for Mastery, from NCETM, provide different kinds of short examples that can be easily incorporated in classroom teaching. Diagnostic Questions by Craig Barton suggest more examples in a standardised form. They are available for online and offline use, including analysis of students’ responses and discussion about misconceptions. Multiple choice questions from local textbooks or exams can also be adapted in different ways for better use in supporting learning. The e-learning platform Desmos Activities is a powerful tool in many occasions and is recommended here specifically for adaptation of multiple choice questions.
Dylan Wiliam is a very influential scholar in the area of formative assessment. His book, Embedded Formative Assessment, gives many useful examples and practical classroom teaching techniques. Malcolm Swan was a productive educational designer. His work includes packages for classroom teaching and professional development. The are available in the Shell Centre for Mathematics Education, Mathematics Assessment Project and National STEM Centre eLibrary.
- NCETM booklets, Teaching for Mastery: Questions, Tasks and Activities to Support Assessment
- Key Stage 3 (S1-S3)
- Key Stage 2 (P1-P6)
- Diagnostic Questions from Craig Barton
- use and adapt multiple choice questions for learning (with examples from public exam in HK)
- Dylan Wiliam's book, Embedded Formative Assessment
- guide and teaching materials from Mathematics Assessment Project (The main author is Malcolm Swan and the links below are similar materials from him.)
- Improving Learning in Mathematics: Challenges and Strategies
- Improving Learning in Mathematics: Teaching Activities and Materials
- examples of setting exercises for learning and assessment
- GeoGebra and Desmos Activities workshop videos
Click the buttons on the right for more videos about this page.
|
Towards flexible teaching
Good mathematics teaching is not defined in a single, prescribed way. It is developed with flexibility, open-mindedness and sensitivity to variation in the students and contexts. In view of the complexity, uncertainty and variety in students’ attributes and learning environments, even new teachers nowadays have to face this challenge of diversifying their teaching. This section suggests various sources of examples and advice for teaching design. They include:
In the following sites, you can find teaching materials and ideas in curriculum or professional development projects, co-developed by teachers.
Some resourceful and productive teacher bloggers:
Jo Boaler promotes a variety of approaches in teaching that address a range of critical issues in mathematics learning, making mathematics accessible and meaningful for all learners, especially those disadvantaged, discouraged or demotivated. She offers useful tips, messages and resources in her website and books, explaining the power of growth mindsets among students (and even teachers and parents), which could bring about substantial changes in the culture and practice of mathematics education.
Good mathematics teaching is not defined in a single, prescribed way. It is developed with flexibility, open-mindedness and sensitivity to variation in the students and contexts. In view of the complexity, uncertainty and variety in students’ attributes and learning environments, even new teachers nowadays have to face this challenge of diversifying their teaching. This section suggests various sources of examples and advice for teaching design. They include:
- local and overseas curriculum or professional development projects based on teacher collaboration;
- blogs and sites of individual practicing teachers showing their continual effort to share and enrich their teaching in their own styles and contexts;
- educators' promotion of multifaceted mathematics pedagogy based on research and development.
In the following sites, you can find teaching materials and ideas in curriculum or professional development projects, co-developed by teachers.
- Catering for Students' Learning Diversity through Rich Tasks and Collaborative Learning
- You can find a collection of 18 rich tasks with guidelines and sample student work from trials in classrooms. Note how they address learner diversity and encourage collaboration.
- Supporting the Learning and Teaching of Mathematics for Non-Chinese Speaking (NCS) Students in Primary Schools
- This ongoing project and the previous one below (for secondary students) develops diversified teaching materials and approaches, making maths accessible to more students, both mainstream and disadvantaged (not necessarily limited to NCS students). Currently, emphasis is put on engaging activities, algorithms with understanding, cultural characteristics, fluency with depth and flexibility, meaningful and mindful practice or exercise.
- The current project (2020) focuses on cultural and linguistic diversity.
- Supporting mathematics learning of NCS secondary students (2015-2017)
- gMath (GeoGebra applets in tablets)
- This is not merely a project promoting e-learning. It is an example of successful school-based development. Through the design and use of applets, we can see effective customisations of curriculum materials and adaptive teaching strategies based on the school context.
- Hong Kong FlippEducators
- This is a community of local teachers promoting flipped learning for all subjects. Many examples are related to mathematics. The emphasis is put on means to active learning, which is not necessarily limited to video making.
- International Math-teacher Professionalization Using Lesson Study
- You can access the Lesson Study Library for details of shared lessons, including videos in some cases (after free registration). You can learn from the explanation of the design and evaluation of each lesson and appreciate the collaboration of teachers (even across countries, from both east and west).
- Teaching Mathematics for Social Justice
- Check the framework inside the front page, which outlines the 5 key features behind the developed teaching ideas that may enhance students' engagement and agency by making mathematics more meaningful and relevant. They are illustrated by resources within the project and from other sources (collaborative problem-solving activities).
- Content and Language Integrated Learning (CLIL)
Some resourceful and productive teacher bloggers:
- Resourceaholics (Jo Morgan)
- Median (Don Steward)
- Mathematics, Learning and Technology (Colleen Young)
- Great Maths Teaching Ideas (William Emeny)
- Inquiry Maths (Andrew Blair)
Jo Boaler promotes a variety of approaches in teaching that address a range of critical issues in mathematics learning, making mathematics accessible and meaningful for all learners, especially those disadvantaged, discouraged or demotivated. She offers useful tips, messages and resources in her website and books, explaining the power of growth mindsets among students (and even teachers and parents), which could bring about substantial changes in the culture and practice of mathematics education.