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go to Treasure Trove in the CDI web site

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go to Treasure Trove in the CDI web site

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Mathematics Education Section - Resources - Treasure Trove

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Most of the books in this padlet can be accessed online via HKUL

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Teaching Secondary School Mathematics Techniques And Enrichment Chapter 1

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Su, F. E. (2020). Mathematics for human flourishing. Yale University Press. https://doi.org/10.12987/9780300248814

related links:

author

original blog post

blog post in Chinese

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based on Swan, Boaler, Wiliam, Posamentier, ...

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Adapting and extending secondary mathematics activities : new tasks for old : Prestage, Stephanie

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Adapting and extending secondary mathematics activities : new tasks for old : Prestage, Stephanie : Free Download, Borrow, and Streaming : Internet Archive

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Thinkers : Free Download, Borrow, and Streaming : Internet Archive

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Follow this link to the main resource page for KS3.

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5 practices for orchestrating productive mathematics discussions : Smith, Margaret Schwan

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5 practices for orchestrating productive mathematics discussions : Smith, Margaret Schwan, author : Free Download, Borrow, and Streaming : Internet Archive

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open Improving Learning in Mathematics in Evernote

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Access all PD materials in Evernote

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Teaching mathematics : Max A. Sobel : Free Download, Borrow, and Streaming : Internet Archive

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open McGrane & McCourt (2020) in Evernote

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Questions, tasks and activities to support assessment in KS3

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Thinking mathematically : Mason, John, 1944- 

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Thinking mathematically : Mason, John, 1944- : Free Download, Borrow, and Streaming : Internet Archive

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Mathematical Etudes

Instant Maths Ideas

for more teaching ideas, see his blog posts and professional articles

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Mathematical Etudes are creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises.

Click here to take a look.

This website contains a free collection of over 40 starting points (beginnings) for mathematical activity. They could be used with learners aged around 11 upwards as a part of normal mathematics lessons or as something 'a little different'. Someprompts are provided to help learners find mathematics to work on and some briefteacher's notes are also offered, indicating possible mathematics that could emerge.

This popular series of three books of lesson ideas, published by Nelson Thornes, is now available free. The three volumes address Number and Algebra, Shape and Space, and Data Handling and ICT.

I have written over 300 articles, including both academic papers and articles for teacher professional journals, as well as 13 books. Many of these contain lesson plans and teaching resources.

Click and here here to take a look.

"Colin Foster ... has now established himself as one of the leading mathematics educationalists in the country."

Editorial (2019). Mathematics in School, 48(3), 1.

Dr Colin Foster MA(Cantab), PhD, PGCE, CMathTeach, SFHEA

I am a Reader in Mathematics Education in the Department of Mathematics Education at Loughborough University, UK. I am Editor-in-Chief of the International Journal of Mathematical Education in Science and Technology and I am a member of the Editorial Board of Research in Mathematics Education. I am a Director of Shell Publications Ltd and President of the Mathematical Association.

Previously, I was an Associate Professor and Director of Research in the School of Education at the University of Leicester, and before that I was a Senior Research Fellow and then Assistant Professor in the Centre for Research in Mathematics Education at the University of Nottingham. Before being an academic, I taught mathematics in secondary schools for 12 years. My first degree and PhD are from Magdalene College, Cambridge, and I obtained my PGCE from the University of Cambridge Faculty of Education.

I have been designing mathematical tasks and writing books and articles for mathematics teachers for over 15 years. During 2005-2008, I co-edited the journalMathematics Teaching, published by the Association of Teachers of Mathematics.

Alongside my research, I direct the Loughborough University Mathematics Education Network, sometimes lecture mathematics to undergraduates and teach pre-service teachers on the PGCE secondary mathematics course at Loughborough University, supervise masters and PhD students and lead professional development for mathematics teachers. I write regularly for the magazineTeach Secondary and for mathematics teacher professional journals, includingMathematics in School, published by the Mathematical Association, and Mathematics Teaching, published by the Association of Teachers of Mathematics. I was a member of the Department for Education Expert Group for the mathematics national curriculum and I am an examiner for Cambridge Assessment.

I am a Chartered Mathematics Teacher, a Fellow of the International Society for Design and Development in Education, a Senior Fellow of the Higher Education Academy and a member of the British Educational Research Association, the International Group for the Psychology of Mathematics Education, the National Council of Teachers of Mathematics and the Association of Mathematics Education Teachers.

Before mathematics education, I worked in chemistry. Click for my thesis and a related paper.

If you are interested in studying for a PhD in an area relating to my research interests, then please email me with your ideas.

Research Conferences and seminars

International Society for Design and Development in Education Virtual Conference, Webinar. Designing a fully-resourced, coherent, research-informed school mathematics curriculum. https://www.youtube.com/watch?v=wsFxwIhaSe8

Association of Teachers of Mathematics / Mathematical Association meeting, University of Leicester. Rich mathematics from closed questions. Click for a blog about this session.

English Schools Foundation, South Island School, Aberdeen, Hong Kong. Rich, open tasks for learning mathematics.

Mathematics Education Blog

© Colin Foster 2022

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Mathematical Etudes are creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises. Click here to take a look. This website contains a free collection of over 40 starting points (beginnings ) for mathematical activity.

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Although manipulatives and representations are commonly used in primary mathematics or have been historically considered the reserve of lower prior attainers, they can be equally valuable for revealing mathematical structures at secondary level for all students.

We have produced guidance for some of the most useful representations for Key Stage 3 mathematics. Each guidance document details:

what they are

why they are important

how they might be used.

Click the following links to download the guidance documents.
Please note some of the links to NCETM content in the documents below may not work. You can quickly find where the links point using the search tool on this website. If you cannot find what you're looking for, contact info@ncetm.org.uk.

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Using mathematical representations at KS3

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Guidance for some of the most useful representations for Key Stage 3 mathematics.

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Resources for Teaching Mathematics 14-16

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Resources for Teaching Mathematics 14-16

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The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students' mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress. The tools are relevant to any curriculum that seeks to deepen students' understanding of mathematical concepts and develop their ability to apply that knowledge to non-routine problems.

More about the Math Assessment Project

100 lessons for formative assessment, some focused on developing math concepts, others on solving non-routine problems. A Brief Guide for teachers and administrators (PDF) is recommended reading before using these lessons for the first time.

A set of 94 exemplar summative assessment tasks to illustrate the range of performance goals required by CCSSM. The tasks come with scoring rubrics and examples of scored student work.

Complete summative test forms and rubrics designed to help teachers and students monitor their progress using a range of task types similar to the 'Tasks' section.

5 Prototype modules that encourage groups of teachers to explore the practical and pedagogical concepts behind the materials, such as formative assessment, collaborative learning and the use of unstructured problems.

The Teaching for Robust Understanding of Mathematics (TRU Math) suite is a set of tools with applications in Professional Development and research based around a framework for characterizing powerful learning environments.

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The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students' mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress.

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open Boaler, J. (2016) in Evernote

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open Mason, J. & Johnston-Wilder, S. (2006)  in Evernote

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KS3 Key Ideas (Core Concepts) exemplified

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KS3 Key Ideas (Core Concepts) exemplified

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The KS3 Mastery Professional Development Materials are made up of six themes. These cover 17 core concepts, collectively containing numerous key ideas. All of these are listed in the overview documents which can be found on the core concept webpages, accessed from the Secondary Mastery Professional Development materials main page.

Each overview document breaks the concept down into several key ideas, and details pedagogical principles and practices. 52 of these key ideas are discussed extensively in sections called 'Exemplified key ideas'.

To help teachers translate the professional development content of all these exemplifications into their classroom practice, we have put together PowerPoint slide decks. These combine slides marked for use in the classroom with students, and slides focusing on the pedagogy, suitable for planning discussions in departments.

Each PowerPoint deck concentrates on one exemplified key idea and includes slides pointing to:

Prior learning

Misconceptions

Representations and structure

Key vocabulary.

You can download all 52 slide decks below. They are organised into six zip files, where each file contains all the slide decks for the key ideas in the overarching theme of the national curriculum.

All this material is mirrored in the KS3 mathematics teaching guidance published by the DfE in autumn 2021.

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The KS3 Mastery Professional Development Materials are made up of six themes. These cover 17 core concepts, collectively containing numerous key ideas. All of these are listed in the overview documents which can be found on the core concept webpages, accessed from the Secondary Mastery Professional Development materials main page.

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also in HKUL, Eng/Chin ebooks

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How to solve it; a new aspect of mathematical method : Pólya, George, 1887-1985 : Free Download, Borrow, and Streaming : Internet Archive

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Understanding Lesson Study for Mathematics

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Understanding Lesson Study for Mathematics

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Archer, R., Morgan, S., & Swanson, D. (2020). Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning (1st ed.). Routledge. https://doi-org.eproxy.lib.hku.hk/10.4324/9781351048286

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Understanding Lesson Study for Mathematics

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Archer, R., Morgan, S., & Swanson, D. (2020). Understanding Lesson Study for Mathematics: A Practical Guide for Improving Teaching and Learning (1st ed.). Routledge. https://doi-org.eproxy.lib.hku.hk...

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Readings from the NRICH site

Enriching Sec Curriculum

Articles for Sec Teachers (Rich Tasks and Pedagogy)

Low Threshold High Ceiling

Thinking Mathematically

Mathematical Habits of Mind

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Resources for Teaching Mathematics 11-14

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Resources for Teaching Mathematics 11-14

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open Small & Lin (2010) in Evernote

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open Wiliam, D. (2018) in Evernote

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open McCrea, E. (2019) in Evernote

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open Techniques for Motivation and check other books from Posamentier in Evernote

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Recorded by experienced teachers, these videos offer advice and ideas for colleagues, especially less experienced colleagues such as NQTs, or non-maths specialists, and TAs/tutors teaching small groups.

Particularly useful for Covid recovery, they cover key learning points, assessing prerequisite knowledge, key questions, language, representations and common misconceptions and pitfalls. They also include lesson ideas and activities for students.

Each video is accompanied by a supporting document of notes, explanations and further resources, and the PowerPoint slides used in the video. These resources are below the video playlist and can be downloaded as zip files.

"I have found these extremely helpful. As an NQT, these resources have been very useful to help me sequence topics so that students can gain a better understanding, and they also give me really good ideas for the language to use when explaining."
- Secondary Maths NQT
The video below is the first in a playlist. Click on the dropdown option below to view the other available videos. If you wish to download any of the videos, you can do so from the Vimeo showcase.

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Videos and resources for teaching Key Stage 3 maths topics

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Teaching Mathematics through Problem Solving

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Teaching Mathematics through Problem Solving

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Takahashi, A. (2021). Teaching mathematics through problem-solving : A pedagogical approach from Japan (Studies in mathematical thinking and learning). New York, NY: Routledge.

http://find.lib.hku.hk/record=HKU_IZ51628585660003414

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Takahashi, A. (2021). Teaching mathematics through problem-solving : A pedagogical approach from Japan (Studies in mathematical thinking and learning). New York, NY: Routledge. http://find.lib.hku.hk/...

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The Essential Guide to Secondary Mathematics

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The Essential Guide to Secondary Mathematics

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The YouCubed Web site

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Information about diagnostic maths activities to help teachers assess understanding and lay foundations for KS3

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Comparison of the Junior Secondary Mathematics Curriculum Content (1999 vs 2017)

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Comparison of the Junior Secondary Mathematics Curriculum Content (1999 vs 2017)

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The open-ended approach : a new proposal for teaching mathematics

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The open-ended approach : a new proposal for teaching mathematics : Free Download, Borrow, and Streaming : Internet Archive

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George Polya Mathematical Discovery : George Polya : Free Download, Borrow, and Streaming : Internet Archive

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MATHEMATICAL DISCOVERY On understanding, learning and teaching problem solving Combined EditionbyGeorge Polya Professor Emeritus of Mathematics Stanford...

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Effective Techniques to Motivate Mathematics Instruction pages Cover - 9

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Math Instruction for Students with Learning Problems

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Math Instruction for Students with Learning Problems

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Groth, R. (2012)

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Learning and doing mathematics : Mason, John, 1944- 

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Learning and doing mathematics : Mason, John, 1944- : Free Download, Borrow, and Streaming : Internet Archive

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Making Mathematical Micro-decisions

Equity, Diversity, Inclusion and Belonging

Traditional and Progressive Models

Variation Theory

Using Realistic Contexts

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Rethinking support for curriculum design in maths by developing a flexible and interconnected digital framework to help reimagine mathematics education.