Resources and Research

Free Classroom Math Posters

The three math posters linked here are used in many International schools. Two of them were created by teachers at the International School of Düsseldorf. The first series of posters look at the essential elements of what makes a good Mathematician, and therefore what goals every math lesson should encapsulate. The second series of posters develops an Inquiry cycle that is useful to teach all lessons, but in particular for Elementary Mathematics. The Final Poster links you to the fantastic website ‘Mashup Math’ and in child friendly speech looks and how to employ a growth mindset in Mathematics in your classroom.

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A (Math) Inquiry Cycle: 
Classroom Posters

A Good Mathematician:
Classroom Posters

Learning Math with a Growth Mindset: Classroom Poster

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Article: Linking the IB PYP Math 
Programme to Numicon 

Curriculum Mapping Booklet:
Linking Numicon to the PYP

Numicon Impact Report 2011:
Reviewing Perceptions

Numicon Case Studies:
Reviewing Specific Schools

Purchase Numicon
Resource: From OUP Direct

Numicon Information & Resources

Numicon is a multi-sensory Concrete, Pictorial, Abstract (CPA) approach to teaching and learning mathematics. It combines the latest research with playful pattern-based materials to form a holistic approach to mathematics, which helps uncover deep conceptual understanding. Numicon can either complement or enhance an existing schools curriculum and syllabus, or be used as a curriculum unto itself. Published by the good people at Oxford University Press, Numicon is something that really works, and accordingly has been strongly advocated by the various schools and in some research articles, of which you can download here, or access with the links provided. 

The Numicon approach is strongly aligned with the International Baccalaureate, Primary Years Program (IB PYP), and its mathematics Scope and Sequence. Available for download here is an article that explicitly shows those connections. Also available is a booklet that helps curriculum map the IB PYP to the Numicon Teacher Resource Handbooks. David is a certified Numicon Consultant specialising in International Schools. You can contact him for any enquiries or further information about Numicon.

Research:
Brain Science and Math Education

Provided here, are a few academic journal articles and book references. This list is by no means exhaustive. It is more of a ‘the tip of the iceberg’ of what research is coming through in the last 10 years that links Brain Science to Educational Pedagogy and  Mathematics. As copyright licences allow, some articles are available for download here. Otherwise, they are linked. The books link to Amazon for purchasing options. Increasingly, the research is proving that there are ways of teaching that are more effective than others to ensure deep learning, retention, as well as reduce anxiety and fear. These newer longer-term academic case studies generally advocate for a multi-sensory approach to teaching and learning such the CPA approach that is strongly advocated by Numicon, the PYP, Singapore Maths, and many other National Curriculums. If you want an expert to summarise, and synthesise this information for your faculty in an accessible way, and show how it can apply and work immediately in your classrooms, then you have come to the right place. Ask David for a quote to deliver a live e-learning or inset workshop customised for your school.

Guide & Research:
Concrete, Pictorial, Abstract (CPA)

A Harmonised Conceptually Based approach to Teaching and Learning Mathematics

Provided here is a guide David has written for public viewing that explains how to teach mathematics using an inquiry cycle that embraces the Concrete, Pictorial, Abstract (CPA) approach to teaching and learning. It explains the steps that are shown in the posters available above and references the seminal works that David has linked for you below. Also linked for your reference are a couple of academic journal articles about the CPA approach, and its impact upon teaching and learning. The articles all consistently show that using this approach reduces student anxiety and fears of math, as well as assisting with dyscalculia, and promoting a deeper relational understanding of the essential mathematical concepts. Further, despite this shift in focus, the CPA approach does not impact upon a summative, skill-based assessment scores. These articles, form only the smallest fraction of what is now available out there. However, the trends and importance to teaching are becoming increasingly clear. Schools should adopt a CPA approach to teaching and learning mathematics in elementary classes. It is this approach that is increasingly advocated as the most evidence based best practice pedagogy now available. 

Research Base:
Seminal Works & Core Books

In David’s workshops, a frequent question he is asked is which influential books form his core research base or have most informed his practice and workshops. Here linked are five of those core books. Three of these books are considered seminal works that help form the pillars of a hands-on approach to teaching and learning mathematics developed from the field of cognitive psychology. Their authors are likely known to all teachers and academics, Jerome Bruner, Zoltan Dienes, and Richard Skemp. The other two references are from contemporary authors Jo Boaler, and David Sousa who are helping develop and refine this approach to teaching and learning mathematics, and show ideas of how it could be employed in todays’ classrooms. These modern influencers have harmonised the cognitive psychology theories of decades past with an evolved understanding of how the brain learns from a neuroscience perspective.

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