Archive for July, 2021

Numicon resources

Posted on: July 28th, 2021 by jnovakowski

Numicon is a research-based collection of resources to support the teaching and learning of mathematics, published by Oxford University Press in the United Kingdom. Several research case studies can be found on their website HERE.

Numicon is based on the Concrete, Pictorial, Abstract (CPA) model of learning mathematics. This is also sometimes known as the CRA model in the USA (Concrete, Representational, Abstract) and are BC curriculum uses the language of Concrete, Pictorial, Symbolic (CPS).

There are teaching resources, both physical and online, student books and the materials that are called “apparatus”. I have been particularly intrigued by what are called the Numicon Shapes after seeing many twitter posts by Simon Gregg that include them.

An individual set of Numicon Shapes includes the numbers 1-10 as in the picture below.

A box of 80 Numicon Shapes is also available:

I have created some investigation cards to use with the Numicon Shapes.

There area also number lines and other tools available to use with the Numicon Shapes. One tool I have invested in is the baseboards which are great for creating symmetrical or “double” designs on or for visualizing and making 100 in different ways..

The Numicon Shapes apparatus can be ordered directly through the Oxford University Press website HERE but I have also found them available in Canada online through Chapters Indigo and Amazon.

A collection of free online resources are available through Oxford University Press HERE and I have collated some of them here:

We hope to have a district Numicon Shapes kit available soon through the District Resource Centre.


Froebel’s Gifts

Posted on: July 22nd, 2021 by jnovakowski

I have always been curious to learn more about Froebel’s work and this summer I decided to do a bit of a deep dive and read more and play with the materials.

Friedrich Froebel lived in the 19th century in Germany and developed the first kindergartens. The Froebelian approach has been adapted all over the world and is based on the following principles:

  • respect
  • connectedness
  • play, talk and first-hand experiences
  • creativity
  • freedom and guidance
  • play outdoors
  • community
  • positive relationships
  • well-informed and qualified educators

Although these principles may seem what is typical is most early childhood education settings now, they were radical ideas at the time.

The blocks that Froebel developed and how children engage with them are grounded in three ideas connected to the above principles:

  • forms of life – using the blocks to create and represent things and events from the world around them
  • forms of beauty – focus on the aesthetic, symmetry, pattern, order, design, etc
  • forms of knowledge – exploring mathematical forms and scientific concepts such as size, shape, area, stability and balance
forms of life: connecting to architecture
forms of knowledge: thinking about fractions
forms of beauty: symmetry and design

Froebel’s Gifts are early play materials intended for use by individual students and designed by Froebel and made by artisans in the communities where the kindergartens were. The German Froebel designed the first six “play gifts” (spielgabe or shortened to gabe) as educational materials that children would progress through and make connections as they played and built with the geometric solids . Further gifts followed and Froebel then developed what he called “occupations” to extend the learning experiences of the gifts. The occupations included weaving, sewing and working with clay. The occupations often transformed the materials unlike the gifts which were intended to go back in their boxes to be used again and again.

The following photographs are of Gifts 1-6 which focuses on the “solids”or what may also be called 3D geometric shapes.

The progression of the gifts and occupations begin with 3D solids, move to 2D shapes then to lines, then to points and then circle back to using lines, points and 2D shapes to create 3D shapes. This progression is connected to the contemporary research of van Hiele’s hierarchy of geometric thinking.

There are clear connections to our mathematics curriculum as students learn about describing and comparing both 2D and 3D shapes. There is also a focus on spatial reasoning in how the gifts are used as students move the shapes, observe them from different perspectives, compose and decompose and transform their orientation.

One of the many interesting stories I came across on the impact of these gifts was about architect Frank Lloyd Wright. His mother was a Froebelian educator and he has distinct memories of playing and building with the the three distinct maple wood blocks. He commented that those shapes were “in” him through those early experiences and inspired many of his designs.

Two books that I read this summer:

Some resources I found online that were helpful include:

  1. Froebel Gifts

This site explains each gift in detail including forms of life, knowledge and beauty. Videos are included. A brief introduction to kindergarten and the Froebel philosophy are included.

2. Froebel Trust (UK)

This website has a lot of information about the history of Froebel’s philosophy and the use of the gifts. It also includes current research and resources to support early learning. There are a set of downloadable pdf “pamphlets” including one on Froebel gifts and block play that makes connections to how blocks are often used in current early childhood settings.

3. Garden of Children Project

The Garden of Children Project looks at the Froebelian approach in the USA and has collected video, transcripts, images and interviews in order to compile a documentary. Short video clips can be viewed on the website here:

Online stores that I ordered materials from:

  1. Red Hen Toys (American – needed to email to sort out shipping to Canada)

They have a page/tab dedicated to Froebel Materials included books, gifts and occupations and related materials.

2. Thinkamajigs (Ontario)

They have a Froebel tab in their shop which has the gifts and some of the occupations.

Current math education research is highlighting the importance of spatial reasoning to overall mathematics development and achievement. See here if you are interested in reading more. The more I learn about the Froebelian approach, I am reminded how these ideas have been highlighted since the 19th Century. We just sometimes let things drop or prioritize other areas of learning when we need to remember to think more holistically and that learning in ultimately about relationships and connections. I am thinking about ways to share these “gifts” with students and thinking of other ways to use these ideas and will share these investigations on twitter and Instagram.