Posts by ibenson

Conceptual Mathematics

by on May 19, 2023 2:29 pm
One approach to mathematics is to regard it as comprising distinct aspects: algebra – the manipulation of symbols, geometry – dealing with shape and position, and logic – making arguments. Conceptual mathematics, or category theory, combines all of these. It is about the structure of arguments, and deals with algebra geometrically. While category theory only… Read more Conceptual Mathematics

Equational reasoning: A systematic review of the Cuisenaire–Gattegno approach

by on May 19, 2023 2:12 pm
The Cuisenaire–Gattegno (Cui) approach to early mathematics uses color coded rods of unit increment lengths embedded in a systematic curriculum designed to guide learners as young as age five from exploration of integers and ratio through to formal algebraic writing. The effectiveness of this approach has been the subject of hundreds of investigations supporting positive… Read more Equational reasoning: A systematic review of the Cuisenaire–Gattegno approach

Science of Education

by on June 15, 2020 1:54 pm
Recent research in educational neuroscience has provided evidence for a computational theory of learning which has a close affinity to Gattegno’s Science of Education. Below is my review of Stanislas Dehaene’s new book “How We Learn. The New Science of Education” which discusses these findings in detail. Book-ReviewDownload

Representing Functional Relationships

by on June 27, 2019 6:53 pm
The study of permutations and combinations of Cuisenaire rods has proved to be a rich source of mathematical tasks motivating abstraction through algebraic symbol systems as well as mathematical generalisation. In this article I take a rod permutation problem and show how teachers can use this task to support generalisation by employing a new formalism… Read more Representing Functional Relationships


by on June 19, 2019 8:38 pm
Caleb Gattegno’s contribution to mathematics education ranged from innovation in the school curriculum (“Algebra First”) to a theory of learning – the Science of Education. Where a “bit” might be said to be a unit of study in information theory, a gene in biology, or an atom in physics — Gattegno’s scientists of education study… Read more Awareness

Hello world!

by on June 19, 2019 7:42 pm
In these three articles teachers describe the benefits of learning and teaching with early algebra and how algebraFirst can be extended so that learners can write small computer programs. Getting started with early algebra Experiences with early algebra   Using Haskell with 5-7 year olds