ibenson

AI as a component in the action research tradition of learning-by-doing

In this pre-print we consider learning mathematics through action research, hacking, discovery, inquiry, learning-by-doing as opposed to the instruct and perform, industrial model of the 19th century. A learning model based on self-awareness, types, functions, structured drawing and formal diagrams addresses the weaknesses of drill and practice and the pitfalls of statistical prediction with LLMs.… Read more AI as a component in the action research tradition of learning-by-doing

Interventions to improve equational reasoning

The ability to reason about equations in a robust and fluent way requires both instrumental knowledge of symbolic forms, syntax, and operations, as well as relational knowledge of how such formalisms map to meaningful relationships captured within mental processes. A recent systematic review of studies contrasting the Cuisenaire-Gattegno (Cui) curriculum approach vs. traditional rote schooling… Read more Interventions to improve equational reasoning

Conceptual Mathematics

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

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

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

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

Awareness

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!

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