All children need occasional experiences with mathematics that are complex, accessible and surprising: to appreciate mathematical patterns and beauty and to learn conceptual connections that span across grades.
George Gadanidis, PhD
This is not a frill — it is their right — and our responsibility as parents and teachers.
Mathematics is big. Children’s minds are bigger.
MATHEMATICS EVERY CHILD NEEDS, Volume 1 (#1-4)
Mathematics Every Child Needs was inspired by and created for Amelia & Nella.
Proceeds used to offer free resources to parents & children.
COMPLEX, ACCESSIBLE, SURPRISING MATHEMATICS
Over many years, I have spent numerous mornings and afternoons co-teaching in grades K-9 classrooms, engaging children with mathematical ideas that are complex, accessible, and surprising, like, “You can hold infinity in your hand”, “Odd numbers hide in squares” and “Parallel lines can meet.”
Volumes 1-2 of Mathematics Every Child Needs offer 8 of these mathematical ideas as conceptual art, in the form of placemats.
As a parent, you may use the placemats on your kitchen table to invite math to breakfast, lunch and dinner.
As a teacher, you may use the placemats with students working in pairs and small groups. You may also post them in your classroom as mathematical art.
The placemats come with investigation tasks (in English, French & Spanish). The teaching guide provides solutions, as well as extensions, some in the form of coding puzzles.
MATHEMATICS WORTHY OF ATTENTION
In the youngest classrooms (typically K-4), children often shared their learning at home, and parents sent feedback to teachers in the form of “What did your child share with you?” and “What did you learn?” Parent comments included, “I loved her excitement and her complete understanding and explanation of it all”, “I was surprised how easily my son grasped it all”, and “I want more homework like this!”
Some student and parent comments were turned into lyrics and songs, and for several years we performed them in math concerts for Ontario schools, funded by the Fields Institute for Research in Mathematical Sciences.
WHY MANY ADULTS DISLIKE MATHEMATICS
As children, we entered school mathematically curious and capable. Yet, in the years we spent in school, many of us somehow learned to dislike and even fear mathematics.
An important reason for this sad predicament is that some of our conceptions of education are wrong. For example, Jean Piaget (2008/1972) developed the theory of stages of cognitive development by incorrectly assuming that young children are concrete thinkers and that they cannot handle abstract thinking until much later in life.
Kieran Egan (2002) noted that if children cannot naturally abstract from a very young age, they would not be able to develop language. The word “dog” is an abstraction. It represents many different types of “dog”: big, small, long hair, short hair, friendly, threatening, etc. Children naturally and effortlessly abstract the essential characteristics of “dog” and tell it apart from “cat” or “wolf”.
Underestimating children often leads to making mathematics easy-to-learn: a diet of school mathematics that is simple, tedious and not worthy of their attention. Children occasionally need mathematics that offers them the pleasure of thinking hard.
Fernández-Armesto (1997) lamented that “generations of school children, deprived of challenging tasks because Piaget said they were incapable of them, bear the evidence of his impact” (p. 18).
REFORM, OCCASIONALLY
Reforms often put a lot of focus on better pedagogy and very little focus on better mathematics. Pedagogy is important. However, pedagogy alone cannot make shallow mathematics deeper: it can only sugarcoat it.
Our reform model focuses on occasionally offering students well-designed mathematics experiences that are complex, accessible, surprising and emotionally engaging (Gadanidis, Borba, Hughes, Lacerda, 2016).
Such experiences live fruitfully in future experiences (Dewey, 1938) by raising expectation and anticipation — for students, parents and teachers — of the intellectual and emotional rewards — the pattern, beauty and wonder — that mathematics can offer.
Try this activity on infinity: https://learnx.ca/mt/infinity-overview. We first designed this experience when grade 3 teachers asked for ideas for teaching area representations of fractions.
AI & HUMAN INTELLIGENCE
In the current era of AI, where mathematicians and computer scientists use the best mathematics available to design algorithms for machine learning, the least we can do is offer children — the future of our society — mathematics that is worthy of their potential, at least occasionally.
RESEARCH
Variations of the activities in Mathematics Every Child Needs have been used in a number of research and outreach projects and publications with colleagues in Canada, Brazil and Norway: Marcelo Borba (UNESP), Janette Hughes (Ontario Tech University), Siri Krogh-Nordby (OsloMET University), Immaculate Namukasa (Western University) and Ricardo Scucuglia (UNESP).
MATH TRAVELS
Mathematics Every Child Needs was initially published in 2024 as Math Travels, and was offered freely to Faculties of Education across Canada, Brazil and Norway, and to school districts that have participated in research and outreach projects (with placemat tasks translated to Portuguese by Ricardo Scucuglia and to Norwegian by Siri Krogh-Nordby). The new title explicitly identifies the goal of this mathematics learning and teaching resource.
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- Dewey, J. (1938). Experience & education. NY: Collier Books.
- Egan, K. (2002) Getting it Wrong from the Beginning: Our Progressive Inheritance from Herbert Spencer, John Dewey, and Jean Piaget. New Haven, CT: Yale University Press.
- Fernández-Armesto, F. (1997). Truth: A History and a Guide for the Perplexed. London, UK: Bantam Press.
- Gadanidis, G., Borba, M., Hughes, J. and Lacerda, H. (2016). Designing aesthetic experiences for young mathematicians: A model for mathematics education reform. International Journal for Research in Mathematics Education, 6(2), 225-244.
- Piaget, J. (2008). Intellectual evolution from adolescence to adulthood. Human Development 51(1), 40-47. (Original work published 1972).
AUTHOR
I am Professor of Mathematics Education at Western University and Lifetime Fellow of the Fields Institute for Research in Mathematical Sciences.
I have also worked as teacher of mathematics, science, and computer science, as mathematics and computer science department lead, as district-wide mathematics coordinator, and as content and digital resource developer for various publishers.
I enjoy co-teaching and co-learning in mathematics classrooms.
ART
Art by Aileen Lin & Ann Langeman. Design by George Gadanidis.
Variations of some of the placemats (#2 & 3) were previously designed as research performances by George Gadanidis, rendered artistically by Ann Langeman, with the original art donated to schools.