Mathematics that is beautiful and a source of wonder!
by George Gadanidis, PhD
ABOUT Mathematics Every Child NeedS
I have spent hundreds of 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 1-3 of Mathematics Every Child Needs offer 12 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 or small groups. You may also display them in your classroom.
The placemats come with investigation tasks. This teaching guide provides solutions, extensions, and coding puzzles.
The placemats offer students, parents and teachers opportunities to learn mathematics in-depth, by making connections among concepts, and seeing trajectories across grades.
MATHEMATICS WORTHY OF ATTENTION
In the youngest classrooms (typically K-4), children often share their learning at home, and parents send feedback to teachers in the form of “What did your child share with you?” and “What did you learn?” Parent comments include, “I loved her excitement and her complete understanding and explanation of it all”and “I was surprised how easily my son grasped it all”.
In some cases, student and parent comments are 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, many of us somehow learned to dislike or even fear mathematics. An important reason for this sad predicament is that some of our theories 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 simply concrete thinkers and they cannot handle abstract ideas until much later in life.
Kieran Egan (2002) has noted that children would not be able to develop language if they could not naturally abstract from a very young age. For example, the word “dog” is an abstraction that represents many different types of “dog” (big, small, friendly, fierce, etc.) and children effortlessly abstract the key characteristics of “dog” to recognize it as different from other four-legged creatures.
Children need mathematics that offers them the pleasure of thinking hard, along with conceptual surprises and insights.
REFORM, OCCASIONALLY
Our research-based reform model focuses on occasionally engaging students with 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.
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).
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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.
- 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.