{"id":14,"date":"2026-01-25T00:22:39","date_gmt":"2026-01-25T00:22:39","guid":{"rendered":"https:\/\/learnx.ca\/um\/?page_id=14"},"modified":"2026-03-21T10:52:56","modified_gmt":"2026-03-21T10:52:56","slug":"cover","status":"publish","type":"page","link":"https:\/\/imaginethis.ca\/u\/","title":{"rendered":"Understanding mathematics"},"content":{"rendered":"\n

For teachers, parents, and curious learners of every age<\/strong><\/h2>\n\n\n
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The height of time and other mathematical waves.<\/figcaption><\/figure>\n<\/div>\n\n\n

Let\u2019s be honest: most of us know some<\/em> math\u2014maybe even a respectable amount\u2014but often we\u2019re just skimming the surface, with very little understanding.<\/p>\n\n\n\n

This resource peels back the curtain on everyday mathematics, revealing the surprising, interconnected world that lies beneath, in ways that are understandable and easy to communicate to others.<\/p>\n\n\n\n

Take a look through it. Have fun with it. And share it with someone who enjoys a good \u201cwait\u2026 what?\u201d moment as much as you do.<\/p>\n\n\n\n

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The wonder of it all<\/h2>\n\n\n
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As you read these words, the planet beneath your feet is racing around the Sun at nearly 100,000 km\/h<\/strong>, carrying you along without so much as a wobble in your coffee cup. And our Sun\u2014our entire solar system\u2014is itself sweeping around the center of the Milky Way at an astonishing 850,000 km\/h<\/strong>, taking about 230 million years<\/strong> to complete a single cosmic lap. All the while, the Milky Way is drifting through the vast dark at something like 1.5 million km\/h<\/strong>.<\/p>\n\n\n\n

And despite the cold and emptiness out there\u2014roughly \u2013270\u00b0C<\/strong>\u2014we live warm, busy, incredible lives inside a thin atmospheric cocoon that protects us so completely we hardly notice it\u2019s there.<\/p>\n\n\n\n

Inside this shelter, across thousands of years of curiosity, imagination, and the sheer human need to understand, we\u2019ve created mathematics of breathtaking depth and elegance. The kind of mathematics that lets us land on the Moon. The kind that powers artificial intelligence systems. The kind that helps us model galaxies, predict weather, design vaccines, and send signals across oceans and into space.<\/p>\n\n\n\n

Yet somehow, amid all this wonder, we often give young children\u2014our future explorers and thinkers\u2014mathematics that is tiny, flattened, and sometimes just plain wrong.<\/p>\n\n\n\n

We teach children to calculate surface area and volume of cylinders, cones and cubes…
But we don’t invite them to ponder: why elephants have big ears<\/strong>\u2014
and what unexpected connection might mathematics have to that question?<\/p>\n\n\n\n

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Why do elephants have big ears?<\/figcaption><\/figure>\n\n\n\n

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We tell children, \u201cParallel lines never meet<\/strong>,\u201d
without giving them the chance to discover that on a sphere\u2014on the very planet they stand on\u2014those lines curve, embrace, and eventually cross.<\/p>\n\n\n\n

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Parallel lines never meet is an assumption, not a theorem. Different assumptions create different geometries.<\/figcaption><\/figure>\n\n\n\n

<\/p>\n\n\n\n

We tell them, \u201cYou can\u2019t hold infinity in your hand<\/strong>\u201d,
instead of engaging them to imagine all the clever, playful ways they actually can.<\/p>\n\n\n\n

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You can hold infinity in your hand!<\/figcaption><\/figure>\n\n\n\n

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We often flatten mathematics\u2014pressing all its colour and life out of it\u2014until it becomes something forgettable, something easy to dismiss.<\/p>\n\n\n\n

But that is not what mathematics truly is.<\/p>\n\n\n\n

Mathematics holds surprises hiding in plain sight, and ideas that reveal themselves when children are given the chance to investigate and understand deeply. When they can make connections across concepts, notice relationships, and follow their curiosity, math stops being a list of individual things to learn and becomes a landscape\u2014wide, rich, and full of wonder.<\/p>\n\n\n\n

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Understanding in depth<\/h2>\n\n\n\n

Mathematics reveals its beauty when we explore it deeply.<\/p>\n\n\n\n

For this to happen, teachers and parents play a vital role. When we<\/em> develop strong, connected understandings of mathematical ideas\u2014how concepts relate, grow, and build on one another\u2014we create the conditions for children to experience mathematics as an exciting journey rather than isolated bits of knowledge.<\/p>\n\n\n\n

You don’t have to learn everything at once. Start with a favourite deep activity.<\/strong><\/p>\n\n\n\n

Occasional, well-designed mathematics experiences can have lasting impact, raising expectation and anticipation of what mathematics can offer.<\/strong><\/p>\n\n\n\n

This resource is an invitation to begin that journey.
It offers starting points, insights, and explorations designed to spark curiosity, strengthen understanding, and open doors to the deeper side of mathematics.<\/p>\n\n\n\n

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A historical problem<\/h2>\n\n\n\n

Our struggle with developing mathematical understanding is not new.
It is a long\u2011standing, widespread pattern\u2014crossing cultures, continents, and centuries.<\/p>\n\n\n\n

We have good intentions.
But without recognizing the importance of deep mathematical insight, we often find ourselves in an impossible position. It\u2019s as if we are caterpillars\u2014who know only the surface of leaves and branches\u2014doing our best to teach butterflies how to fly. <\/p>\n\n\n\n

We care.
We try.
But without mathematical depth, our efforts do not take flight.<\/p>\n\n\n\n

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For teachers, parents, and curious learners of every age Let\u2019s be honest: most of us know some math\u2014maybe even a respectable amount\u2014but often we\u2019re just skimming the surface, with very little understanding. This resource peels back the curtain on everyday mathematics, revealing the surprising, interconnected world that lies beneath, in ways that are understandable and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-14","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/pages\/14","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/comments?post=14"}],"version-history":[{"count":48,"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/pages\/14\/revisions"}],"predecessor-version":[{"id":555,"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/pages\/14\/revisions\/555"}],"wp:attachment":[{"href":"https:\/\/imaginethis.ca\/u\/wp-json\/wp\/v2\/media?parent=14"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}