When the Basics Take Shape
Few topics present such a clear link between basic beginner math skills and higher-level learning like geometry. Within this wide branch of mathematics, we go from learning our first shapes to working with complex geometric relationships on grids and in formulas.
Understanding geometry and its graphical representations is fundamental Euclidian geometry, radial measurement, trigonometry, functions and calculus, linear algebra, and much, much more. These branches of math underpin our modern scientific understanding of all kinds of realities in our world: everything from physics to economics to engineering to management forecasting.
And it all starts with a few lines, an angle or two, and a shape.
Visualizing from All Angles
It is easy to see how a visual approach is a critical first step to learning shapes. They are, after all, small pictures. As students progress from primary learning to middle and intermediate grades that prepare them for high school and beyond, we seek to keep the visual approach going. It is much easier for students to relate to the abstraction required at higher levels of study when they can visualize the math behind them.
The junction that divides early geometry—dealing with the basic shapes many of us learn as pre-Kindergarteners—from middle school geometry comes largely when angles are introduced. The first step is to get students comfortable with the idea of calculating and describing angles; in fact, we encourage them to think about the angles they already subconsciously work with. Using metaphors such as a door on hinges, we can teach them the basic terminology necessary to describe angular relationships and how to calculate simple angles.
Students can then practice calculating angles in shapes they are already familiar with, such as triangles and quadrilaterals. In classic Singapore math form, we ask them to tackle problems “from every angle” in order to add to their understanding more deeply. This helps them to ask new questions and understand what they have the power to calculate with the information they are given.
It is a very quick step from fluidly filling in angles among lines and shapes to doing so on a graph. Without even realizing it, they’ve laid the foundations for themselves for trigonometry and calculus. The more readily comfortable a student is with understanding the degrees and angles within a circle, or triangle, or any kind of shape, and doing so on a graph, the more readily they will have epiphanies of understanding when they start to work with the more intimidating buttons on their calculators.
Basic Shapes to Hero Capes
It is incredible to think of our little Polygon-practicing preschoolers as future Pythagoras proficients. Using the Singapore math tools we deeply believe in, we at Mentorhood never teach a concept in isolation. We are always considering how the math we learned today provides the foundation for the concepts we will tackle tomorrow, and the mastery that we will aspire to in the future.
Questions and lessons are designed to provide students with a gateway into intuitive understanding. Math proficiency is obtained not through memorization and formulaic repetition, but through the ability to consider deeper questions and further conclusions beyond a learned concept. We teach with this goal in mind. We are always trying to equip our students to learn through all kinds of perspectives, treating the concepts they learn as three-dimensional objects they can pick up and examine from all sides.
This not only sets the foundation for proficiency in math, which happens to be our favorite subject, but gives the students the tools to have proficiency in learning as a whole, confidence in themselves, and the ability to question and make inferences in whichever areas feel the most intellectually stimulating and satisfying to them.
We teach, therefore, and hope our students learn, from the very core of our favourite shape: the heart.
Welcome to the team, parents—the Singapore Math team! We’re excited to have you on board and we look forward to helping you coach your little ones.
We’re happy to come alongside your learner in their learning journey. And if you want to do more from home, you can check out our ever-growing library of games, now on YouTube!
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In the meantime, if there are specific topics you’re having trouble teaching and you’d like us to cover them, let us know. We’d love to hear from you.