What are the most enjoyable math facts

Homeschooling in Switzerland

Blog Post # 4 by Dr. Cotter, the founder of RightStart:

I want to take some time to discuss the science and art of teaching math. I call it a science because there has been a lot of research into how children learn math in general, and math in particular. I call it an art because every child is different, which requires each teacher to modify the lesson a little to help each and every child.

The role of the teacher

Studies have shown that 40% of what a student learns depends on the teacher. First, let's look at the teacher's beliefs and attitudes. If the teacher shows some math anxiety, the child will very likely adopt some of that anxiety and fear. If the teacher views math simply as facts and rules that should be memorized, the child's math education will be built on shaky foundations. If the teacher believes the myth of a “math person” the child may decide that they are not qualified to do so and will stop trying.

On the other hand:

  • Happy is the child whose teacher is convinced of the importance of mathematics for daily life, future careers and an understanding of our world.
  • Happy is the child whose teacher sees math calculations as a puzzle that has to be solved, tries different methods and looks for different solutions.
  • Happy is the child whose teacher realizes that there is more than one way to do calculations, some are more efficient than others, and not everything needs to be written down.
  • Happy is the child whose teacher dispenses with arithmetic cards and lightning tests and instead practices arithmetic facts based on numerical comprehension and games.
  • Happy is the child whose teacher knows that facts are mastered by thinking and not by blindly following an example or practicing a rule over and over again.
  • Happy is the child whose teacher uses mathematics to help his / her students develop self-confidence and independent thinking.
  • Happy is the child whose teacher understands that a certain amount of frustration is a normal part of learning and encourages the child to stick with it.
  • Happy is the child whose teacher does not constantly distribute rewards (verbally or otherwise), which result in the child relying on the teacher in every small step for certainty rather than on his own thinking.
  • Happy is the child whose teacher realizes that a child develops his concentration by being allowed to concentrate and by being protected from unnecessary disturbance.
  • Happy is the child whose teacher exudes joy and helps the child develop a love for mathematics.

Independent learning

Although one goal of education is the ability to learn independently, the basis of a discipline must first be learned. Going down a black slope on your skis before you learned to control your skis would be a catastrophe. Participating in a triathlon before learning to swim would result in soaked failure. Giving a young child a math workbook and expecting them to automatically master simple math is wishful thinking. They're just learning how to fill in the blanks in the book. Telling a child to watch a math video on their own isn't much better. There is no one there to answer questions and there is no way to check understanding. There is no one there to listen and encourage the child's alternative path of thought. There is no one there to cultivate the need for deep understanding.

Homework

If you look at math as a lot of rules and procedures to memorize, a lot of homework might make sense. Everything we learn by heart without understanding needs very regular repetition in order to stay in our memory. The homework should never be so difficult that the lesson has to be taught again, or worse, that the answers have to be spoon-fed to the child. In RightStart Math, the “homework” mostly includes a game.

The world of math

It's easy to think that the math we learned as a kid is enough for our kids and grandchildren. However, the fact is that today's kids need a different kind of math. You'll need to learn topics in geometry, math equations, probability, statistics, the fractals, and combinatorics to name a few. At the same time, arithmetic is less important because of the calculators and computers.

It's also easy to think that the way we learned math was enough, often just by memorization and without much understanding. On the contrary, we now know that a deep understanding of the concepts removes fear, eases the pressure to memorize, makes advanced math easier to understand, and generally makes math more enjoyable.

Sometimes we see math as just a pen and paper activity. On the contrary, what we write down on paper is often an abbreviation in expressing a concept that can often be found in some form in the real world.

Some of the reasons we read to our children are to: cultivate a love for reading, expand their world, and expand their vocabulary. Similar reasons exist in the realm of mathematics. Use precise wording, especially with younger children: say, for example, ellipse instead of oval and rhombus instead of diamond. Refrain from concluding that squares are not rectangles (because they are), that you cannot take 7 out of 5 (you can: the answer is -2), that the result after a multiplication is always greater than any of the Multipliers (this is not always the case: 2 x 0 = 0, which is not greater than 2).

An interesting fact that researchers recently discovered is that when mathematicians discover the beauty of mathematics, their brains light up in the same areas as artists do when they find the beauty in art. I hope that you and your children have great success in learning and discovering math.

Here is the original article in English.

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I am the (foster) mother of three children. I have been teaching two of them at home since 2014. I also give tutoring lessons. In this blog I write about our homeschool experience. All posts by T.S. Show