FAQ for Parents
The way math is instructed today differs greatly from how current adults had learned it. In order to be able to support students' learning, it is important for parents to understand why we do what we do at school. It is important for children to hear a similar message from home and school. Below are some of the most commonly asked questions with simple answers.
Why don't you teach the standard algorithm? What's wrong with the way I learned it?
The standard algorithm is and efficient way to calculate, but is very easily misunderstood, or incompletely understood. If students think in terms of digits rather than whole number, they often don't notice whether they've made a mistake and struggle to judge the reasonableness of their answer. Memorizing a series of steps, without a conceptual understanding of why those steps work is like learning the sounds of a phrase in a foreign language, without knowing the language itself. Math is a language, and we want children to be able to communicate in it fluently. Learning the standard algorithm too soon or allowing it to be used too often can limit flexibility of student strategy. Once students demonstrate ample conceptual understanding, it can be appropriate for them to use the standard algorithm. At some point in the year, standard algorithm is taught as it is part of the Common Core State Standards.
What about facts, should those be memorized?
Having the basic math facts memorized is crucially important to being a successful mathematician. When students can recall facts quickly, consistently, and accurately, mental energy is freed up to consider the complexities of a particular problem. Knowing those facts allow children to more easily notice patterns and find efficient ways to solve the problem.
What is 'representation' and why is important?
Representation refers to demonstrating the way that someone has solved a problem. It facilitates strategy communication. There are a few representations which tend to work very well, such as the open number line, arrow language, ratio table, area model for multiplication, etc. These also support a deeper understanding of the numerical relationships found in standard algorithms. Even as adults, we probably could deepen our understanding by using some of these representations. As children solve problems and explain their thinking, we show them ways that they could represent what they did. Once they really grasp it, they no longer need that support. As always, we move from concrete to abstract, according to the student's level of understanding.
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