Using Strategic, Efficient Methods

Using Strategic, Efficient Strategies: What is that?

 Students demonstrate flexible thinking through choosing to use a variety of strategies that are best suited to different types of questions. 

Overview

Not all problems should be solved in the same way.  Students need to have a variety of strategies that they can use proficiently when solving problems, which may include the standard algorithm.

This handy checklist can help students know which strategy to use:

• easy to understand?

• easy to apply?

• easy to remember?

• easy to perform accurately?

With experience, students can learn to apply these criteria to their own strategies and develop ways for improving their efficiency and effectiveness.

Over-reliance on memorized addition and subtraction, multiplication and division procedures prevents students from using mathematical reasoning which can lead to students answering a question incorrectly and not be aware of it.

Supporting Students to use Efficient & Strategic Methods 

Student-developed strategies are not necessarily efficient and effective. Educators will need to support students to work through the exploration of the most effective strategies.

For example, a student-generated strategy may require more steps and time than is appropriate. However, students develop and use these strategies because they make sense to them. As students share and compare their strategies, they will become better at finding methods that are both efficient and effective.

An efficient method is one that does not require a page of calculations and more than a reasonable amount of time to produce an answer. An effective method is one that works for all problems of a particular type (i.e., one that is generalizable to many problems using the same operation). Students need to learn to evaluate their own strategies and algorithms on the basis of the following criteria.

Is the strategy:

• easy to understand?

• easy to apply?

• easy to remember?

• easy to perform accurately?

Continued practice and encouraging students to work with the numbers using the most efficient strategy will support students to build flexibility. Educators can also engage in conversations with students to discuss the most efficient strategies to solve given problems, based on the numbers in the question.