The Number Line
“Tools Before Rules”
The number line is an important mathematical tool that used properly can assist teachers, learners and parents to work collaboratively to explore math concepts and applications. Clocks, rulers, tape measurers, and thermometers are examples of simple tools related to the number line. Many board games, as well as athletic events, expand the opportunity to discuss lines in relationship to planes. A football field is a plane. The line of scrimmage is a line on a plane. The monopoly board is a plane – you must count the number on the dice and move in a line with corners. At 3rd grade level students are required to solve more complex problems using the number line.
What proper fraction is half way between ½ and ¾? Although the parent or teacher may have their own method of solving this problem, we want to know how the learners solve the problem using a number line. This is why new assessments (State tests) are more interested in how the learner solved the problem rather than the correct answer. As the complexity of mathematics progressions spiral at each grade level, it will be more important to possess and use cognitive tools. This will only occur with practice, repetition and rehearsals.
There are specific cognitive tools, that with practice over time will move from working memory (short-term memory) to long-term memory. These cognitive tools applied to problems to be solved result in progressions that empower learners to deal with increasing complexity. Educators need to identify and implement the most essential cognitive tools at age appropriate levels and this should be the framework for curriculum development. The number line is an essential cognitive tool of mathematics for learners in grades 1 through 5.
The 21st century and beyond will require learners to be equally adapt and fluent in the language of mathematics (algorithmic) and at the same time be able to think creatively and solve problems that do not fit into a formula to be applied (heuristic). The new common core standards require both.