viiWhen do you know you really understand something? One test is to see if you can
explain it to someone else—well enough that they understand it. Eureka Math routinely
requires students to “turn and talk” and explain the math they learned to their peers.
That is because the goal of Eureka Math (which you may know as the EngageNY math
modules) is to produce students who are not merely literate, but fluent, in mathematics.
By fluent, we mean not just knowing what process to use when solving a problem but
understanding why that process works.
Here’s an example. A student who is fluent in mathematics can do far more than just
name, recite, and apply the Pythagorean theorem to problems. She can explain why a^2 + b^2 = c^2
is true. She not only knows that the theorem can be used to find the length of a right triangle’s
hypotenuse but also can apply it more broadly—such as to find the distance between any two
points in the coordinate plane, for example. She also can see the theorem as the glue joining
seemingly disparate ideas including equations of circles, trigonometry, and vectors.
By contrast, the student who has merely memorized the Pythagorean theorem does
not know why it works and can do little more than just solve right triangle problems by rote.
The theorem is an abstraction—not a piece of knowledge, but just a process to use in the
limited ways that she has been directed. For her, studying mathematics is a chore, a mere
memorizing of disconnected processes.
Eureka Math provides much more. It offers students math knowledge that will serve
them well beyond any test. This fundamental knowledge not only makes wise citizens and
competent consumers but also gives birth to budding physicists and engineers. Knowing
math deeply opens vistas of opportunity.
Students become fluent in math—as they do in any other subject—by following a course
of study that builds their knowledge of the subject, logically and thoroughly. In Eureka Math,
concepts flow logically from PreKindergarten through high school. The “chapters” in the
story of mathematics are A Story of Units for the elementary grades, followed by A Story
of Ratios in middle school, and A Story of Functions in high school.
This sequencing is joined with a mix of new and old methods of instruction that are
proven to work. For example, we utilize an exercise called a “sprint” to develop students’
fluency with standard algorithms (routines for adding, subtracting, multiplying, and dividing
whole numbers and fractions). We employ many familiar models and tools such as the
number line and tape diagrams (aka bar models). A newer model highlighted in the curriculum
is the number bond (illustrated on the following page), which clearly shows how numbers are
composed of other numbers.