Making Connections

It is critically important that students see the relevant connections that exist in math, not only across subject areas but in the real world.  How often we hear students ask, "When will I ever use this again?"  The answer is....every day.

According to Linda M. Gojak, President of the National Council of Teachers of Mathematics,

Instructional programs from prekindergarten through grade 12 should enable all students to:

Gojak comments that "...rather than making sense of mathematical ideas, students focus on remembering procedures or tricks. For example, how many students learn “flip and multiply” to divide fractions but have no idea why it works? Often those who understand why the procedure works struggle to apply it in problem situations. The procedure alone often leads to misconceptions. Students who work from rote memory often invert the wrong fraction, forget to change operations, or even apply the rule when multiplying two fractions. The meaning of operations doesn’t change from whole numbers to fractions. For example, in the early grades, the understanding that students develop of division of whole numbers often rests on the idea that “9 ÷ 3,” for example, asks how many groups of 3 are in 9. As students move to fractions, it is important to provide them with experiences that connect this whole-number understanding to similar examples with fractions: “9/16 ÷ 3/16,” for example, asks how many groups of 3/16 are in 9/16. In this way, students gain a deeper understanding rather than depending on a memorized procedure and can apply division of fractions to a variety of problem-solving situations and real-world applications". 

                                                                                                                                        (NCTM, 2013)

https://www.youcubed.org/resources/tour-mathematical-connections/