Connections

It is the responsibility of teachers to emphasize to their students the interrelatedness of mathematical concepts. By doing so their students will learn more readily as they build upon past mathematical experiences.  Teachers can facilitate this process by modelling the identification of connections during instruction. For instance, when teaching students to measure the surface area of a parallelogram, a teacher might illustrate how, through the addition of a few simple lines, a parallelogram can be divided into a square and two triangles. Following this addition, he or she might ask, "Does the addition of these two lines remind you of any shapes you already know how to find the area of?"

It is also important for students to see how different mathematical functions are related. When teaching multiplication, for instance, it is important for students to recognize how the numerical pattern is shared if a number is added to itself repeatedly. This could allow a student to use an alternative strategy to recall the product of 3x9 when stumped. He or she might think, "Well, I know 3x10 is thirty, so 3x9 must be 3 less...27."

Finally, it is important for students to appreciate how mathematics is relevant in every day life. Whether they plan to run a profitable lemonade stand or they want to calculate the number of hours they need to work before they can buy a new skateboard, mathematics is a indispensable tool.

On review of the Standards for Mathematical Practice (2010), it is clear that the Connections Process Standard relates closely with the following:

Reason abstractly and quantitatively
By making connections between mathematical expressions and real world scenarios, students will be assured of being able to think mathematically with and without a defining context.

Model with mathematics
Students who are able to express real life scenarios using mathematical expressions have an additional tool through which they can examine phenomena and draw reliable conclusions.

Look for and make use of structure
Identifying similarities and patterns help students connect new knowledge to past learning. As mentioned above, students who can identify the inter-relatedness of addition and multiplication can profit from this connection when learning their multiplication tables.

NCTM (2011). Connections Standard. Retrieved from nctm.org.

CCSSI, (2010). Common core standards for mathematics. Retrieved from http://www.isbe.state.il.us.