## Linkages Connect Basic Concepts to Higher Math

Most middle and high school teachers say that they wish their students had a greater facility with multiplication/division concepts, and fractions. In fact, too many students are taught basic operations as a set of procedures. These procedures are language based, directionality challenging and difficult to remember. In workshops and classes, I continually hear, "Gee, I wish I had learned math this way." Many teachers tend to teach math the way they were taught and they will commonly say, "I know how to tell my students to 'do it' but I can't tell them what it means."

If students do not have the skills necessary to begin formal instruction in algebra, they will continually fall further and further behind. They will fail at applications- which is what new standards based curricula are all about. Often the language of instruction is a key to enhancing the meaning. Consider the following phrase: two of three equal parts, we call it two thirds. I meet sixth and seventh grade students who do not know how to name fractions or convey the meaning of numerator and denominator. Asked about perimeter in contrast to area, a student responds: Is that the one where you add or the one where you multiply? Is it any wonder so many of our students are forced to take remedial math courses when they enter college? We are so busy marching to the beat of a timed curriculum that we lose students along the way.

The language of linear functions is similarly important. Knowing that slope intercept is a function, a relationship in which there is a constant rate of change and a starting value, can help students recognize components of y=mx+b AND understand the meaning. Begin with the story problems, asking students to identify what happens once and what happens over and over again. Lead them to the forms and equations as they make sense of real life math. Keep the numbers easy at first until the concept is in place. Linear functions are the entry way to the rest of high school math. They must be thoroughly understood and the student must master the various applications if more complex algebra is to be built from this foundation.

Both algebra and geometry can be taught in a multisensory manner. Color coding for formula components can help when the abstract level of instruction is reached. Summary sheets and graphic organizers will greatly enhance the student's ability to organize and remember what has been learned, but those manipulative objects and "Prove By Construction" activities often have the greatest impact.

If students do not have the skills necessary to begin formal instruction in algebra, they will continually fall further and further behind. They will fail at applications- which is what new standards based curricula are all about. Often the language of instruction is a key to enhancing the meaning. Consider the following phrase: two of three equal parts, we call it two thirds. I meet sixth and seventh grade students who do not know how to name fractions or convey the meaning of numerator and denominator. Asked about perimeter in contrast to area, a student responds: Is that the one where you add or the one where you multiply? Is it any wonder so many of our students are forced to take remedial math courses when they enter college? We are so busy marching to the beat of a timed curriculum that we lose students along the way.

The language of linear functions is similarly important. Knowing that slope intercept is a function, a relationship in which there is a constant rate of change and a starting value, can help students recognize components of y=mx+b AND understand the meaning. Begin with the story problems, asking students to identify what happens once and what happens over and over again. Lead them to the forms and equations as they make sense of real life math. Keep the numbers easy at first until the concept is in place. Linear functions are the entry way to the rest of high school math. They must be thoroughly understood and the student must master the various applications if more complex algebra is to be built from this foundation.

Both algebra and geometry can be taught in a multisensory manner. Color coding for formula components can help when the abstract level of instruction is reached. Summary sheets and graphic organizers will greatly enhance the student's ability to organize and remember what has been learned, but those manipulative objects and "Prove By Construction" activities often have the greatest impact.