Graphic organizers are powerful tools that support conceptual development, language development, and skills acquisition when used appropriately. In the mathematics classroom, they can serve as powerful vehicles that facilitate discussion, provide formative assessment data, and allow students to demonstrate their thinking in creative ways.  

In order to achieve success with the use of graphic organizers, the teacher has to select the appropriate organizer, understand it, plan for how the organizer will be used to promote thinking, and develop appropriate questions and tasks.

Formative assessment is an important tool to take full advantage of, especially in this transitional era of implementing more rigorous standards.

When correctly incorporated into classroom practice, the formative assessment process provides information needed to adjust teaching and learning while they are happening. The process serves as practice for the student and a check for understanding during the learning process. The formative assessment process guides teachers in making decisions about future instruction. 

As we implement higher standards across the country, it has become increasingly important that we identify and use a variety of strategies to assess student learning so that the appropriate interventions may be provided. 

One strategy is to encourage students to reflect on their reasoning and justify their work.  The idea of justifying your work in mathematics has to go beyond the use of inverse operations to “prove” that the calculation was correct. This way of checking is not justification since it does not address the student’s use of metacognition—the thinking about thinking—that goes beyond the use of an algorithm and takes you into their decision-making processes.

I’d like to take you on another journey along the road of the language of mathematics with a stop at the intersection of “math concepts and symbolic notations.”

Sometimes the mathematics conversation is just as confusing to students as this collection of signs is to a driver in an unfamiliar situation. There appears to be a variety of symbols used to identify the different types of roads in the area, just as we have a variety of concepts, operations, and relations that are conveyed through symbolic notations. 

To further complicate the issue, in math we sometimes have a variety of symbols used to convey the same concept or idea. Imagine the student’s dismay when he or she is not familiar with a new symbolic notation that is being used but is familiar (and perhaps proficient) with a different notation. This can certainly be a blow to some students’ math confidence.

Have you ever wondered why it is so difficult to teach mathematics and why it is so difficult for students to grasp the meaning of the words we use in mathematics? If you pause and think about it, mathematics is a very technical subject, and it has a set of vocabulary words that have very precise meanings and sometimes multiple uses within mathematics. Outside of the math class, those same words take on a whole different meaning—oops, there is one of those words: “whole.” Get it?

Well, there are lots of them, and I would like for you to take the seat of the students for a few minutes as you read this and filter the conversation through their ears.