Organizing and Retaining Math Information

Laurian Phillips
Jun 08, 2009

When choosing an appropriate graphic organizer in mathematics, try to keep in mind that it is not about simply having a graphic organizer, but rather having a good graphic organizer that serves the purpose and intent of the lesson. When planning, begin by asking several questions.

  • Is this lesson comprehension based, requiring an organizer that would show sequential steps and the progression from concrete to pictorial to abstract thinking? An organizer for such a lesson might look something like this:

Math Matrix 1

  • Does this lesson rely heavily on new vocabulary, requiring an organizer to convey that vocabulary in student language? If so, maybe choose a Frayer or one similar to the one below:

Math Matrix 2

  • Is this lesson one that will use a technique that will be repeated over and over and will benefit from a mnemonic device or a kinesthetic activity to help students remember?
  • Will the graphic organizer be used as a part of the teaching process, or will the organizer be used as a study tool for students?

These questions are used when planning to teach something like graphing quadratics. Go through the whole process with students and tell them what happens when p is greater than or less than 0, and discuss opposite b over 2a, but really, all they hear is "blah, blah, blah...". Let's face it. We are math people, and we love this stuff. They do not. It is a foreign language to most students. The brain is a pattern seeking device. If we put something in a chant, rhyme, or song, students will be more likely to remember it and use it. You can go online and find any number of tunes to the quadratic formula.

Graphing quadratics typically comes just before the quadratic formula, however, so have them sing math words to the chorus of "Glory, Glory, Hallelujah" to find the vertex of the parabola. The chart shows which words replace the original words.

Math Matrix 3

Put this in a foldable and do a few examples, providing much more meaning. The "blah blah blah" part is still in their notes if they need to go back to them, but you use the song to help them find the vertex. Then, they problem solve to find the other parts of the parabola needed in order to graph it, given the equation. The point is to teach them to think about how to approach the parabola from different points of view rather than simply plug numbers into a formula on a page that they do not understand. Later, when you get to the quadratic formula, teach them the rest of the song. The questions simply guide you as you begin to form the graphic organizer for the lesson. Sometimes you will find that the organizer is a combination of more than one type, or that you need more than one organizer to do the job.

One of the biggest errors teachers make is using a Frayer or some type of foldable and simply having students copy all notes that they would normally put in their notebook on the graphic organizer or in the foldable. This is easy to fix with a simple adjustment. You should not think of the graphic organizer as taking the place of where students would normally take notes in math. They can still take notes in their notebooks with all of the math jargon. The organizer is then used to teach them how to take that math jargon and summarize, putting things in their own words so that it makes sense to them. The organizer is something they can remember and re-create. It uses pictures, charts or diagrams, hence the name "Graphic" Organizer. If you don't use the organizer this way, then it is just the same old notes with a box drawn around them, or the same old stuff on a folded piece of pape r with no evidence to suggest that this is effective. The effectiveness comes from making connections with the content, summarizing, generalizing, and putting in their own words content they can retrieve to help them when needed. The effectiveness also comes from showing students how to retrieve and use this information. Time should be taken to show students how to re-create their graphic organizers to help them retrieve the information they need to answer questions, not just to pull them out and copy information from them.

Remember the purpose and intent of your graphic organizers, and they will be much more meaningful for both you and your students.

See the LEARNING-FOCUSED Math Instruction Collection for more ideas.