Teaching Secrets: Making Math Meaningful for All
While it is considered unacceptable for the average person to lack basic reading and writing skills, people often brag about their inability to “do math.” It is almost a badge of honor to be numerically challenged.
As classroom teachers, we must overcome this attitudinal acceptance of not being successful at math before we can create numerically literate students. We must learn to teach in ways that make mathematics accessible to every child and build our students’ confidence in their capacity to master the knowledge and skills associated with our importantand intriguing!content area.
Having taught 7th grade math for many years, I have discovered some keys to success with my students. These fundamental instructional strategies are easily adapted to any grade level math class.
Purchase a set of student whiteboards for your class. These boards are fantastic for many purposes. I like to use them when I am first introducing a concept to allow students the opportunity to write the steps or process as I am doing it, then practice on their own in a non-threatening environment. Even the most intimidated math-a-phobe seems less concerned about making mistakes when they are easily erased with a paper towel. I also use these boards when reviewing concepts before a quiz or test. Having students complete individual problems, then hold up their boards with answers circled simultaneously, quickly shows me where the misconceptions and allows me to quickly restructure our next step in the review.
Create real-life examples of concepts you are learning. Going beyond the typical ‘story problems’ included in most math textbook series, and generating your own meaningful examples of how topics relate to real life, helps students cement those concepts in their brains. For example, when we study inverse relationships in my classroom, not only do we plot the length and width of a rectangle with a given area (as suggested in the text), I create a group project where students look at earning a set amount of money from a given task. They graph the possibilities in large graph paper, write the equation for the inverse relationship, illustrate it and present it to the class as a group. Having this concrete real-life example gives them something to associate with this often difficult concept, making it “stickier” in their minds.
Use small groups and presentations where students teach each other as well as the entire class. The old adage that you learn something better when you teach it is certainly true in math class. By explaining a concept to another student, the presenter is forced to think more deeply about the process involved in the task at hand. Using large graph paper to create (and illustrate) graphs for a presentation is always a huge hit simply because of the social and artsy nature of making them. Students work together, learning from and with each other, both when they create the product and when they present it. These procedures engage students actively in the thinking processthe goal of every lesson.
Teach the power of “Is your answer logical?” When working out problems with students, look at the answer critically, asking probing questions to lead them to whether or not the answer makes sense in the context of the problem. Students too easily accept the answer in their calculator window just because the calculator said it was the answer. Walk them through logical and illogical answers, and how to hone in on the correct solution simply by eliminating possibilities. Use actual problems solved incorrectly on assignments or tests to have students analyze the process of making mistakes and how to identify where the solution went wrong.
Integrate technology to capture student interest. Many websites offer interactive math activities. One such site is the National Library of Virtual Manipulatives. This site organizes math activities by topic and grade level and offers many simple but engaging tools to explore concepts. Some of the activities lend themselves well to large group instruction, while others are wonderful for students to use individually. Other sites to consider are Interactive Mathematics Miscellany and Puzzles and Cool Math.
Encourage, require, demand re-do’s. Having students rework problems they missed on both tests and daily assignments teaches perseverance. Over time this process will help students identify their mistakes more readily and strengthen their ability to think critically. Another strategy to encourage students to examine problems more closely is to give them the answer upfront and invite them to explain the solution by working backwards. The goal here is to go beyond the traditional teacher demonstrations of how to solve problems and have students learn to work independently, correct mistakes, and move on. Students become mathematical thinkers and build success.
The ultimate goal in each of these strategies is to develop students who enjoy the processes of math, learn to appreciate the complexities of the subject, and find ways to relate math to their everyday lives. Through this process, we can build a generation of adults who are comfortable with mathematics and confident in their numerical abilities.