The problem is that we dive in with formulae before students have their bearings. Let your students get their hands dirty with geometry. They've got to play with the shapes and explore. Beginning adders and subtractors work with manipulatives before they delve into abstract arithmetic. Older students are still beginning geometers. Give them a chance to touch the math and have some fun.
Starting with an IKEA catalog, a hotel furnishing math project was born. Use this project as a tool to differentiate your math instruction and impart some practical knowledge on your students.
The typical cases are usually too simple and students fall into a sense of false security. Rather than truly mastering the skill, students develop pattern recognition that gets them through the common cases. Eliminate this problem by seeking edge cases.
Many wrote in to add that showing work is important as a way of communicating to an audience. But, whether we realize it or not, the only audience many students are performing for is a test scanner. So, teachers, let's put our money where our mouths are and give them a chance to experience that showing steps is vital to communication. And give them this chance daily!
Let's play with linear graphing! First, don't set this up as a direct instruction lesson. That wouldn't be playing. Instead, capitalize on your students' ability to think inductively and recognize patterns. Set up a situation where they can construct their own meaning.
Remembering the formulae for area and circumference of a circle is often a challenge for students due to their surface similarities as well as the additional confusion of radius and diameter. I like to tackle them one at a time and give students a chance to explore the origin of each formula. Let's look at circumference today by utilizing some famous circles from around the world... and beyond!
I'm beginning to teach the dreaded geometry unit featuring complementary, supplementary, adjacent, and vertical angles. Historically a confusing topic, this year is going to be different. I'm going to use a new tactic: cooperative reasoning with a set of "clues."
Looking for some ways to challenge your advanced mathematicians? If you'd like to keep them on the same topic as the rest of your class, consider increasing the complexity of your current unit. If they're in need of more advanced curriculum to keep their creativity flowing, try to bring in novel ways of looking at math.
We must be careful not to admonish our intuitive learners for being intuitive. As teachers of the gifted, we must set up learning environments that are best for our students. And if they're doing it all in their heads (and getting it right!), then the environment needs to change.
Entice your gifted mathematicians with real world data and an authentic problem such as: "Let's say that instead of buying the original iPod, you spent the same amount of money on Apple stock. How much would that stock be worth now?"