Tell a Story
A well-told story can be motivating, can reduce math anxiety by activating theimagination, and can provide a relatable connection from the story's context to the topic (Schiro, 2004). Storytelling also appeals to the nature of field-dependent students, as it puts mathematics in a framework that is realistic or that relates to students' lives (Whitefield, 1995).
For example, there is a well-known story about one of the greatest mathematicians, Carl Friedrich Gauss (1777-1855). When he was in elementary school, Gauss found the sum of the first 100 natural numbers much faster than his teacher anticipated he would. Rather than add the numbers 1 + 2 + 3 + ... + 98 + 99 + 100 in the order in which they are written, he decided to add them in pairs:
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
4 + 97 = 101
50 + 51 = 101
Then he multiplied 101 by 50 (the number of pairs) and found the product 5,050. After providing this relevant anecdote to the class, the teacher can use the procedure to help the students generate the formula for the sum of an arithmetic sequence. The style in which this story is presented is key-not as a rush to get to the derivation of the formula, but as story with interesting embellishments.
- Find Patterns
- Present a Challenge
- Challenge Students' Thinking
- Connect to the Real World
- Tell a Story
- Make Math Fun
- Discuss Surprising Relationships
- Present the Unknown
- Integrate Technology
Make Math Fun
Often, a recreational feature of mathematics that is related to a topic can be motivating. For example, a teacher might inspire an algebraic discussion of number properties by asking each student to select a three-digit number in which the hundreds digit and the ones digit are not the same (for example, 847). The students then write their selected number in reverse order (748) and subtract the lesser number from the greater number (847 - 748 = 99). Having them reverse the digits in the result (099 to 990) and add these two numbers (099 + 990) yields a result they could share with the class.
Those who did not make an arithmetic error should all have arrived at the same answer: 1,089-no matter the number with which they started. Students may be amazed at this unusual number characteristic, and motivated to determine why it works; at the same time, the teacher has produced a thought-provoking introduction to an algebraic investigation.
Discuss Surprising Relationships
The teacher can further cultivate students' interest by discussing the many surprising relationships in mathematics. These curiosities may pique the interest of students and motivate them to determine why they are true. Here, a teacher can have students draw any quadrilateral: the purpose to show the same result among varied shapes. The class can be instructed to join the midpoints of the sides and to observe each other's drawings. In every case, they will get a parallelogram. This can lead to a discussion of the properties of parallelograms.