Chapter 6, page 87
The Importance of Understanding Students’ Alternative Conceptions
When teachers understand their students’ alternative conceptions, they can alter instruction to meet
students’ needs. Very often, when teachers gain a complete understanding of students’ alternative
conceptions, they gain new insights into how to develop instruction (Ballenger & Rosebery, 2003).
Sometimes these insights are surprising. Most elementary school teachers that I have talked with over the
years are unaware that many of their students have dual-earth and hollow-earth conceptions of the earth.
Once teachers realize this, and once they realize that these alternative conceptions are grounded in
children’s beliefs that things must always fall downward and that round things must always look round, it
gives them new ideas about how to develop instruction. For example, they may now realize that
instruction on the earth’s shape might start with instruction on how very, very large round things will look
flat to someone standing on the surface. One way to do this might be to show how the surface of an
extremely large inflatable ball looks flatter and flatter as it expands.
It is important to try to gain a complete understanding of students’ alternative conceptions in order
to understand how to develop instruction. Sometimes students’ prior conceptions form a complex system
of interrelated ideas; we can call this an alternative conceptual system. It is important to understand these
interrelated ideas in order to know how to instruct students. A good example comes from mathematics—
specifically, from students learning fractions. As we examine the alternative conceptual system that makes
learning fractions difficult, we will see that it would be very difficult to teach fractions effectively without
understanding these conceptions (Stafylidou & Vosniadou, 2004).
The alternative conceptual system that interferes with students’ attempts to learn about fractions
is students’ conceptions about the natural number systems. Natural numbers are the whole numbers we
can count—1, 2, 3, 4, and so on; natural numbers do not include fractions such as ½ or 7/15 or decimals
such as 3.29. Students learn about the natural number system at home and in early school grades. Most
children learn the natural number system very well. But then, later in elementary school, their successful
learning of the natural number system gets in the way of learning fractions.
Let’s explore in more detail how this happens. By third or fourth grade, students have mastered
many important ideas about natural numbers. For example, they have learned that 15 is larger than 9.
They have learned how to add, subtract, and multiply. They know that when two numbers are added
together, the sum is larger than the numbers added. They know that 9 is 1 more than 8, that 117 is one
more than 116, and so on. They know that there is no natural number between adjacent numbers (e.g.,
there is no natural number between 23 and 24). They know that you can add numbers by counting them
together; you can add 11 pennies to 6 pennies by putting all the pennies together and counting them all. By
third or fourth grade, students have mastered these ideas and more. A more complete list of what they
have learned appears appear on the left side of Table 6.5.