Chapter 6, page 104
In the early stages of learning to solve problems in an area, students at any age are prone to
organize problems based on surface similarity rather than deep similarity. It can take a very long time to
shift from novice organization to expert organization. Cognitive scientist Michelene Chi has found that
university students who have earned A’s or B’s in university physics courses classify physics problems as
novices do—by surface similarity. In a famous study, students were asked to classify physics problems
involving forces and motion (Chi et al., 1981). The undergraduates classified problems based on surface
similarity—problems with ramps were groups together in one group, problems with pulleys were grouped
together in another group, and so on (see Figure 6.8). In contrast, experts (physics professors) classified
problems according to the solution procedure needed to solve the problems. For instance, a ramp problem
and a spring problem were classified as similar both are solved using Newton’s Second Law. It is
important to note that the undergraduates were still thinking as novices despite very successful completion
of a physics course on forces and motion. The shift from novice to expert organization of conceptions can
take years, even many years.
Implications for Instruction
One instructional implication of research on novice conceptions is that teachers should help students
notice deep similarities between problems and not just surface similarities. One way to do this is to ask
students to reflect on similarities between problems that are different at the surface level. For example, a
fourth grade teacher could ask students what these two problems have in common:
#1. Julio has 3 apples, and then his mother gives him 8 more. How many apples does he have now?
#4. Pam has saved 5 dollars, and now she earns 4 dollars by doing her chores. How many dollars does
she have now?
This question would encourage students to notice that despite the fact that one is about oranges and the
other about money, the two problems are fundamentally similar because both solved by addition. The
teacher can then encourage students to contrast these problems with a third problem that requires
subtraction. By comparing and contrasting problems, students can learn to identify ways in which
problems are similar at a deep level.
Problem 6.5. Understanding students’ thinking. A ninth grade language arts teacher is teaching
his students about the structure of arguments. He gives students the following arguments to
compare and contrast.- Andreas’s paper. We ignore global
warming at our own peril. Glaciers are
melting. The temperature is gradually rising.
The ice caps are diminishing. We may be
reaching the tipping point, and if we do not
act now, it will be too late. Global warming is
a big problem, and we need to take steps to
try to stop it.
2. Michelle’s paper. Global warming is
accelerating, and we need to do something
about it. Core samples from Greenland ice
show a large increase in temperature over
the last 100 years. Some have argued that
there was a decrease in temperatures from
1940 to 1960, when the industrial gases were
rapidly increasing, but you have to look at
long-term trends, and the longer trends show
an increase. Also, many glaciers have
disappeared or decreased by half or more.
Here are several statements written by students. Which are more typical of novices, and which
are more typical of experts. Explain your answers.
#1: Both papers are about global warming. Michelle’s paper is longer.
#2: The first paper has more pieces of evidence, but it doesn’t talk about the source of the