In one experiment, several students were asked to
solve equations based on direct instruction and metaphorical explanations.
Researchers found that many of these descriptions actually led students to
over-think questions and set up problems incorrectly. Much of the issues
revolved around the concept of positive and negative numbers. In most cases,
students avoided setting up equations using negative numbers and attempted to
change the problems to only work with positive integers. Kilhamn argues that
this is not a simple error on the part of the student but a “reluctance to
accept negative numbers.” She further explains that this “is closely linked to
our desire to be able to concretise that which is abstract and understand
negative numbers in terms of concepts such as debts, lifts or temperatures.”
However, many of these “concepts” are difficult to convey to students who lack
correlative experiences.
Kilhamn suggests a change in the way we
explain mathematical theories. By focusing on numbers at an early age, students
can better grasp the key concepts necessary to later approach word problems.
The study further suggests that students recognition of symbology such as
decimals or fractions develops faster than their perception of, say, a pizza
pie cut in half to represent 1/2. Use of metaphors can further cause
issues with the diversification of student experience and cultural
distinctions. This is not to say that students should avoid understanding the
implications of numbers on real life. Yet Kilhamn’s study recognizes that as
kids develop their basic math skills, they should begin with standard symbology
and later gravitate toward correlative experiences; only then can they fully
translate these concepts into their day to day life.
This presents a unique challenge for
teachers. How can we focus on this set of basic symbology and still make math
fun? Repetition and game driven math equations can continue to build conceptual
skills without distracting students from the problems at hand. Outside
education and math tutoring can
further reaffirm these concrete principles outside of the classroom. When
students find certain problems challenging, math
tutors can cater to a student’s
set of experiences and change their approach accordingly. Here at Five Points
Learning, we believe in the opportunity to create an adaptive learning
environment and overcome the confusions that arise in the classroom. Perhaps
vague words and metaphors are not the sole reason for confusion. Instead, how we
use these tools to explain problems can make a huge difference in the way
students retain information. After all, each child has their own method of
comprehending material, and it is up to us to harness and foster this potential
for learning.
