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.