A CONSTRUCTIVIST PATHWAY TO REFRESHING MATHEMATICAL UNDERSTANDING

Many people find mathematics hard or even scary.The 2012 PISA report identified that roughly a third of students around the world feel actual panic having to do math --a ratio that seems to be in line with figures found in the 1970s.The proportion of the population who do not panic from math but still find the subject difficult or unappealing is higher still.The global pandemic and remote education further exacerbated this problem.Meanwhile the world is becoming ever more mathematical and computational, increasing the expected quantitative understanding of the people to meaningfully participate in modern society.These dual effects cause an increasingly widening knowledge and skills gap that need to be addressed at all levels of education.This paper discusses an optional workshop provided for freshmen students before starting university at a small liberal arts school.The purpose of this was to increase mathematical understanding and reduce math anxiety.The approach integrated basic programming skills in the form of block programming with a re-discovering of mathematical thinking.The class started by introducing the creativity of programming, aimed at driving engagement and excitement about the experience.The class then leveraged the simple programming understanding gained at the beginning (especially variables, loops, conditional statements and functional concepts) to re-create basic mathematical concepts, thus connecting the students' interests and majors through block programming and computational thinking to algebraic thinking.The class empowered the students by being able to "create" mathematics, leading to a more integrated understanding.The mathematics content of the course reviewed the key pre-college level quantitative skills, specifically focusing on problem areas that often arise for freshmen university students (function concept, proportions).Utilizing a constructivist approach, the students didn't simply review these topics, instead they re-discovered them through constructing them themselves: a number is just a loop, the basic operations are just loops applied in sequence or embedded in each other, the prime factors of a number are just the previously constructed division operators inside a loop, etc.