How Well Do High-Achieving Undergraduate Students Understand School Algebra?

Area of Science:

• Mathematics Education
• Cognitive Science

Background:

• Assessing foundational mathematical knowledge is crucial for tertiary success.
• Understanding student comprehension of core algebraic principles informs pedagogical strategies.

Purpose of the Study:

• To evaluate the grasp of school algebra among high-achieving undergraduates in Ireland.
• To identify specific areas of difficulty within basic algebraic concepts for this student cohort.

Main Methods:

• Development and online administration of a 31-item algebra comprehension test.
• Analysis of responses from 327 first-year undergraduates in mathematics modules.
• Focus on the performance subset of high-achieving students.

Main Results:

• High-achieving undergraduates generally exhibit a strong understanding of school algebra.
• A specific test subsection on valid solutions for equations and inequalities proved disproportionately challenging.
• This topic represents a significant area of concern for even advanced students.

Conclusions:

• While overall algebraic proficiency is high, the difficulty with equations and inequalities warrants further investigation.
• Findings highlight potential gaps in advanced algebraic understanding that may impact tertiary mathematics progression.
• Recommendations for pedagogical adjustments and further research are discussed.