Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

Area of Science:

• Educational Psychology
• Mathematics Education
• Cognitive Science

Background:

• National assessments in the Netherlands indicate a two-decade decline in primary school (Grade 6) arithmetic achievement.
• Complex and written arithmetic problems show a notable decrease in student performance.

Purpose of the Study:

• To explain the significant decrease in complex division achievement.
• To investigate the evolution of student strategies in solving division problems between 1997 and 2004.

Main Methods:

• Latent variable modeling, specifically latent class analysis and explanatory Item Response Theory (IRT).
• Analysis of student strategies (four categories) and achievement scores (correct/incorrect) from 1997 and 2004 assessments.
• Year of assessment used as a covariate in latent class analysis.

Main Results:

• A shift in strategy was observed from 1997 to 2004, moving from the traditional long division algorithm to less accurate methods, such as stating an answer without calculation.
• This strategic shift was particularly pronounced in boys.
• Explanatory IRT analyses confirmed that the three primary strategies employed were significantly less accurate in 2004 compared to 1997.

Conclusions:

• The decline in complex division achievement is linked to a shift towards less effective problem-solving strategies.
• Educational interventions may need to address the decline in algorithmic proficiency and promote accurate strategy use in mathematics.