Personal Need for Structure and Fractions in Mathematical Education

Area of Science:

• Cognitive Psychology
• Educational Psychology
• Mathematics Education

Background:

• Individual cognitive variables significantly influence academic performance.
• Understanding the relationship between cognitive traits and specific mathematical knowledge is crucial for effective pedagogy.
• The personal need for structure (PNS) is a cognitive individual variable that may impact learning outcomes.

Purpose of the Study:

• To investigate the relationship between a student's personal need for structure (PNS) and their knowledge of fractions.
• To determine if cognitive individual variables correlate with mathematical knowledge in university students.
• To analyze the specific factors of PNS in relation to fraction problem-solving abilities.

Main Methods:

• An experiment was conducted with 162 university students in Nitra, Slovakia.
• The study measured personal need for structure (PNS) using a scale and assessed mathematical knowledge through a fraction test.
• Item Response Theory (IRT) models were employed to analyze the relationships between PNS factors and fraction test performance.

Main Results:

• A statistically significant negative correlation was found between performance on the fraction test and scores on the PNS scale.
• Higher success rates in solving fraction problems were associated with lower overall scores on the personal need for structure scale.
• This negative correlation extended to the subfactors of the PNS scale.

Conclusions:

• The findings indicate that students who excel in understanding fractions tend to have a lower personal need for structure.
• This suggests that cognitive individual variables, like PNS, play a role in mathematical achievement, particularly in areas like fraction comprehension.
• Further research could explore the implications of this relationship for instructional strategies in mathematics education.