Prior math achievement and inventive production predict learning from productive failure

Area of Science:

• Educational Psychology
• Mathematics Education

Background:

• Constructivist instruction is often perceived as more effective for students with higher prior domain knowledge.
• Investigating the efficacy of specific constructivist approaches across diverse student achievement levels is crucial.

Purpose of the Study:

• To examine the relationship between prior math achievement and learning outcomes in Productive Failure (PF).
• To determine if inventive production mediates the effect of prior achievement on learning in PF.

Main Methods:

• Two quasi-experimental, pretest-intervention-posttest studies were conducted in Singapore public schools.
• Students with varying prior math achievement designed solutions to complex problems before receiving instruction.
• Learning was assessed post-intervention, with a focus on inventive production and prior achievement.

Main Results:

• Students with significantly different prior math achievement showed similar levels of inventive production.
• Inventive production demonstrated a stronger association with learning from PF than prior math achievement.
• These findings were consistent across different mathematical topics.

Conclusions:

• Productive Failure (PF) is a valuable instructional approach for diverse learners in mathematics.
• Encouraging inventive production is essential for effective learning, irrespective of students' initial math abilities.
• The study challenges the notion that constructivist methods exclusively benefit high-achieving students.