Ordinal models to analyze strategy sophistication: Evidence from a learning trajectory efficacy study

Area of Science:

• Cognitive Psychology
• Educational Psychology
• Developmental Psychology

Background:

• Traditional assessment of early math interventions often relies on the proportion of correct responses.
• This approach may overlook crucial information about children's developing problem-solving processes.
• There is a need for methodological advancements to analyze the sophistication of children's mathematical strategies.

Purpose of the Study:

• To propose a shift in focus from response correctness to the sophistication of problem-solving strategies in early mathematics intervention research.
• To provide methodological guidance for researchers analyzing strategy data.
• To investigate the effectiveness of arithmetic Learning Trajectory (LT) instruction on strategy sophistication.

Main Methods:

• Utilized data from a randomized teaching experiment with kindergarteners.
• Developed a coding system for problem-solving strategies amenable to analysis.
• Explored and applied ordinal statistical models to characterize arithmetic strategies.
• Analyzed the impact of LT-aligned instruction versus a teach-to-target skill condition.

Main Results:

• Arithmetic strategy development is best modeled as a sequential, stepwise process.
• Children receiving LT instruction demonstrated significantly more sophisticated strategies at post-assessment compared to the control group.
• Introduced 'latent strategy sophistication' as a novel metric, showing moderate correlation (r=0.58) with traditional Rasch factor scores.

Conclusions:

• Strategy sophistication provides unique and complementary information to traditional correctness-based scores in intervention studies.
• The findings support the expanded use of strategy sophistication analysis in evaluating early mathematics interventions.
• This approach offers a more nuanced understanding of child outcomes in mathematics education.