Constructing Mathematical Meaning through Authentic Nutrition Problems in Higher Education

Technical Summary: Constructing Mathematical Meaning through Authentic Nutrition Problems in Higher Education

Problem Statement
The study addresses a persistent challenge in interdisciplinary STEM education: mathematics often appears in courses without becoming an explicit object of "sense making." In nutrition education, mathematical tasks frequently devolve into procedural applications (e.g., substituting numbers into formulas) rather than requiring students to coordinate quantities, interpret representations, and justify disciplinary claims. The research questions how undergraduate nutrition students construct mathematical meaning when engaging with authentic problems involving proportionality, percentages, functions, and data interpretation. Specifically, the study investigates whether aggregate assessment scores can capture the quality of mathematical reasoning or if they mask critical gaps between procedural accuracy and valid inference.

Methodology
The research employed a qualitatively driven convergent mixed-evidence case study design within a "Mathematics for Nutrition" course (NCMA-0016) at a public university in Panama during the 2026 academic semester. The study involved 60 students (46 women, 14 men).

• Data Corpus: The analysis integrated multiple evidence sources:
  • The official course plan.
  • Four distinct team video transcripts (approx. 7–12 minutes each) covering nutrition labels, anthropometric indicators, meal planning, and survey data analysis.
  • A linked portfolio from one team (Team 5) containing survey calculations and reflections.
  • Four handwritten artifacts from Team 5 demonstrating proportional measurement, unit rates, and linear modeling.
  • De-identified assessment records for all 60 students.
• Analytical Framework: The study utilized a four-lens theoretical framework:
  1. Schoenfeld: For analyzing resources, strategies, monitoring, and control in problem solving.
  2. Silver: For examining problem posing, mathematical production, and flexibility.
  3. Li: For assessing interdisciplinary STEM learning and transfer.
  4. Marzano-Kendall: For organizing cognitive demand and assessment evidence (self-system, metacognitive, cognitive processing, knowledge domains).
• Analytical Procedures:
  • Qualitative: Video transcripts and artifacts were segmented into "episodes" and coded for resources, strategies, representations, monitoring, problem formulation, and disciplinary integration. The analysis focused on the "Team 5" case as an emblematic example of both high-quality procedure and structural breakdown.
  • Quantitative: Descriptive statistics, Pearson/Spearman correlations, and hierarchical regression were used to analyze assessment records. A provisional formative composite, MKACI-P, was constructed from nonredundant course signals (cognitive foundation, analytic/communication, knowledge utilization, and opportunity-to-engage) to serve as a bounded complement to qualitative findings, not a validated latent scale.

Key Results

1. Procedural Accuracy vs. Valid Inference: The central finding is the coexistence of correct mathematical procedures with invalid quantitative inferences. In the emblematic Team 5 case, students correctly calculated marginal percentages from survey data (102 respondents) but subsequently averaged overlapping indicators and converted these averages into person-level counts and a ratio without joint-frequency evidence. This resulted in a "polished" presentation containing a fundamentally invalid model.
2. Task-Dependent Competence: Mathematical competence was found to be task-dependent. The same team demonstrated sound proportional reasoning, unit-rate logic, and correct interpretation of slope/intercepts in other artifacts (e.g., menu cost modeling, protein intake functions) but failed to monitor assumptions when the task required statistical aggregation of overlapping categories.
3. Limitations of Aggregate Grades: Assessment records showed a high-performing cohort with ceiling-concentrated scores. While the MKACI-P composite correlated with end-of-course measures ($r = .762$), the rank correlation was weaker ($\rho = .336$), and high composite scores did not guarantee valid modeling in authentic tasks. Aggregate grades failed to expose the inferential errors visible in the video and artifact analysis.
4. Evidence of Monitoring: Explicit scrutiny of assumptions was rare. Monitoring and control were most visible when students diagnosed unit errors or questioned the sufficiency of a single screening indicator (e.g., BMI), but these critical checks were often absent when students moved from data description to disciplinary claims.

Key Contributions

• Empirical: The study documents how nutrition students mobilize proportional, functional, graphical, and inferential reasoning across authentic tasks, highlighting that correct calculation does not equate to valid disciplinary modeling.
• Theoretical: It integrates four distinct theoretical perspectives (Schoenfeld, Silver, Li, Marzano-Kendall) to distinguish between executing a procedure, understanding structure, drawing warranted inferences, and critically examining assumptions.
• Methodological: It demonstrates that video-derived episodes and student artifacts must lead the explanatory narrative, with grade analytics serving only as bounded triangulation. It argues that group products (videos) cannot substitute for individual mathematical evidence regarding metacognitive monitoring.

Significance and Claims
The paper claims that effective mathematics-in-STEM learning becomes visible only when students coordinate quantities, representations, assumptions, and disciplinary meanings rather than merely obtaining correct values. The study proposes a meaning-making assessment cycle for higher education that includes:

1. Authentic problem posing.
2. Visible mathematical production.
3. Teacher attention to assumptions and model limits.
4. Cognitively differentiated assessment (distinguishing between retrieval, analysis, and utilization).
5. Revision and transfer tasks.

The authors position mathematics not as a decorative tool but as an integrative practice essential for examining and justifying disciplinary claims. They conclude that while authentic contexts and collaborative products are valuable, they must be paired with assessment strategies that make the reasoning and assumptions inspectable, rather than relying on aggregate scores or production value alone. The study modestly asserts that its findings contribute to reframing effective STEM learning around sense making, modeling, and critical reasoning, while acknowledging limitations regarding the single-cohort design and the inability to reconstruct individual negotiation trajectories from edited transcripts.