Learning trajectories for graph comprehension and covariational reasoning as frameworks for mathematics-in-science integration¶

Theory · All theories
Evidence · 6 claims (6 for) · 1 study (1 causal), q2 · 0 of 1 report an effect size · 6 claims rest on one study

Description¶

The report articulates two learning trajectories framing mathematics in OpenSciEd investigations. Graph comprehension is "the ability to read, interpret, and obtain meaning in graphical representations of data," with three levels: Informational (extracting information directly represented), Relational (finding relationships across multiple pieces of information), and Interpretive (making interpretations and predictions beyond the data). Covariational reasoning is "the mental processes involved in coordinating how two varying quantities change in relation to each other," with levels of Existence, Direction, and Amount/Rate of change. These trajectories grounded the student assessment design and teacher professional learning.

Design Implications¶

Context¶

Requirements¶

• Teacher knowledge of the trajectories to anticipate student ideas and craft prompts that advance thinking
• Assessment rubrics aligned to trajectory levels to measure student outcomes

Constraints¶

• The report notes findings may not generalize beyond eighth-grade physical science units and the GC and CoV mathematical domain

Target Learners¶

• middle school science students

Target Learning Objectives¶

• graph comprehension
• covariational reasoning
• using data as evidence for scientific claims

Claims¶

• Gc Consistent Cov Varied Across Lessons [+M]
• Teachers varied in Data Routine enactment, with Sensemaking about the Data least common, and sensemaking activities were strongly associated with open-ended questioning [+W]
• Delayed Treatment teachers more frequently simplified GC/CoV-lean lessons in ways that removed opportunities for figuring out, while Treatment teachers added graphing-skill opportunities [+W]
• The two teacher groups did not differ on released-math tasks; both groups made pretest-to-posttest gains, suggesting math-in-science-context tasks better capture OpenSciEd math reasoning [+W]
• Many teachers' knowledge of students' GC and CoV increased in sophistication over the school year, and teachers reported the professional learning and just-in-time supports were helpful [+W]
• Treatment-group students increased significantly more than Delayed Treatment students on math-in-science-context tasks from pretest to midtest and pretest to posttest [+W]

Related Theories¶

Examples¶

• Four recommendations for deepening mathematics integration in science investigations
• The Data Routine: a four-element structure for student engagement with data in science investigations

Key Sources¶

• McElhaney, K. W., Hodkowski, N. M., McMahon, L. H., Jacobs, J., Penuel, W. R., Anton, G., Henson, K., Urban, R., & Parker, D. A. (2025). Promoting Mathematical Reasoning in OpenSciEd Middle School Curriculum Units. Digital Promise. https://digitalpromise.dspacedirect.org/items/4ea4b3c5-c663-4484-8727-258bff346d2d. doi:10.51388/20.500.12265/281