The NSF MSP Culturally Relevant Ecology, Learning Progressions, and Environmental Literacy project focuses on the critical education juncture of middle through high school (grades 6-12). Universities and research centers associated with four Long Term Ecological Research (LTER) programs across the nation are collaborating with school districts to a) define essential pathways for achieving environmental science literacy, and b) to develop and test teacher professional development programs that help accomplish this ambitious goal through innovative instruction in the sciences in middle and high schools.  This poster focuses on our study of the impact quantitative reasoning (QR) has upon students' development of environmental science literacy.

The Quantitative Reasoning Theme Team for the project has established a QR Theoretical Framework to guide the development of QR assessment items for the learning progressions in the Carbon, Water, and Biodiversity strands. We are defining QR for the MSP LTER project as all mathematical and statistical processes that support student understanding of the carbon cycle, water cycle, and biodiversity. For this project QR will include areas identified in the literature under the titles of quantitative literacy, numeracy, mathematical literacy, civic literacy, cultural literacy, mathematical or statistical reasoning, problem solving, and mathematical modeling. The QR Theme Team has determined three components of QR across which assessment items will be created:

• Quantitative Literacy (QL): ability to manipulate and calculate, apply algorithms, possess number sense and estimation skills including understanding small and large numbers, employ proportional reasoning including working with ratios and percentages, and calculate basic descriptive statistics. These are primarily the arithmetic skills required to be a literate citizen.
• Quantitative Interpretation (QI): ability to interpret mathematical models, ability to interpret multiple representations of real world situations including tabular, graphic, analytic, and verbal representations, and determine correlation and causality. These are primarily the algebraic processes required to be a literate citizen, though it includes geometric, statistical, and discrete mathematical processes as well.
• Quantitative Modeling/Logic (QM/L): ability to logically reason with quantitative information, capacity to create a model representing a real world situation including geometric and analytic models, problem solving, and conducting statistical inference with hypothesis testing. These are primarily the pre-calculus, calculus, and statistics processes required to be a citizen scientist.

While the level of cognitive challenge overall grows as a student moves from QL through QI to QM/L, all levels incorporate significant cognitive barriers for teachers and students. For example, the QL process of proportional reasoning is well established in the literature as a major barrier for students, a lack of which results in an inability to work with rational numbers, ratios, and rates of change. On the QI level students often struggle with moving between multiple representations. While moving from a table to a graph requires only point plotting, moving from a table to an equation means creating a mathematical model, and moving from a graph to an equation takes an understanding of families of functions.