Robert L. Mayes

Quantitative Reasoning Learning Progressions for Environmental Science: Developing a Framework

Quantitative reasoning is a complex concept with many definitions and a diverse account in the literature. The purpose of this article is to establish a working definition of quantitative reasoning within the context of science, construct a quantitative reasoning framework, and summarize research on key components in that framework. Context underlies all quantitative reasoning; for this review, environmental science serves as the context.In the framework, we identify four components of quantitative reasoning: the quantification act, quantitative literacy, quantitative interpretation of a model, and quantitative modeling. Within each of these components, the framework provides elements that comprise the four components. The quantification act includes the elements of variable identification, communication, context, and variation. Quantitative literacy includes the elements of numeracy, measurement, proportional reasoning, and basic probability/statistics. Quantitative interpretation includes the elements of representations, science diagrams, statistics and probability, and logarithmic scales. Quantitative modeling includes the elements of logic, problem solving, modeling, and inference. A brief comparison of the quantitative reasoning framework with the AAC&U Quantitative Literacy VALUE rubric is presented, demonstrating a mapping of the components and illustrating differences in structure. The framework serves as a precursor for a quantitative reasoning learning progression which is currently under development.

Quantitative Reasoning in Environmental Science: A Learning Progression.

The ability of middle and high school students to reason quantitatively within the context of environmental science was investigated. A quantitative reasoning (QR) learning progression was created with three progress variables: quantification act, quantitative interpretation, and quantitative modeling. An iterative research design was used as it is the standard method for the development of learning progressions. The learning progression was informed by interviews of 39 middle and high school students from 5 schools in the Western USA using QR assessments. To inform the lower anchor, intermediate levels, and upper anchor of achievement for the QR learning progression, an extensive review of the literature on QR was conducted. A learning progression framework was then hypothesized. To confirm the framework, three QR assessments within the context of environmental literacy were constructed. The interviews were conducted using these QR assessments. The results indicated that students do not actively engage in quantitative discourse without prompting and display a low level of QR ability. There were no consistent increases on the QR learning progression either across grade levels or across scales of micro/atomic, macro, and landscape.

Quantitative Reasoning in Environmental Science: Rasch Measurement to Support QR Assessment

The ability of middle and high school students to reason quantitatively within the context of environmental science was investigated. A quantitative reasoning (QR) learning progression, with associated QR assessments in the content areas of biodiversity, water, and carbon, was developed based on three QR progress variables: quantification act, quantitative interpretation, and quantitative modeling. Diagnostic instruments were developed specifically for the progress variable quantitative interpretation (QI), each consisting of 96 Likertscale items. Each content version of the instrument focused on three scale levels (macro scale, micro scale, and landscape scale) and four elements of QI identified in prior research (trend, translation, prediction, and revision). The QI assessments were completed by 362, 6th to 12th grade students in three U.S. states. Rasch (1960/1980) measurement was used to determine item and person measures for the QI instruments, both to examine validity and reliability characteristics of the instrument administration and inform the evolution of the learning progression. Rasch methods allowed identification of several QI instrument revisions, including modification of specific items, reducing number of items to avoid cognitive fatigue, reconsidering proposed item difficulty levels, and reducing Likert scale to 4 levels. Rasch diagnostics also indicated favorable levels of instrument reliability and appropriate targeting of item abilities to student abilities for the majority of participants. A revised QI instrument is available for STEM researchers and educators.

Quantitative Reasoning Learning Progression: The Matrix

The NSF Pathways Project studied the development of environmental literacy in students from grades six through high school. Learning progressions for environmental literacy were developed to explicate the trajectory of learning. The Pathways QR research team supported this effort by studying the role of quantitative reasoning (QR) as a support or barrier to developing environmental literacy. An iterative research methodology was employed which included targeted student interviews to establish QR learning progression progress variables and elements comprising those progress variables, development of a QR learning progression framework, and closed-form QR assessments to verify the progression. In this paper the focus is on development of the current iteration of the QR learning progression, including a brief discussion of the first and second iterations that provide a look into the development of a learning progression. The focus is on the latest iteration, with a detailed discussion of the progress variables: Quantitative Act (QA), Quantitative Interpretation (QI), and Quantitative Modeling (QM). The elements that constitute these progress variables which arose from our analysis of qualitative interview data and quantitative assessment data are provided. Discussion of the evolution of the QR assessment to document students’ abilities to utilize the progress variables occurs concurrently with explanation of the learning progression development. The most recent QR assessment focused on QI. The data from this assessment will provide additional information to revise the learning progression QI progress variable. A similar effort is planned for the QA and QM progress variables.

Quantitative Reasoning in the Context of Energy and Environment

This book provides professional development leaders and teachers with a framework for integrating authentic real-world performance tasks into science, technology, engineering, and mathematics (STEM) classrooms. We incorporate elements of problembased learning to engage students around grand challenges in energy and environment, place-based leaning to motivate students by relating the problem to their community, and Understanding by Design to ensure that understanding key concepts in STEM is the outcome. Our framework has as a basic tenet interdisciplinary STEM approaches to studying real-world problems. We invited professional learning communities of science and mathematics teachers to bring multiple lenses to the study of these problems, including the sciences of biology, chemistry, earth systems and physics, technology through data collection tools and computational science modeling approaches, engineering design around how to collect data, and mathematics through quantitative reasoning. Our goal was to have teachers create opportunities for their students to engage in real-world problems impacting their place; problems that could be related to STEM grand challenges demonstrating the importance and utility of STEM. We want to broaden the participation of students in STEM, which both increases the future STEM workforce, providing our next generation of scientists, technologists, engineers, and mathematicians, as well as producing a STEM literate citizenry that can make informed decisions about grand challenges that will be facing their generation. While we provide a specifi c example of an interdisciplinary STEM module, we hope to do more than provide a single fi sh. Rather we hope to teach you how to fi sh so you can create modules that will excite your students.

The 21st Century STEM Reasoning

The integration of Science, Technology, Engineering, and Mathematics (STEM) programs within the educational framework and the creation of STEM-designated schools and academic/career pathways represent a national trend meant to prepare students for the demands of the 21st century while addressing future workforce needs. Often, however, the STEM disciplines are taught within silos independent of each other. Students miss the opportunity to participate in the interrelationship among the STEM disciplines, resulting in missing opportunities to build critical reasoning skills. The Real STEM Project focuses on the development of interdisciplinary STEM within the school and community. Interdisciplinary STEM is characterized by sustained professional development that is job-embedded and competency-based, and on the development of student reasoning abilities across contexts. To accomplish this, interdisciplinary STEM should strive to be inclusive when it comes to the multiple STEM disciplines, embrace authentic teaching strategies that are based on real-world problem-solving through hands-on student engagement, and structured around the three Ps: project-based, place-based, and problem-based. To assist in developing an interdisciplinary STEM program, this article concludes with a focus on five primary reasoning modalities that best capture the spirit of interdisciplinary STEM: complex systems reasoning, science model-based reasoning, technology computational reasoning, engineering design-based reasoning, and quantitative reasoning.

Energy and Environment Performance Task

We have presented an overview of the QR STEM project so STEM professional development leaders and teachers reading this have a sense of the big picture, including our goals, methods, and expected outcomes. We now turn to providing a detailed discussion of leading teachers in developing a performance task within the context of energy and environment using the Understanding by Design assessment framework (Wiggins and McTighe, 2005).

Quantitative Reasoning: Changing Practice in Science and Mathematics

In the summer of 2007 Jimm Myers, Mark Lyford, and I were working at the University of Wyoming on projects to improve secondary and post-secondary science and mathematics education. Jimm, a distinguished professor of Geology, was integrating real-world problem-based tasks into introductory level geology courses.

Pedagogical Framework: A Pathway to Citizenship Preparation

In Chapter 1 we provided a framework for our work in QR STEM. In this chapter we walk through the process of collaborating with teachers in developing a unit driven by a performance task with a focus on the context of energy and environment. We have selected the very broad areas of energy and environment as fields from which to select topics.

Quantitative Reasoning in Stem

In Chapter 1 we introduced our framework for quantitative reasoning, which includes the components of the act of quantification, quantitative literacy, quantitative interpretation, and quantitative modelling. Here we want to provide specific examples within science contexts of elements of QR within each of these components.