# Grand Challenge 1:

**How does quantitative thinking help geoscientists and citizens better understand the Earth, and how can geoscience education move students toward these competencies?**

### Rationale

The ability to think quantitatively is an important part of what transforms an introductory student into a geoscience major and then into a professional geoscientist. Employers value quantitative thinking. Quantitative thinking may be a sweet spot for GER research, in that there is rich trove of math education research to build upon. The set of recommended strategies listed below is not meant to comprehensively cover the entirety of geoscience quantitative thinking; we have prioritized strategies that we think offer the highest leverage and that will produce a strong foundation upon which future efforts can build.

The literature in quantitative reasoning outside of geoscience is extremely rich, including contributions in mathematics, mathematics education, statistic education, engineering education, computer science education, and educational psychology. Good starting points include Ashcraft (2002), Madison (2014), & Wing (2006). Several sources have indicated that modest gains in student attitudes can be achieved with some effort (Wismath & Worrell 2015; Lipka & Hess 2016; Follett et al., 2017; Ricchezza & Vacher, 2017). However, results are mixed and not all interventions have produced desired results (Sundre et al. 2012; Mayfield & Dunham 2015). Research on quantitative reasoning specifically within geoscience education is a fertile field for future work (Vacher, 2012; Ricchezza & Vacher, 2017).

### Recommended Research Strategies

**Collaborate with mathematics education researchers and quantitative literacy experts.**There is already a large community outside of the geosciences who has thought about issues of quantitative thinking, and we want to be able to build on their efforts rather than start from scratch. Two anticipated research process outcomes from such collaborations would be gains in: (a) vocabulary and constructs with which to talk about how experts and novice participants in our studies are thinking and learning and (b) insights about mathematical habits of mind and partnering to better understand how these habits of mind come into play in thinking about the Earth. The following are example contact points to initiate collaborative research with mathematics education researchers and quantitative literacy experts:- National Numeracy Network
- Research in Undergraduate Mathematics Education
- Transforming Post-secondary Education in Mathematics
- EDC Math Education group: authors of Cuomo, Goldenberg, & Mark, 1996.
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**Research how novices and experts take an Earth phenomenon that they understand holistically or experientially and transform it into a mathematical representation**(e.g., word equation, mathematical equation, mathematical or computational model; Figure 2). Personal experiences as educators tell us that this is a skill that many students lack, and it is generally not being taught in math classes. For geoscience majors, this is an essential skill for doing original research. For non-majors, this is a valuable life skill. There is very little research on this, and also not much guidance for educators. Models include the work of W.-M. Roth (e.g., Roth & Bowen, 1994) and the 1990's vintage Jasper Woodbury series (Vanderbilt, 1992).**Research what quantitative habits of mind expert geoscientists use in understanding the Earth.**Research suggests that habits of mind are more enduring and transferable than specific skills. We do not know what the geoscience careers of the future will entail, or what specific skills might be needed. Habits of mind should prepare students for whatever specific tasks are required. We and our math colleagues have put a lot of effort into teaching math skills; we now want to move beyond teaching quantitative skills to teaching quantitative habits of mind. This topic is seriously under-researched.**Work towards a community consensus on what quantitative skills and habits of mind are needed to function effectively as a citizen of the planet.**Many of the critical Earth-related problems facing humanity can be broadly understood at either a qualitative or quantitative level; for example climate change, resource depletion, and resilience in the face of natural disasters. However, to move beyond merely understanding the problems, so as to be able to weigh the costs and benefits of conflicting paths forward, requires quantitative thinking. There is not a consensus on what the elements of such thinking should be, but the traditional algebra-calculus sequence seems not to be an optimal match. Deciding what needs to be learned is a necessary pre-cursor to designing a comprehensive research program in this area. This could be approached as a community discussion. Or it could be approached as a research question, looking out in the world at what kinds of tasks and decisions citizens face in the context of Earth/human interactions, and what quantitative capacities are needed to succeed at these tasks and make wise decisions.**Research what learning experiences can help students with poor math preparation or attitudes feel the power of math**to answer questions or solve problems they care about concerning the Earth. Extensive literature in and out of the geosciences and uncounted personal experiences as educators tell us that many of our students enter our classes or our major(s) with a negative attitude about math (e.g., math anxiety, math phobia) combined with a lack of proper math preparation, that leads to math avoidance (Wenner & Baer, 2015; Maloney & Beilock, 2012). This shuts them off to the rich possibilities of the power of math to solve problems and open entire career opportunities they had not considered before. Improving quantitative thinking about the Earth is important for all students, but we prioritize this population for research attention because the problems here are so gigantic and so important, and because we think that this can be a pathway to transform math from "something I hate" into "something I want and need."**Collaborate with assessment experts**to develop and validate assessments for the learning goals articulated in Strategies 2 and 5, and to begin to shape the findings of Strategies 3 and 4 into assessable constructs. There are few to no tested, validated, research-grade assessment instruments that tackle quantitative reasoning in the context of Earth education. The building of such assessments requires both deep knowledge of the Earth and serious expertise in assessment; collaboration will be helpful. It might be possible to: (a) build Earth content into existing quantitative reasoning assessments, or (b) increase the quantitative component of existing Earth literacy assessments, or (c) formalize and validate assessments that have been developed as summative or formative assessments for coursework. Any of these pathways would need to begin with a clear articulation of learning goals and of what student behavior and/or product would demonstrate that each learning goal had been met. This is a long path; all the more reason to start sooner rather than later.