Quantitative Reasoning Skills Research Articles

Predicting Public Personnel Selection Examination Achievement: A Data Mining Approach

This research investigates the predictive variables related to the Public Personnel Selection Examination (KPSS), utilized for recruitment in public institutions and organizations. The study explores predictor variables' importance levels by analysing longitudinal data, including examinees' high-stakes exams, demographic information, and educational backgrounds. It compares the prediction performances of machine learning algorithms such as artificial neural networks, random forest, support vector machine, and k-nearest neighbour. The findings reveal that the quantitative test of the graduate education exam is the most influential predictor, closely followed by the mathematics test of the university entrance exam. These results highlight the importance of quantitative reasoning skills in predicting KPSS achievement. Additionally, variables related to undergraduate programs and universities demonstrate significant importance in predicting KPSS achievement. Notably, the artificial neural networks model demonstrates superior predictive accuracy compared to other models, indicating its effectiveness in KPSS prediction. This research sheds light on important predictors of KPSS achievement and provides valuable insights into the effectiveness of different prediction models.

Is everything everywhere? A hands-on activity to engage undergraduates with key concepts in quantitative microbial biogeography.

The ubiquity and ease with which microbial cells disperse over space is a key concept in microbiology, especially in microbial ecology. The phenomenon prompted Baas Becking's famous "everything is everywhere" statement that now acts as the null hypothesis in studies that test the dispersal limitation of microbial taxa. Despite covering the content in lectures, exam performance indicated that the concepts of dispersal and biogeography challenged undergraduate students in an upper-level Microbial Ecology course. Therefore, we iteratively designed a hands-on classroom activity to supplement the lecture content and reinforce fundamental microbial dispersal and biogeography concepts while also building quantitative reasoning and teamwork skills. In a class period soon after the lecture, the students formed three-to-five-person teams to engage in the activity, which included a hands-on dispersal simulation and worksheet to guide discussion. The simulation involved stepwise neutral immigration or emigration and then environmental selection on a random community of microbial taxa represented by craft poms. The students recorded the results at each step as microbial community data. A field guide was provided to identify the taxonomy based on the pom phenotype and a reference to each taxon's preferred environmental niches. The worksheet guided a reflection of student observations during the simulation. It also sharpened quantitative thinking by prompting the students to summarize and visualize their and other teams' microbial community data and then to compare the observed community distributions to the idealized expectation given only selection without dispersal. We found that the activity improved student performance on exam questions and general student satisfaction and comfort with the biogeography concepts. Activity instructions and a list of needed materials are included for instructors to reproduce for their classrooms.

Infusing Quantitative Reasoning Skills into a Differential Equation Class in an Urban Public Community College

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of infusing QR into mathematics courses and provide insights for educators looking to adopt similar strategies in their teaching.

Human Influence On Global Climate: Legal Protection For Sustenance Of Life On Earth

Changes in solar irradiance may have affected global climate, the importance of the climate change issue stems from the impact of changes in climate on human and natural systems. The two most well-known consequences of climate change are an increase in global-mean temperature and a rise in sea level. The primary components of sea-level rise are thermal expansion and the melting of small glaciers. However, there are other changes in climate could be as important, or even so, than changes in the mean climate state. These include changes in precipitation and climate variability, particularly changes in the intensity and/or severity of extreme events such as droughts, floods, or tropical storms.
 Physics deals with the structure of matter and how the fundamental constituents of the universe interact. The impact of humans on the environment revolves around the need of physical science to understand how human beings change a natural system, an understanding of global warming and the associated climate change. Hence, physicists will approach numerous troubles from more than one direction. Physicists had to constantly keep attentive to changes, to visualize one factor going on in nature, to discover new phenomena and to document it in order that they will describe it later. Thus studying physics strengthens quantitative reasoning and problem solving skills. The environment is the natural world but with toxic chemicals, spacecraft, and nuclear bombs, humans seem to be moving further and further away from what could be called 'natural' every day. As physics strengthens quantitative reasoning and problem-solving skills, it should be dealt transdisciplinary with Law will surely helps in reducing human influence on global climate and render legal protection for sustenance of life on earth. Hence the paper concentrates on the importance of application of physical principles to environmental problems and the proactive role played by judiciary in different countries in protecting life on earth by adopting policies relating to climate change, enhancing ethical principles by setting regulations and standards for operating industries.

Modeling and Measuring Domain-Specific Quantitative Reasoning in Higher Education Business and Economics

Quantitative reasoning is considered a crucial prerequisite for acquiring domain-specific expertise in higher education. To ascertain whether students are developing quantitative reasoning, validly assessing its development over the course of their studies is required. However, when measuring quantitative reasoning in an academic study program, it is often confounded with other skills. Following a situated approach, we focus on quantitative reasoning in the domain of business and economics and define domain-specific quantitative reasoning primarily as a skill and capacity that allows for reasoned thinking regarding numbers, arithmetic operations, graph analyses, and patterns in real-world business and economics tasks, leading to problem solving. As many studies demonstrate, well-established instruments for assessing business and economics knowledge like the Test of Understanding College Economics (TUCE) and the Examen General para el Egreso de la Licenciatura (EGEL) contain items that require domain-specific quantitative reasoning skills. In this study, we follow a new approach and assume that assessing business and economics knowledge offers the opportunity to extract domain-specific quantitative reasoning as the skill for handling quantitative data in domain-specific tasks. We present an approach where quantitative reasoning – embedded in existing measurements from TUCE and EGEL tasks – will be empirically extracted. Hereby, we reveal that items tapping domain-specific quantitative reasoning constitute an empirically separable factor within a Confirmatory Factor Analysis and that this factor (domain-specific quantitative reasoning) can be validly and reliably measured using existing knowledge assessments. This novel methodological approach, which is based on obtaining information on students’ quantitative reasoning skills using existing domain-specific tests, offers a practical alternative to broad test batteries for assessing students’ learning outcomes in higher education.

Exploring the Relationship between Quantitative Reasoning Skills and News Habits

Because people are constantly confronted with numbers and mathematical concepts in the news, we have embarked on a project to create journalism that can support news users’ number skills. But doing so requires understanding (1) journalists’ ability to reason with numbers, (2) other adults’ ability to do so, and (3) the attributes and affordances of news. In this paper, we focus on the relationship between adults’ news habits and their quantitative reasoning skills. We collected data from a sample of 1,200 US adults, testing their ability to interpret statistical results and asking them to report their news habits. The assessment we developed differentiated the skills of adults in our sample and conformed to the theoretical and statistical assumption that such skills are normally distributed in the population overall. We also found that respondents could be clustered into six distinct groups on the basis of news repertoires (overall patterns of usage, including frequency of news use overall and choice of news outlets). As often assumed in the literature on quantitative reasoning, these news repertoires predicted quantitative reasoning skills better than the amount of quantification in the outlets, but they still predicted only a small fraction of the variance. These results may suggest that news habits may play a smaller or less direct role in quantitative reasoning than has previously been assumed. We speculate that the presence (or absence) of quantification in everyday activities – namely work and hobbies – may be a better predictor of adults’ quantitative reasoning, as may additional dimensions of news habits and affective responses to numbers.

Diverging Paths: Exploring the Association Between Initial Math Pathways and College Students’ Subsequent Math Performance

Math pathways are an increasingly common policy reform where students choose a traditional math pathway (involving Algebra and/or Calculus) or an alternate math pathway more applicable to students' fields of study, namely Statistics or Liberal Arts Math with quantitative reasoning skills. We use data from all first-time-in-college students in the Florida College System to conduct an inverse-probability regression adjustment examining whether student's initial enrollment in different gateway math pathways influences subsequent math performance. We find the Liberal Arts pathways may increase the likelihood of students passing the first gateway course, but Algebra pathways tend to result in greater longer-term coursetaking success.

Integrating Community Ecology Into the Study of Parasites: Exploring the Effect of Host Behavior on Parasite Transmission Rates

Organismal life cycles are often presented as a set of facts to memorize in undergraduate biology courses. This approach is cognitively demanding for students and fails to convey how central life cycle diversity is in shaping ecological and evolutionary processes. Understanding the causes and consequences of life cycles is especially important when studying parasites with multiple life cycle stages for passing through diverse hosts. We designed a two-part lab activity to help our students gain a better understanding of the ecological interactions driven by parasite life cycles. Part I is a structured guide to reading a peer-reviewed journal article. Part II is a guided exercise in summarizing and interpreting mock experimental data involving a trematode parasite life cycle. These assignments helped students (1) understand how parasite life cycles shape ecological interactions with their hosts, (2) practice making predictions about species interactions using core ecological principles, and (3) practice quantitative reasoning and graph literacy skills by visualizing and interpreting data. We first used this activity as a self-guided lab exercise for an upper-division undergraduate parasitology class that switched from in-person to asynchronous-remote mid-semester. The stepwise structure of the activity allowed us to pinpoint the links in the chain of biological reasoning where students struggled most to guide target topic reviews in subsequent lectures. Here, we provide a summary of the activity, our experience with the activity, and suggestions for adapting the activity for a synchronous-remote or in-person class.

Three Research-Based Quantitative Reasoning Modules for Introductory Organismal Biology Laboratories

We have designed three laboratory modules for an introductory organismal biology course with an emphasis on quantitative reasoning and data analysis skills. Module 1 tests for dimorphism in crayfish chelae using a paired statistical design. Module 2 tests for allometric growth of tapeworm hook structures using a regression model. Module 3 tests for differences in stomatal densities between two groups of plants using a two-sample statistical approach. For all three modules, we emphasize the use of confidence intervals to draw statistical conclusions about hypotheses. Knowledge about the basic biology of animals and plants is required, including arthropods, platyhelminths, and vascular plants. Background reading on dimorphism, allometry, and transpiration provides the necessary foundation to develop questions and hypotheses. Some familiarity with R is necessary for both students and instructors, although the activities can be modified for analysis with Excel or another statistical package. These modules can be taught independently or together as a unit within a course. As stated in the AAAS document, <em>Vision and Change: A Call to Action</em>, the ability to use quantitative reasoning is a core competency that must be developed by all biology students. These modules address the call for instruction in quantitative reasoning and provide a hands-on active introduction to key tools that will be required to build students&rsquo; statistical repertoire in more advanced courses. <em>Primary Image:</em>&nbsp;A highlight of the three modules used in our introductory organismal biology course, including the use of calipers to test for dimorphism in the size of crayfish chelae (upper right), a leaf impression (lower right) from a hydrangea plant (lower left) used to test hypotheses about stomata densities, and the image of an <em>Echinococcus </em>tapeworm (upper left) to test hypotheses about allometry.&nbsp;&nbsp;

Iron supplementation given to nonanemic infants: neurocognitive functioning at 16 years

ABSTRACT Objective There is concern that high iron uptake during the critical period of early brain development carries potential risks, especially for nonanemic infants. This study examined the neurocognitive functioning of 16-year-olds who were nonanemic as infants and received iron supplementation. Methods We studied 562 Chilean adolescents (M 16.2 years; 52.7% female) who participated in a randomized controlled iron supplementation trial in infancy. Between 6 and 12 months, 346 consumed an iron-fortified formula (12.7 Fe mg/L) or, if primarily breastfed, liquid vitamins with 15 mg elemental iron as ferrous sulfate, and 216 consumed unmodified cow milk without iron or liquid vitamins without iron if primarily breastfed. Results Compared to adolescents in the no-added iron condition in infancy, those in the iron-supplemented condition had poorer visual-motor integration, quantitative reasoning skills, and incurred more errors on neurocognitive tasks. Consuming larger amounts of iron-fortified formula in infancy was associated with lower arithmetic achievement. Of adolescents who had high hemoglobin at 6 months (Hb ≥ 125 g/L), those in the iron supplemented condition had poorer performance on arithmetic, quantitative reasoning, and response inhibition tests than those in the no-added iron condition. Of adolescents who had marginally low 6-month hemoglobin (Hb > 100 and < 110 g/L), those who received no-added iron incurred more errors on a visual searching task than those in the iron-supplemented condition. Conclusion The physiologic need for iron during the period of rapid and critical brain development in young infants should be considered vis-à-vis the risks associated with supplementing nonanemic infants with high levels of iron. Clinical Trials number: NCT01166451

The Conceptualization of Quantitative Reasoning among Introductory Biology Faculty

ABSTRACTQuantitative reasoning (QR) skills have become a critical competency for undergraduate biology students, and recommendations for curricular reform urge QR training throughout undergraduate biology programs. Much research has been directed at course design, pedagogy, and student challenges in QR, but less research has been directed toward understanding how biology faculty conceptualize the QR skills they are called upon to teach. We conducted in-depth, semistructured interviews with 15 participants teaching introductory biology courses to learn how faculty conceptualize QR at the introductory level. Using phenomenology, responses were coded to establish inductive codes. We found that two themes emerged from the coded conceptualizations: sophisticated, cognitively complex QR skills and basic QR skills. Participants placed emphasis on the more complex QR skills as being important in the undergraduate curriculum, beginning at the introductory level. Participants’ conceptualizations of QR aligned with skills called for in curriculum reform, but the perceived notion of “basic” for some skills may not align with the literature. This suggests that more is needed in aligning faculty conceptualization of QR with curriculum, pedagogy, and assessment.

Familiarize Your Students with Life at the Microscopic Scale

Developing students’ understanding of cells and the microscopic scale is an important goal of biology education. Cells are the building blocks of multicellular organisms, and most of Earth’s biodiversity is found at the microscopic scale. Developing an understanding of the microscopic scale requires that students use their quantitative reasoning skills. Here, resources are presented that help students develop their quantitative reasoning skills and improve their understanding of the small scale of microscopic life. The crosscutting concept, Scale, Proportion, and Quantity, and the science and engineering practice, Using Mathematics and Computational Thinking, are highlighted. The development of students’ quantitative reasoning skills in biology is universally recognized as an important outcome of biology education.

Ability-related political polarization in the COVID-19 pandemic

In two large-scale longitudinal datasets (combined N = 5761), we investigated ability-related political polarization in responses to the COVID-19 pandemic. We observed more polarization with greater ability in emotional responses, risk perceptions, and product-purchase intentions across five waves of data collection with a diverse, convenience sample from February 2020 through July 2020 (Study 1, N = 1267). Specifically, more liberal participants had more negative emotional responses and greater risk perceptions of COVID-19 than conservative participants. Compared to conservatives, liberal participants also interpreted quantitative information as indicating higher COVID-19 risk and sought COVID-related news more from liberal than conservative news media. Of key importance, we also compared verbal and numeric cognitive abilities for their independent capacity to predict greater polarization. Although measures of numeric ability, such as objective numeracy, are often used to index ability-related polarization, ideological differences were more pronounced among those higher in verbal ability specifically. Similar results emerged in secondary analysis of risk perceptions in a nationally representative longitudinal dataset (Study 2, N = 4494; emotions and purchase intentions were not included in this dataset). We further confirmed verbal-ability-related polarization findings on non-COVID policy attitudes (i.e., weapons bans and Medicare-for-all) measured cross-sectionally. The present Study 2 documented ability-related polarization emerging over time for the first time (rather than simply measuring polarization in existing beliefs). Both studies demonstrated verbal ability measures as the most robust predictors of ability-related polarization. Together, these results suggest that polarization may be a function of the amount and/or application of verbal knowledge rather than selective application of quantitative reasoning skills.

Analysis of a COVID-19 Clinical Trial to Emphasize Experimental Design and Quantitative Reasoning in an Introductory Biology Course.

Increasing student exposure to primary literature in early biology coursework can enhance scientific literacy and quantitative reasoning skills. The efficacy of primary literature discussion is heavily impacted by article selection, as student engagement is optimal with material that is topical and has clear relevance to real world issues. During the COVID-19 pandemic, the prevalence of COVID-19–related scientific research in the mainstream media makes it an ideal topic for current discussion in entry-level biology courses. Here, we present an activity developed to facilitate a remote, synchronous discussion of an open access clinical trial publication on the experimental drug remdesivir in the treatment of COVID-19 (Beigel et al., 2020, N Engl J Med https://doi.org/10.1056/nejmoa2007764). The activity, which is amenable to adaptation for other research articles, emphasizes concepts in experimental design, statistical analysis, graphical interpretation, and the structure, content, and organization of typical sections of a primary research article. Importantly, the activity highlights the utility of the classroom response tool Pear Deck, a Google Slides add-on, for creating engaging literature discussions that can be readily adapted to a wide variety of teaching modalities.

Exploring Hubble Constant Data in an Introductory Course

Popular accounts of exciting discoveries often draw students to physics and astronomy, but at the introductory level it is challenging to connect with these in a meaningful way. The use of real astronomical data in the classroom can help bridge this gap and build valuable quantitative and scientific reasoning skills. This paper presents a strategy for studying Hubble’s law and the accelerating expansion of the universe using actual data. Along with understanding the physical concepts, an explicit goal is to develop skills for analyzing data in terms of a model.

Dual language supports for dual language learners? Exploring preschool classroom instructional supports for DLLs' early learning outcomes

Dual language learners (DLLs) - children who are learning and developing two languages - are among the fastest growing groups of young children in the United States and currently compose a third of the public preschool population. Although evidence suggests that preschool education is beneficial for DLLs, little is known about which instructional supports in the preschool classroom best promote DLLs’ early learning skills. Drawing on a newly-collected sample of Spanish-speaking DLLs in an English-dominant, mixed-delivery public preschool system for children in low-income families (Head Start; school-based pre-k), this paper focuses on two instructional dimensions of the preschool classroom expected to support DLLs’ learning: supports for home language and supports for English acquisition. We test for associations between these classroom supports and DLLs’ English language skills, quantitative reasoning skills assessed in English, and home language skills at the end of the preschool year, and whether any such associations are moderated by the proportion of DLLs in the classroom. Controlling for baseline skills, results indicate positive associations between classroom supports for home language and quantitative reasoning skills and Spanish expressive vocabulary skills at the end of preschool. Associations varied by proportion of DLLs in the classroom. Supports for English acquisition did not predict any outcomes. This study adds to an emerging body of research suggesting classroom instructional supports for DLLs’ home language may be important not just for the maintenance of children's home language, but also for the acquisition of foundational pre-math skills. Additionally, findings suggest support for home language is possible even in preschool classrooms where the teacher does not speak the home language. The DLL composition of the classroom also warrants attention as a moderator of these associations.

A Comparison of Students’ Quantitative Reasoning Skills in STEM and Non-STEM Math Pathways

Quantitative Reasoning (QR) is essential for today’s students, yet most higher education institutions have not effectively addressed this issue. This study investigates students’ quantitative reasoning in STEM and Non-STEM math pathways using a non-proprietary, NSF grant-funded instrument, the Quantitative Literacy & Reasoning Assessment (QLRA). Participants were students enrolled in at least one college-level math pathway course at a large public institution in the southeastern US. The results showed a significant difference between STEM and Non-STEM students’ QLRA scores, with STEM students (n = 244, M = 27%, SD = 16.21%) scoring, on average, about 6% higher than Non-STEM students (n = 295, M = 21.1%, SD =11.38%). STEM students who were further along in their math sequence, i.e. Pre-calculus/Trigonometry and Calculus I, had a higher QLRA score than those taking the gateway math courses in that pathway. Non-STEM students who took additional math courses also had a higher QLRA score than those in the entry-level math course. However, the students overall had relatively low QR skills (n = 539, M = 23.78%, SD = 14.07%). These results highlight the need for an increased understanding of the math pathways initiative and its relationship with quantitative reasoning. Thoughtful and deliberate scrutiny of curriculum and pedagogy is important in all math pathways as it relates to the development of quantitative reasoning skills.

The Effectiveness of Model Rocketry to Teach Science and Quantitative Content to Students in a Non-Science Majors Course at the College Level: An Example from a Planetary Geology Course

Engaging non-science majors in a college-level science course can prove challenging. In turn, this can make it difficult to effectively teach science and math content. However, topics related to planetary exploration have a unique way of capturing one’s imagination and may serve to robustly engage non-science majors. In this contribution, I 1) describe a model rocketry lab module, I have created and implemented into an introductory-level planetary geology course and 2) quantify student learning gains as a result of this module. This module builds on model rocketry lesson plans for science and math coursework at the K-12 level (e.g., [1] [2]) and involves students working in groups to 1) design and build model rockets to carry out a theoretical mission that addresses a science question the students have developed, 2) launch their rockets and collect related data, 3) synthesize and evaluate their data, and 4) report their results in both oral and written forms. The tasks of building and launching the model rocket serve as a vehicle that allows students to employ the scientific process while learning about planetary mission design and applying geologic and quantitative skills useful to answering a science-related question. Quantification of student learning gains shows that through this lab module, students significantly improved their quantitative and scientific reasoning skills. Results from student questionnaires showed a significant increase in student interest and confidence in addressing scientific questions as well as an understanding of how planetary missions are designed and conducted.

Pitfall Traps &amp; Diversity Indices: Using Quantitative Reasoning to Test Edge Effect Theory

Students learning the skills of science benefit from opportunities to move between the scientific problems and questions they confront and the mathematical tools available to answer the questions and solve the problems. Indeed, students learn science best when they are actively engaged in pursuing answers to authentic and relevant questions. We present an activity teachers can use in the classroom to introduce the concepts of species richness and diversity. We break down the history and logic behind the two primary statistical tools ecologists use to quantify species diversity: Simpson's and Shannon's diversity indices. With hypothetical data, we show how students can learn about and practice the calculations. We then describe an activity where students collect authentic ecological data with pitfall traps while learning some arthropod systematics and practicing their newly acquired quantitative reasoning skills, all within the context of edge effect ecology and habitat conservation. The entire activity reinforces for students how interesting and helpful mathematical models and quantitative reasoning in science can be for understanding biological phenomena, but also for generating more questions, and for designing additional data-collection techniques and experiments.

Conceptualizing Integrative Agricultural Education: Introductory Framework for Integrating Mathematics in Agricultural Curriculum

A curriculum framework to support the integration of academic content to support students’ development of 21st century skills including critical thinking and problems solving skills is notably absent from agricultural education. An integrative agricultural education framework is conceptualized through a review of literature in STEM education to establish integrative teaching practices. A focus on the development of students’ quantitative reasoning skills through agriculture content hones the focus of the curriculum framework. Quantitative reasoning is the ability to confidently approach unique and complex problems in a real-life context by applying mathematical skill, knowledge, and reasoning. The integrative agricultural education framework developed was used to design an evaluative rubric for teachers, administrators, and curriculum designs to use as a tool for building both integrative teaching and mathematics into agricultural education curriculums intentionally and fluidly.