Proses Penalaran Kuantitatif Menggunakan Kerangka Referensi Siswa Ditinjau Dari Gender

The results of previous studies showed that the ratio of the differences in the level of quantitative reasoning abilities between male students and female students was quite significant. While the frame of reference refers to a series of mental actions through which individuals can regulate the processes and products of quantitative reasoning. Therefore, there are two main objectives of this study, namely to show whether or not there are differences in quantitative reasoning products using a frame of reference between male and female students, then to describe the process of quantitative reasoning using a frame of reference between male and female students. Using Sequential Mixed Methods, this study examined 58 students of class VIII junior high school. The research was conducted in two phases, namely the quantitative phase which included statistical data analysis using the Mann Withney Test to determine whether there were differences in the product of quantitative reasoning using the frame of reference for male and female students. Then the qualitative phase includes a description of the quantitative reasoning process using a frame of reference for male and female students. The results of the study stated that there were differences in the product of quantitative reasoning between male and female students. This is indicated by the results of statistical tests in the quantitative phase, while the qualitative phase found that male students were able to analyze the formulas that were determined according to the results of their own interpretation of the information provided implicitly or explicitly in the questions compared to female students. Keywords: Quantitative Reasoning, Frame of Reference, Gender Abstrak Hasil penelitian sebelumnya menunjukan rasio perbedaan tingkat kemampuan penalaran kuantitatif antara siswa laki-laki dan siswa perempuan yang cukup signifikan. Sedang kerangka referensi merujuk pada serangkaian tindakan mental yang melaluinya individu dapat mengatur proses dan produk dari penalaran kuantitatif. Oleh karenanya, ada dua tujuan utama dari penelitian ini, yaitu menunjukkan ada atau tidak-nya perbedaan produk penalaran kuantitatif menggunakan kerangka referensi antara siswa laki-laki dan perempuan, selanjutnya mendeskripsikan proses penalaran kuantitatif menggunakan kerangka referensi antara siswa laki-laki dan perempuan. Menggunakan Sequential Mixed Methods penelitian ini mengkaji 58 orang siswa kelas VIII SMP. Penelitian dilakukan dengan dua fase, yaitu fase kuantitatif meliputi analisis data statistik menggunakan uji Mann Withney Test untuk mengetahui adakah perbedaan produk penalaran kuantitatif menggunakan kerangka referensi siswa laki-laki dan perempuan. selanjutnya fase kualitatif meliputi, deskripsi proses penalaran kuantitatif menggunakan kerangka referensi siswa laki-laki dan perempuan. Hasil penelitian menyatakan ada perbedaan produk penalaran kuantitatif antara siswa laki-laki dan perempuan. Hal ini ditunjukkan oleh hasil uji statistik pada fase kuantitatif, sedangkan fase kualitatif menemukan bahwa siswa laki-laki lebih dapat menganalisis rumus/formula yang ditentukan menurut hasil interpretasinya sendiri terhadap informasi yang diberikan secara implisit maupun eksplisit dalam soal disbanding siswa perempuan. Kata Kunci: Penalaran Kuantitatif, Kerangka Referensi, Gender.

A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning

The concept of derivative is used in many areas including applied problems and requiring mathematical modelling in different disciplines. One of the most important approaches for teaching the derivative is to support students in visualizing the concept. Also, it is necessary to shift researchers and teachers’ focuses to students’ dynamic mental actions while learning derivative in order to conduct effective teaching process. With this necessity, I focused on the perspective of quantitative reasoning related to the graphical approach to the derivative. This study aims to reveal a calculus student’s mental actions related to the graphical approach to the derivative. The data were collected from a first-year calculus student engaged in the task requiring graphical interpretation of the derivative. Results showed that the student’s understanding of the slope shaped her inferences about the tangent line because the quantity of ratio is prior knowledge for learning the instantaneous rate of change. Besides, as the student had the idea of correspondence related to the concept of function, she had difficulties in interpreting the global view of the derivate. This result suggests that having global view of the derivative requires a strong understanding of function and rate.

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.

Surveying the Landscape of Numbers in U.S. News

The news arguably serves to inform the quantitative reasoning (QR) of news audiences. Before one can contemplate how well the news serves this function, we first need to determine how much QR typical news stories require from readers. This paper assesses the amount of quantitative content present in a wide array of media sources, and the types of QR required for audiences to make sense of the information presented. We build a corpus of 230 US news reports across four topic areas (health, science, economy, and politics) in February 2020. After classifying reports for QR required at both the conceptual and phrase levels, we find that the news stories in our sample can largely be classified along a single dimension: The amount of quantitative information they contain. There were two main types of quantitative clauses: those reporting on magnitude and those reporting on comparisons. While economy and health reporting required significantly more QR than science or politics reporting, we could not reliably differentiate the topic area based on story-level requirements for quantitative knowledge and clause-level quantitative content. Instead, we find three reliable clusters of stories based on the amounts and types of quantitative information in the news stories.

Fibrational bisimulations and quantitative reasoning: Extended version

Bisimulation and bisimilarity are fundamental notions in comparing state-based systems. Their extensions to a variety of systems have been actively pursued in recent years, a notable direction being quantitative extensions. In this paper we enhance a categorical framework for such extended (bi)simulation notions. We use coalgebras as system models and fibrations for organizing predicates—following the seminal work by Hermida and Jacobs. Endofunctor liftings are crucial predicate-forming ingredients; the first contribution of this work is to extend several extant lifting techniques from particular fibrations to $\textbf {CLat}_\wedge $-fibrations over $\textbf {Set}$. The second contribution of this work is to introduce endolifting morphisms as a mechanism for comparing predicates between fibrations. We apply these techniques by deriving some known properties of the Hausdorff pseudometric and approximate bisimulation in control theory.

Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs

Extending the popular answer set programming paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs) where standard rules are equipped with modal operators which allow to express conditions on literals for being known or possible, that is, contained in all or some answer sets, respectively. ELPs thus deliver multiple collections of answer sets, known as world views. Employing ELPs for reasoning problems so far has mainly been restricted to standard decision problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set. Second, we present a novel system that is capable of efficiently solving the underlying counting problems required to answer such quantitative reasoning problems. Our system exploits the graph-based measure treewidth and works by iteratively finding and refining (graph) abstractions of an ELP program. On top of these abstractions, we apply dynamic programming that is combined with utilizing existing search-based solvers like (e)clingo for hard combinatorial subproblems that appear during solving. It turns out that our approach is competitive with existing systems that were introduced recently.