Six Principles for Quantitative Reasoning and Modeling

Weber, Eric; Ellis, Amy B.; Kulow, Torrey; Özgür, Zekiye

doi:10.5951/mathteacher.108.1.0024

Cited by 20 publications

(12 citation statements)

References 2 publications

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“…Quantitative reasoning has a focus on quantity and quantity relationships, which means approaching mathematical topics from certain mathematical attitudes that emphasize activities such as measurement, conceptualization of quantities, and establishing mathematical relationships (Thompson, 1993). This is supported by the opinion of (Ramful, 2009;Weber et al, 2014) who say that quantitative reasoning is the basis supporting students in modelling mathematical phenomena because it provides a means for students to create relationships between quantities, create new quantities, and make conclusions with quantities.…”

Section: Introductionmentioning

confidence: 99%

Students' Thinking Processes Connecting Quantities in Solving Covariation Mathematical Problems in High School Students of Indonesia

Wang

Nusantara

Qohar

et al. 2020

Participatory Educational Research

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The purpose of this study was to describe students' thinking processes in relating quantities to the problem of covariation in the process of solving mathematical problems. This study used a descriptive exploratory approach within the scope of qualitative research involving 87 students as prospective subjects from three different high schools. The schools were chosen from three different areas; where two schools were on Sumbawa island namely in Bima district and Bima town. The subject described was chosen by giving assignments related to the covariation problem. Data obtained from the answer sheets from the subjects while doing think aloud, the results of task-based interviews, and field notes. Supporting equipment for video and audio recording was used to take data of think aloud and interview. Data analysis was conducted retrospectively by combining answer sheets, think aloud, interview results and field notes with reference to APOS theory. The results obtained from students' thinking processes in connecting the quantities of covariation were two, namely Connecting Quantity by direct analytic and equation analytic. In general, it was found that students connected quantities in covariation problem solving by linking changing-quantity along with the changes in other quantities internally or externally through mathematical analysis to form new quantities based on quantitative operations.

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Section: Introductionmentioning

confidence: 99%

Students' Thinking Processes Connecting Quantities in Solving Covariation Mathematical Problems in High School Students of Indonesia

Wang

Nusantara

Qohar

et al. 2020

Participatory Educational Research

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“…Perhaps the first step to enhancing students' quantitative reasoning skills in biology is to identify contexts that afford quantification [77] that would be meaningful for students and require QR. Real world problems, such as the COVID-19 example, are often relatable to students and serve as meaningful contexts that can motivate learning, but even problem contests that are loosely based in reality (e.g., goldfish tragedy of the commons scenario) can garner significant interest and engagement.…”

Section: Motivating Problem Contexts That Afford Quantificationmentioning

confidence: 99%

A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology

Mayes¹,

Owens²,

Dauer³

et al. 2022

ACM

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Biology is becoming more quantitative. If we are to support the future of quantitative biology, then the next generation of biologists must be prepared to consistently integrate quantitative reasoning into subject matter that has traditionally been considered through a qualitative lens. We introduce a quantitative reasoning framework and discuss the importance of quantitative modeling in biology. The framework includes the Quantitative Act as a support for Quantitative Modeling and Quantitative Interpretation. The QM BUGS diagnostic instrument was developed to assesses undergraduate biology students' abilities to create and apply models employing pre-calculus mathematics. A brief discussion of our research findings based on implementation of the instrument include the lack of student ability to develop quantitative models. We present items from the instrument as examples of the Quantitative Act elements: variable quantification through identifying variable and attributes, measurement, variation, quantitative literacy, and context. We also provide items representing quantitative modeling and quantitative interpretation. We then view quantitative biology from K-12 and collegiate perspectives, including instructional practices for teaching quantitative biology, motivating problem contexts that afford quantification, instructional strategies of repetition, scaffolding, peer teaching and learning, direct instruction and teacher moves on the K-12 level, as well as identifying five competencies for the next generation of biologists which require QA abilities.

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“…Dalam penerapannya, penalaran dipengaruhi oleh aktifitas kognitif dan kemudian terwujud dalam berbagai bentuk, salah satunya adalah 660| penalaran kuantitatif. Penalaran kuantitatif merupakan proses kognitif untuk menggambarkan tindakan mental seorang siswa dalam memahami masalah matematika, mengonstruksi kuantitas dari masalah, menghubungkan, memanipulasi, dan menggunakan kuantitas dalam memecahkan masalah (Ellis, 2011;Moore, 2014;Weber et al, 2014).…”

Section: Pendahuluanunclassified

Generalisasi Dalam Penalaran Kuantitatif Siswa Melalui Pemecahan Masalah Pecahan

Wang

2021

AJPM

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Tujuan penelitian ini adalah mendeskripsikan penalaran kuantitatif dalam proses generalisasi dan cara siswa dalam menghubungkan kuantitas. Jenis penelitian ini adalah penelitian kualitatif dengan pendekatan deskriptif eksploratif. Penelitian dilakukan pada siswa sekolah menengah (kelas 9) di daerah kabupaten Bima, Nusa Tenggara Barat. Penelitian ini melibatkan 35 orang siswa yang telah memperoleh materi pecahan sebagai subjek penelitian. Subjek yang deskripsikan pada hasil penelitian sebanyak 2 orang yang merepresentasikan dari subjek penelitian dan dilakukan proses seleksi dengan memberikan tes berupa soal pemecahan masalah pecahan sebanyak 2 nomor. Siswa yang terpilih berdasarkan representasi pemecahan masalah dan atas rekomendasi dari guru matematika terhadap siswa yang memiliki kemampuan menjelaskan secara lisan. Data penelitian dikumpulkan dari hasil representasi siswa dan hasil wawancara, kemudian dianalisis secara komprehensif untuk mengidentifikasi penalaran kuantitatif siswa. Hasil penelitian menunjukan: 1) penalaran kuantitatif siswa dapat menghasilkan generalisasi pola bilangan; 2) siswa menghubungkan kuantitas dengan menggunakan rasio ekuivalen; 3) siswa merepresentasikan masalah pecahan dapat menggunakan bentuk kesetaraan. Penelitian ini menemukan bahwa kuantitas atau unit dari pecahan matematika dapat membentuk suatu pola bilangan melalui proses perbandingan kuantitas.

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Six Principles for Quantitative Reasoning and Modeling

Abstract: Modeling the motion of a speeding car or the growth of a Jactus plant, teachers can use six practical tips to help students develop quantitative reasoning.

Cited by 20 publications

References 2 publications

Students' Thinking Processes Connecting Quantities in Solving Covariation Mathematical Problems in High School Students of Indonesia

Students' Thinking Processes Connecting Quantities in Solving Covariation Mathematical Problems in High School Students of Indonesia

A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology

Generalisasi Dalam Penalaran Kuantitatif Siswa Melalui Pemecahan Masalah Pecahan

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