Modeling as a Decision-Making Process

Bleiler-Baxter, Sarah K.; Stephens, Diane; Baxter, Wesley A.; Barlow, Amy

doi:10.5951/teacchilmath.24.1.0020

Cited by 8 publications

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“…Bleiler‐Baxter and colleagues (2017) developed a task aimed at promoting modeling with mathematics as a means to experience modeling as a decision‐making process. Students were provided with wait times for amusement park rides during various moments in a day; albeit, the table with the wait times is incomplete.…”

Section: Background and Conceptual Framesmentioning

confidence: 99%

A design process for developing agricultural life science‐focused model eliciting activities

Bostic

Clark

et al. 2020

School Sci & Mathematics

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INTRODUCTION Agricultural literacy, inclusive of technology, science, and human dimensions, involves civic, cultural, and economic understandings (Knobloch et al., 2007; Meischen & Trexler, 2003). Organizations such as the National Center for Agricultural Literacy (NCAL, 2013) have emphasized the importance of agricultural literacy in the K-12 classrooms, moving past narratives of farming to a more national global perspective of conservation and humanitarian issues (Hess & Trexler, 2011; Trexler et al., 2013). The NCAL defines meaningful agricultural life science (AgLS) topics through five key topics: (1) agriculture and the environment, (2) culture, society, economy, and geography, (3) food, health, and lifestyle, (4) plants and animals for food, fiber, and energy, and (5) science, technology, engineering, and math. However, classroom implementation of complex socio-scientific issues is challenging, particularly at the elementary level (Sadler & Zeidler, 2005) where teachers might struggle to glean what foundational knowledge young students have. One potential avenue for growing student resources and understandings of complex AgLS topics is the use of Model-Eliciting Activities (MEAs; Lesh et al., 2000). Aligned with both Common Core State Standards Initiative ([CCSSI]; 2010) and Next Generation Science Standards ([NGSS]; 2013), MEAs are important mathematical tasks that promote reasoning, sensemaking, problem solving, and content learning (Consortium for Mathematics and its Applications

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Section: Background and Conceptual Framesmentioning

confidence: 99%

A design process for developing agricultural life science‐focused model eliciting activities

Bostic

Clark

et al. 2020

School Sci & Mathematics

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“…We did not interpret the groups to make full use of the contexts. The last column in Table 2 shows that we interpreted the performance of most of the activities as applications of mathematics (or "modelling mathematics" (Bleiler-Baxter et al, 2017)). Many of the essential modelling subprocesses (Blum & Leiß, 2006) lacked in the descriptions of the implementations.…”

Section: Discussion Of Resultsmentioning

confidence: 99%

“…The problem was introduced in three steps: presenting a newspaper article to familiarise the students with the problem, asking readiness questions about the article, and presenting the problem and corresponding data tables. Bleiler-Baxter et al (2017) stressed the importance that teachers distinguish between "modelling mathematics" and "modelling with mathematics" to meet expectations in the 2010 curriculum (the Common Core State Standards Initiative). They claimed that using concrete materials or visual representations to illustrate mathematics ("modelling mathematics") is not comparable to the activity of making assumptions and approximations to analyse and conclude about a real-world situation, the practice of authentic modelling.…”

Section: Literature Reviewmentioning

confidence: 99%

Using decision theory to understand preservice teachers’ implementations of mathematical modelling

Hansen

2022

Math Ed Res J

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In this study, we aim to explain choices that groups of preservice teachers made to implement modelling tasks in primary school. We found that the preservice teachers decided to facilitate everyday-inspired contexts for the tasks and that this could be explained by their reasoning that modelling is supposed to be an activity close to reality. Essentially, the groups preferred two different approaches to introducing students to the tasks: (1) by inviting students to physically participate in situations related to their local communities that were familiar to them (e.g. trash picking), and (2) through pre-structured problems that were recognisable to students (e.g. estimation of the number of beads in an irregular box). We found evidence that the preservice teachers tended towards avoiding focusing on possible mathematical answers to the tasks. This could be explained by lacking experience with how to find approximate solutions, or that the preservice teachers were engaged in observing students’ solution strategies and mathematical behaviour.

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“…Some of the reason why teachers so rarely do such tasks, as Borromeo Ferri (2010) states, are time constraints and their perception that mathematical modelling tasks are to demanding or complex. Research shows that when students have opportunities to do mathematical modelling tasks, they are able to reason mathematically, improve their problem-solving abilities and make connections to real-world problems (Bleiler-Baxter et al, 2017). Mathematical modelling is undoubtedly challenging and complicated for teachers, but many studies show and point to its benefits for students.…”

Section: Discussionmentioning

confidence: 99%

What Is and What Is Not Mathematical Modelling in Primary School: Opinions of Slovenian and Croatian Primary School Teachers / Što jest, a što nije matematičko modeliranje u razrednoj nastavi: mišljenja slovenskih i hrvatskih učitelja razredne nastave

Sabo Junger,

Lipovec

2022

Croatian Journal of Education

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Every day we encounter various obstacles and tasks that we solve with the help of mathematics, consciously or unconsciously. Mathematical modelling in teaching is an important interactive process in which students are introduced to problems from the real world and their environment. All education is slowly striving for students' better education on problem-solving, including mathematical modelling, but this is not yet the practice in the lower grades of elementary schools. Our research describes what mathematical modelling actually is in primary school and its advantages and difficulties, all from the point of view of the primary school teachers themselves. The research was conducted on 1000 primary school teachers from Croatia and Slovenia. The study results show almost no differences according to the originating country even though we expected some since Slovenia had previously introduced mathematical modelling into its curricula. Results also indicate that teachers are fairly uneducated on the topic of mathematical modelling, and the difficulties that could arise from its introduction into the classroom. It can also be reported that teachers are eager and ready for education on a given topic, and in the vast majority show interest in additional much-needed education.Key words: cross-country comparison; mathematical models; mathematics; teacher education; primary school---Svakodnevno se susrećemo s raznim preprekama i zadatcima koje svjesno ili nesvjesno rješavamo uz pomoć matematike. Matematičko modeliranje u nastavi važan je interaktivan proces u kojem se učenici upoznavaju s problemima iz stvarnoga svijeta i svojega okruženja. Čitavo obrazovanje polako teži boljem obrazovanju učenika o temi rješavanja problema, uključujući matematičko modeliranje, ali to još nije praksa u nižim razredima osnovnih škola. Naše istraživanje opisuje što je zapravo matematičko modeliranje u osnovnoj školi te njegove prednosti i poteškoće, sa stajališta učitelja razredne nastave. Istraživanje je provedeno na 1000 učitelja razredne nastave iz Hrvatske i Slovenije. Rezultati istraživanja ne pokazuju gotovo nikakve razlike prema zemlji podrijetla, iako smo ih očekivali budući da je Slovenija prethodno uvela matematičko modeliranje u svoje kurikule. Rezultati također ukazuju na to da su učitelji prilično neobrazovani po pitanju matematičkoga modeliranja i poteškoća koje bi mogle nastati njegovim uvođenjem u učionice. Također se može izvijestiti da su učitelji željni i spremni za obrazovanje o navedenoj temi te u većini pokazuju interes za dodatno, prijeko potrebno, obrazovanje o matematičkom modeliranju.Ključne riječi: matematika; matematički modeli; međudržavna usporedba;obrazovanje učitelja; osnovna škola

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Modeling as a Decision-Making Process

Abstract: Using simplification, relationship mapping, and situation analysis as a framework, we offer vignettes of student discussions about the Theme Park task to highlight their key choices as they model with mathematics.

Cited by 8 publications

References 0 publications

A design process for developing agricultural life science‐focused model eliciting activities

A design process for developing agricultural life science‐focused model eliciting activities

Using decision theory to understand preservice teachers’ implementations of mathematical modelling

What Is and What Is Not Mathematical Modelling in Primary School: Opinions of Slovenian and Croatian Primary School Teachers / Što jest, a što nije matematičko modeliranje u razrednoj nastavi: mišljenja slovenskih i hrvatskih učitelja razredne nastave

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