Investigation of middle school seventh-and eighth-grade students' modelling skills. (original) (raw)
Related papers
Exploring Secondary Students' Modelling Competencies
The Mathematics Enthusiast, 2020
Mathematical modelling is a very important component in the teaching and learning of mathematics. In Malaysia, educators require more exposure to mathematical modelling it is still a new pedagogical method in classrooms. Modelling tasks that require students to construct a mathematical model would be a good start in developing modelling competencies. In this study, the authors investigate three mathematical modelling competencies of secondary students in the state of Selangor through a qualitative analysis of 20 students (divided into four groups) responses based on one modelling task developed by the researchers. The three modelling competencies we focus in this study are (1) making assumption; (2) computing and interpreting solution; and (3) mathematical reasoning. Our findings indicate that most students were basic users while a small percentage reached the proficient users level. With more engagement with the modelling tasks, students would able to acquire the modelling competencies and also develop their modelling skills. This would contribute to the meaningful learning of mathematics.
Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 2022
One of the main purposes of teaching mathematics is to enable students to solve real-life problems and relate mathematics to real-life situations. As a way of facilitating the teaching of mathematics, it should be applied in lessons with mathematical modeling activities of real life problems. The aim of this study is to determine the views of primary school 4th grade students who have experienced mathematical modeling activities for 9 weeks and their suggestions for future modeling activities.The participants of the study are 12 students selected by purposive sampling method among 69 students attending the 4th grade of a public school in Konya in the 2019/2020 academic year. As a result of the study, students; In addition to positive opinions such as increasing the interest of mathematical modeling activities in the lesson, increasing their success in mathematics lessons and improving their social skills, they also expressed negative opinions such as long questions, problems in group work and insufficient time.
Journal of pedagogical research, 2023
Educators have long emphasized the importance of relating mathematics to everyday life situations. During the primary school years, mathematical modeling activities play an important role in this regard. Through a mathematical modeling activity prepared in accordance with the length and area measurement learning outcomes in the primary school 4th-grade mathematics curriculum, the purpose of this study was to determine students' mathematical modeling competencies. The study adopted a qualitative approach using a teaching experiment model. The study involved three students selected from 33 in a state primary school through criterion sampling. Farmer Uncle Hüseyin model eliciting activity (MEA) was given to the focus group to work on, and the whole process was videotaped. Each video recording was transcribed in detail. Transcriptions, student handouts, and researcher field notes were analyzed using the mathematical modeling competencies cycle developed by Blum and Kaiser and adapted by Maaß (2006). Modeling competencies of students were found to be at different levels. Based on the study, the students' warm-up activities, the context of the MEA, and their previous modeling experiences all contributed to the students' representation of different levels of modeling competency. Due to the frequent use of multiple-choice questions in their classrooms, students also had difficulty interpreting qualitative data and understanding the mathematical task they were given.
Mathematical modelling in the early school years
Mathematics Education Research Journal, 2005
In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of 3rd-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (d) How the children developed important mathematical ideas; and (e) Ways in which the children represented their mathematical understandings. Making modelling, generalization, and justification an explicit focus of instruction can help to make big ideas available to all students at all ages. (Carpenter & Romberg, 2004, p. 5). We face a world that is shaped by increasingly complex, dynamic, and powerful systems of information, such as sophisticated buying, leasing, and loan plans that appear regularly in the media. Being able to interpret and work with such systems involves important mathematical processes that have been under-emphasized in many mathematics curricula. Processes such as constructing, explaining, justifying, predicting, conjecturing, and representing, as well as quantifying, coordinating, and organising data are becoming all the more important for all citizens. Mathematical modelling, which traditionally has been the domain of the secondary school years, provides rich opportunities for students to develop these important processes. A model may be defined as "a system of conceptual frameworks used to construct, interpret, and mathematically describe a situation" (Richardson, 2004, p. viii). By engaging in mathematical modelling students identify the underlying mathematical structure of complex phenomena. Because mathematical models focus on structural characteristics of phenomena (e.g. patterns, interactions, and relationships among elements) rather than surface features (e.g. biological, physical or artistic attributes), they are powerful tools in predicting the behaviour of complex systems (Lesh & Harel, 2003).
Mathematical Modelling Education in East and West, 2021
The goal of this study is to recognize the implicit and explicit features in the practices of mathematical modelling with teachers ofpublic schools in Bogotá-Colombia. To do this, a questionnaire was designed, considering two categories, which emerge from the theoretical analysis from the onto semiotic, epistemic and didactic approach. The study was carried out with thirty mathematics teachers who have extensive experience in teaching mathematical modelling in ninth grade. The data was collected using the Google Docs platform and analyzed under descriptive statistics in relation to the theoretical framework.
Group Modelling Competencies of Seventh Grade Mathematics Students
International Journal for Mathematics Teaching and Learning
In recent years many curricula all over the world have included modelling competencies and their promotion (Kaiser & Brand, 2015). There is, however, a need within the current modelling literature domain to investigate what modelling competencies are and how they vary in mathematically weak and strong groups of students. This study examined how mathematical modelling competencies displayed in seventh grade students working in two groups. It was qualitative in nature and it took competencies from existing literature into a detailed analysis of the modelling situation. The findings firmly supported the premise that strong group exhibit higher levels of modelling competencies than weak group. The differences in the levels of groups were more apparent in competencies of a sense of direction, planning and monitoring, understanding, mathematising, and validating. Recommendations for further studies include studies of heterogenous groups and further teacher development in the field of mode...
Students’ mathematical modelling behaviors: Strategies and competencies
2019
Mathematical modelling has recently taken the spotlight in mathematics education as a means to prepare students for the challenges they face in the modern world, and there have been numerous proposals on the modelling cycles describing students' approaches to solve modelling tasks. Within these proposed modelling cycles, researchers emphasize the importance of building a real model to describe the real situation and the application of extra-mathematical knowledge to highlight the relationship between reality and mathematics. However, the concept of extramathematical knowledge and the process to establish a real model have only been described in broad strokes and these descriptions lack details. This thesis aims to add to the descriptions of extra-mathematical knowledge and the process to develop a real model based on empirical data by closely examining students' mathematical Modelling behaviors. To achieve these goals, I administered two rudimentary mathematics complex tasks, a special type of tasks that present a complex situation but allow the audience to apply their well-worn tools in mathematics to establish a solution, to two groups of junior secondary school students. These tasks allow me to tip the balance of between reality and mathematics in mathematical modelling in order to focus on students' modelling behaviors. With regard to the process leading to a real model, my analysis indicates that students hold different intentions in building a real model and these intentions affect the strategies they use and therefore their modelling process and the quality of their solutions deeply. In the analysis of these strategies, I also apply flow theory to understand these intentions. As for extra-mathematical knowledge, my analysis demonstrates that extra-mathematical knowledge is a multi-faceted, complex construct composed of various competencies, that contains different characteristics and can deeply affect students' engagement with the tasks.
A glimpse of reality - what mathematical modelling at secondary school could look like
2013
Any use you make of these documents or images must be for research or private study purposes only, and you may not make them available to any other person. Authors control the copyright of their thesis. You will recognise the author's right to be identified as the author of this thesis, and due acknowledgement will be made to the author where appropriate. You will obtain the author's permission before publishing any material from their thesis.
Introducing Mathematical Modelling to Secondary School Teachers: A Case Study
2008
In the search for an effective approach to make mathematics education relevant, interesting and beneficial to students, mathematical modelling has emerged as an approach that has the potential to enhance students" mathematical thinking in a creative manner. While this may be so, it is important that teachers be adequately prepared so that they too have the experience doing mathematical modelling themselves. This paper discusses an attempt by a group of teachers who were undergoing an in-service course to model a simple knot. The three emergent themes arising from the case study were (1) the experience of creative and collaborative problem solving, (2) learning mathematics through mathematical discourse, and (3) the concern for time in the modelling process.
2021
A mathematical client-driven task known as Model-Eliciting Activities was implemented with students of different levels of achievement (i.e., low, average, and high) at the high-school level. The study strived to prove that Model-Eliciting Activities can be solved by students at any achievement level and be used as an assessment tool. Students collaborated in teams of three to develop solutions that met the client’s needs. The model-solutions were compared and contrasted among several dimensions and achievement levels, considering the quality of the final product-solution based on the Quality Assessment Guide, the intermedia product composed of the type of models created, the strategies followed, and the elements of the mathematical construct. A Model & Modeling perspective was considered as a framework in which students’ teams comprised the cases studied and analyzed. Findings show that students were able to create and elaborate models-solutions regardless of the level of achieveme...