Investigating mathematical modeling competencies of primary school students: Reflections from a model eliciting activity (original) (raw)
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Mathematical Thinking and Learning
A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to provide opportunity for the prospective teachers to experience the Common Core Mathematical Practice Model with Mathematics and begin to develop competency in modeling. Their work and reflections displayed a range of proficiency in several competencies associated with the modeling process. Examples of their work illustrating these ranges are provided. The prospective teachers expressed both struggle and rewards during the process, and reflected on challenges for teaching modeling. The results suggest that infusing modules in existing courses can be an effective way to elevate prospective teachers from unfamiliarity with modeling to noticeable levels of proficiency in various modeling sub-competencies.
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.
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.
MAA Reviews, MathDL, 2013
This book stems from the 13 th International Conference on the Teaching of Mathematical Modeling and Applications (ICTMA 13). The first part focuses on research into what it means for students to understand models and modeling processes (6 sections, comprising 23 chapters), while the second part considers what is needed for modeling activities to be productive in classrooms (5 sections, comprising 30 chapters). The authors come from many countries: South and the U.S. This book is a veritable fount of information about modeling in classrooms at all levels from elementary through university. In addition, it has chapters dealing with how teachers develop models of modeling (Chapters 30-46) and how new technologies influence modeling in classrooms (Chapters 47-51).
The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a mathematical modelling test. The phenomenographic method and descriptive analysis were used in analysing the data. As a result of the study, it was determined that there was a significant change in the knowledge, skills, and opinions of prospective teachers on mathematical modelling. Therefore, it was considered that it would be appropriate to feature mathematical modelling in the teaching curriculum in universities’ faculties of education for prospective teachers to use in their courses.
Exploring the Nature of Mathematical Modeling in the Early Grades
2020
This working group will engage PMENA members to better understanding the nature of mathematical modeling in the early grades while considering the student perspective and recognizing the importance of teachers knowing their students and the contexts that are meaningful to their students. We will investigate how PK-6 teachers demonstrate the interdisciplinary nature of mathematical modeling, the diversity of mathematical approaches taken by student modelers, and the multiple pathways the teacher can use to elicit den mathematical thinking. We will explore how mathematical modeling bridges equity and social community in teaching and learning mathematics for all students. Exemplar tasks that em ha i ed local con e and a ed in o den f nd of kno ledge and student artifacts ill be ha ed o ill a e he child e ec i e and he de elo men al og e ion. The e topics will facilitate group discussions exploring the learning progression for mathematical modeling thinking and habits of mind that can develop for emergent mathematical modelers from an early grade. Finally, based on the interests of the participants, we will devote work time to finding synergistic collaborative topics to pursue for future research and practice.
Investigating the Role of Modeling Practices on Mathematical Literacy
Bartın University Journal of Faculty of Education
The mathematical literacy or competence notion in PISA deals with the capacity of students to analyze, reason and communicate efficiently as they pose, formulate, solve and interpret mathematical problems in a variety of situations. The best way to improve mathematics literacy is that students have the necessary mathematical knowledge and different problem solving strategies, know when and how to use these strategies, and work with activities that involve different contexts of interest. When considered in this respect, teachers have an important role in the development of students' mathematical literacy. The aim of this study was to investigate the mathematics literacy status of Mathematics Teacher Candidates through PISA questions. The mathematical literacy status of pre-service teachers was examined within the scope of conceptual, operational and contextual questions and in terms of gender, academic grade point average and mathematical modeling. At the same time, semi-structur...
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.
Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers’ difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers’ knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers’ knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.
Developing prospective mathematics teachers’ knowledge of the modelling approach
Scientia in educatione, 2018
Modelling is considered an important approach that requires prospective teachers to be qualified both in modelling competencies and in pedagogical knowledge. In order to investigate the development of these competencies, we examined 49 prospective mathematics teachers studying in a course that included a sequence of modelling activities. During the course, groups of 5–6 participants engaged in these modelling activities as learners. The data include two sets of reports by the prospective teachers on their observations of a recorded modelling activity carried out by a group of five 6th grade students. The first set of reports was collected before the prospective teachers worked on any modelling activities, while the second set was collected after they had engaged in the modelling activities. The findings indicate that, prior to working on modelling activities, most of the prospective teachers described the students’ modelling activity as a linear process and focused on the final math...