Math Trail Research Articles

Learning Numeracy around School Environment Supported by Mobile Math Trails using Problem-Based Learning Model

Learning Numeracy around School Environment Supported by Mobile Math Trails using Problem-Based Learning Model

Project-based learning through augmented reality-assisted math trails at Blenduk Church to promote mathematical literacy

Mathematical literacy ability is one of the indispensable abilities in the development of mathematics education today. Currently, the mathematical literacy ability of students in Indonesia is still low. In the field of education, the era of society 5.0 has a great impact, so education must be able to produce human resources who have good mathematical literacy and are able to apply technology well with their literacy abilities. This study aims to determine how the quality of a project-based learning model with math trails assisted by augmented reality in the context of Blenduk Church is able to promote students' mathematical literacy. The research method used is design research. The data were analysed using qualitative and quantitative data analysis techniques. Qualitative data analysis techniques were used to analyse the results of student response questionnaires after conducting project-based learning with augmented reality-assisted math trails at Blenduk Church. Meanwhile, quantitative analysis techniques are used to analyse students' mathematical literacy skills obtained from student test results before and after conducting project-based learning with augmented reality-assisted math trails at Blenduk Church. However, further research is needed on the development of augmented reality-assisted learning instruments and media in other contexts to promote students' literacy skills.

Development of a Mathematical Experience from a STEM and Sustainable Development Approach for Primary Education Pre-Service Teachers

Advances in education are increasingly important, and it is necessary to look for methodological strategies that enhance the value of mathematics in society and promote integrated training that helps students reason critically and rigorously. In this sense, math trails with a focus on STEM and sustainable development are a good resource to connect mathematics with the environment in a transversal way with other disciplines. A total of 35 postgraduate students in secondary education and 30 undergraduate students in primary education participated in this research and received a training course from experts in mathematics teaching. During the experience, the graduate students designed trails that were tested by the undergraduate students after a prior review by three in-service primary teachers. Likert scale questionnaires and open questions were asked of the students to evaluate the training received and the execution of the experience. Likewise, it was also decided to hold a debate with the participants and a guided interview with in-service teachers to assess the possible application of the resource in primary education courses. The results show a very positive assessment of the experience and allow us to support this approach to promote a change in the teaching–learning of mathematics in the last years of primary education.

Literature Review: Inquiry Social Complexity-STEAM Model Based on Math Trail-Virtual Reality Activity Nuanced with Javanese Culture in Improving Critical Thinking Ability

Purpose of the study: Analyse various literature studies on the Inquiry Social Complexity-STEAM model based on Math Trail-Virtual Reality activities with Javanese cultural nuances in improving students' critical thinking skills. Methodology: This research method uses a literature review. Researchers look for data from books, journals, or relevant research articles and include them in the findings and discussion section to reach a conclusion. This research uses descriptive qualitative data analysis techniques to study literature by describing the results of sources obtained either through books, journals, or related research articles. Main Findings: The syntax of inquiry social complexity STEAM learning model based on math trail virtual reality activities with Javanese cultural nuances can be concluded that each syntax encourages students to find, investigate, construct, and integrate the knowledge gained to form better critical thinking skills by accommodating all aspects of students' abilities with different levels to participate in every aspect and step of learning. Novelty/Originality of this study: The addition of the STEAM approach, especially in the Inquiry Social Complexity Learning model, and math trail-based activities using virtual reality technology that has never been done before or integrated into a maths classroom.

DESIGN WORKSHEETS MATH TRAIL TO OUTDOOR LEARNING MATHEMATICS

The aim of the research carried out was to produce valid mathematics trail worksheets for outdoor learning. This research is a design research type of development study using two stages of initial evaluation and formative evaluation from Tessmer, namely prototyping, self-evaluation, expert review, one-to-one, small group, and field test. The research discussed in this article has reached the expert review stage. Data collection uses walkthrough and documentation techniques. The results of this research are math trail worksheets that are valid according to the validator's comments and suggestions and have been declared valid by the validator at the expert review stage. In this research, the results were obtained from validators consisting of 3 lecturers and 2 mathematics teachers. From the language aspect, the average validation result was 3.45 in the very valid category, from the appearance aspect, the average was 3.32 in the valid category, and from the presentation aspect, the average was 3.53, very valid. The average of the 3 aspects obtained was 3.45 in the very valid category. In the LKS material, the result was 3.56 in the very valid category and in the problem solving construct, an average of 3.44 was obtained in the very valid category. So the worksheet developed can be concluded to be valid by the validator.

Out of Doors and Outdoors

Abstract This study examines STEAM learning outside the classroom: necessary preparations, how students cope with ‘mobile learning’, and how motivation changes while working on problem-based STEAM tasks. Further, the authors provide examples of tasks without and with technology support, and compare two mobile applications, Actionbound and MathCityMap, supporting outdoor math trails. The study started in 2017 by collecting data based on observations about students’ motivation and views on outdoor mathematics and has been carried on ever since by collecting data mainly from lower secondary school classes involving 90 students. As the authors also gave workshops on STEAM to pre-service teachers, they questioned the participants (a group of 13) about their experiences with STEAM, technology, and outdoor mathematics. The authors found that ‘mobile learning’ and STEAM tasks enhance students’ motivations, however, pre-service teachers have little experience and may need more support during their studies to implement STEAM and technology, hence the authors aim to design such courses.

Mobile Math Trails: An Experience in Teacher Training with Mathcitymap

Mobile Math Trails: An Experience in Teacher Training with Mathcitymap

Mathematical Modelling Ability in Outdoor Learning with Mobile Math Trails

Mathematical Modelling Ability in Outdoor Learning with Mobile Math Trails

How digital tools support the validation of outdoor modelling results

Mathematical modelling addresses numerous demands of modern mathematics education: The learning of mathematics is directly linked to reality and hence to real objects. At the same time, these tasks are very challenging for students, especially when their own solution process needs to be validated and refined. Studies even show that some students do not validate their results at all. Recent research has shown that digital tools can enhance the support of modelling activities in different ways. In this paper, we take the modelling step of validation into a deeper account and explore the potential of MathCityMap, a digital tool for outdoor mathematics education. Hereby, its automatic solution validation by means of a predefined interval and assessment of the result’s quality are taken into consideration. The modelling activities of secondary school students are compared on a quantitative and qualitative level – half of the students working with the MathCityMap app and half of them solving the tasks without any digital support. Based on the quantitative results, we can see that the app functionalities for elaborative feedback are used to varying degrees: While student groups frequently access the hints, the sample solution is hardly accessed. Moreover, our analysis can show the value of corrective app feedback. Student groups that used the app solved a comparable number of problems, but failed significantly less often than student groups that worked on math trails without the app. The qualitative results show that in particular the solution validation forces the students to proceed with a second run in the modelling cycle if a result is valued as wrong in the app. In addition, it helps the students to assess their own result in terms of its correctness. Based on the combined results, we draw conclusions about the app usage in mathematical modelling tasks.

Active learning strategies for an effective mathematics teaching and learning

Learning is an active enterprise, where three dimensions stand out, cognitive, social, and physical, and, in addition, not all students learn in the same way. Grounded on these ideas, this article reports a study that aims to understand and characterize the performance of pre-service teachers when experiencing active learning strategies during their mathematics classes. The participants were 48 future teachers of primary education (3-12 years old) that experienced paper folding, a gallery walk, and a math trail as active learning strategies. We followed a qualitative methodology, collecting data though observations, written productions, and photographic records. The analysis involved a qualitative and inductive approach resorting to content analysis. The results of the study show that the participants valued these experiences, due to their potential in the development of a diversity of mathematical concepts and abilities, and throughout them showed traits of cognitive, social, and physical engagement. Active learning provided collaborative work and mathematical communication enabling the emergence of different strategies to solve the proposed tasks. The participants were able to reflect and be aware of their ideas, mistakes, and difficulties, as well as of others, in a non-threatening environment, where movement was highlighted for not being a popular dimension in mathematics classes. Although more research is needed, the results encourage the use of active learning strategies as a valuable approach to teaching and learning.

Critical Co-Investigators of Math Trails: Reflections from a Student and Teacher

Critical Co-Investigators of Math Trails: Reflections from a Student and Teacher

Engaging STEM Learning Experience of Spatial Ability through Activities with Using Math Trail

Math trail is a type of outdoor activity conducted in groups. Group members work together, communicate, and find common and best strategies for solving problems. Thus, it combines the use of mathematics in real life with a pleasant walk. Pupils have the opportunity to explore mathematics linked to real objects, solving standard and non-standard problems. Teachers, in turn, can use mathematics in this way as a tool to connect it to other STEM disciplines. This article first describes the results of research aimed at assessing spatial ability and mental rotation in students at technical vocational schools in Slovakia. A stereometry test was solved by 455 students. We then created a mathematical walk aimed at developing students’ spatial ability. The experiences presented in the article may be helpful as other mathematics’ popularization stimuli. We believe that when students are engaged in problem-based learning activities that are related to STEM disciplines, in particular, by connecting with the subjects in the problem context of the real world, STEM disciplines may become more important for students. Interdisciplinary STEM learning imitates authentic real-world problem-solving.

Indonesia-Germany MathCityMap training: Shifting mobile math trails teacher training to a hybrid environment

The purpose of this study is to explore how MathCityMap training for teachers can be designed and implemented in a hybrid setting. Design research has been carried out involving teachers from 34 provinces in Indonesia. A four-day model training program for indoor and outdoor activities in a hybrid setting has been designed. The core concept of designing modeling tasks and math trails, as well as the introduction to MathCityMap, were delivered in a hybrid mode between Indonesia and Germany. The activity continued with the development of MathCityMap Trails in city parks. Post-training activities were conducted in their respective places of origin, in schools, and in city parks. Participants have successfully designed trails in both their schools and the city parks where they live supported using Learning Management System. The findings of the MathCityMap team's review indicate that most of the trails fulfilled the requirements. The trainee teachers then disseminate their knowledge and experience to their colleagues. They also used MathCityMap Trails for classroom learning as well as other activities such as MathCityMap competitions and public educational activities. The hybrid environment helps to accelerate the attainment of training objectives while also broadening the program's reach and network.

The City as a Tool for STEAM Education: Problem-Posing in the Context of Math Trails

This study presents an experience that combines problem-posing and Math Trails in the context of future teachers’ instruction. Pre-service teachers in the third year of their studies were faced with the design of tasks to be included in Math Trails for primary school students. The study analyzes, from a quantitative approach, 117 tasks contained in 11 Math Trails. The analysis was performed on the basis of classification variables (grade, mathematical content and object or real element involved in every task) and research variables which provide information about the nature of the tasks (procedural vs. problem-solving, level of cognitive demand, degree of contextualization, openness and creativity). Additionally, relationships between the different categories of analysis have been studied. The results reveal certain biases in the tasks in relation to the contents addressed (an abundance of tasks with a geometric component and a scarcity of tasks involving algebra or probability concepts). Most of the tasks are presented in a real context. However, a higher percentage of procedural tasks than problem-solving tasks is observed, with a predominance of low openness, creativity and cognitive demand. These results provide useful lines of work to address difficulties faced by future teachers in the STEAM field.

Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails

Tasks are a key resource in the process of teaching and learning mathematics, which is why task design continues to be one of the main research issues in mathematics education. Different settings can influence the principles underlying the formulation of tasks, and so does the outdoor context. Specifically, a math trail can be a privileged context, known to promote positive attitudes and additional engagement for the learning of mathematics, confronting students with a sequence of real-life tasks, related to a particular mathematical theme. Recently, mobile devices and apps, i.e., MathCityMap, have been recognized as an important resource to facilitate the extension of the classroom to the outdoors. The study reported in this paper intends to identify the principles of design for mobile theme-based math trails (TBT) that result in rich learning experiences in early algebraic thinking. A designed-based research is used, through a qualitative approach, to develop and refine design principles for TBT about Sequences and Patterns. The iterative approach is described by cycles with the intervention of the researchers, pre-service and in-service teachers and students of the targeted school levels. The results are discussed taking into account previous research and data collected along the cycles, conducing to the development of general design principles for TBT tasks.

Professional Development in Mathematics Education—Evaluation of a MOOC on Outdoor Mathematics

In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers’ professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished using MOOCs. By taking into account the MOOC “Task Design for Math Trails”, with 93 finalists, we analyze the learning progress of 19 selected case studies from different nations and learning levels by taking into account their answers in a pre- and post-questionnaire and their posts on a specific communication message board, with a special focus on the MOOC’s topics’ task design for outdoor mathematics and the digital tool MathCityMap. The analysis is performed using different quantitative and qualitative approaches. The results show that the teachers studied have benefited from professional development, which is evident in the expansion/evolution of their knowledge from a content, pedagogical, and technological perspective. Finally, we formulate consequences for professional development in STEM education, and conclude the paper with limitations to be drawn and a perspective for further research.

O (re)descobrimento do conhecimento matemático fora da escola a partir de uma trilha de matemática: um estudo fundamentado na etnomodelagem

Este artigo teórico disserta sobre a contribuição do Programa Etnomatemática e a sua conexão com a Modelagem Matemática em sua perspectiva sociocultural por meio da Etnomodelagem no contexto das Trilhas de Matemática, que tem como objetivo principal trilhar caminhos diferenciados para o desenvolvimento dos processos de ensino e aprendizagem em Matemática. As Trilhas de Matemática podem ser consideradas como uma proposta para a ação pedagógica em que os professores utilizam práticas extraescolares para que os alunos possam perceber a aplicação do conhecimento matemático em tarefas realizadas fora das salas de aula, em pontos específicos nas ruas de suas cidades. Desse modo, existe a necessidade do desenvolvimento de módulos de atividades matemáticas extracurriculares, para que se possam criar situações-problema enfrentadas no cotidiano dos alunos e no âmbito escolar, que estão baseadas nos fenômenos presentes na vida diária de suas comunidades, que visam torná-los sujeitos ativos e críticos nos processos de ensino e aprendizagem em Matemática por meio de uma análise reflexiva dos ambientes sociocultural e natural. Então, este artigo busca analisar e discutir a perspectiva sociocultural da Etnomodelagem, que objetiva auxiliá-los na leitura de sua realidade, direcionando-os para uma melhor compreensão de seu entorno por meio da participação nas Trilhas de Matemática, possibilitando-lhes uma interação aprofundada com o próprio mundo.

Students’ modelling processes when working with math trails

Students’ modelling processes when working with math trails

Developing mathematical skills and moral behavior through cultural artifacts: a study of math trail activities at Patan Durbar Square in Nepal

Nepalese education is often inclined towards rote memorization and teacher centered instruction and learning processes. In this regard, how can instruction be actively made more effective as a key idea as researchers take this into account when conducting research in this area. This study forms an ethnographic case study of one of the schools that is transforming itself from a traditional book-based teaching and learning approach to a curriculum specific child friendly learning process. As researchers and teacher trainers we have been involved in teacher training programs for numbers of schools in Nepal. What we have observed during the four years of involvement is that the training solely do not make changes in the school system. This program is helping teachers in making instructional activities that allows them to galvanize their work for increased student involvement. This research also indicates how moral behavior can be developed through math trail activities where students do field work in groups for different objectives. Children develop their understanding through day to day activities where the perspective of different contexts, culture and ethnic groups play a vital role. At this point, we started working on excursion-based instruction. The change in instruction forces them to design activities and projects that demand children to work in outside school context with curricular objectives. It ensured opportunities for participating in hands-on activities and experiential learning. Finally, this research supports the assumption that mathematical knowledge, skill and moral behavior can be developed through different cultural project-based instructional activities and cultural artifacts and practices are key to ensure effectiveness of learning.

LEARNING MATHEMATICAL MODELLING WITH AUGMENTED REALITY MOBILE MATH TRAILS PROGRAM: HOW CAN IT WORK?

The aim of this study is to investigate how an augmented reality mobile math trails program can provide opportunities for students to engage in meaningful mathematical modelling activities. An explorative research design was conducted involving two mathematics teachers and 30 eight grades in Semarang, Indonesia. An Augmented Reality Mobile Math Trails App was created, and several math trail tasks were designed, then students run the activity. Data were gathered by means of participatory observation, interviews, questionnaires, tests, and worksheets. Data analysis began with the organisation, annotation, description of the data and statistic tests. The findings indicate that an educational program was successfully designed, which offered students a meaningful mathematical experience. A mobile app was also developed to support this program. The mobile app with augmented reality features is helpful for students as a tool that bridges the gap between real-world situations and mathematical concepts in problem-solving following the mathematical modelling cycle. The program thus contributes to a higher ability in mathematical modelling. The study identified a link between instrumented techniques in programs and mathematical modelling, as built during the instrumentation process. Further studies are essential for project development and implementation in other cities with different situations and aspects of study.