This theoretical paper describes how Community-based Mathematical Modeling can advance equity and cultivate civic empathy in elementary school settings. We provide a framework for community-based mathematical modeling instruction consisting of five goals: facilitating connections, fostering engagement, promoting rigor, cultivating civic empathy,…

This paper brings together studies on the future and design methodologies to develop a novel proposal for prospective analysis in the field of education. We apply mixed research methods in combination with design methodologies to open up new routes for studying the evolution, impact and behaviour of trends in future scenarios. Our research is…

To address the upcoming reform curriculum initiative following competency-based learning in Vietnam, this study examines how variations of a contextualized task allow students to experience the mathematical modelling process. We explore how Grade 10 students respond to tasks with different levels of authenticity when they first attempt such tasks.…

In 2016, we (seven high school students from a school in Plock, Poland) participated in the CERN Beamline for Schools competition. Together with our team coach, Mr. Janusz Kempa, we submitted a proposal to CERN that was selected as one of two winning proposals that year. This paper describes our experiment from the early days of brainstorming to…

While aggregate reasoning is a core aspect of statistical reasoning, its development is a key challenge in statistics education. In this study we examine how students' aggregate reasoning with samples and sampling (ARWSS) can emerge in the context of statistical modeling activities of real phenomena. We present a case study on the emergent ARWSS…

The use of method of imitational modeling to study forming the empirical knowledge in pupil's consciousness is discussed. The offered model is based on division of the physical facts into three categories: 1) the facts established in everyday life; 2) the facts, which the pupil can experimentally establish at a physics lesson; 3) the facts which…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Drawing strategies are widely used as a powerful tool for promoting students' learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling…

In this article we analyse: 1) one-component models of training; 2) the multi-component models considering transition of weak knowledge in strong and vice versa; and 3) the models considering change of working efficiency of the pupil during the day. The results of imitating modeling are presented, graphs of dependences of the pupil's knowledge on…

The authors explore how one teacher uses play and enacts the Effective Teaching Practices as a way to increase student engagement and autonomy and to meet learning goals when teaching mathematics with interactive simulations.

Many studies mentioned the deductive nature of Mathematical Induction (MI) proofs but almost all fell short in explaining its potential role in the formation of the misconceptions reported in the literature. This paper is the first of its kind looking at the misconceptions from the perspective of the abstract of the deductive logic from one's…

This study was designed to examine predictors of instructional beliefs related to problem solving that influence mathematics in-service teachers' practices in the Chilean context. A total of 713 in-service mathematics teachers from various elementary schools participated in the survey study during 2015 and 2016. Results showed that teachers'…

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

The goal in this article is to support teachers in better understanding what it means to model with mathematics by focusing on three key decision-making processes: Simplification, Relationship Mapping, and Situation Analysis. The authors use the Theme Park task to help teachers develop a vision of how students engage in these three decision-making…

Students of mathematics teacher candidates are required to have good math and communication skills. Therefore, students of mathematics teacher candidates need to have good imagery modalities like the rational-irrational function graph. To get the imaginary student of mathematics teacher candidate in describing the rational-irrational function…