A central goal of physics education is to teach problem-solving competency, but the description of the nature of this competency is somewhat fragmentary and implicit in the literature. The present article uses recent historical scholarship on Arnold Sommerfeld and Enrico Fermi to identify and characterize two positions on the nature of physics…

This paper explores the integration of STEM activities in teaching and learning, emphasizing the importance of innovative pedagogical approaches in effectively introducing theoretical concepts, such as variables and functions, and merging them with practical applications. Drawing on existing literature, this study investigates the integration of…

Mathematics is a particularly notable domain in which to understand the role of body movement for improving reasoning, instruction, and learning. One reason is that mathematics ideas are often expressed and taught through disembodied formalisms--diagrams and symbols that are culturally designed to be abstract, amodal, and arbitrary (Glenberg et…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

While one branch of literature is replete with investigations of problem solving and another branch frequently investigates student use of dynamic mathematics environments (DMEs), most of the studies in both of these fields consider whether or not students can solve problems. Far fewer number of studies consider the cognitive processes associated…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be…

This study is to reveal the construction process of student representation in solving of ill-structured geometry problems. The three phases involved in the construction process are interpreting the problem, giving opinions, and concluding. A total of four high school students participated in Surabaya and Sidoarjo in this qualitative study. They…

Productive struggle--expending effort to make sense of something beyond one's current level of understanding--aids in learning mathematics concepts and procedures. In this study, we surveyed 197 parents with children in the 1st to the 5th grade on their beliefs about productive struggle. Beliefs were assessed via questionnaire and rating of a…

We review literature relevant to using technology in the teaching/learning of mathematics to highlight four roles of effective technology use: (a) promoting cycles of proof; (b) presenting and connecting multiple representations; (c) supporting case-based reasoning; and (d) serving as a tutee. We then discuss how they intersect with good…

Conceptual understanding is one of the main concerns of mathematics education. Numerous research have discussed student understanding of algebraic concepts, linear equations in particular. This research was drawn upon in order to develop a new approach for teaching and learning linear equations based on the equivalence concept, one that aims to…

This article discusses the importance of visual models in problem solving, in the scope of rational numbers. We seek to highlight the potential of this approach, as a structuring theme in the mathematical development of students in elementary education and the connections it allows to establish. In order for students to be mathematically competent…