The Role of Teachers’ Knowledge in the Use of Learning Opportunities Triggered by Mathematical Connections

Connecting Mathematics and Science in Primary School STEM Education: Modeling the Population Growth of Species

“…The analysis of intra-mathematical and extra-mathematical connections shows that the establishment of intra-mathematical connections serves as the basis for the establishment of complex extra-mathematical connections, in agreement with (De Gamboa et al [32]). While the EMC1 connection was mediated by the pupils' previous ideas about the phenomenon in a superficial way, in the EMC2 connection the mathematical contents played a semiotic role, based on intra-mathematical connections with treatment in a graphic register and with conversion between tables and graphs.…”

“…The notion of mathematical connection is associated with a deep and lasting understanding of mathematics (Smith, M., Bill, V., and Raith, M. L. [24]; Hiebert and Carpenter [25]). The consensus in the mathematics education community on the importance of making connections for the learning of mathematics led to their explicit incorporation by the National Council of Teachers of Mathematics in the curricular standards of the U.S. (NCTM [26]) and also to the appearance of a line of research devoted to the characterisation of mathematical connections (e.g., Businskas [27]; Duval [28]; Evitts [29]; Eli [30]; De Gamboa and Figueiras [31]; De Gamboa et al [32]; Rodríguez-Nieto et al [33]).…”

El papel de las conexiones intra-matemáticas en el aprendizaje de los números decimales

“…El interés creciente por las conexiones matemáticas ha llevado a los investigadores en Educación Matemática a explicitar una conceptualización para tal noción, permitiendo una caracterización de diferentes tipos de conexiones matemáticas (p. e. Businskas, 2008;De Gamboa et al, 2023;Dolores-Flores y García-García, 2017;Eli et al, 2011;Hatisaru, 2023;Rodríguez-Nieto et al, 2023). En este estudio, atendiendo a la naturaleza de los datos, se utiliza un marco de conexiones construido de manera inductiva (De Gamboa y Figueiras, 2014;De Gamboa et al, 2020). Este marco surge a partir de la observación sistemática de sesiones reales de clase, y presenta diversos tipos de conexiones matemáticas coincidentes con las ya reportadas en la literatura, a la vez que introduce nuevos tipos.…”

Literature review on networking of theories developed in mathematics education context

“…Just as research has been carried out on networking or theoretical connections, there have also been works focused on mathematical connections, which is a relevant topic in mathematics education because the establishment of connections contributes to the understanding of mathematical concepts (De Gamboa et al, 2020Gamboa et al, , 2021. Most of the research work on establishing connections has been carried out on key calculus concepts such as the derivative (Rodríguez-Nieto et al, 2021a, 2021b, 2021c, 2022, the derivative and its relationship with the integral (García-García & Dolores-Flores, 2019, 2021), the rate of change ; and on functions, such as exponential and logarithmic function (Campo-Meneses & García-García, 2020;Campo-Meneses et al, 2021), quadratic function (Businskas, 2008).…”

“…Extended theory of mathematical connections: In the ETC, a mathematical connection is defined from a cognitive process perspective where a person establishes links or relationships between mathematical objects such as meanings, concepts, characteristics, representations, procedures with each other and with real life situations that may be framed in other scientific disciplines (García-García & Dolores-Flores, 2018). Mathematical connections have been classified into two groups (Figure 8 De Gamboa et al (2020) state that extra-mathematical connections are based on intra-mathematical connections and are important for students and inservice teachers in problems-solving in the classroom. Mathematical connections of the ETC is described below:…”