Exploring mathematical connections of pre-university students through tasks involving rates of change

ABSTRACT

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration.

KEYWORDS:

• Mathematical connections
• rate of change
• slope
• velocity
• speed
• acceleration
• pre-university students

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Crisólogo Dolores-Flores http://orcid.org/0000-0002-2748-6042

Martha Iris Rivera-López http://orcid.org/0000-0001-5597-0758

Javier García-García http://orcid.org/0000-0003-4487-5303

Notes

1 Junior High School in Mexico corresponds with the 7th, 8th and 9th grade, pre-university level includes the 10th, 11th and 12th grade, this level is equivalent to Senior High School of the USA.

Additional information

Funding

This work was supported by Consejo Nacional de Ciencia y Tecnología (Conacyt) and Gobierno del Estado de Guerrero [grant number: 249538].