Relate before calculate: Students’ ways of experiencing relationships between quantities
The aim of this article is to contribute with findings concerning students’ ways of experiencing general mathematical structures and, in particular, relationships in additive structures.When students discern relationships in additive structures, it may lead to positive consequences for students’ future ability to perform calculations in addition and subtraction tasks. In the study, semi-structured interviews were conducted with students in grades 3, 8, and 9. An illustration showing a set of different quantities was the starting point during the interviews, together with an opening question regarding how the diverse quantities could be equalised. After the students’ discussions, they were asked if this could be described mathematically using written symbols. The students’ expressions concerning the phenomenon “relationships between quantities” were analyzed using phenomenography as an analytical tool. According to phenomenography, there are a limited number of ways in which a phenomenon can be experienced. Further, it is not about exploring how many individuals hold a specific experience that is of interest. In the case of this article, it is about capturing qualitatively different ways of experiencing the phenomenon relationships between quantities. Despite no specific numbers being presented, many students attributed specific numbers and values when expressing relationships between quantities. The students expressed general mathematical structures only to a limited extent and, in those cases, mostly only after encouragement from the interviewer. Following the phenomenographical analysis, the students’ ways of experiencing “relationships between quantities” are: as something that has to be calculated, or as something that has to be related. The first of these was most common in all grades. In this study, one critical aspect was identified, namely, that quantities are related to each other, additively. Instead of introducing mathematics with a focus on answer-oriented tasks, it is essential to introduce mathematics based on general structures such as additive structures. Even if the students are not familiar with such a mathematical “culture”, it is worth it. This was confirmed in our study.
Jane Tuominen, et al. "Relate before calculate: Students’ ways of experiencing relationships between quantities." Didactica Mathematicae 40 (2018): null. <http://eudml.org/doc/292885>.
@article{JaneTuominen2018,
author = {Jane Tuominen, Charlotta Andersson, Lisa Bjorklund Boistrup, Inger Eriksson},
journal = {Didactica Mathematicae},
keywords = {general mathematical structures; relationships; part-whole; additive structures; quantities; phenomenography; ways of experiencing; critical aspect},
language = {pol},
pages = {null},
title = {Relate before calculate: Students’ ways of experiencing relationships between quantities},
url = {http://eudml.org/doc/292885},
volume = {40},
year = {2018},
}
TY - JOUR
AU - Jane Tuominen
AU - Charlotta Andersson
AU - Lisa Bjorklund Boistrup
AU - Inger Eriksson
TI - Relate before calculate: Students’ ways of experiencing relationships between quantities
JO - Didactica Mathematicae
PY - 2018
VL - 40
SP - null
LA - pol
KW - general mathematical structures; relationships; part-whole; additive structures; quantities; phenomenography; ways of experiencing; critical aspect
UR - http://eudml.org/doc/292885
ER -
You must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.
