Algebraic and fractional thinking in collective mathematical reasoning

Abstract

This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the El´konin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic thinking. Further analysis showed that these arguments were characterised by interplay between fractional and algebraic thinking except in the conclusion stage. In the conclusion and the evaluative arguments, these two types of thinking appeared to be intertwined. Another result is the discovery of a new type of argument, identifying arguments, which deals with the first step in task solving. Here, the different types of arguments, including the identifying arguments, were not initiated only by the teachers but also by the students. This in a multilingual classroom with a large proportion of students newly arrived. Compared to earlier research, this study offers a more detailed analysis of algebraic and fractional thinking including possible patterns within the collective mathematical reasoning. An implication of this is that algebraic and fractional thinking appear to be more intertwined than previous suggested.

A Systematic Review on Algebraic Thinking in Education

“…In one study (Pourdavood et al, 2020), the relationship between mental computational activity and algebraic thinking was examined. In another study (Eriksson & Sumpter, 2021), algebraic thinking and mathematical reasoning were investigated. The other focus of the studies was understanding and measuring algebraic thinking.…”

“…In many studies (Agoestanto et al, 2019;Apsari et al, 2020;Obara, 2019), "interview" has been used as a data collection tool to verify and support the data obtained. In-class observation (Afonso & Mc Auliffe, 2019) and video recordings Eriksson & Sumpter, 2021;Venenciano et al, 2020) were also used to determine the algebraic thinking levels of the students.…”

“…Some studies (Agoestanto et al, 2019;Apsari et al, 2020;Obara, 2019) have employed "interview" as a data gathering strategy to verify and substantiate the data acquired. Additionally, in-class observation (Afonso & Mc Auliffe, 2019) and video recordings Eriksson & Sumpter, 2021;Venenciano et al, 2020) were employed to ascertain the students' algebraic thinking.…”

Profil Miskonsepsi Mahasiswa dalam Memahami Konsep Pecahan dengan menggunakan Certainty of Response Index

“…Jika ditinjau darp proses belajar, Stephen & Clements (McKevett et al, 2020) menyatakan bahwa mempelajari pecahan cenderung difokuskan pada aspek prosedural dibandingkan memberikan pemahaman mendalam pada siswa. Kompleksitas pecahan menjadi bagian yang tak dapat diabaikan dalam proses pembelajaran (Eriksson & Sumpter, 2021;Lee & Hackenberg, 2014;McKevett et al, 2020), bahwa tidak ada bidang matematika di sekolah yang kaya, kompleks, dan sulit untuk diajarkan seperti pecahan.…”

The Effect of Numerical Literacy Activities in Problem Based Learning Environment toward Mathematical Reasoning Ability of Elementary School Students

“…The ability to use logic is essential in understanding mathematics. In learning mathematics, students should be able to connect their knowledge with the knowledge they are still learning (Eriksson & Sumpter, 2021). For this reason, students' mathematical reasoning abilities must continue to be developed, which impacts achieving maximum learning outcomes.…”