Athens Journal of Education - Volume 7 - Issue 3 - The Impact of Mental Computation on Children’s Mathematical Communication, Problem Solving, Reasoning, and Algebraic Thinking

Oct 15, 2026

Uploaded by Marglet

The study examines how mental computation in a third-grade classroom relates to algebraic thinking, mathematical reasoning, and students’ problem-solving and communication. Using classroom observations, field notes, students’ verbal and written communications, and interviews, the research runs in two phases: establishing talk roles, rules, and expectations, then building a classroom community that supports participation, active listening, students’ voices, and multiple perspectives. Results indicate verbal communication strengthens problem-solving, reasoning, and communication. The findings also emphasize the need for competent, caring teachers who understand students’ backgrounds and have strong pedagogical knowledge.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

AccessFree to download

Introduction

Literature Review

Methodology and Study Context

Results

Discussion and Significance

Athens Journal of Education-Volume 7, Issue 3, July 2020 – Pages 241-254 The Impact of Mental Computation on Children’s Mathematical Communication, Problem Solving, Reasoning, and Algebraic Thinking By Roland Pourdavood􀀍 , Kathy McCarthy† & Tess McCafferty‡ Moving from arithmetic to algebraic thinking at early grades is foundational in the study of number patterns and number relationships. This qualitative study investigates mental computational activity in a third grade classroom’s and its relationship to algebraic thinking and reasoning. The data sources include classroom observations, field notes, students’ verbal and written communications, and interviews. The study occurs in two phases; phase one includes establishing roles, rules, and expectations regarding how to talk about mathematical ideas; and phase two involves creating a classroom community that encourages participation, active listening, students’ voices, and multiple perspectives. The findings of the study suggest that students’ verbal communication enhances their problem-solving, reasoning, and communication. In addition, the findings suggest that creating learning opportunities for all students to do sophisticated mathematics requires competent and caring teachers who know their students’ backgrounds, who understand the subject, and have strong pedagogical knowledge. Keywords: algebraic reasoning, communication, children’s mathematical thinking, mental computation. Introduction Mental computation refers to the process of working on a problem in one’s head and obtaining the exact or approximate answers mentally, without the use of paper, a calculator, or other means (Jordan, Glutting, & Ramineni 2010; Heirdsfield, 2011). Mental computation is important for children to learn, but the focus should not be limited to helping children develop mental computation strategies, but also to develop higher order thinking, reasoning, and critiquing, along with the ability to make sense of numbers and number operations (Carvalho & da Ponte 2013; Erdem & Gurbuz, 2015; Erdem, Gurbuz, & Duran, 2011) . It isan important thinking process because it enables children to: learn more in depth about how numbers relate to each other, make decisions about procedures, and create strategies for calculating (Tsao, 2011; Everett, Harsy, Hupp, & Jewell, 2014). Mental computation is the most common form of computation used in everyday life. It is used for quick calculations and estimations, but is more than 􀀍Professor, Cleveland State University, USA. †Third Grade Teacher, Campus International School, USA. ‡Third Grade Teacher, Campus International School, USA. [https://doi.org/10.30958/aje.7-3-1](https://doi.org/10.30958/aje.7-3-1) doi=10.30958/aje.7-3-1 Vol. 7, No. 3 Pourdavood et al.: The Impact of Mental Computation … mental arithmetic. When calculating mentally, students select from a range of strategies depending on the presenting problem (Bacon, 2012). As they develop their repertoire of strategies, students select those that are more efficient and effective for them. These thinking processes provide learners opportunities to construct relational understanding and algebraic thinking (O’Nan, 2003; Parrish, 2010, 2011; Obersteiner, Reiss, & Ufer, 2013; Morin, 2017). Algebra has been considered advanced mathematics for centuries and is typically taught in early middle school in the United States with the rationale being that middle school students have already mastered fundamental arithmetic and are prepared to use their cumulative acquired knowledge in mathematics towards algebraic concepts (Katz & Parshall, 2014; Pyke & LeFevre, 2011) . Research has informed academia of the advantages of introducing algebraic thinking in early elementary years to foster a formidable learning of vital mathematics concepts in which children can then understand and apply to their future education (Gargiulo & Metcalf, 2013) . The National Council of Teachers of Mathematics (N

FAQs

What does “mental computation” mean in this study?

It refers to working on a problem in one’s head to obtain exact or approximate answers without paper, a calculator, or other tools.

How did the study investigate the relationship between mental computation and algebraic thinking?

It used a qualitative approach with classroom observations, field notes, students’ verbal and written communications, and interviews across two phases of classroom setup and community building.

What key finding links mental computation to students’ learning outcomes?

Students’ verbal communication was found to enhance problem-solving, reasoning, and mathematical communication, supporting development of algebraic thinking.

Oct 15, 2026

Uploaded by Marglet