This paper examines the relationship between student engagement and mathematical justification in school settings. Drawing on secondary literature, it defines student engagement across behavioral, academic-cognitive, and social-psychological dimensions, then connects engagement levels to student performance in mathematics. The paper explains mathematical justification as the process of supporting solutions with reasoning and evidence, and argues that engaged students develop stronger justification skills. It surveys instructional strategies — including teachable moments, explorative versus instruction-based teaching, active learning, field-dependent and independent learning styles, and mathematical scaffolding — that teachers can use to increase engagement and, in turn, improve students' mathematical reasoning and sense-making abilities.
The paper demonstrates effective use of secondary source synthesis: the author draws on a range of peer-reviewed works — Parsons & Taylor, Werndl, Michel et al., Brewster & Fager — and weaves them into a coherent argument rather than summarizing each source in isolation. Each citation is used to advance a specific claim, illustrating how literature reviews can build cumulative, evidence-based arguments.
The paper opens with an introduction defining student engagement and situating mathematics as the subject under focus. A methodology section justifies the use of secondary data. The literature review covers types, measurement, and importance of engagement, followed by a dedicated section on mathematical justification. A facilitation section surveys five instructional strategies. The paper concludes with a combined discussion and recommendations section that applies all prior concepts to classroom practice.
The concept of student engagement is strongly related to reduced dropout rates in schools. Students who participate actively in class have strong chances of passing their courses and earning good grades. Despite these advantages, the task of motivating and encouraging students to participate grows more challenging each year. There has been considerable ambiguity in defining the term student engagement. Recently, however, Parsons and Taylor (2011) defined student engagement as the willingness of a student to participate in school activities — such as attending classes, submitting homework, and answering questions posed by the teacher. This definition relates student engagement to compliance (Parsons & Taylor, 2011).
In the same work, Parsons and Taylor also described student engagement as the intensity and quality of a student's participation. This second definition treats student engagement as a comparative scale measuring the emotional attachment a student has to school activities and to the teacher (Parsons & Taylor, 2011).
Student engagement depends on many factors, one of which is teaching style. Teachers can make coursework more interesting and engaging by introducing varied activities and tasks. Effective teaching strategies can therefore act as a lever to boost both grades and participation (Parsons & Taylor, 2011).
Mathematics is a fundamental subject used across almost all scientific disciplines. Its increasing importance has raised the demand for capable mathematicians able to address the challenges of the modern technological era. Accordingly, it is essential that students perform well in mathematics.
There is a strong relationship between good student performance and engagement in school activities. When student engagement increases in mathematics classes, results in the subject improve, better equipping students for the demands of a technology-driven world. Student engagement in mathematics also leads to stronger mathematical justification.
Justification in mathematics means supporting one's work with evidence. Students should be able to justify their solutions in mathematics class. This highlights the importance of student engagement: when teachers encourage participation, students can communicate their mathematical ideas and prove their reasoning. As a result, students improve their mathematical skills, which in turn supports their further studies (Parsons & Taylor, 2011).
The purpose of this study is to investigate the concept of student engagement and to establish a relationship between student performance in mathematical justification and student engagement. The study explores the research of various authors and identifies strategies to encourage students to participate in school activities. The paper centers on two major questions:
1. Why is academic justification an important part of mathematical justification?
2. How does a mathematics student benefit when a teacher uses best practices and student engagement strategies?
Based on these questions, the study investigates the relationship between student engagement and mathematical justification, and identifies strategies that teachers and administrators can employ to improve both.
This study relies primarily on secondary data — data collected by parties not directly involved in the present research, available in written or electronic form. The use of secondary data offers several advantages (McCaston, 2005). First, it is relatively inexpensive to access, store, and use, and is sometimes available at no cost. Second, it allows the researcher to engage with the work of leading authors in the field. Third, exploring secondary data provides direction and a guiding framework for the research. Finally, secondary data is relatively easy to obtain through internet searches that yield a large volume of relevant articles (McCaston, 2005).
A potential drawback of secondary data is the risk of irrelevancy, since other authors' work may not align precisely with the research topic. To minimize this risk, considerable care was taken in selecting articles for this study. Only peer-reviewed work was included, and outdated sources were excluded.
Student engagement, as defined by Parsons and Taylor (2011), is the willingness of students to engage in school activities. A second definition frames it as the intensity with which a student participates in those activities. The latter definition is more qualitative and allows student engagement to serve as a comparative scale (Parsons & Taylor, 2011).
Parsons and Taylor describe three types of student engagement (Parsons & Taylor, 2011):
Behavioral Engagement refers to non-academic engagement — participation in extracurricular activities and sports.
Academic-Cognitive Engagement refers to purely academic involvement. A student is considered academically engaged when he or she submits homework on time and participates actively in class.
Social-Psychological Engagement refers to the emotional attachment a student develops to the school, teachers, and peers (Parsons & Taylor, 2011).
Student engagement is difficult to measure with precision, as the degree of interest a student has in a given topic cannot be assessed with complete accuracy. Nevertheless, Parsons and Taylor (2011) identify two techniques used by researchers to measure engagement levels:
Self-report: Students who are interested in a subject report that interest to the researcher and answer questions about it. Students who are not interested can similarly report their situation and provide reasons (Parsons & Taylor, 2011).
Teacher rating: The teacher's perspective is used to gauge academic engagement. According to teachers, class participation and grades are the primary indicators of engagement, and teachers' remarks on these dimensions provide substantial information about a student's engagement level (Parsons & Taylor, 2011).
Mathematical justification refers to the act of supporting mathematical claims and ideas using facts and formulae. It is crucial because it forms the foundation of mathematical learning and practice. The entire discipline of mathematics rests on proofs and rigorous calculation; students who cannot justify their steps and calculations will never master the subject (Holdan & Lias, 2009).
Justification matters to the teacher as well. In most cases, the teacher is less interested in the final answer than in the method by which the student arrived at it. Mathematical justification of steps and formulae is therefore an important part of mathematical study (Werndl, 2009; Members of The National Council of Teachers of Mathematics, 2009).
As described in the work of Charlotte Werndl (2009), mathematical reasoning involves the following three steps, which do not necessarily occur in a fixed order:
Conjecturing: The student uses given facts or assumptions to draw preliminary conclusions about the problem. These conclusions are tentative and are not yet certified as correct (Werndl, 2009).
Generalizing: The student identifies a relationship between the current problem and previously solved problems, seeking a common link so that similar problems can be solved in a consistent way (Werndl, 2009).
Justifying: The student explains the reasoning behind each step taken. Justification completes mathematical reasoning. If a student does not understand why a particular formula applies, any reasoning offered will be hollow. The student may arrive at the correct answer, but the method will be flawed (Werndl, 2009).
Mathematical reasoning supports the student in proving claims. If a student asserts that a certain formula applies to a given scenario, reasoning is required to convince others. Without it, the claim amounts to little more than a guess. Martin et al. also identify mathematical reasoning as the basis of sense-making in mathematics: a student who can provide correct mathematical reasoning has genuinely understood the underlying concept (Members of The National Council of Teachers of Mathematics, 2009).
The connection between mathematical reasoning and student engagement is direct. A student who is deeply engaged in studies and school activities will be better at mathematical justification, because engagement drives genuine understanding of concepts and formulae. Moreover, the engaged student will communicate justifications more effectively as a result of greater confidence. Academic engagement thus benefits mathematics students in both forming and articulating their justifications (Members of The National Council of Teachers of Mathematics, 2009).
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