Justification in Mathematics (JiM)

Project Number
OER 01/16 CBL

Project Duration
June 2016 - October 2018

Status
In-Progress

Abstract
Mathematics as a discipline calls for students to be able to examine and evaluate the validity of facts, articulate their reasons for employing a certain method to solve a mathematical task, and substantiate any arguments put forth. So justification, alongside mathematical reasoning, is one of the crucial process skills that enables students to carry out all those activities. Through the activities, students acquire mathematical knowledge and skills. Getting students to justify is also one powerful means to gain deeper insight into their thinking and reasoning. Mathematical reasoning and justification are therefore essential and inseparable components of any mathematical activity. When students are able to analyse, reason and communicate ideas clearly as they perform the mathematical activity, they are considered mathematically literate. Mathematical literacy is crucial for the development of two 21st century competencies as identified by MOE: critical thinking and communication skills. This is why there has been a focus in recent years on mathematical reasoning in the teaching of mathematics in Singapore to better prepare students to meet the immense challenges in the 21st century. Mathematical reasoning and justification are however not new process skills. They have been included under the Processes component in the Singapore Mathematics Framework for many years. Yet many students do not know how to navigate justification successfully. This is confirmed by evidence from GCE O and N level examiners’ reports which frequently highlight student difficulty in constructing a clear and acceptable justification. A recent informal discussion with a small group of mathematics teachers has found them attributing student difficulties to several student-related factors, ranging from inexperience in dealing with justification tasks to lack of good command of the English language to express justifications and unfamiliarity with the use of correct mathematical terminology. The JiM project will set out to investigate the students', as well as the teachers', understanding of justification. It comprises four inter-related stages. The first stage sets out to investigate the ways upper secondary school students (15 – 16 years old) in both the Express and Normal (Academic) courses and secondary school mathematics teachers justify mathematical claims through a paper-and-pencil test. This project will focus on upper secondary school students because it is this group of students who would have been introduced to most of the content specified in the mathematics curriculum. The second stage will explore their judgement of an acceptable justification through a questionnaire comprising tasks used in the paper-and-pencil test. Each task will present a few justifications. The students will then have to pick the one that they believe will receive the best mark from their teacher. Similarly, the teachers will have to select the one that they believe will be awarded the best mark by them.

Funding Source
NIE

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