PREP Workshop Report: Expository Writing

A significant part of the job of a mathematician involves writing - between research papers, expository writing, grant applications, letters of recommendation, and materials for our teaching, I know that I spend much of my days writing something or other. Yet most of us are never really trained to write mathematics, and even in our jobs we rarely find time to talk about the actual writing of the mathematics which has taken place. With this in mind, I chose to attend a PREP workshop held by the Mathematical Association of America at their headquarters in Washington, DC dedicated to the art of mathematical exposition. [excerpt

Developing Students Ability To Write Mathematical Proof By Polya Method

Both writing and reading a proof is equally not easy. Some mathematicians attested that students found difficulties in mathematical proving. Mathematics and mathematics education experts like Jones (1997, 2001), Weber (2001), and Smith (2006) found that difficulty in proof writing is due to: lack of theorem and concept understanding, lack of proving ability, and there is a teaching-learning process that unites with the subject. So, it is truly needed that class of writing proof in order to help to generate students’ ability to do mathematical proving. Polya method is going to be that purpose. Keywords: mathematics proof, Polya metho

Rubric supported journal writing in mathematics : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies (Mathematics), at Massey University

Using an Action Research model, this project followed the implementation of a journal writing programme in mathematics, in a grade three (year 4) class. The effect of journal writing, as a formative assessment tool upon a single teacher's approach to the teaching and assessment of mathematics in her textbook-based, whole class mathematics programme, is the focus of the study. The teacher who participated in this project looked towards the journal writing programme to assist her in making changes to her teaching and assessment practises in mathematics, in an effort to bring them in line with her performance based approach to other areas of the curriculum. Using Greenwood's (1993) criteria for mathematical thinking, rubrics were designed to make mathematical thinking a focus of her teaching and assessment in mathematics. Several changes in the teacher's approach to the teaching and assessment of mathematics were observed within the study period and continued sustained changes were realised in the longer term. In addition, aspects of her teaching and assessment practices that were not observed to change are discussed. The suggestion is made that the potential of journal writing to be used to extend and challenge the mathematical thinking of students may be partly dependent upon the depth and breadth of the mathematical knowledge of the teacher

Writing Mathematical Proofs

This text is intended to serve as an IBL style workbook to be used in an undergraduate introductory proof writing course. It covers direct, contrapositive, contradiction, biconditional, existence, uniqueness, induction, and set equality proofs while also covering fundamental topics from number theory, elementary real analysis, functions, and sets with infinite cardinality. It is assumed that the audience has attained a degree of mathematical maturity and has had some exposure to sets and logic, but knowledge of calculus or linear algebra is not required

Detecting multiple authorship of United States Supreme Court legal decisions using function words

This paper uses statistical analysis of function words used in legal judgments written by United States Supreme Court justices, to determine which justices have the most variable writing style (which may indicated greater reliance on their law clerks when writing opinions), and also the extent to which different justices' writing styles are distinguishable from each other.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS378 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Copying equations to assess mathematical competence: An evaluation of pause measures using graphical protocol analysis

Can mathematical competence be measured by analyzing the patterns of pauses between written elements in the freehand copying of mathematical equations? Twenty participants of varying levels of mathematical competence copied sets of equations and sequences of numbers on a graphics tablet. The third quartile of pauses is an effective measure, because it re- flects the greater number of chunks and the longer time spent per chunk by novices as they processed the equations. To compensate for individual differences in speeds of elementary operations and skill in writing basic mathematical symbols, variants on the measure were devised and tested

Use Mathematical Writing as a Practical Approach to Increase Students’ Problem Solving Skills: A Case Study

In mathematical problem solving, students’ written work mostly reveals their mathematical algorithm skills and has very little information about their reasoning skills of the problem solving process. This study extends the features of mathematical writing that integrate the language and mathematical thinking to increase students’ mathematical problem solving skills. The main feature of this study is the use of mathematics writing workbook as a practical approach to guide the students in the problem solving process. Thirty Foundation students in Engineering participated in a six weeks of writing to solve mathematical problems. An exploratory case study analysis was used to examine the written contents of the participants’ mathematical writing workbook, the performance of their formal test as well as their perceptions of mathematical writing. The trace of work in the workbooks showed that mathematical writing has somehow given some impact on these students to visualize, aware and recognize their problem solving behaviors in words

WRITTEN MATHEMATICAL COMMUNICATION SKILLS ON OPEN-ENDED PROBLEMS: IS IT DIFFERENT BASED ON THE LEVEL OF MATHEMATICS ABILITY?

This study aims to describe students' written mathematical communication skills in open-ended problems based on their mathematical abilities. This research was conducted at grade VII-A of SMPN 1 Pamekasan. This research uses descriptive qualitative research. The instruments used were the Mathematical Ability Test (MAT), Written Mathematical Communication Skills Test (WMCST) on open-ended problems, and Interview Guidelines. The results showed that subjects with high and moderate mathematical ability were able to meet three indicators of written mathematical communication skills, namely being able to express mathematical ideas through writing, demonstrate and convey visually; able to understand, interpret and evaluate mathematical ideas in writing, as well as in other visual forms; and able to use mathematical notations in the structure to write down ideas and relationships with situation models in writing. Meanwhile, subjects with low mathematics ability can fulfill 2 out of 3 indicators of written mathematical communication skills, namely being able to express mathematical ideas through writing, demonstrate and convey visually; unable to understand, interpret and evaluate mathematical ideas in writing or other visual forms; and able to use mathematical notations in the structure to write ideas and relationships with situation models.This study aims to describe students' written mathematical communication skills in open-ended problems based on their mathematical abilities. This research was conducted at grade VII-A of SMPN 1 Pamekasan. This research uses descriptive qualitative research. The instruments used were the Mathematical Ability Test (MAT), Written Mathematical Communication Skills Test (WMCST) on open-ended problems, and Interview Guidelines. The results showed that subjects with high and moderate mathematical ability were able to meet three indicators of written mathematical communication skills, namely being able to express mathematical ideas through writing, demonstrate and convey visually; able to understand, interpret and evaluate mathematical ideas in writing, as well as in other visual forms; and able to use mathematical notations in the structure to write down ideas and relationships with situation models in writing. Meanwhile, subjects with low mathematics ability can fulfill 2 out of 3 indicators of written mathematical communication skills, namely being able to express mathematical ideas through writing, demonstrate and convey visually; unable to understand, interpret and evaluate mathematical ideas in writing or other visual forms; and able to use mathematical notations in the structure to write ideas and relationships with situation model