Pre-service Primary Mathematics Research Articles

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning process. The present research aims to assess the mathematical content knowledge of 194 prospective teachers about fraction word problems faced by students at the Primary Education stage, based on the Mathematics Teachers′ Specialized Knowledge (MTSK) model. By means of the preservice teachers’ written answers, we explored their knowledge and identified the associated error to fraction word problems (one-step and multistep) in which the fraction has a meaning as an operator. Preservice teachers showed some difficulties when working with this content, difficulties that were intensified when they solved multistep problems. The most common error founded in both types of problems is related to the meaning of fraction as operator. The results show a weak prior mathematical content knowledge and as a consequence, it is necessary to establish preventive actions in the training degrees since an insufficient mathematical content knowledge prevents them having a proper didactic knowledge.

The process of problem posing: development of a descriptive phase model of problem posing

The aim of this study is to develop a descriptive phase model for problem-posing activities based on structured situations. For this purpose, 36 task-based interviews with pre-service primary and secondary mathematics teachers working in pairs who were given two structured problem-posing situations were conducted. Through an inductive-deductive category development, five types of activities (situation analysis, variation, generation, problem-solving, evaluation) were identified. These activities were coded in so-called episodes, allowing time-covering analyses of the observed processes. Recurring transitions between these episodes were observed, through which a descriptive phase model was derived. In addition, coding of the developed episode types was validated for its interrater agreement.

The ‘Mathematics Problem’ and preservice post primary mathematics teachers – analysing 17 years of diagnostic test data

In the mathematics education literature, subject matter knowledge is well recognized as the cornerstone of a mathematics teacher’s knowledge base. Though the ‘Mathematics Problem’, the declining standards of students’ mathematical abilities upon entering tertiary education, is well documented in many countries, its effect on preservice mathematics teachers has not yet been analyzed to date. Therefore, we analyze 17 years of data (1997–2013) from a mathematics diagnostic test taken by preservice post primary mathematics teachers (n = 365) during their first mathematics class in a teacher training institution. Our analysis shows that the mathematical knowledge of preservice teachers has declined in all of the assessed core areas of arithmetic, algebra, geometry and calculus, with the more recent years of 2007–2013 showing more rapid decline than the years before. In fact, the average-performing preservice teacher in 1997 achieved a higher score than almost all preservice teachers in more recent years.

Metaphors as boundary objects in preservice primary teacher mathematics education

Metaphors as boundary objects in preservice primary teacher mathematics education

Dynamic learning approach to studying curve stitching on a unit circle

In this article, we report a study on how students learn elementary number theory concepts via pre-constructed activities of curve stitching on a unit circle. By using a dynamic learning approach, students were able to observe and guess the patterns of curve- stitching figures and explore how they were related to the total number of points on the circle and the interval between any pair of connected points. The subjects were pre-service and in-service primary mathematics teachers majored in mathematics or information technology in a BEd programme offered by the Hong Kong Institute of Education. We also discuss some teaching and learning issues related to this topic.

Analysis of Instruments Measuring Values of Mathematics Education

Abstract Research conducted in the affective domain of mathematics education found that affective variables such as attitude, motivation, anxiety, beliefs and values were strongly linked to the quality of teaching and learning of mathematics. Unfortunately values seem to receive the least attention although it is one of the most stable affective domains. This is due to the fact that most people viewed mathematics as value-free, where in fact it has various values related to it. This paper fills in the missing literature on values in mathematics, particularly in the area of values assessment in mathematics education. The literature review indicated the absence of psychometrically based instruments which adopted holistic well defined constructs in mathematics education between the years 1985 and 2012. The five related instruments were reviewed on definitions of constructs and sub-constructs, designs of instruments, theoretical bases, samples, validity and reliability processes. Definitions on constructs and sub-constructs were found to be mainly based on the western education philosophy and the definition by Bishop (1988) is the most referred to and used by researchers from Australia, Turkey, and Taiwan. Four out of five instruments used survey method to measure values in mathematics education. Targeted respondents were found to be mainly the pre-service and in-service primary and secondary mathematics teachers. Only two out of five instruments went through rigorous processes to enhance validity and reliability. This study is an initial step in developing instrument measuring values in mathematics education for the Malaysian education system which is based on faith and religion as stipulated by the National Educational Philosophy which is not aligned with the western culture. The paper proposed the model of instrument which is in line with the Malaysian Educational Development Plan.