Assigning mathematics instruction time in secondary schools: what are the influential factors?

Similar to countries such as the Netherlands and the United Kingdom, secondary schools in Ireland can decide how to allocate instruction time between curriculum subjects. Although there are national guidelines available from the Department of Education and Skills (DES), the majority of schools make their own decisions about how much time they allocate to different subjects. This results in variations between the amounts of time allocated to teaching mathematics in different schools and between different year and class groups within the same school. Decisions regarding time allocation are generally taken by the school management. This means that the ethos of the school and the individual opinions of school management can determine the amount of mathematics that students experience throughout their second level education. The aim of this study is to evaluate the most influential factors that management considers when assigning instruction time in Irish secondary schools. For the purpose of this research, seven possible factors were identified and 400 deputy principals from a stratified sample of secondary schools around Ireland were asked to select their top three. Timetabling constraints, the availability of mathematics teachers and the perceived importance of the subject were found to be the most influential factors.     

Assessing ‘functionality’ in school mathematics examinations: what does being human have to do with it?

This article analyses aspects of the process of developing ‘functional’ assessments of mathematics at the end of compulsory schooling in England. A protocol that was developed for scrutinising assessment items is presented. This protocol includes an indicator of the ‘authenticity’ of each assessment item. The data are drawn from scrutiny of 589 assessment items from thirty-nine formal unseen examinations taken by students aged sixteen, and the article illustrates ways that mathematics is presented in different contexts in examinations. We suggest that currently the ‘human face’ of the questions may serve to disguise routine calculations, and we argue that, in formal examinations, connections between mathematics assessments situated in context and functional mathematics have yet to be established.     

Declining participation in post-compulsory secondary school mathematics: students’ views of and solutions to the problem

We analysed multivariable calculus students' meanings for domain and range and their generalisation of that meaning as they reasoned about the domain and range of multivariable functions. We found that students' thinking about domain and range fell into three broad categories: input/output, independence/dependence, and/or as attached to specific variables. We used Ellis' actor-oriented generalisations framework to characterise how students generalised their meanings for domain and range from single-variable to multivariable functions. This framework focuses on the process of generalisation – what students see as similar between ideas in multiple contexts. We found that students generalised their meanings for domain and range by relating objects, extending their meanings, using general principles and rules, and using/modifying previous ideas. Our findings suggest that the domain and range of multivariable functions is a topic instructors should explicitly address.     

Time allocated to mathematics in post-primary schools in Ireland: are we in double trouble?

Mathematics educators and legislators worldwide have begun placing a greater emphasis on teaching mathematics for understanding and through the use of real-life applications. Revised curricula have led to the time allocated to mathematics in effected countries being scrutinised. This has resulted in policy-makers and educationalists worldwide calling for the inclusion of double class periods on the mathematics timetable. Research from the United States suggests that the introduction of double or block periods allow for the objectives of revised curricula to be realized. The aim of this study, which is set in the school context, is first to ascertain if schools in Ireland are scheduling double periods for mathematics at both lower post-primary level (Junior Cycle) and upper post-primary level (Senior Cycle). It also seeks to determine if there is a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods and to get insights from teachers in relation to their opinions on what can be achieved through the introduction of such classes. Questionnaires were sent to 400 post-primary schools (approximately 1600 teachers) which were selected using stratified sampling techniques. It was found that 8.7% of mathematics teachers reported the provision of double periods at Junior Cycle while 55% reported that double periods were included on their timetable at Senior Cycle. The study also identified a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods. Finally, teachers felt that double periods allowed for new teaching methodologies, which were promoted by the revised curricula, to be implemented and teaching for understanding was also more feasible. In essence, it was found that double periods have an influence on the mathematical experience of post-primary students as well as the teaching approaches employed.     

Running to keep up with the lecturer or gradual de-ritualization? Biology students’ engagement with construction and data interpretation graphing routines in mathematical modelling tasks

Through a commognitive lens, we examine twelve first-semester biology students’. engagement with graphing routines as they work in groups, during four sessions of Mathematical Modelling (MM). We trace the students’ meta-level learning, particularly as they fluctuate between deploying graphs for mere illustration of data and as sense-making tools. We account for student activity in relation to precedent events in their experiences of graphing and as fluid, if not always productive, interplay between ritualised and exploratory engagement with graph construction and interpretation routines. The students’ construal of the task situations is marked by efforts to keep up with lecturer expectations which allow for changing degrees of student agency but do not factor in the influence of precedent events. Our analysis has pedagogical implications for the way MM problems are formulated and also foregrounds the capacity of the commognitive framework to trace de-ritualization and meta-level learning in students’ MM activity.