Outcomes and Indicators of Success in First Year Calculus

Beginning and end of module surveys were used to collect data from students on demographics, prior (school) learning experiences and their levels of maths anxiety (following ethical approval from the REC). The surveys also included items asking students to rate their engagement with and experiences of various learning activities and aspects of their Calculus module (e.g. blended-learning, mastery learning approaches). 

Further data on students’ completion of and attainment levels on assessments was gathered through loop. Two postgraduate mathematics students worked on the project as research assistants to clean and then undertake a preliminary analysis of the data collected, following which they summarised their findings. 

This informed a more in-depth data analysis by the project team in order to provide information on the effectiveness of the newly-adopted approaches and the variety of activities used in the modules. 

A research report has been written on our findings in relation to the mastery learning approach used: this has been accepted for presentation at the Research in Mathematics Education in Ireland (MEI) conference (taking place in Oct 2025) and will be published in its proceedings. A report on other aspects of the project will be submitted to the smec 2026 conference.

To provide some context for the description of the impact of the project, ‘mastery learning’ is based on a belief that all students can achieve the same level of content mastery when provided with sufficient time and appropriate resources. Key elements of mastery learning programmes include 
•        the administration of a diagnostic pre-teaching assessment to determine whether students have the prerequisite knowledge and skills to succeed on the programme and the subsequent provision of an opportunity to remediate these gaps before continuing with the programme, 
•        the inclusion of regular formative assessments to allow students’ progress to be monitored systematically and regular feedback to be given (assessment for learning), 
•        the opportunity for students to retake assessments, which can serve as a powerful motivational tool.

The revision of the MS146 & MS150 modules encompassed all of these elements. 

Another feature common to many mastery learning programmes is the provision of learning materials, organised into coherent lesson units, through which students move at their own pace. For MS146/MS150, these lesson units were provided in the form of pre-recorded mini lectures, associated problem sets and supplemental recommended reading which were made available week-by-week on loop. 
 

In relation to the mastery learning approach adopted, 83% of survey respondents agreed or strongly agreed that they found it useful to be able to resit certain components of summative assessment, showing the degree to which they appreciated this initiative and the second chance to succeed that it afforded them. This is supported by data gathered on the number of students who availed of these resit opportunities. For each such assessment component, the majority of students who availed of the opportunity to resit were able to improve on their grade, indicating that the feedback they received and the revision opportunities they were provided (before the assessment was retaken) were successful in helping them remedy their individual learning difficulties.

Furthermore, 68% of respondents found the weekly (optional) formative assessments provided useful, while 58% found the Foundations Unit useful. The latter was made available to students whose pre-teaching diagnostic test score suggested deficiencies in their prerequisite knowledge. It provided them with the opportunity to remediate these deficiencies before continuing with the module with the aim of creating the conditions necessary for successful completion of the module.

MS146 & MS150 were delivered using a blended-learning approach through the provision of learning materials on loop, complemented by weekly face-to-face plenary Q&A sessions and small group tutorials. This blended-learning approach allowed us to be adaptive and flexible in terms of when and where students engaged with the course materials. Also loop’s capacity to make different sets of materials available to different groups of learners effectively affords the creation of individualised pathways through a module. This approach addresses DCU’s strategy to commit to greater “flexibility in provision, pathways, access and curriculum to address a diversity of learner needs and emerging system priorities”. The blended-learning approach seems to be appreciated by students with the majority of our survey respondents reporting that they found the provision of recorded lectures useful (61% agreed or strongly agreed while only 17% disagreed or strongly disagreed) and 78% reporting engaging with these resources every or most weeks.

Findings from the project have been used to inform further minor revisions to the first year MS146/MTH1030 & MS150/MTH1033 Calculus modules, for instance, in terms of the structure and scheduling of summative assessments and the focus of the weekly face-to-face sessions. More broadly, a similar mastery learning approach has now also been adopted on another first year Calculus module taken by students on other programmes (MTH1088).   
 

Our experiences of the initiatives undertaken for the MS146 & MS150 Calculus modules will continue to inform our own teaching both on these modules and in other areas. Moreover, our findings are being shared with other lecturers within the School of Mathematical Sciences with a view to applying what we have learned more widely and incorporating mastery learning and blended-learning approaches to other modules where appropriate.

We will also continue to monitor the effectiveness of the approaches taken by gathering and analysing feedback from students on the relevant modules. 

The research literature reports that obstacles often inhibit the use of mastery-learning as an instruction method in terms of the provision of opportunities to retake assessments – for instance, the production and grading multiple versions of tests/assessments at various stages of a course. While these issues may have seemed insurmountable and prohibitive initially, especially for large group modules, we realised that they could be resolved through the use of technology. For our Calculus modules, Loop facilitated automated grading and provision of feedback, as well as the creation of multiple versions of quizzes by means of its 'randomised question' and 'wildcards within questions' features. An initiative that would previously have been onerous or even impossible was made feasible by the capacity and capability of technology.

Careful thought as to how course materials are organised and made available can facilitate a move from passive to active learning.  The way in which we organised the delivery of the MS146 & MS150 modules, together with their blended-learning nature, meant that a ‘flipped-classroom’ approach was effectively enacted: students were required to watch pre-recorded videos, complete associated problems and engage in formative assessments each week before attending a face-to-face plenary Q&A session and were thus more actively engaged in the learning process. Active learning has been shown to be particularly beneficial across STEM disciplines but also in improving outcomes for women and other underrepresented groups in mathematics. The increased focus on critical thinking skills we adopted also actively involved students as they engaged in inquiry-based activities and worked together to solve non-routine problems during tutorial sessions. This is important as the inclusion and promotion of techniques that support active and participatory learning, critical thinking and the development of key skills is one of the key principles of education for sustainable development.