Although our first-year undergraduate mathematics courses in applied sciences cover similar topics, teaching a multi-disciplinary cohort can present challenges. Students have different levels of ability: they may have experienced a gap in their education, or lack the foundational competencies to navigate and engage in a course effectively.

On the other hand, high achieving students already adept at mathematical thinking can be disadvantaged by the slow pace of teaching.

To address these issues, a blended learning model was developed to teach these modules. This comprised a set of pre-recorded lectures and in-person engagement sessions, along with formative and summative online quizzes.

The inclusivity of the learning environment and the blended design activities were measured against the following five principles.

Transition

Modules were supported by foundational-level quizzes that targeted certain mathematical abilities and competence. Pre-recorded lectures helped to facilitate the transition into higher education studies and bridge gaps in prior education. Learners appreciated the resourceful nature of this model.

Playful and intriguing

Playful learning was introduced by creating online quizzes that had similar functionality to video gaming. As a result, students described the learning as ‘stress free and fun’ and believed quizzes were beneficial in developing their skills and confidence. Occasional in-class group competitions were also incorporated.

Factors that support inclusivity in a learning environment

Cognitive engagement

Each quiz comprised randomly chosen problems from a pool of questions designed for each topic. For each re-attempt, variables (mathematical symbols) randomly picked a value from a given range. The randomised nature of each quiz made it more educational activity than assessment, increasing students’ intellectual engagement and mental resilience, while maintaining the theme of playful learning.

Learners described the quizzes as ‘ideal’, ‘an interesting method of assessment’ and ‘a good way’ to assess understanding. They also appreciated the clear structure for submitting work, which helped them to plan their workload.

Feedback

Each quiz question was supported by detailed feedback about how to tackle a similar mathematical problem, and the mathematical concepts used. Students were also directed to pre-recorded lectures relating to the same topic to help them prepare for subsequent attempts. Feedback appeared after each attempt, regardless of outcome, encouraging the students to revise their understanding and reflect on their own performance.

Monitoring progress

The students were able to track their progress through each of the learning activities. They felt this structured design and clarity of instruction kept them informed on what to expect in each session, highlighting the benefits of the pre-session preparatory stage in creating more time to deal with questions during in-person sessions.

The careful consideration of these principles was essential in creating a harmonious learning environment that not only stimulated the students’ thinking, but also taught them how to critically reflect on their own ways of learning.

The interactive involvement of the students comprised the major part of the course design. Students received immediate feedback on their formative and summative online quizzes with clear, step-by-step guidance on how to solve similar types of questions. General feedback at the end of each quiz attempt also provided a clear reference to the learning outcomes.

Additionally, the design of the module was supported by clear ground rules (ie students’ responsibilities prior, during and after scheduled hours), which were communicated weekly. This allowed students to plan their workload and manage their self-directed study hours efficiently at each stage.

A blended model example

Pre-session tasks:

Task 1: Watch lecture recordings of the topic taught (eg Differential Calculus and Applications).

Task 2: Attempt and practise examples displayed in the videos.

During-session tasks:

Task 1: Use interactive seminar sessions efficiently and effectively, reflect on your understanding, and self-assess your progress by the end of each week.

Task 2: Attempt the problems of the exercise sheet provided; consider working with peers during in-class assessments or exercises.

Post-session tasks:

Task 1: Attempt formative/summative quizzes.

Task 2: Read, analyse and understand the feedback attached to each question before each re-attempt.

This structured plan helped learners to constructively engage in their learning experience and reflect upon it, helping to create an inclusive learning environment whilst supporting the students’ diverse subject competency levels.

Reflections

Introducing a blended learning approach was beneficial as it guaranteed a better student outcome, both academically and on a personal level, and helped achieve a more sustainable implementation of academic resources.

Reflecting on this approach has proved useful in helping to understand how educational interventions – whether a ‘simple’ change (such as an increase in the number of ‘in-person’ teaching sessions), or a ‘major’ one (such as redesigning a module) – could have a positive impact on students’ learning experience and overall module satisfaction.

While teaching through blended learning has attracted greater attention for a variety of reasons, it brings the potential for massive educational and professional rewards.

Read more about Dr Melkonian’s approach and the theory underpinning it.