How can educators identify teaching models for modules they teach?

This article is written by Dr Houry Melkonian, Senior Lecturer in Mathematics at the College of Engineering, Mathematics and Physical Sciences of the University of Exeter.

With the current advancements in technology, online teaching and learning is becoming an inevitable educational model, which, if used sensibly, can empower the existing educational system both at schools and higher education institutions. This integration becomes advantageous when it is employed to support the traditional interactive teaching and not to diminish it. Online teaching and learning complements in-class teaching endeavour and brings different prospects to the existing experience which has been known and used for centuries. The world is becoming digitalised and nowadays things are done so differently compared to how they were before. The ability to access knowledge and education remotely is an advantage when equipped with the appropriate pedagogy.

So, how do we maintain a healthy and sustainable educational culture within the context of virtualisation? We need to understand that the digital world, with its pros and cons, has blended and settled into the traditional way of living, so it is almost impossible to deny its presence. However, it is our responsibility to decide on the amount of involvement it exerts, the quality of the content it offers and the efficiency in performance it entails.

As educators, it is our duty to identify teaching models, for the modules we teach, that foster the learning needs of our students. Models that enhance not only their ability to perform mathematics, but also encourage resilience and cognitive flexibility through a sense of togetherness.

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Supporting a diverse maths classroom

Most first-year undergraduate mathematics courses for applied sciences cover similar topics, and teaching a multi-disciplinary cohort may sometimes cause some disruptions in the functionality of the module structure. This could be due to many reasons: diversity in maths competency levels, the mixed discipline speciality in the same class, lack of subject-related prior experience, education gap (a deferral in studies; employment; sabbatical gap, etc.), or because of the different entry requirements for each discipline.

Research by (Winberg 2008, p. 364) on the academic identity of engineers in the context of Higher Education, suggests that ‘Teaching practices that are strongly associated with disciplinary norms and values are unlikely to undergo radical changes, but traditional practices can be enhanced as lecturers find ways to balance their engineering and educational identities’. The mixed disciplinarity of diverse maths-abilities represented by a cohort is usually one of the main challenges we face when teaching mathematics.

According to Duncan-Howell et al. (2009), ‘When the lens of identity is applied to the multi-disciplinary cohorts in undergraduate and postgraduate units, it assists in identifying learning needs’. The element of learning through engagement accompanied with an inclusive structure of the curriculum design is key to a diversified, deep and sustainable learning experience. Consequently, a blended learning model was developed to teach these modules, which comprised a set of pre-recorded lectures and in-class targeted-engagement sessions, in addition to the employment of a set of formative and summative online quizzes and a final exam. The motive for this intervention was to foster an approach that effectively aligns with the disciplinarity requisites of each unit by incorporating an attitude that supports diverse subject competency levels within the class cohort.

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Research by Hunt and Chalmers (2013, p. 117) shows that the blended design of a subject (including the learning activities and the teaching material), should be ‘organised in accordance with an effective model of instruction’, that encourages ‘the innovative use of technologies in teaching’. The structured plan of this model helped learners to constructively engage in and reflect on their learning experience contributing to the creation of an inclusive learning environment.

Inspired by (Broughan C. and Hunt L., 2012) citing, ‘Inclusive learning and teaching in higher education refers to the ways in which pedagogy, curricula and assessment are designed and delivered to engage students in learning that is meaningful, relevant and accessible.’ (Hockings 2010, p.1). The inclusivity of the learning environment and the activities of the blended design of the modules were measured against the following five principles:

a) Transition:

Modules were supported by foundational-level quizzes that target certain mathematical abilities and competence. The pre-recorded lectures were designed to help facilitate the transition into higher education studies, which can play an important role in bridging existing gaps in prior education. Also, during the in-class sessions, a selection of maths problems were addressed and the concepts taught were put into practice. Learners appreciated the resourceful nature of this model, and they engaged well with this activity.

b) Playful and intriguing:

The functionality of the online quizzes were analogous simulations of video gaming, which created a joyful aspect of patient learning among the learners. It was found that ‘When playful learning promotes a state of flow, it will increase intrinsic drive because of a sense of effortlessness between joy, learning and acquiring skills, just as we see when progressing through levels of a game’ (Koeners and Francis (2020), p. 153). Learners described learning as ‘stress free and fun’, and quizzes are beneficial ‘to develop skills and confidence’. Occasional in-class group competitions were also incorporated within the sessions which learners expressed an interest for, describing them as mathematically ‘compelling’.

c) Cognitive engagement:

Each quiz comprised a set of randomly chosen problems from a pool of questions designed per topic. Questions were generated in a way where in each reattempt, variable(s) (mathematical symbol(s)) were set to randomly pick a value from a given range. The randomised character of each quiz made it become more of an educational activity, rather than just an assessment, as it increased students’ intellectual engagement and resilience, while the factor of joyous learning was maintained. Learners described the quizzes as ‘ideal’, ‘interesting method of assessment’ and ‘a good way’ to ensure and assess ‘understanding’, expressing an appreciation to the clear and ‘regular structure of hand in dates’ which has helped to ‘plan for the workload’.

d) Feedback:

Each question in the quiz was supported by detailed feedback about how to tackle similar types of mathematical problems. It provided a clear indication of the mathematical concepts used and the topics covered per question. The students were also directed to the pre-recorded lectures related to the same topic to prepare for next attempts. The feedback attached was set to appear after the completion of each attempt regardless of the outcome, which encouraged the students to revise their understanding and reflect on their own performance.

e) Monitoring progress:

The students were able to track their own learning progress through the learning activities involved in the model. Learners expressed an appreciation to the structure design of the blended learning model and how the clarity of instructions informed on ‘what to expect in each session’, highlighting the benefits of the pre-session preparatory stage which helped in having ‘more time to deal with questions’ during in-person sessions.

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This careful and rational consideration of these principles was essential to create a harmonious learning environment that triggers not only the students’ thinking, but it teaches 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. The students received immediate feedback on their formative and summative online quizzes with a clear step-by-step guidance on how to solve similar type of questions. The general feedback provided at the end of each quiz attempt has also provided a clear reference to the learning outcomes.

Additionally, the design of the module was supported by clear ground rules (i.e., students’ responsibilities prior, during and after scheduled hours) communicated on a weekly basis. This was important since it allowed the students to plan for the workload and to manage their self-directed study hours efficiently at each stage of their learning. A research study (Hale, J., Grenny, J. and Swedberg, L., 2020) demonstrates the rules that can be used to ‘avoid a passive lecture and engage the group’. Also, another pedagogical research by Angelo, T. (2012, p. 108) shows that students ‘learn deeply in ways that lead to independence and further learning’ when they take part in ‘deliberative practice’ which according to Hattie (2009, p. 30), cited in (Hunt and Chalmers, 2013, p. 108), is a ‘practice focused on improving particular aspects of the target performance, to better understand how to monitor, self-regulate and evaluate their performance, and reduce errors’.

Example model: Mastering weekly learning goals

Here we provide an example of a model which can help learners acquire a clear picture of overall learning goals for the week.

Pre-session tasks:

Task 1: E.g., Watch Lecture Recordings of the topic taught (e.g., Differential Calculus and Applications).
Task 2: E.g., Attempt and practice 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: E.g., Attempt the problems of the exercise sheet provided; consider working with peers during in-class exercise sessions.

Post-session tasks:

Task 1: E.g., Attempt formative/summative quizzes.
Task 2: E.g., Read, analyse and understand the feedback attached to each question before each re-attempt.

Teaching Models

Factors that support inclusivity in a learning environment (hover mouse to zoom in)


The introduction of the Blended Learning approach as a mode of delivery was essential to guarantee a better student outcome academically as well as on a personal level. It also contributed to achieving a more sustainable implementation of academic resources. The practice of reflecting on this phenomenon was useful as it helped in understanding how educational interventions, whether it is just a ‘simple’ change (i.e., an increase in the number of ‘in-class’ teaching sessions), or a ‘major’ one (i.e. re-designing a module), could have a positive impact on students’ learning experience and the overall module satisfaction. Today, teaching through blended learning has attracted greater attention for various reasons, but most importantly, for the massive educational and professional rewards it brings and embeds into the academic exercise.


  • Angelo, T. 2012, ‘Designing subjects for learning: practical research-based principles and guidelines’, in L Hunt & D Chalmers (eds), University teaching in focus: a learning-centres approach, ACER Press, Melbourne, pp. 93-111.
  • Broughan C. and Hunt L. 2012, ‘Inclusive teaching’, in in L Hunt & D Chalmers (eds), University teaching in focus: a learning-centres approach, ACER Press, Melbourne, pp. 182-198.
  • Duncan-Howell, J. A., McDonald, F. and Lewis, B. (2009), ‘Identity and disciplinarity: Multi-disciplinary student cohorts in higher education’, European Conference on Educational Research, pp. 28-30, University of Vienna, Vienna.
  • Hale, J. and Grenny, J. with commentary from Swedberg, L. (2020), ‘How to Get People (Students) to Actually Participate in Virtual Meetings (Classes)’, Harvard Business Publishing Education, [online] Available at: (Accessed: 8th March 2022)
  • Hattie, J. (2009 ), Visible learning: A synthesis of over 800 meta-analyses related to achievement, Routledge, New York.
  • Hockings, C. 2010, Inclusive learning and teaching: research synthesis, Higher Education Academy, York.
  • Hunt, L. and Chalmers, D. (2013), University teaching in focus: a learning-centred approach, ACER Press, Melbourne.
  • Koeners, M. P. and Francis, J. (2020), ‘The physiology of play: potential relevance for higherEducation’, International Journal of Play 9(1), pp. 143-159.
  • Winberg, C. (2008), `Teaching engineering/engineering teaching: interdisciplinary collaboration and the construction of academic identities’, Teaching in Higher Education 13(3), pp. 353-367.

Acknowledgement: H Melkonian thanks Dr Pallavi Banerjee (Graduate School of Education - University of Exeter) and the Technology Enhanced Learning Department (University of Exeter) for the generous support.

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