An important aspect of education is to promote higher-order thinking skills to learners. However, in the lecture environment, learners are passively engaged and it is unlikely for higher-order thinking to occur. Although interventions such as "clickers" can be used to increase engagement in lectures, this does not necessarily promote higher-order thinking. Approaches such as collaborative learning are better suited for this but there is little room to use such methods in the short time frame of a lecture. With recent advances in the capabilities of smart mobile devices and their growing penetration rate among the student cohort, it is possible to take advantage of these devices to design a system to promote higher-order thinking skills in the lecture environment. We present the design of a mobile-app-based collaborative learning system named "myVote" and a process for its usage. Our aim is to present a theoretical paper that discusses the relevant learning theories used in designing the system as well as describe a process to use the system to achieve collaborative learning at varying levels of thinking. We demonstrate the usefulness and flexibility of the system through three scenarios involving different levels of thinking, ranging from lower- to higher-order. Although the scenarios are in the context of IT education, the system is versatile enough to be adapted for education in general and also non-educational settings, such as business-like environments. Our contribution is a framework for using mobile apps and collaborative learning theories within a lecture environment to encourage higher-order thinking in learners. Although a potential limitation of the system is that it may not be appropriate for teaching more technical IT materials, such as programming and SQL code snippets, the problem can be recasted in a different format such as pseudocode in order to facilitate teaching in these areas. (Contains 4 figures and 1 table.)