Pre-Service Teachers’ Implementation of Physical and Virtual Manipulatives

With the accessibility of virtual manipulatives (apps and applets) in classrooms, it is necessary to reassess how these advancements may impact the learning process and research efforts. A possible approach is a framework that combines the well-known concrete (C), pictorial (P) and abstract (A) learning levels (CPA) with a proposed Virtual-level (V) (CPAV). The V-level includes digital and dynamic (non-static) components, which allows students’ virtual interaction with digital tools such as images, words, numbers and graphs. It also involves different sublevels: Virtual-Concrete, Virtual-Pictorial and Virtual Abstract. The framework will be discussed and demonstrated using easily available apps and applets (for example, NCTM Illuminations and National Library of Virtual Manipulatives). It is very important to understand what is involved in a virtual manipulative tool in order to provide for students’ learning needs. We will discuss mathematics pre-service teachers’ understanding and possible misconceptions of the framework while developing lesson plans and assessment activities. Several improvements are recommended in order to avoid participants’ misunderstandings. Most pre-service teachers demonstrated the ability to identify the levels involved in the instructional activities for the C, P and A levels in pre-, post and follow-up-tests, and lesson plans, but had a harder time with the V-sublevels. Participants are encouraged to bring their own iPads and computers.