These introductory lessons include ideas, techniques, and best practices that I experimented with while teaching in Singapore. All lessons integrated the Concrete-Virtual and Virtual-Pictorial-Abstract (C-V and V-P-A) approach to encourage students to use concrete experiences to construct knowledge, communicate their reasoning, and relate their understandings to real-world mathematics. You can find the links to the detailed lesson plans and my personal reflections below. 

1. Introductory Bar Graph Lesson 

2. Introductory Angles Lesson

Key limitations and considerations include: 

• Using virtual manipulatives as a supplement, complement, or in lieu of concrete manipulatives

  • “Once conceptual understanding is effected with concrete manipulative, the subsequent use of virtual manipulatives seems to facilitate bridging to the abstract” (Hunt et al., 2011, p.6)

  • Providing opportunities for 3D representational awareness since nearly everything students interact with in their daily lives is in 3D

• Choosing the most appropriate virtual manipulatives 

  • Synchronous vs. asynchronous instruction and activities

• Understanding students’ familiarity with technology 

• Understanding the particular group of students and their abilities in thinking, problem-solving, and metacognitive skills

• Factoring in students’ development of fine motor skills, muscle control, spatial thinking and reasoning, hand-eye coordination, directional awareness