Learning-by-teaching has been identified as one of the more effective approaches to learning. Recently, educational researchers have investigated virtual environments in order to utilize the learning-by-teaching pedagogy. In a face-to-face learning-by-teaching situation, the role of the learners is to teach their peers or instructors. In virtual environments, learners take an active role by teaching a computer agent, which is referred to as Teachable Agent (TA). Although the current TA systems have shown their effectiveness on students' learning, there are some challenges associated with learner-computer interaction methods. One of the most popular interaction methods between the learner and the system is a concept map approach. The learner teaches TA by creating information structures by drawing and editing their concept map. However, the learner can teach TA rather constrained topics, such as concept-related materials or causal effects. It is difficult for TA systems to be utilized in different types of learning along with concept-related areas. Therefore, new approaches or methods for communication between a human learner and TA systems are required. This project aims to suggest a virtual learning-by-teaching environment. A communication method (i.e., a symbol manipulation approach) was adopted in this system. The method facilitates the interaction between the learner and the computer agent, specifically for K-12 students' mathematics learning. The design and development process is described, and future research areas are discussed.