Research and information about mathematics and learning mathematics has evolved over the last hundred years. In the first half of the 20th century, much of the attention was paid to computational approaches such as hands-on training and incidental learning (Brownell, 1947; Thorndike, 1924). This emphasis can certainly be attributed to the lack of available technology coupled with society's needs for efficient computing (Jones et al., 2002). The development of new mathematics in the second half of the 20th century represented a shift in position for mathematics educators and researchers. The shift occurred towards the structure of mathematics (Jones & Coxford, 1970), as well as reflecting current needs and the state of mathematics at that time. Questions have arisen about what the focus of the content should be and what the class structure should entail. Advances in knowledge and technology characterize the 21st century. Kiong and Yong (2001) point out that these advances highlight the need for a restructuring of mathematics education. Researchers accentuate imaginative methods in learning and teaching mathematics that can promote problem-solving skills, higher-order thinking skills, independent learning, collaboration, and communication skills. The skills and processes emphasized in the mathematics curriculum in the past will not be sufficient in the knowledge-based era now present in our world. What is certain is that mathematics is indispensable for generalizing, modeling and understanding the world in which we all function and interact. Furthermore, mathematics has paved the way for increased scientific and technological advancements. The end result is that there has been considerable attention to mathematics... halfway through the article... when a mathematical concept is presented under conditions in which the relevant variables remain constant but the irrelevant variables are changed the ability to generalize it has improved. The principle of constructiveness states that students should be allowed to construct their own concepts by manipulating concrete materials in order to form mathematical relationships. Through interactions with the learning environment the principles attributed to Dienes highlight the importance of learning mathematics. The phrase “mathematics is not a spectator sport” would apply to theories developed by Dienes that the school environment must include the physical and mental involvement of the student (Post, 1981). Dienes' influence can also be found in the work of Lesh & Doerr (2003) and their work related to authentic model design and model elicitation activities.