Research on and information about mathematics and the learning of mathematics has evolved over the last one hundred years. In the first half of the 20th century much of the focus was on computational approaches such as drill and practice and incidental learning (Brownell, 1947; Thorndike, 1924). This emphasis can certainly be attributed to the lack of technology available along with the needs of society for efficient computation (Jones et al., 2002).
The development of the new math in the second half of the 20th century was a positional change for mathematics educators and researchers. The shift was towards the structure of mathematics (Jones & Coxford, 1970) as well as reflecting the current needs and state of mathematics at the time. Questions arose regarding what the content focus should be and what should the structure of the classroom involve. Advances in knowledge and technology characterize the 21st century. Kiong & Yong (2001) emphasize that these advances bring forth the need for a restructuring in mathematics education. The researchers accentuate imaginative methods in the learning and teaching of mathematics that can promote problem-solving skills, higher-order thinking skills, independent learning, collaboration, and communication skills. The skills and processes emphasized in 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 indispensible in generalizing, modeling, and understanding the world in which we all function and interact. Furthermore, mathematics has led the way for an increase in scientific and technological advancements. The end result is that there has been a significant amount of focus on mathematics teaching and learning on the part of theorists, researchers, and educators.
Mathematics educators must continue to develop and incorporate a deeper understanding of their students’ cognitive development, which will in turn improve the mathematical competency of the student. When classroom teachers become more aware of how their students process, remember, and learn mathematical information, positive learning environments can be created for their students.
The purpose of this paper is to provide a brief introduction to three theorists, Lev Vygotsky, Richard Lesh, and Zoltan Dienes in terms of an interpretation as to how their research has influenced the design of a mathematics classroom and some of the methods used to aid effective student understanding. The concluding remarks will be the author’s beliefs about college-level instruction in the context of a mathematics environment in accordance with the aforementioned theorists.
Lev Vygotsky was an early twentieth century theorist who contributed significantly to the foundation for understanding cognitive development as he focused on the social, cultural, and historical processes in the development of the learner. Vygotsky stressed active engagement with the...