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 ...
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... when a mathematical concept is presented under conditions in which the relevant variables remain constant but irrelevant variables are changed the ability to generalize is enhanced. The constructivity principle states that students should be allowed to build their own concepts by manipulating concrete materials in order to form mathematical relations.
Through interactions with the learning environment is how the principles attributed to Dienes stress the importance of learning mathematics. The phrase “mathematics is not a spectator sport” would apply to the theories developed by Dienes in that the classroom environment must include physical and mental involvement of the student (Post, 1981). The influence of Dienes can also be found in the work of Lesh & Doerr (2003) and their work related to the design of authentic models and model-eliciting activities.
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