26 July 2011

Young Children Need Basic Concepts to Build Upon

A recent study from the University of Missouri's David Geary, provides some suggestions for better preparing young children for later study in mathematics:
Numbers, counting, and low-level arithmetic are three basic competencies that are vital to later success in math, and students should have these key math skills in first grade in order to be successful in math in fifth grade, according to a long-term study released by psychologists at the University of Missouri (UM).

“Math is critical for success in many fields, and the United States is not doing a great job of teaching math,” David Geary, UM’s Curator’s Professor of Psychological Sciences, who led the research team, said in a statement. “In order to improve basic instruction, we have to know what to instruct.”

Researchers monitored 177 elementary students from 12 different elementary schools from kindergarten to fifth grade, and intend to continue monitoring them through high school. Students who understood the number line and some basic math facts in the beginning of first grade showed faster growth in math skills over the next five years.

“It is important that children understand the meaning of Arabic numerals, that is, the quantities they represent and be able to quickly translate quantities into numerals and numerals into quantities. [The study] also highlights the importance of knowing basic facts and the number line,” Geary said. _eschoolnews
The longitudinal study by the University of Missouri referred to above, which will follow 177 students from kindergarten through high school, may well provide learning specialists and psychologists with much valuable information on how to help students learn math and other important topics. But it is important that the researchers remove as many possible confounders as possible before drawing any conclusions. IQ, SES, EF, and other confounding factors might easily be ignored by some researchers. David Geary is a top psychologist, however, and is not likely to overlook such basic concepts in the planning and data analysis phases.

There are a large number of free online helper sites which provide exposure to these basic math concepts. For example, Visual Math Learning provides a number of basic lessons in the very topics highlighted by the study. Lessons in natural numbers, counting, and a number of lessons in low level arithmetic are all provided free of charge.

The Khan Academy is a most helpful online math learning site which provides lessons from very basic levels to far more advanced areas of math.

Math is a lot more than numbers, counting, and simple arithmetic, of course. The understanding of all sorts of dynamic patterns and relationships in the modern world require some level of math learning. Very young minds can be prepared for many of these advanced concepts merely by exposure -- just as very young minds which are exposed to languages are better prepared to use languages as they mature.

The longitudinal U. Missouri study discussed above will be helpful, but a lot more is needed. Although we have a rough idea of the time frame for developmental windows in the learning of language and the training of executive function, we have far less understanding of the timing of developmental windows for later intuitive understanding of advanced math concepts, or world class musical abilities. It is likely that the best of the best were given early starts, but how early, and what type of start is best? No one knows.

It is important that a civilisation whose future existence of abundant prosperity is dependent upon the skillful use of advanced mathematical concepts, learns to train its young to develop these skills at the most advantageous times.

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