<jats:p>Teaching concepts relating to rational numbers is a challenging task for most teach... more <jats:p>Teaching concepts relating to rational numbers is a challenging task for most teachers. National assessments show that many students in the United States have a poor understanding of rational numbers. For example, on the 1996 National Assessment of Education Progress only 50 percent of fourth graders could answer correctly how many fourths make a whole, only 45 percent could identify a diagram illustrating the equivalence of two fractions, only 21 percent could compare fractions, and only 10 percent could show how three figures can be partitioned (Arbaugh et al. 2004, Wearne and Kouba 2000).</jats:p>
<jats:p>During their first mathematics methods course, many prospective elementary teachers... more <jats:p>During their first mathematics methods course, many prospective elementary teachers confront their previous conceptions about mathematics and its teaching for the first time. This juncture makes the course important in their evolution as teachers of mathematics. Prospective teachers in a mathematics methods course must develop the ability to reflect on their actions, beliefs, knowledge, and attitudes. Writing in a mathematics methods course fosters reflection in a natural way; it serves as a tool for documentation, analysis, and discussion to help prospective teachers internalize what they learn and reach new levels of comprehension. At the same time, what teachers in training write gives teacher educators a window into their reflection and growth process.</jats:p>
Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first appr... more Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first approximation to the square root of a number to obtain a second, much better approximation. This article will show that their method is remarkably efficient. We use geometric algebra, much like the Babylonians might have done, to give a visual rationale for the method and its efficiency.
<jats:p>Teaching concepts relating to rational numbers is a challenging task for most teach... more <jats:p>Teaching concepts relating to rational numbers is a challenging task for most teachers. National assessments show that many students in the United States have a poor understanding of rational numbers. For example, on the 1996 National Assessment of Education Progress only 50 percent of fourth graders could answer correctly how many fourths make a whole, only 45 percent could identify a diagram illustrating the equivalence of two fractions, only 21 percent could compare fractions, and only 10 percent could show how three figures can be partitioned (Arbaugh et al. 2004, Wearne and Kouba 2000).</jats:p>
<jats:p>During their first mathematics methods course, many prospective elementary teachers... more <jats:p>During their first mathematics methods course, many prospective elementary teachers confront their previous conceptions about mathematics and its teaching for the first time. This juncture makes the course important in their evolution as teachers of mathematics. Prospective teachers in a mathematics methods course must develop the ability to reflect on their actions, beliefs, knowledge, and attitudes. Writing in a mathematics methods course fosters reflection in a natural way; it serves as a tool for documentation, analysis, and discussion to help prospective teachers internalize what they learn and reach new levels of comprehension. At the same time, what teachers in training write gives teacher educators a window into their reflection and growth process.</jats:p>
Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first appr... more Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first approximation to the square root of a number to obtain a second, much better approximation. This article will show that their method is remarkably efficient. We use geometric algebra, much like the Babylonians might have done, to give a visual rationale for the method and its efficiency.
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