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The general consensus of large-scale studies that compare traditional mathematics with reform mathematics is that students in both curricula learn basic skills to about the same level as measured by traditional standardized tests, but the reform mathematics students do better on tasks requiring conceptual understanding and problem solving. [3]
However, when the logical reasoning tests measured students' understanding of part-to-whole relations, the Waldorf students also outperformed the public school students. [9] Although the study noted the Waldorf students' enthusiasm for science, the science curriculum itself was viewed as "somewhat old-fashioned and out of date, as well as ...
This goal was the reason for teaching arithmetic in bases other than ten in the New Math, despite critics' derision: In that unfamiliar context, students couldn't just mindlessly follow an algorithm, but had to think why the place value of the "hundreds" digit in base seven is 49.
The Mathematics Tutor (Beal, Beck & Woolf, 1998) helps students solve word problems using fractions, decimals and percentages. The tutor records the success rates while a student is working on problems while providing subsequent, lever-appropriate problems for the student to work on.
The transition from activities to the formal Mathematical systems is guided by a variety of general insights and ideas. Another approach for defining mathematics is to use its methods. For example, an area of study is often qualified as mathematics as soon as one can prove theorems—assertions whose validity relies on a proof, that is, a ...
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