Mathematics for science or vice versa?

The reader might feel that a rather fine distinction is being drawn here. What possible difference does it make whether science is integrated with mathematics or mathematics with science? This is not an idle question, and the answer is as follows. Practical applications of mathematics to everyday situations (as in any of the numerous examples found in the curricula cited in the first paragraph) are primarily motivated by the mathematical concepts to be taught. The selected situations tend to be fictional or hypothetical, conjured to fit the mathematical purpose. Where real-world data are used, there is often no scientific motivation for the situations studied, nor for the questions that are asked of the data. For the purpose of science teaching then, there is a need to design new quantitative learning situations which are geared towards an understanding of the world.