Of adding oranges and apples: how non-abstract representations may foster abstract numerical cognition

Of adding oranges and apples: how non-abstract representations may foster abstract numerical cognition

INTRODUCTION The realm of numbers constitutes just one of many fields of mathematical cognition, but arguably a pivotal one. It is also among those core domains of knowledge that—while being prepared for unfolding in the human species (Feigenson et al., 2004; Hyde, 2011)—nonetheless requires cultural mediation to unfold to its full potential: Not only is the availability of a conventionalized c...

Adding Apples and Oranges

We define a unit system for end-user spreadsheets that is based on the concrete notion of units instead of the abstract concept of types. Units are derived from header information given by spreadsheets. The unit system contains concepts, such as dependent units, multiple units, and unit generalization, that allow the classification of spreadsheet contents on a more fine-grained level than types...

Adding apples and oranges: alignment of semantic and formal knowledge.

We show that the same mechanism that mediates analogical reasoning (i.e., structural alignment) leads to interpretive "content effects" in reasoning about arithmetic word problems. Specifically, we show that both college students and textbook writers tend to construct arithmetic word problems that maintain systematic correspondence between the semantic relations that people infer from pairs of ...

Comparing apples and oranges ...

The most comprehensive and often-cited statistic about the U.S. economy is gross domestic product (GDP), the sum of all goods and services produced in the United States. Estimates of GDP are the featured statistics in the National Income and Product Accounts, the construction of which involves the collection and aggregation of an immense amount of data. In the construction of real GDP, complica...

Comparing apples and oranges.