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Pattern generalization is considered one of the prominent routes for in-troducing students to algebra. However, not all generalizations are al-gebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this arti-cle I suggest a characterization of algebraic generalizations. This char-acterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples.

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Deriving maps of phytoplankton taxa based on remote sensing data using bio-optical properties of phytoplankton alone is challenging. A more holistic approach was developed using artificial neural networks, incorporating ecological and geographical knowledge together with ocean color, bio-optical characteristics, and remotely sensed physical parameters. Results show that the combined remote sensing approach could discriminate four major phytoplankton functional types (diatoms, dinoflagellates, coccolithophores, and silicoflagellates) with an accuracy of more than 70%. Models indicate that the most important information for phytoplankton functional type discrimination is spatio-temporal information and sea surface temperature. This approach can supply data for large-scale maps of predicted phytoplankton functional types, and an example is shown.