This study investigated mathematics teachers' interpretation of higher-order thinking in Bloom's Taxonomy. Thirty-two high school mathematics teachers from the southeast U.S. were asked to (a) define lower-and higher-order thinking, (b) identify which thinking skills in Bloom's Taxonomy represented lower-and higher-order thinking, and (c) create an Algebra I final exam item representative of each thinking skill. Results indicate that mathematics teachers have difficulty interpreting the thinking skills in Bloom's Taxonomy and creating test items for higher-order thinking. Alternatives to using Bloom's Taxonomy to help mathematics teachers assess for higher-order thinking are discussed.

BackgroundSeriation is a procedure that orders stimuli according to structure within a proximity matrix. The method was developed within electrical engi-

A practical concern for many existing tests is that subscore test lengths are too short to provide reliable and meaningful measurement. A possible method of improving the subscale reliability and validity would be to make use of collateral information provided by items from other subscales of the same test. To this end, the purpose of this article is to compare two different formulations of an alternative Item Response Theory (IRT) model developed to parameterize unidimensional projections of multidimensional test items: Analytical and Empirical formulations. Two real data applications are provided to illustrate how the projection IRT model can be used in practice, as well as to further examine how ability estimates from the projection IRT model compare to external examinee measures. The results suggest that collateral information extracted by a projection IRT model can be used to improve reliability and validity of subscale scores, which in turn can be used to provide diagnostic information about strength and weaknesses of examinees helping stakeholders to link instruction or curriculum to assessment results.

Behavioural disorders present extreme problems for clients and careers. In this article, the authors discuss a definition of challenging behaviour. Types of behaviour classified as 'challenging' and possible responses to them, are also considered. Some of the points are illustrated with short case studies.

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