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There is a compelling need to develop an algebra teacher self‐efficacy instrument (ATSEI) as algebra continues to be considered a gatekeeper course for postsecondary educational and career opportunities, which is seen as a crucial piece in closing the achievement gap. This paper reports on the development and validation of the ATSEI, an instrument that measures two domains, Efficacy To Do School Algebra (Knowledge Efficacy, KE‐A) and Efficacy to Teach Algebra (Personal Teaching Efficacy, PTE‐A) along six categories. Four of the categories represented content standards (variables, functions, patterns, and modeling) and two of the categories represented process standards (technology and concrete models, and multiple representations). Through conducting an exploratory factor analysis across two phases, the instrument was reduced and refined from an initial 118 items developed from a curriculum analysis to 36 items that reflected two significant categories, Functions and Technology. The ATSEI measure is validated for in‐service mathematics teachers and thus provides an instrument to examine need and impact in professional development venues. The specificity of the ATSEI allows those working with teachers to be better able to support them in the field and in return positively influence the learning outcomes of the students they teach. [ABSTRACT FROM AUTHOR]

Abstract: Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan operator algebras; they are far more similar to associative operator algebras than was suspected. We initiate the theory of such algebras. [ABSTRACT FROM AUTHOR]