This paper presents the model, The Mathematics Teacher's Specialised Knowledge (MTSK). It acknowledges earlier contributions to understanding and structuring teachers' knowledge, in particular, the special debt owed to Shulman's notion of pedagogical content knowledge and to Ball and collaborators' Mathematical Knowledge for Teaching (MKT) influential for the specialised nature of one of its sub-domains. Our research with teachers has led us to explore the characteristics of MKT and to refine the descriptors relating to its sub-domains, a task which has underlined the difficulty involved in unambiguously delimiting the boundaries which separate these. As a result, and taking into consideration a broader view of the specialised nature of the teacher's mathematical knowledge, we propose a framework which, whilst respecting the major domains of Content Knowledge and Pedagogical Content Knowledge, regards the specialisation in respect of mathematical knowledge as a property which is inherent to the model and extends across all sub-domains.

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Resumen El profesor desempeña un papel crucial en la articulación de los Espacios de Trabajo Matemático. El modelo de conocimiento del profesor que aquí se presenta (denominado Mathematics Teacher’s Specialised Knowledge) propone una estructuración de dicho conocimiento basada en la noción de ‘especialización’. Esta estructuración, particularmente la consideración de sus componentes (subdominios), permite comprender el conocimiento que el profesor pone en juego en la transición entre los distintos Espacios (idóneo, personal y de referencia) de Trabajo Matemático, así como las relaciones entre estos.

BACKGROUND Some cervical/vaginal Papanicolaou (Pap) smears previously diagnosed as normal in women with a high grade squamous intraepithelial lesion (HSIL) are found to contain abnormal cells on retrospective review. This study characterized and quantitated such cells in 100 Pap smears. METHODS One hundred prior negative Pap smears from 49 women with a newly diagnosed HSIL were rescreened, as were 107 negative Pap smears from 100 women with normal subsequent smears. Cases were assorted randomly so that the rescreener was unaware of the subsequent follow‐up. RESULTS All 12 Pap smears found to contain atypical mature and immature metaplastic cells belonged to the group with a subsequent HSIL (P = 0.001). In addition, 18 of the 100 previously negative Pap smears (18%) had immature metaplastic cells without nuclear atypia compared with 4 of 107 Pap smears (4%) in the control group (P = 0.0007). CONCLUSIONS This study supports the observations of other authors that atypical metaplastic cells, especially those of the immature type, are associated with HSIL. These cells most likely are HSIL lesional cells, which are not easily recognizable as such. Immature metaplastic cells without atypia also were shown to be associated significantly with HSIL in this study. These cells may be unrecognizable lesional cells or a marker of increased risk for HSIL and deserve further study. [See editorial on pages 45–7, this issue.] Cancer (Cancer Cytopathol) 1999;87:56–9. © 1999 American Cancer Society.