This study explored Israeli elementary school mathematics teachers' perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents' main needs are associated with strengthening their didactical knowledge capability of dealing with emotional aspects that relate to pupils' learning of mathematics. Although most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. In light of Israeli pupils' relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.

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Proving and refuting mathematical claims constitute a significant element in the development of deductive thinking. These issues are mainly studied during geometry lessons and very little (if at all) in lessons of other mathematical disciplines. This study deals with high school students' perceptions of proofs in the geometry. The study explores whether students know when to use a deductive proof and when an example is sufficient for proving or refuting geometrical claims. The findings indicate that in cases of simple claims, the students corroborate them by using a deductive proof. However, when the claim is more complex, the students tend to present both a proof and an example. Moreover, they are unsure whether using an example can constitute a method for proving a mathematical claim, believing that in mathematics everything must be proven. They believe that examples are used merely for illustration purposes rather than as a means of convincing. The research conclusions support the need for deepening and developing the students' distinction between cases where examples are insufficient and cases where an example is sufficient for proving a claim.

This article deals with an intervention unit which focused on the positive effect of integrating poems, stories and fables (the literary genre) for improving mathematical language, fostering the teaching of mathematics language, increasing satisfaction with the process and strengthening the relationship between use of daily language and mathematics language. The study was conducted amongst pre-service mathematics teachers, specialising in literacy activities designed to foster mathematics language. One of the study outcomes was a ‘bank’ of words with double meanings which can result in misguided perceptions and common errors. Another outcome was a pool of ideas for literacy activities in mathematics which can develop wide, integrative activities. Exposure to and awareness of such a bank of words may help mathematics education practitioners to cope with difficulties in mathematics teaching and learning.<p><strong>How to cite this article:</strong> Patkin, D. (2011). The interplay of language and mathematics. <em>Pythagoras</em>, <em>32</em>(2), Art. #15, 7 pages. http://dx.doi.org/10.4102/pythagoras.v32i2.15</p>

This study aims to explore in-service preschool teachers' attitudes towards and beliefs about geometry and its teaching and to investigate their knowledge of shapes and solids. The study uses a mixed descriptive approach employing quantitative and qualitative research methods. Thirty-four Israeli preschool teachers of children aged 3-6 from 34 different preschools and kindergartens participated in the study and responded to a questionnaire comprised of closed and open items. Regarding their attitudes and beliefs, the preschool teachers were asked about: the meaning of geometry; affinity for geometry, importance of geometry; need to use accurate mathematical language, and about their enjoyment of engaging young children in activities connected with learning geometry. As to the knowledge of shapes and solids, the preschool teachers were asked to describe or define shapes and solids, name shapes and solids and distinguish between rectangles and other shapes. The results illustrate that most of the preschool teachers like geometry or expressed a neutral position towards geometry, but some hate geometry. Most of the preschool teachers comprehend the importance of engaging in activities that relate to geometry in preschool and enjoy involving young children in activities connected with learning geometry. As to the use of accurate language, most of the preschool teachers maintain that accurate mathematical language should be applied when preschool children aged 3-6 deal with shapes and solids. Yet, only about half of them believe that it is necessary to use accurate language when the children are at an earlier age. Certain preschool teachers lack the knowledge to name shapes and solids, even those which are part the mathematics curriculum for ages 3-6. They exhibited difficulties in using accurate mathematical language when describing shapes and solids, and were influenced by the shapes' visual appearance rather than by their definitions and properties. It is recommended that preschool teachers attend further development programs so they can appropriately involve young children in activities connected to learning geometry, as required by the curriculum.