Textbooks and other materials are used extensively in mathematics lessons and they influence to a large extent how students think about mathematics and come to understand its meaning (Valverde, et al, 2002). It is therefore important to analyse such materials and their use in order to ensure that what is offered to students is a rich, coherent and connected learning experience. In this presentation we use the concept of 'connectivity' as a tool for developing a framework to investigate textbook tasks, and we subsequently apply this tool to analyse selected textbooks in England, France and Germany. In a previous study (Pepin and Haggarty, 2001; Haggarty and Pepin, 2002) we have investigated similarities and differences of mathematics textbooks and how these linke to teachers' use of textbooks in English, French and German lower secondary mathematics classrooms. A growing interest in the research literature on 'mathematical understanding' and 'connectivity' (Hiebert et al, 1997, Hiebert and Carpenter, 1992), and in relation to this in mathematical tasks (Henningsen and Stein, 1997; Doyle, 1988) offered in textbooks , encouraged us to develop an analytical tool, based on the concept of 'connectivity' (Pepin and Haggarty, submitted), and subsequently re-analyse the textbooks on that basis. Textbooks which were originally identified as amongst the ones most frequently purchased for years 7 (6ème, Jahrgang 6), 8 (5ème, Jahrgang 7) and 9 (4ème, Jahrgang 8) were chosen for re-analysis. The topic of 'directed numbers' was selected for a more detailed analysis, because this topic was regarded as relatively self-contained and likely to be taught as a new topic, particularly in years 7 and 8. In particular, individual tasks were analysed with respect to1. context embeddedness, familiar situations- tasks which make connections with what students already know, 'real life';2. cognitive demand/formal statements/generalisations- tasks which emphasise relational rather than procedural understanding, tasks which make connections with the underlying concepts being learnt;3. mathematical representations- tasks which make connections within mathematics and across other subjects, tasks which connect different representations.A literature review related to mathematical tasks in textbooks, the analysis of those tasks, and the connections, connectedness and mathematical knowledge offered through tasks and worked examples, highlights the importance of making connections, if learning is to take place. Based on this review of the literature, we develop a tool for analyzing mathematical tasks in textbooks, and present a set of criteria that can be applied to tasks in the analysis of textbooks.What is apparent from the analysis of mathematical tasks, using the 'connectivity' tool, is that none of the textbooks analysed across the three countries fully meets all the criteria identified from the literature as important for mathematical understanding. What then becomes important is the central role of the teacher in mediating the text in an enhancing and enriching way, and therefore in ensuring that teachers' awareness of the issues is raised so that they are alerted to make connections which the textbook may have failed to do. More importantly perhaps, we argue that different countries provide different (mis)representations of mathematics for their students in school textbooks. Despite perhaps gaining proficiency at certain kinds of procedures and tasks, in particular English students -compared to their French and German colleagues- may well have gained at best a fragmented sense of the mathematics and understood few if any connections that tie together the procedures they had studied in textbooks. It can be argued that through these disconnected and impoverished activities students are likely to develop perspectives on mathematics that may impede them in their use and acquisition of other mathematical knowledge. Doyle, W. (1988) Work in Mathematics Classes: the content of student thinking during instruction, Educational Psychologist, 23(2): 167-80. Haggarty, L. and Pepin, B. (2002) 'An investigation of mathematics textbooks and their use in English, French and German Classrooms: who gets an opportunity to learn what?' British Educational Research Journal 28 (4). Hiebert, J. and Carpenter, T. (1992) Learning and teaching with understanding, in D.A. Grouws (ed) Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan. Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., and Human, P. (1997) Making sense- Teaching and Learning Mathematics with Understanding, Portsmouth, NH: Heinemann. Henningsen, M. and Stein, M.K. (1997) Mathematical Tasks and Student Cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning, Journal for Research in Mathematics Education, 28 (5): 524-49. Pepin, B. and Haggarty, L. (2001) 'Mathematics textbooks and their use in English, French and German classrooms: a way to understand teaching and learning cultures', Zentralblatt for the Didactics of Mathematics, 33 (5). Pepin, B. and Haggarty, L. (submitted)- Textbooks, tasks and connectivity: developing an analytical tool, submitted to Educational Studies in Mathematics. Valverde, G.A., Bianchi, L.J., Wolfe, R.G., Scmidt, W.H. and Houng, R.T. (2002) According to the Book- Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Kluwer Academic Publishers., e.g. Educational Studies in Mathematics Education