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Sequences and series is one of the mathematical topics that are related to everyday life. The topic is also taught at several levels of education in Indonesia. However, many students still experrienced difficulties in learning this topic. This study uses an interpretive paradigm that is part of the Didactical Design Research (DDR). This research aims to analyze students’ learning obstacles on the topic of sequence and series using the onto-semiotic approach. To do so, written test consists of five questions related to the conceptual understanding of an arithmetic sequences and series was administered to 23 students from one of the senior high schools in Kota Tangerang Selatan followed by interviews with 4 students. The results show that learning obstacles are classified into epistemological, ontogenic, and didactical obstacles. Based on the onto-semiotics approach, the students had difficulties in defining a mathematical idea on sequences and series topics. They could convert a problem into mathematical model but were confused to use a proper procedure. It can be concluded that students still experience obstacles in learning sequences and series topic. The results of this study can be used by teachers as considerations in designing learning situation on the topic of sequence and series.

Let be a totally ordered abelian group and I an order ideal in . We prove a theorem which relates the structure of the Toeplitz algebra T ( ) to the structure of the Toeplitz algebras T (I) and T ( /I). We then describe the primitive ideal space of the Toeplitz algebra T ( ) when the set ( ) of order ideals in is well-ordered, and use this together with our structure theorem to deduce information about the ideal structure of T ( ) when 0 → I → → /I → 0 is a non-trivial group extension.2000 Mathematics Subject Classification. 46L55.Introduction. Let be a totally ordered abelian group with positive cone + , and denote by {e x : x ∈ + } the usual basis for the Hilbert space 2 ( + ). For each x ∈ + , there is an isometry T x on 2 ( + ) such that T x e y = e x+y for all y ∈ + .The Toeplitz algebra of is the C * -subalgebra T ( ) of B( 2 ( + )) generated by the isometries {T x : x ∈ + }. These Toeplitz algebras include as special cases the algebras studied by Coburn [7] and Douglas [8], and generalisations to various classes of partially ordered groups have attracted a great deal of attention in recent years (see [12,13,10,11], for example).In [4], we considered the problem of describing the ideal structure of T ( ), and found that a crucial ingredient is the set ( ) of order ideals in , which is itself totally ordered under inclusion. We showed that the primitive ideals of T ( ) are parametrised by the disjoint union X( ) := { I : I ∈ ( )} of the duals of the discrete abelian

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This research is conducted to obtain a description of students' difficulties in understanding and applying Pythagorean theorem based on the onto-semiotic approach. This research applies a qualitative approach with phenomenology interpretation design. Research data were collected using test and interview methods. The research result was deducted from students' answer sheets and interviews. Participants involved in this study were as many as 25 students of UPI Lab School Junior High School Bandung, who had learned Pythagorean theorem, 4 of which also participated in the interview. It showed that students found it complicated to comprehend definition, describe symbols or notations of mathematical objects, and interpret mathematical objects. Meanwhile, in solving problems related to the application of the Pythagorean theorem, students could describe procedure, algorithm, and technique in solving questions well.