Seyda Uysal

Kathleen M Clark
email: kclark@fsu.edu

Using history of mathematics to inform the transition from school to university: Affective and mathematical dimensions

Keywords: Transition from school to university, emotions, affective dimensions, history of geometry

In this paper, we briefly describe an intervention that addressed the transition from school mathematics to university mathematics by making students aware of concept changes in the history of geometry. We provide a description of the intervention (called the ÜberPro Seminar), the context and setting for the study, and the data sources that informed our work. Then, we focus on one particular data source and describe initial stages of our analysis and sample findings. In our findings, we share only a small glimpse into the affective experience students described when reflecting on the transition from school to university. We conclude with a discussion of some of the patterns that began to emerge from our analysis and we propose connections to current work on the transition from school to university mathematics and future direction for our research.

Introduction

The transition from school mathematics to university mathematics has received increased attention in recent years in a variety of contexts (Clark & Lovric, 2009;[START_REF] Gueudet | Investigating the secondary-tertiary transition[END_REF][START_REF] Kosiol | Which) mathematics interest is important for a successful transition to a university study program[END_REF]. On the one hand, several research efforts have focused on "the" transition; that is, examining undergraduate students taking courses at the moment they transition to university (see for example, [START_REF] Kosiol | Which) mathematics interest is important for a successful transition to a university study program[END_REF]. Some studies focus on questions of whether or why students persist in either mathematics or other STEM-related fields (e.g., Di [START_REF] Martino | The mathematical crisis in secondary-tertiary transition[END_REF] and others may approach the transition problem from a deficit model perspective. That is, there may be an emphasis on the lack of sufficient background knowledge on the part of students who move from secondary mathematics to tertiary mathematics. On the other hand, examples in the literature examine specific junctures that prove to be obstacles for students transitioning to university mathematics, such as students beginning coursework that focuses primarily on proof (e.g., courses in Analysis, Abstract Algebra, etc.). From either of these two perspectives, the transition may seem more discrete; that is, at one particularly time pointe.g., the change from the last mathematics course taken in high school to the first course at university, or, the change from courses to be considered more computational at university (e.g., Precalculus or Calculus) to more proof-oriented (such as Abstract Algebra). In our work, the transition problem, or, in German, ÜbergangsProblematik, is considered as a continuous phenomenon. That is, we do not consider the transition occurring at one particular moment in time. Instead, students may experience aspects of transition throughout their time at university. In this context, it may be more appropriate to consider a (as opposed to the) transition problem or multiple transition problems.

The research described in this paper originates from an experiment conducted in 2015, when we1 began work on the design, development, and implementation of a seminar for undergraduate mathematics students who were preparing to teach mathematics. The theoretical foundation of the seminar included the hypothesis that:

The change from an empirical-object oriented to a formal-abstract belief system of mathematics constitutes a crucial obstacle for the transition from school to university. On epistemological grounds, similar changes regarding different natures of mathematics can be described for the history of mathematics (e.g., in the development of geometry). Student analysis of the historical belief change can support them on their individual transition from school to university and back to school again. [START_REF] Witzke | ÜberPro-A seminar constructed to confront them from school to university mathematics, based on epistemological and historical ideas of mathematics[END_REF] In this paper, we share a very brief overview of research literature focused on transition from school mathematics to mathematics at university, describe the evolution of the seminar that began in 2015, and provide a description of a study conducted on the most recent implementation of it. Finally, we share selected findings for the research question: In what ways do seminar students, when confronted with the historical development of mathematics, recognize their own transition?

The study

The seminar

The seminar, "Addressing the Transition Problem from School to University Mathematics" (or, the ÜberPro (taken from the German term) Seminar), was first implemented as a three-day intensive seminar in Spring 2015. Readings and seminar activities were designed and piloted with 20 preservice mathematics teachers at a medium-sized university in Western Germany. We used geometry as the topic of the seminar's mathematical content and the seminar activities included engaging students in reading and discussing excerpts from student task transcripts, textbooks, learning standards documents, and historical resources, as well as working on various tasks prompted by historical sources and content. From its inception, the aim of the ÜberPro Seminar was to promote students' awareness of the changes regarding the nature of mathematics from school to university as means to support their own transition from the changing mathematical and institutional context in high school to those at university. This was accomplished through the sequence of seminar sessions on examining beliefs about mathematics promoted in school and university mathematics textbooks, the nature of Euclidean Geometry (with an in-depth examination of proofs of the Pythagorean Theorem), the development of projective geometry, the failure of the parallel postulate (leading to the development of non-Euclidean geometry), and the formalism of Hilbert's geometry. Additionally, students were reminded of the hypothesis (given above) during each session so that explicit connections between it and seminar content could be drawn. Gueudet and colleagues (2017), in literature focused on the transition from school to university mathematics contexts, have described certain boundary objects which may play a significant role in helping students to "make this transition" (p. 108).2 However, we share the same view as described by [START_REF] Gueudet | Transitions in mathematics education[END_REF], that the transition problem cannot be easily "smoothed out" and that it probably should not be smoothed out, because it gives the opportunity to reflect on one's own beliefs, knowledge, and affect in mathematics during the transition. A unique attribute of the ÜberPro seminar course is in the potential of utilizing the case of the historical development of geometry to provide a means of support as students consider their own beliefs about mathematics in light of the changes in beliefs (e.g., nature) of mathematics that have occurred over time. The description of the first implementation of the ÜberPro Seminar (Spring 2015) has appeared elsewhere [START_REF] Witzke | ÜberPro-A seminar constructed to confront them from school to university mathematics, based on epistemological and historical ideas of mathematics[END_REF], as well as the modifications to extend the initial intensive seminar into a semester-long seminar experience that was implemented in Summer 2016 [START_REF] Witzke | Addressing the transition from school to university: Evolution of a seminar emphasizing historical sources and student reflections[END_REF]. We propose that in light of the instructional materials (e.g., textbooks) that students face in school mathematics, they are more likely to acquire an empirical belief system. Yet, at university, students are likely to obtain a formalistic belief system based upon the instructional materials found there. Epistemologically, both of these experiences provide parallels to specific historical conceptions of mathematics, which we sought to highlight as the fundamental components for the design of our "transition problem" seminar for students. Yet, we wish to emphasize that we do not propose that the formal-abstract approach is exclusive to learning mathematics at university. Instead, the development of our hypothesis and the intervention we developed is based on survey and interview experience, as well as support from literature that there are certainly differences in the discourse, tasks, and nature of mathematics at university when compared to school, and this difference often materializes as empirical-object (school) versus formal-abstract (university).

Setting and context

The research described here took place during the Summer 2017 semester at the same institution as the pilot seminar and the first semester-long version of the seminar. The seminar course was offered to pre-service mathematics teachers and these students also had the opportunity to take a similarlydesigned seminar on probability [START_REF] Stoffels | evolutions in probability theory: students reflecting their own beliefs about mathematics by dealing with original sources from 20th century development of probability theory[END_REF].

Data sources and participants

There are several data sources that informed our research on the Summer 2017 ÜberPro Seminar, including audio recordings and observer-participant notes from each seminar session (taken by the second author), all course materials used with seminar participants (designed by the instructorresearchers involved with each of the three implementations of the ÜberPro Seminar), and weekly submissions of reflection journals by the seminar participants. In this paper, we focus on the student participants' reflection journals. Over the course of the 12-week semester, students were asked to respond to 59 reflection journal prompts. The reflection journal prompts were varied, with some focused purely on the transition from school to university mathematics and others focused on topics in geometry, on the historical development of geometry, or related to the participants' future teaching of mathematics. In summer 2017, 19 students participated in the ÜberPro Seminar. However, for this paper we consider the data for 14 of the 19, for whom we have responses to the reflection journal prompts. The mean age of these 14 students (8 male and 6 female) was 23 years and the mean semester at university was 6. It is also important to note that three of the students (1 male, 2 female) were considered as "expert" students because they had previously completed the ÜberPro Seminar on probability. In the reflection journal excerpts that follow, these students are identified with an "E" at the end of their code number.

Data analysis

In order to prepare the reflection journal prompt responses for coding, student responses were first translated from German into English through the assistance of Google Translate. Then, responses were revised for grammatical accuracy by the second author, who has some German language proficiency. Of the 59 reflection journal prompts, we focused on a subset of eight that provided us with student responses that reflected more affective dimensions of students' experiences in the transition from school to university mathematics. Based on these criteria and for the purposes of this paper we narrowed the set of reflection journal prompts further from eight to two, as prompts of interest for this paper. In doing so, we ensured that sufficient data remained and we were able to pay attention to the principle of theoretical saturation [START_REF] Merriam | Qualitative research: A guide to design and implementation[END_REF]. Next, we reviewed all 14 students' responses to the reflection journal prompts of interest and we approached the coding of students' responses to the journal reflection prompts using aspects of Grounded Theory (Strauss & Corbin, 1990). We first completed line-by-line coding to determine aspects of recognition of their own transition from school to university mathematics (e.g., difficulties with content; differences in content, structure, or environment; reference to formal versus abstract belief systems). During line-by-line coding we also made analytical notes on each response, to assist with the next stage of coding in which we sought to determine themes. In the second stage of the data analysis, we focused on the two specific prompts (prompts 4.1 and 12.6, given in the "Initial findings" section) that explicitly asked student participants about the recognition and awareness of the transition problem during their undergraduate mathematics studies. We were most interested in coding words and expressions within students' responses which might potentially reflect emotional aspects of the transition (e.g., emotionally-charged phrases and expressions) and these were noted by the two authors independently. We then met to discuss controversial interpretations for the purpose of establishing trustworthiness which contributes to the credibility of the study [START_REF] Creswell | Qualitative inquiry and research design: Choosing among five approaches[END_REF][START_REF] Lincoln | Naturalistic inquiry[END_REF]. Ultimately, the purpose of the second stage of the data analysis was to identify and categorize repetitive and similar expressions and to highlight the themes in participants' reflections.

Initial findings

The focus for this paper was to highlight participants' experience in the ÜberPro Seminar relative to their recognitione.g., emotionally, mathematicallyof their own positioning in transitioning from school to university mathematics. We purposefully selected the two reflection journal prompts because they asked for participants to explicitly reflect on their own transition early in the semester (prompt 4.1 from week 4) and at the end (prompt 12.6 from week 12). Thus, we were able to examine the ways in which participants described aspects of the transition, both early in the seminar experience, and after having engaged with seminar content designed to make explicit the beliefs changes in students (over their mathematical trajectory) and in mathematics (using the example of the historical development of geometry). The two prompts are: Q4.1: Think about your own transition from school to university and reflect this on the basis of the transition problem hypothesis presented in the seminar.

Q12.6: Explain the transition problem referring to the completed seminar. What consequences can be derived for university and school? Include what you have learned on your personal transition experience and how to deal with it in the future. You can also refer back to the seminar's underlying hypothesis on transition issues.

Investigating patterns: How do students recognize their transition?

As described, 14 students' responses to the reflection prompts (prompts 4.1 and 12.6) were analyzed based on semester of enrollment, gender and age of the participants, and the general frequency of some expressions such as "change of viewpoint," "rapid," "difficulty," and "new ways of dealing with mathematics." For the purpose of this paper, we share only a brief collection of the type of affective experience students described when reflecting on the transition from school to university. In general, students felt confronted by the view of formal, abstract mathematics at university. Twelve of 14 students either implied or explicitly articulated that mathematics taught in school was a quite different experience from university mathematics, which refers to the gap between school and university mathematics. For example, Student 7360 described the following:

As part of my transition from school to college, I was confronted with a new way of dealing with mathematics: While I met mathematics in school mostly in the context of concrete computing tasks and applications, and only met a little proof, I was confronted with a definition-theoremproof-example-mathematics, which was based on a strict formal approach and an axiomatic structure. The procedure was strictly axiomatic and I knew little until now. A special change was also in the now much higher value of proof. While there was hardly a lesson in school without examples (tasks) and hardly any lesson with proof, the picture was now the other way around: in the university, there was hardly a lecture with sample exercises and hardly a lecture without proof […] (Response to journal reflection prompt 4.1) Similar to Student 7360, other seminar students emphasized that more empirical examples were encountered in high school mathematics whereas university mathematics included more formal definitions and abstract proofs. Moreover, the students believed that they needed to change their view of mathematics to be able to comprehend formal abstract university mathematics. According to their responses, the ways in which students expressed their emotions toward this transition between school to university was fairly intense. Students who had or experienced an unpleasant transition frequently used descriptors such as "bumpy," "big hurdle," "very bad transition," "incredibly challenging," "struggling," "sudden" and "rapid change," and these terms capture the magnitude of the emotions that students associated with the transition from school to university. Some students mentioned the high drop-out rates of peers due to the change of view from empirical to formal mathematics as a consequence of a difficult transition. One of the "expert" students (Student 1612E) expressed his experience as:

My own transition to university confirms the hypothesis of the seminar. It was a big hurdle and took some time to get used to the formalism and the level of abstraction of academic mathematics. I myself have finally mastered the transition; however, I know some who found the hurdle to be too high and have quit their studies. (Response to journal reflection prompt 4.1) Another participant, Student 1609, identified the "rapid change" in views of mathematics as a defining feature of the transition, but he also compared the transition that students endure with the change in views that occurred in the development of geometry:

The rapid change from an empirical-object view or view of mathematics to a formal-abstract one is one of the most influential reasons that the transition problem is such an important issue today. I assert as well that every student must [go] through this phase of ignorance and acquire new knowledge, in order to first understand what is being conveyed in the lectures at university. In my opinion, there is a great deal in common between the transition from school to university and the historical development of geometry. This has developed from an empirical-objective conception to a formal-abstract one. As with the transition problem, there is added complexity in the evolution of geometry and it becomes more in-depth as time passes. (Response to journal reflection prompt 12.6) In a similar way, Student 1905 drew upon the seminar content (i.e., the historical development of geometry) to situate her view of the transition problem, and to note a key difference for her experience at university (e.g., "a rigid conception is used"):

In the historical development of geometry, one finds mathematicians who represent an empirical-object view and mathematicians who represent a formal-abstract view. So, there are different views of geometry in the past. Here I see a difference [in views] to the transition from school to university. While [at university] only a rigid conception is used, in the history one finds a multiplicity of geometrical conceptions. I see a commonality in the transition. The conceptions that we find today between school and university can also be found in the development of geometry. (Response to journal reflection prompt 12.6) As a final example, we present the characterization that Student 7536E (another "expert" student) offered in her response to journal reflection prompt 12.6:

The transition problem from school to university is clearly recognizable, especially in mathematics. Geometry also has a strong evolution behind it and is based on different views. The biggest difference is probably between Euclidean and non-Euclidean geometry, which also differentiates the school material and the university material. In these different views, the relationship to reality and truth always plays a decisive role. [START_REF] Gueudet | Investigating the secondary-tertiary transition[END_REF] observed that "[u]niversity is seen as a new world, or at least a new country, with a new language and new laws that make the novice student feel like a foreigner" (pp. 242-243). Indeed, ÜberPro Seminar students' responses revealed that they experienced palpable difficulty in dealing with a new way of mathematical thinking, which might be analogous to learning a new language. The expression of "change of viewpoint" was referred to either explicitly or implicitly by the seminar students, which we found interesting in our analysis. The change in students' viewpoint also gives us cues concerning historically different views in mathematics. On the other hand, the repetitive use of expressions regarding the change of viewpoint from empirical to formal validates the inconsistency between secondary and university mathematics, which makes it harder to initiate a schema [START_REF] Rumelhart | Schemata: The building blocks of cognition[END_REF] to make cognitive connections between prior knowledge and abstract/theoretical mathematics. Failing to adjust to the change of viewpoint is most likely to affect students' dispositions toward formal mathematics in terms of attitude, emotion and belief, which is examined as "affective factors" by Di [START_REF] Martino | The mathematical crisis in secondary-tertiary transition[END_REF]. Therefore, the severe difficulties which potentially lead to dropout of students from STEM-related undergraduate programs without obtaining a degree seem to be problematic due to their connection to psychological strain from an individual standpoint (Di [START_REF] Martino | The mathematical crisis in secondary-tertiary transition[END_REF]. In our future work we plan to design interventions for our local context (Florida State University), in which we will continue to use the context of history of mathematics as a means to bridge the gap between secondary and university mathematics. Additionally, we will explicitly address student dispositions and emotional response to the transition to investigate whether such supporting features assist students in avoiding the most severe aspects of the transition. We believe that from the educational perspective, keeping the impact of affective factors in mind could contribute to students' weathering of transition problems (particularly in STEM-related fields) and hence, positively impact student achievement. Therefore, in our continuing open-ended analysis, we seek to investigate additional methods of data collection and analysis that will enable us to further contribute the growing body of research on students' transition from school to university mathematics in ways that highlight and honor the emotional and affective aspects of transition, and ways in which they may be mediated and remedied by interventions such as the ÜberPro Seminar.

Discussion

Conclusion

We determined that a need to address and reflect on students' emotional dispositions emerged when students were prompted to articulate how they recognized their own transition during the ÜberPro Seminar. Furthermore, this intervention may have contributed to the promotion of metacognitive thinking about students' own transition and gave them agency in partially managing the remainder of their transition process.

The original research was conducted by the second author with colleagues Witzke, Struve, and Stoffels (see alsoWitzke, Clark, Struve, & Stoffels,

2018).

It is important to note that we do not subscribe to the notion that such a transition can be "made." That is, students experience a personal trajectory through the transition, and there are interventions (e.g., the ÜberPro Seminar) which may be enacted that aid in supporting students during this trajectory.


Olov Viirman
email: olov.viirman@hig.se

Magnus Jacobsson
email: magnus.jacobsson@math.uu.se

Epistemological characteristics influencing didactic choices in course planningthe cases of Basic Topology and Differential Geometry

Keywords: University mathematics, course design, epistemological analysis, mathematical and didactic praxeologies, didactic co-determination

Epistemological characteristics influencing didactic choices in course planning -the cases of Basic Topology and Differential Geometry

Olov Viirman, Magnus Jacobsson

What influences university mathematics teachers' didactical choices?

University mathematics education (UME) research is increasingly engaged with questions concerning teaching, and university mathematics teachers' (UMTs) teaching practices, as seen, for instance, in the growing amount of research investigating factors influencing UMTs' didactical choices when planning and preparing courses or individual lectures. Some of these factors are individual, depending upon the UMT's own educational background, research practice, and beliefs about mathematics and students (e.g. [START_REF] Hernandes-Gomes | Teaching Calculus in engineering courses. Different backgrounds, different personal relationships[END_REF][START_REF] Tabchi | University teacher-researchers' practices: The case of teaching Discrete Mathematics[END_REF]. Some concern more general pedagogical issues, such as the specialisms of different student groups [START_REF] Bingolbali | Factors shaping mathematics lecturers' service teaching in different departments[END_REF], available textbooks and other educational resources [START_REF] Mesa | Textbook mediation of teaching: an example from tertiary mathematics instructors[END_REF], or the choice to adhere to particular instructional design principles (Andrade-Aréchiga, [START_REF] Andrade-Aréchiga | Assessing effectiveness of learning units under the teaching unit model in an undergraduate mathematics course[END_REF]. Others again are institutional, such as imposed reform initiatives [START_REF] Stieha | Stirring the pot: Supporting and challenging general education science, technology, engineering, and mathematics faculty to change teaching and assessment practice[END_REF] or the dominant epistemology of the institution (Barquero, Bosch & Gascon, 2013). Here, however, we will consider a different factor that we believe deserves further study: the inherent structure of the particular mathematical domain covered by the course. This paper grew out of conversations between the first author, a UME researcher, and the second author, a research mathematician at a large Swedish university. His research is in topology and geometry and he has been teaching university mathematics for twenty years, at all levels from beginning undergraduate to doctoral courses. While planning and conducting two different courses, Basic Topology (BT) and Differential Geometry (DG), both aimed at second or third year mathematics majors, he was struck by the extent to which the character of the two topics influenced the way he chose to design and teach the courses. To study the particularities of this influence, we adopt an institutional perspective, the Anthropological Theory of the Didactic (ATD) (e.g. [START_REF] Bosch | Doing research within the anthropological theory of the didactic: the case of school algebra[END_REF]. In what follows, we will present an epistemological analysis of the topics, aimed at describing how their different epistemological characters affected the didactical choices made during course design. First, however, we introduce the aspects of the ATD pertinent to the analyses in this paper.

A praxeological perspective on mathematics teaching

ATD "offers a general epistemological model of mathematical knowledge where mathematics is seen as a human activity of study of types of problems" (Barbé, Bosch, Espinoza & Gascon, 2005, p. 236). This activity consists of, on the one hand, the practical block (or praxis) of tasks to be solved and techniques for solving them and, on the other hand, the knowledge block (or logos) providing "the mathematical discourse necessary to justify and interpret the practical block" (ibid, p. 237). This block consists of technologies referring directly to the techniques used and theory justifying the technology and organizing the discourse. An example of a task could be finding the instantaneous rate of change of a certain function at a given point. This task can be solved using different techniques, for instance, calculating the slope of the tangent line to the function at the point. This technique can be justified, for instance, using the definition of the derivative using difference quotients, a technology in turn part of a theory of differential calculus. Together the tasks, techniques, technologies and theories form mathematical praxeological organisations (MO's) or simply praxeologies. In fact, ATD "considers that the notion of praxeological organisation can be applied to any form of human activity, and not only to mathematics" (ibid, p. 239). Hence, the practice of teaching (and learning, for that matter) can be described using didactic praxeological organisations (DO's). The teacher's didactic praxeology is used to help students engage with a particular MO. As any praxeology, it consists of a practical block composed of types of didactic tasks and didactic techniques, and a knowledge block formed by "a didactic technologicaltheoretical environment" (ibid, p. 239). Praxeologies develop within institutions. Indeed, it is a basic tenet of ATD that "human practices and human knowledge are entities arising in institutional settings. (…) As institutions are made of people, institutional praxeologies evolve because of the changes introduced by their subjects" (Bosch, 2015, p. 52). Such evolution is subject to conditions that enable or facilitate the development of a certain praxeology in a given institutional environment, and constraints hindering or impeding its development. "The notions of condition and constraint are relative to the position assumed by a person in a given institution. A condition becomes a constraint when it cannot be modified by the person in this position, at least not in the short run." (Barquero, Bosch & Gascón, 2013, p. 313) These conditions and constraints occur at different levels of didactic co-determination (ibid, p. 314):

Civilisation↔Society↔School↔Pedagogy↔Discipline↔Domain↔Sector↔Theme↔Question

The levels from Discipline to Question concern the particularities of the specific discipline and the way it is structured, while the levels from Pedagogy to Civilisation concern how societies organise the study of disciplines (ibid.). [START_REF] Barbé | Didactic restrictions on the teacher's practice: the case of limits of functions in Spanish high schools[END_REF] use the case of the teaching of limits of functions in Spanish high schools to show how teachers' practices are conditioned by various restrictions, both mathematical and didactical. At the university level, Bosch, Gascón and Nicolas (2016) use the case of the teaching of Group Theory "to illustrate two different ways of questioning the mathematical content to be taught: a first one based leaving the global structuring of the content untouched; and a second one requiring a complete deconstruction and reconstruction of the knowledge to be taught" (ibid, p. 256). In light of the above, we aim to investigate possible relationships between the Mathematical Organisations and the development of the Didactic Organisations in the courses Basic Topology and Differential Geometry. Before presenting an epistemological analysis of the two domains, we will briefly describe the context in which the study took place.

Epistemological analysis and didactical considerations

Both the BT and the DG courses are included in a mathematics program, typically attracting about 30 students each year. Additionally, the courses also attract some students from other programs, for instance, engineering and physics. Prerequisites for both courses include Introductory Algebra, Calculus in one and several variables, and Linear Algebra. When planning the courses, the second author worked with already determined syllabi, although he had control over the choice of textbook [START_REF] Munkres | Topology[END_REF] for BT, and Do Carmo (2016) for DG). At the department where he works, the more advanced courses are usually taught in a Definition-Theorem-Proof (DTP) format [START_REF] Weber | Traditional instruction in advanced mathematics courses: a case study of one professor's lectures and proofs in an introductory real analysis course[END_REF], and although this is not enforced, there are few institutional incentives for radical changes in the teaching format. Hence, the courses discussed here were also taught in this format. The analysis that follows developed through conversations between the authors, and hence reflects the way the second author thinks about and chose to teach the courses. Still, this largely corresponds with how the courses are typically taught, as suggested for instance by the fact that already established syllabi were used.

The main object of study in BT is the class of topological spaces and continuous maps. The course introduces the notions of point-set topology, for instance, compactness, connectedness, and separation properties, in a systematic axiomatic fashion. The main object of study in DG, on the other hand, is the (mostly local) geometry of (curves and) surfaces. It starts with the geometry of surfaces in 3-space and proceeds via the fundamental forms and Gauss' Theorema Egregium (Gauss curvature is preserved under isometric transformations) to the notion of abstract surface geometry with examples such as the flat torus and the hyperbolic plane, which have no isometric embeddings into 3-space. The aim of BT is to structure the class of topological spaces, which is vast and mostly unknown to the students beforehand, into tractable subcategories introducing a comprehensive (and traditional) set of definitions. In contrast, DG concerns itself largely with the production of tools for the analysis of geometric properties of the intuitively relatively accessible collection of all surfaces, building on the students' knowledge of curves and surfaces (in 3-space) from previous courses in the calculus of several variables. DG thus works its way from a concrete setting towards the beginning of a more abstract theory, while BT may be said to go in the other direction. Definitions serve largely different purposes in the two courses. In BT, their main purpose is to establish a vocabulary for the class of topological spaces, which allows for effectively breaking it down into more tractable subclasses. Compactness, separation properties, connectedness and countability properties are all definitions of this type. Few interesting things can be said about all topological spaces. The notions above allow for the study of subclasses (e.g. locally compact Hausdorff spaces) about which interesting theorems can be proved. In DG, on the other hand, definitions establish the tools to make precise distinctions in a setting where the object of study is well known. The first and second fundamental forms, various curvatures and the Gauss map are all examples of this; with their help, it becomes possible to analyse the geometric properties of the surface quantitatively. The particularities of definitions in the BT course have consequences for the use of examples as well. The first role of examples in BT is to show how the few topological spaces that the student has already encountered in earlier courses fit into the general framework that the course provides. For instance, is an example of a Hausdorff space. The second role is to expand the known collection of topological spaces, and in particular, to show that new definitions are not empty. For instance, equipped with the Zariski topology is an example of a -space which is not Hausdorff. It is unlikely that the student has heard of the Zariski topology before. Moreover, in the context of the BT course its relevance in other mathematical domains (e.g. algebraic geometry) cannot be properly discussed. Instead, its presence in the course serves to motivate the definition. In this context, the role of the concept is primary and the example secondary. In fact, one might say that the topic of the BT course is as much the established ways of rendering the category of topological spaces understandable, as it is the topological spaces themselves. On the contrary, in the DG course the role of the examples is mainly to illustrate the different mathematical techniques involved. Hence, examples mostly consist of concrete calculations, much as in earlier calculus courses (e.g. explicitly computing geodesics on a surface of revolution by solving the appropriate differential equation). With a slight exaggeration, one might say that in DG the examples precede the definitions, which are there for the sake of understanding the examples, whereas in BT the definitions precede the examples, which serve the purpose of understanding the definitions. The aim of the BT course, that is, structuring the class of topological spaces and developing a vocabulary for this purpose, has implications also for the type of theorems the course contains. In a sense, most of the theorems are of a technical nature; clarifying the definitions and the properties of the spaces that satisfy them. At least in the beginning of the course they are very elementary, and could easily be given as exercises to students, even at this level. Indeed, we are aware of at least one textbook where the theory is developed with most proofs given as exercises for the reader [START_REF] Viro | Elementary topology[END_REF]. Most of the course is introductory and the theorems proved are thus reasonably easy for the students to follow, with a few exceptions, which (unsurprisingly) occur in the more structured areas, notably in the part concerning metric spaces. The DG course, on the other hand, with its aim of analyzing the geometric properties of surfaces, contains more complex theorems requiring more advanced proof techniques from analysis (relying on relatively advanced theorems, e.g. the implicit function theorem). Where the BT course has mostly technical theorems, The DG course has at least two central, historically and philosophically significant theorems which can provide structure for the course to be built aroundthe Theorema Egregium and the Gauss-Bonnet Theorem (which connects the curvature of a compact surface with its Euler characteristic). The above differences have direct consequences for the way the material is presented to the students. BT is presented in a strictly axiomatic fashion. The whole course unfolds deductively from the definition of topological space. This is a consequence of the extreme generality of this notion and the fact that very few examples are known beforehand. The course requires no prerequisites apart from basic set theory, although a certain degree of mathematical maturity is necessary, due to the degree of abstraction involved. Proofs consist of set theoretical arguments to show that a certain class of spaces or maps has certain properties, while examples consist of the same, but for specific spaces or maps. As mentioned above, the vocabulary is as much an object of study as the particular examples of spaces the course includes. In fact, one reason for developing this vast general theory without much prior knowledge of the objects it describes is that this vocabulary in itself is so useful, that once mastered (even if only through toy examples of little independent value) it is applicable as soon as the student happens upon a topological space in their later studies. DG, in contrast, admits a looser structure, since it is possible to rely on students' previous knowledge and intuition in the presentation of the material and since the course is about closer analysis of a known class of objects. Indeed, it has clear prerequisites of Calculus of several variables and Linear Algebra, which are both necessary and sufficient. This implies that the rich collection of tools of infinitesimal calculus and linear algebra are available for use. Hence, the arguments used in proofs have a very different flavour from those in BT, more akin to standard basic calculus. In DG, definitions are typically motivated by conceptual arguments, relying to a large extent on the student's preconceptions and intuitions. The conceptual meaning of the central definitions can usually be (and often is) explained even without concrete examples, relying on the students' grasp of earlier courses. For instance, the relevance of the geodesic concept can be argued by the wish to generalize the meaning of `straight line' (or motion with zero resultant force). Similarly, just by sketching some pictures the ideas behind principal curvatures or the Gauss map can be conveyed. In contrast, the explanation of definitions in BT cannot rely very much on preestablished intuition, since there are very few examples that the students are familiar with beforehand. Instead, the definitions in BT are presented as a fixed vocabulary to be digested and understood. The point of many of the definitions is seen only in hindsight, when they prove themselves useful in proving theorems. For example, few students immediately understand the definition of first countability of spaces. The relevance becomes clearer when the connection with sequences in the space is explored in more detail. In praxeological terms, the MO underlying the DG course takes its starting point in the praxis, in tasks aimed at understanding the behaviour of surfaces, as objects already familiar to the students, and in techniques used to carry out these tasks. The course develops technology justifying the techniques but the idea of a general theory of abstract Riemannian manifolds is presented only toward the end of the course and is not extensively developed. From a didactical perspective, the fact that students are already familiar with the objects and techniques of the course enables the lecturer to build on this familiarity when presenting arguments and explanations. The MO underlying BT, on the other hand, is structured much more around the logos. A theory of topological spaces, with an elaborate set of technologies, is developed around one main task, namely, classifying topological spaces, and using techniques mostly taken from set theory. In a sense, the BT course is all about logos. The tasks of the taught MO are to a large extent "toy examples", developed in order to support the learning of the theory, rather than being of interest in their own right. Indeed, the BT course is largely about developing technologies that can then be applied elsewhere, to justify techniques for dealing with topological spaces in other settings. In conclusion, we suggest characterizing the DG course as praxis-driven, whereas the BT course is logos-driven.

Conclusions and discussion

In this paper, we have analyzed the epistemological characteristics of two university courses aimed at second and third year mathematics students: Basic Topology and Differential Geometry. We have shown how the different theoretical starting points of the courses, with BT being logos-driven and DG praxis-driven, had consequences for the design of the courses. Here, however, a caveat is needed. We are aware that the MO's that we have described above to some extent are mixtures of the scholarly MO's underlying the courses and the transposed MO's actually taught in the classroom. However, preserving a strict separation is difficult, and we believe that the mixture does not significantly alter the gist of our argument. In fact, the difficulty of adequately separating the two might go some way towards explaining the observation made by [START_REF] Florensa | Helping lecturers address and formulate teaching challenges: an exploratory study[END_REF], that when university lecturers reflect upon their own practice, content-related didactic considerations often seem to be lacking. We see this paper as a small step towards such content-related didactic reflection. In terms of didactic co-determination, we have presented an example of how the domain, and thus the discipline, influences pedagogy. If content of the type included in the BT course is to be presented to students, this poses constraints on the type of pedagogy available. It makes it more difficult, for instance, to make use of students' previous experience and knowledge, and to provide motivation through showing applications of the theory. On the other hand, the mostly self-contained nature of the material, its axiomatic structure, and the relative accessibility of the proof techniques employed, makes a course such as BT suitable for a form of teaching that inducts students into the practices of formal proof. Through use of the DTP format, the lecturer can model this part of mathematical practice (see for instance [START_REF] Viirman | The function concept and university mathematics teaching[END_REF] and can provide students with tasks that lets them engage in such practice in a manageable setting. A course such as DG is less suitable for this, since the proof techniques required are much more complex. However, the way it takes its starting point in relatively accessible, practical problems invites an inquiry-oriented approach, where these problems serve as starting points for the handling of content. This approach appears to be less suitable for the BT course, although one might conceive of a course taking as its starting point the overall question of how to categorize topological spaces. Still, even from this starting point, the course would probably enfold in much the same manner as the course discussed in the present paper. Moreover, we wish to emphasize that the differences in the MO's underlying the two courses should not be seen as mainly influencing the temporal organisation of the material. One could imagine another instance of DG, consistent with the course syllabus but maybe not didactically ideal for the intended students, where the starting point is an abstract definition of Riemannian surface and the extrinsic geometry of surfaces in 3space would appear as embedding theory. However, the course would still be praxis-driven, focused mainly on developing the technology for justifying techniques used for solving geometrical problems. Similarly, BT could be set in the opposite order, starting with several examples of topological and metric spaces arising in natural contexts, and only then introducing suitable notions to understand their similarities and differences. This would be an interesting but likely somewhat ineffective way of teaching the same material, consistent with the course syllabus. Still, the course would be logos-driven in that the main purpose of the examples would be the development of the theory. In other words, the temporal order of definitions and examples could be inverted, but this does not alter their different epistemological status in the courses.

The analysis we have presented here should be seen only as a first step. For instance, one might ask whether other mathematics courses taught at university fit within the two patterns described here. One example of a type of course that does not seem to do so is the Calculus of Variations course at the second author's department. Roughly speaking, it consists of showing how a single central technique (the variational principle) can be applied in a large variety of settings in different areas of mathematics and the applied sciences. At first glance, it would seem as if the logos block would play a very different role in such a course compared to the ones under scrutiny in this paper, and it might be enlightening to examine this case further. Moreover, a more detailed analysis of the interplay between the DO and the scholarly and taught MO in a particular course would require data analysis that we did not engage with in the writing of this paper. This could involve, for instance, an examination of the role of textbooks and other didactic resources on the development of the DO as well as analysis of tasks given to students and of the potentially constraining role played by established assessment practices. Moreover, a deeper understanding of the DO would require empirical data on the teacher's and students' practices. The work presented in this paper is not intended as the type of more radical rethinking of the organization of content suggested, for instance, by Bosch, Gascón and Nicolas (2016). We have done some thinking on alternative ways of course design, cutting "against the grain", so to speak, of the established structuring practices according to mathematical domain. One might consider, for instance, a course on "classification", looking at various ways of structuring classes of mathematical objects in different domains. However, any such radical rethinking would risk encountering major difficulties because of institutional constraints, particularly in early courses taken by students from many different programs, and would thus, at least at first, probably only be possible in relatively high-level courses aimed at future research mathematicians. Still, just thinking about such alternative ways of organizing content may aid in the content-related didactical reflection requested by [START_REF] Florensa | Helping lecturers address and formulate teaching challenges: an exploratory study[END_REF], by forcing us to question established ways of structuring content, and how this structuring might influence the ways in which we can teach.


Guillaume Tisserant

Mathieu Roche

Violaine Prince

Mining Tweet Data -Statistic and semantic information for political tweet classification

Keywords: Text Mining, Classification, Tweets

INTRODUCTION

This paper deals with detection of important words in a document, and how to use them for classification. Importance is a notion that is not predefined. It depends on the task goal and features, as well as on the user's intentions. Textual data are extremely difficult to analyze and classify, according to [START_REF] Witten | Data Mining: Practical machine learning tools and techniques[END_REF]. The supervised learning algorithms require to know the class associated with each document (e.g. theme for document classification, polarity for sentiment analysis, and so forth). The inputs of these algorithms are "package" of language features representing the document to be classified. Once the learning phase is complete, the trained model can assign a class to a " package of features " unlabeled. The quality of the classification given by the algorithm will therefore depend not only on the quality of the learning algorithm, but also on how the transmitted data is represented [START_REF] Guyon | An introduction to variable and feature selection[END_REF].

To sketch an overview of the question to be tackled, in the first instance, we run a brief survey of the different research methods description of textual data suitable for supervised learning. Then, we present GENDESC, a statistical method to select features to the purpose of text classification (Section 3). In Section 4, we compare information given by GENDESC with information extracted of tweets with "semantic" methods. Every new step needs to be confirmed: Thus, the GENDESC method is evaluated in Section 5, focusing on the quality of its proposed features. Finally, we draw the current balance of our work and present some perspectives in Section 6.

GENERALISATION OF TEXTUAL FEATURES

In the abundant literature about text mining, the traditional method of representation of textual data is the "bag of words" model: Words are considered as features used as inputs in the learning algorithms [START_REF] Salton | Introduction to Modern Information Retrieval[END_REF]. Despite its popularity, this method has many limitations. First, it highlights a large number of features : The matrix of features is larger than the number of terms appearing in the corpus, even though short texts like tweets do not provide many features per document (Sriram et al., 2010a). Secondly, it loses all the information related to the position of the words and their syntactic roles in the sentence, as well as all the information related to the context. This information can be sometimes crucial.

Several researchers have stressed the importance of having more general features than words. Experiments have shown the possibility of using the radical or the lemma of each word [START_REF] Porter | An algorithm for suffix stripping[END_REF], or the POS-Tag [START_REF] Gamon | Sentiment classification on customer feedback data: noisy data, large feature vectors, and the role of linguistic analysis[END_REF]. But these methods are not satisfactory. Lemma is not an important generalization, as generalizing words with lemmas cannot significantly decrease the number of features. POS-TAG is an important generalization which destroys all semantic information. It can be useful for a specific task like grammatical correction, but is unadapted for ev-ery word in a generic text classification task. For purposes of classification on specific tasks, some studies like [START_REF] Joshi | Generalizing dependency features for opinion mining[END_REF] propose to generalize specific words (determined according to their grammatical role) by substituting a more general feature and keeping the other in their natural form. In this kind of method, words are selected to be generalized using information based on their classification type. GENDESC, our method, is independent of the classification task. Its goal is to improve the quality of the classification of textual data, when deprived of any knowledge on the classification task.

GENDESC APPROACH

The approach we propose is in two steps. The first one determines the grammatical function of each word in the corpus (Section 3.1). The second step consists in selecting the words which will be generalized (Section 3.2).

Partial Generalization

The objective of our work is to generalize words whose POS tag (in its context of appearance) is more useful than the word itself for the classification task. A POS tag (i.e. verb, noun, adjective, etc.) is a class of objects that behave similarly when it comes to the sentence building. So, replacing a word by its tag comes to delete a semantic contents and keep the grammatical role. This task needs to explore a few tracks to determine the words that must be generalized. We start by replacing the words that appear in few documents by their POS tag. Those that appear often are deemed relevant for classification and are directly used as features.

Take for example the corpus of Figure 1. It contains 14 documents, each consisting of a single sentence describing a semantic relationship type (h: hyperonym; s: synonym). In this context, the aim of classification is to predict the relationship associated to each document (here, sentence). From the example in Figure 1, we obtain, for each word, the number of documents containing it. Actually, the example is built with short sentences like tweets.

Then, for each word of the sentence, the POS-tag is computed.

• Example of Sentence:

The molecular data is also sometimes called a gene clock or evolutionary clock. Noun ; JJ:

Adjective ; To generalize some words of a sentence, we have tested some ranking functions which can assign a value to each word. If this value is smaller than a threshold, the word is generalized. The function used in the first example is the number of documents of the corpus that contains the word. So the threshold represents a minimum number of documents that must contain the word.

KDIR2014-InternationalConferenceonKnowledgeDiscoveryandInformationRetrieval

According to our example, if we consider 4 as a threshold, all the words that appear in less than 4 documents will be replaced by their POS-tag found at the previous step (see Table 2).

The initial sentence of our example, with this ranking function and a threshold at 4, is generalized as follows: The /JJ /NNS is /RB /RB called a /NN /NN /CC /JJ /NN .

We show below the same example with all possible generalization thresholds.

• threshold at 1 (we do not replace any word): The molecular data is also sometimes called a gene clock or evolutionary clock.

• threshold at 2: The molecular /NNS is also /RB called a /NN /NN or /JJ /NN .

• threshold at 3: The /JJ /NNS is also /RB called a /NN /NN or /JJ /NN .

• We can observe that, before the threshold becomes too important, the relevant information (for the relationship type given by the sentence) becomes more evident than in the full sentence. The less relevant words are the first to be generalized, and the words that give the semantic type of the relation ("is" and "called") are generalized only when the threshold is high. From threshold 4 to 6, a "definition" pattern appears : "The X is called a Y". This pattern is a strong clue for a semantic relationship between X and Y, and thus helps classifying the document. Thus, the question of the threshold value relevance appears: In section 5 we discuss the definition of different thresholds. Note we can combine this method with a filter to delete stop-words.

Ranking Function

In this example, we have tested the DF (Document Frequency) function, to generalize specific words. The more present text containing the word in the corpus, the higher its DF. We have tested some other ranking functions. For each function, we have tested several thresholds which will be discussed in Section 5.

IDF: Inverse Document Frequency

The IDF function (formula (1)) is the inverse function of DF [START_REF] Jones | A statistical interpretation of term specificity and its application in retrieval[END_REF].

IDF(x) = log
number of documents in the corpus DF(x)

(1) The more present a text containing the word is in the corpus, the lower its IDF is. Thus, the words with high DF value are those with a low IDF value. So, words generalized with a low threshold become those requiring a high threshold to be generalized. IDF function generalizes common words that appear in classes, which are therefore not interesting for classification.

For example, the IDF of the word is, which appears in many documents (i.e 12 sentences of the corpus of Figure 1) is log( 1412 ) = 0.07 while IDF of word for is log( 142 ) = 0.8

TF: Term Frequency

TF is the term frequency in a document [START_REF] Luhn | A statistical approach to mechanized encoding and searching of literary information[END_REF].

The more often a term appears in the document, the lower its probability of being generalized. This function can be interesting because if a word appears many times in the same document, the word can be useful to classify documents.

D: Discriminence

The idea of D measure (formula ( 2)) is that a word which appears many times in the same class and never in other classes, is relevant for classification. For example, for semantic relationship classification, if a word appears often in documents that contain synonymy relationship, and never in other documents, then this word is probably relevant for synonymy relationship identification. D measure (see formula ( 2)) corresponds to the computation of T F × IDF where all documents belonging to the same class are considered as a single document.

D(x) = nbOccClass(x) nbOccCorpus(x) (2)
• nbOccClass(x) is the number of occurrences of word x in the class that most often contain x

• nbOccCorpus(x) is the number of occurrences of x in the entire corpus

Combination of Functions

It is possible to combine some functions. For example, the combination of the functions D and DF highlights words that both appear often and indicate a particular class. We can expect than the words with high DF × D value are relevant for document classification.

Similarly, all functions described above can be combined together. For example, the function D × IDF emphasizes the words that appear rarely and are distributed very unevenly between classes. T F can be combined with all other functions. We tested these different functions with different thresholds. The efficiency of each function will be discussed in Section 5.

ANALYSIS OF FEATURES GIVEN BY GENDESC

Linguistic Features and Semantic Information

Semantic information is very difficult to use in text classification context, since semantic disambiguation is an crucial requirement before feeding semantic data

to an automatic process: The meaning of a word is generally complicated to take into account for learning algorithms.

But it is the main information used by humans when they analyze documents. So it is probably the most important information to use in text processing.

In this paper, we focus on the semantic "importance" of a word in a document. The following subsections highlight endogenous (see Section 4.1.1) and exogenous (see Section 4.1.2) semantic information.

Endogenous Semantic Information

An endogenous method aims at using information contained in documents.

Different approaches allow the detection of words with high semantic information [START_REF] Faure | Knowledge acquisition of predicate argument structures from technical texts using machine learning: The system asium[END_REF][START_REF] Hirano | Detecting semantic relations between named entities in text using contextual features[END_REF]. Some methods consist of exploiting syntactic information in order to induce semantic information [START_REF] Faure | Knowledge acquisition of predicate argument structures from technical texts using machine learning: The system asium[END_REF][START_REF] Béchet | How to combine text-mining methods to validate induced verb-object relations?[END_REF]. For instance, all the objects of the verb to eat can be gathered in a same concept food.

Other approaches use meta data, e.g. labels of HTML pages. For instance, the title and keyword labels can highlight significant features.

In social networks (e.g. Twitter) HashTags represent a semantic information useful for tweet classification [START_REF] Conover | Predicting the political alignment of twitter users[END_REF][START_REF] Ozdikis | Semantic expansion of hashtags for enhanced event detection in twitter[END_REF][START_REF] Costa | Defining semantic meta-hashtags for twitter classification[END_REF]. HashTags are words highlighted by people who write tweets. This information can be considered as keywords. As an example, in 2012, the HashTag #2012 was used by many people to precise their tweet concern the presidential election. Other people use name of their favorite candidate to highlight their political opinion. Thus, the HashTag #Obama has been massively used to mark a support of Barack Obama. Supporters of the republican party have used #RomneyRyan2012, as a reference to the candidature of Mitt Romney for the presidential position and of Paul Ryan for the vice presidential role. Some HashTags are less explicit, like #Forward2012, exploited by the Obama campaign.

Exogenous Semantic Information

Exogenous methods rely on external sources of information to improve analysis of documents [START_REF] Sriram | Short text classification in twitter to improve information filtering[END_REF]. There is a lot of documents representing semantic information, e.g., ontologies, lexicons, semantic networks, and so on. We use the lexicalsemantic network called JeuxDeMots (JDM) [START_REF] Chamberlain | Using games to create language resources: Successes and limitations of the approach[END_REF]. It is based on the serious game principle in order to construct a large lexical-semantic KDIR2014-InternationalConferenceonKnowledgeDiscoveryandInformationRetrieval network. JDM is the most important semantic network for the French language. It is totally built by players.

Moreover, JDM contains a game named Politit to generate political orientation of words. The construction of this game is very simple: Words are presented with six political orientations (i.e. far left, ecologist, left, center, right, far right). The user has to click on the orientations having most connections with the word. The user can skip the word if he considers it without semantic connection with a political orientation.

Comparison of Approaches

We argue that words considered relevant by a statistical analysis must contain important semantic aspects. So the aim of this section is to compare features returned by GENDESC (i.e. statistical method) with approaches using semantic characteristics. More precisely, we compare words given with D formula, HastTag, and PolitIt.

We can see in Figure 2 that a high proportion of HashTag words are considered relevant with GENDESC. In addition, more than 50% the words of PolitIt that appear in the corpus are also considered relevant with GENDESC. Experiments of Section 5.2 describe different types of words (e.g. Person, Location, and so on) given with the methods (i.e. GENDESC, HashTag, PolitIt).

EXPERIMENTS

Classification with GENDESC

Experimental Protocole

We chose to tackle a problem of classification in order to predict a political orientation of a tweet. We have used a corpus composed of 1500 tweets distributed between five political parties. The goal is to classify tweets based on the political party of the user.

In order to check the effectiveness of GEN-DESC, we tested three different learning algorithms: Bayesian classification algorithm, decision trees, and an algorithm based on SVM (Support Vector Machine). This point will be discussed at the end of this section 5.

Different functions have been tested to choose words which must be generalized. We can see that the quality of a function is almost independent of the learning algorithm.

Table 3 shows results obtained using NaiveBayes algorithm with different functions and different generalization thresholds. We used as baseline a classification with bag-of-words as features, obtaining an accuracy of 46.80%.

Function and Threshold

Table 3 shows that only D function is actually relevant for the choice of words which can be generalized. Other functions generally provide lower results than use of bag-of-words such as features, whatever the threshold. For the D function, the optimal threshold is 0.3. 46.26 45.44 43.83 43.63 Our previous work [START_REF] Tisserant | Gendesc : Vers une nouvelle reprsentation des donnes textuelles[END_REF] confirmed the interest of our method for classification tasks with different corpora.

Machine Learning Algorithms

Three algorithms were tested in their version implemented in Weka [START_REF] Hall | The weka data mining software: an update[END_REF]) :

• The Bayesian algorithm is NaiveBayes

• The decision tree is C4.5

• The algorithm based on SVM applied is SMO (Sequential minimum optimization)

These algorithms are used with default parameters of Weka using cross-validation (10-fold).

Experiments with several learning algorithms were run, in order to compare their performance. Table 4 shows the obtained results. SMO has the best performance and the algorithm based on decision trees has the lowest performance, whether using words as features or those obtained with GENDESC.

HashTag Generation

Another attractive issue of GENDESC concerns the HashTag generation [START_REF] Mazzia | Suggesting hashtags on twitter[END_REF]. Since HashTags are neither registered nor controlled by any user or group, it is difficult for some users to determine appropriate HashTags for their tweets [START_REF] Kywe | On recommending hashtags in twitter networks[END_REF]. We have first compared the type of words given by GENDESC with the HashTag of the corpus, and then, we investigate if words selected with GENDESC in the corpus can be used as possible HashTags.

Types of Features Given with GENDESC

This section describes the types of features (e.g., named entities and HashTags) extracted with different systems. Table 5 has been built with 25 words of each category manually annotated. It shows the different types of words returned with our systems. For example, data given by PolitIt contain a lot of political organisations.

We have compared the set of named entities given by the systems with the similarity measure Cosine. Table 6 presents the obtained results. GENDESC PolitIt GENDESC ∩ PolitIt 52% 76% 92%

Table 7 has been built thanks to hashtags.org website1 . We have taken 25 words for each category in order to study how many are used more than a hundred time per day on average. Words selected with GENDESC are words with high D value. PolitIt words are those which have been attached with one political party by most of players. Measures have been done in July 2014, more than two years after the corpus acquisition.

This table shows that more than 50% of words with high value of D are used as Hashtags. However, the words that come from PolitIt are more relevant for Hashtag generation because of the specificities of the application. Note that the intersection of GENDESC and PolitIt gets a better result than using PolitIt words.

CONCLUSION AND FUTURE WORK

In this paper, we proposed a representation of textual data that improves classification of document methods by generalizing some features (words) to their POS category when these words appear as less discriminant for the task. Our results show that this approach, called GENDESC is appropriate when classification is at stake, regardless of the nature of its criteria. We have also demonstrated that D, Discriminence, is a measure that can be relevant to find semantically important words in a corpus. In our future work, we plan to use semantic information to improve classification.

In previous work, we proved that n-grams can be combined with GENDESC to slightly improve the classification [START_REF] Tisserant | Gendesc : Vers une nouvelle reprsentation des donnes textuelles[END_REF]. HashTag can probably be generated with n-grams of words with high D value. So we plan to use these n-grams in order to construct new Hashtags (e.g. kdir 2014 → #kdir2014). They could be useful to detect Hash-Tags which combine several concepts associated with n-grams returned with GENDESC (i.e. n-grams of words and/or Hashtags). As an example, a lot of tweets contain both HashTag #Iran and word nuclear, and they are often close to each other. The system should detect that #IranNuclear could be an interesting HashTag for all these tweets, which evoke the Iranian nuclear issue. If enough people use the proposed HashTag, they could follow news about "Iranian nuclear" more easily.

Figure 2 :

 2 Figure 2: Venn diagram showing number of common words in the different information sources.

Table 1 :

 1 number of instance of each word.

	This practice of adding minerals to herbal medicine is
	known as rasa shastra. (s)
	The ellipsis is called wielokropek. (s)
	The pancreas is a sort of storage depot for digestive
	enzymes. (h)
	Walnuts and hickories belong to the family Juglandaceae.
	(h)
	In both group the anterior tagma is called the ceprhalotho-
	rax. (s)
	Biochemistery, sometimes called biological chemistery, is
	the study of chemical processes in living organisms. (s)
	Inhalational anthrax is also known as Wooksorters' or
	Ragpickers' disease.(s)
	Biology is a natural science concerned with the study of
	life and living organisms. (h)
	This part of biochemistry is often called molecular biology.
	(h)
	Biological classification belongs to the science of zoologi-
	cal systematics. (h)
	The philosophy of biology is a subfield of philosophy of
	science. (h)
	An MT is also known as a Medical Language Specialist or
	MLS. (s)
	The molecular data is also sometimes called a gene clock
	or evolutionary clock. (s)
	Word	Amount of documents
		containing the word
	is	12
	the	9
	of	8
	a	6
	called	5
	biology, science
	as, know, or, also	3
	study, this, molecular
	for, sort	2

Stotting, for instance, is a sort of hopping that certain gazelles do when they sight a predator. (h) Figure 1: Semantic relationship corpus

•

  Example of the Previous Sentence Tagged with PoS: The/DT molecular/JJ data/NNS is/VBZ also/RB sometimes/RB called/VBN a/DT gene/NN clock/NN or/CC evolutionary/JJ clock/NN ./.

	In this example, the POS-tags are:
	RB:	Adverb;
	DT:	Determiner ;
	VB:	Verb ;
	VBN: Verb, past participle ;
	VBZ: Verb, 3rd ps. sing. present ;
	NN:

Table 2 :

 2 Generalisation.

	word	POS-tag	Number of	feature
			documents
			which contain
			the word
	The	/DT	9	The
	molecular	/JJ	2	/JJ
	data	/NNS	1	/NNS
	is	/VBZ	12	is
	also	/RB	3	/RB
	sometimes	/RB	1	/RB
	called	/VBN	5	called
	a	/DT	6	a
	gene	/NN	1	/NN
	clock	/NN	1	/NN
	or	/CC	3	/CC
	evolutionary	/JJ	1	/JJ
	clock	/NN	1	/NN

Table 3 :

 3 Accuracy according to measures and thresholds.

	Threshold	0.1	0.3	0.5	0.7
	D	46.80 50.24 49.19 47.38
	DF	46.32 45.44 43.90 43.70
	IDF	47.47 41.95 26.85 25.10
	T F	19.62 19.62 19.62 19.62
	DF × D	46.32 44.37 43.36 43.22
	D × IDF	49.40 35.50 20.13 20.13
	T F × D	46.80 46.26 43.22 45.37
	T F × IDF 39.66 28.19 22.80 21.95
	T F × DF

Table 4 :

 4 Results obtained with different learning algorithms.

	Method	GENDESC Bag-of-words
	SMO	55.30	52.33
	NaiveBayes	50.24	46.80
	C4.5	38.52	43.43

Table 5 :

 5 Word classification in % with : -Word with highest D value by using GENDESC -Word most referenced in PolitIt -HashTag most frequent in the corpus

	Approaches GENDESC PolitIt HashTag
	Person	16	28	4
	Location	28	16	12
	Political	4	28	8
	Organisation
	Non political	8	4	20
	Organisation
	Other	44	22	56

Table 6 :

 6 Similarity of different group of words.

	Cosine( GENDESC, Politit)	0.73
	Cosine( GENDESC, HashTag) 0.90
	Cosine(HashTag, Politit)	0.59
	Towards HashTag Generation
	We show that words selected by people as HashTags
	contain important semantic information. Note that
	HashTag generation is a totally different task than
	classification; This enables to identify semantic infor-
	mation in messages.

Table 6 and

 6 Figure 2 highlight that ungeneralized words with GENDESC are close to HashTags. So we argue these words could be interesting as Hashtags. To validate this hypothesis, we have studied if words with high D values are currently used in Twitter as HashTags.

Table 7 :

 7 Connexions between hashtags.org, PolitIt, and GENDESC.

http://www.hashtags.orgKDIR2014-InternationalConferenceonKnowledgeDiscoveryandInformationRetrieval