Ruth Druart's educational portfolio: 2011

Teaching fractions to grade 3 at Marymount International School: Reflecting on and developing present teaching techniques.

Introduction

After having taught fractions to a 3^rd grade middle maths group during the last academic year, I felt concerned that many of the children had not really understood the concept behind fractions. This manifested itself in their inability to generalise out and to use fractions in everyday life situations. Furthermore I had two years previously taught fractions to a middle maths group in grade 5. I had found at the time that very few of them could manipulate fractions, even though this had been covered in grade 3 and again in grade 4. It appeared that the skills taught (adding fractions, ordering fractions, finding equivalent fractions) were skills that many of the children could only master for a limited time after the methodology was taught. In fact the teachers are often heard to complain that the children forget everything after the summer, and we always need to start again every September. This indicates to me that the children had not understood the concept of fractions, but could merely follow the mechanics of working with them shortly after having been shown the methodology. Is this really what the teacher intended? It certainly isn’t what I want to achieve with my class. I expect and hope that the children will have understood the concepts behind the methodology, and will therefore have better retention with regard to the operations.

In this assignment I will examine my current teaching methods with regard to the teaching of fractions, by looking at the learning theories behind my teaching; and I will also seek to find a better way to move forward with my teaching by investigating the different learning theories.

My Method for teaching fractions to third grade

I introduce fractions by drawing a circle and dividing it up into equal parts, starting with two halves, then three thirds, then four quarters, etc. I ask them to name the parts, and then I give them the vocabulary that goes with the fractions, such as numerator and denominator.

They then do exercises from the text book, where they need to identify shaded parts of a whole, using fractions. I then mark and correct their work individually. When most of the class seem to have mastered this I introduce the idea of equivalent fractions. This is done using mathematical manipulatives, in the form of magnetic strips; this enables them to visually realise, for example, that two thirds is equivalent to four sixths. They then make diagrams in their books to show equivalent fractions, followed again by exercises from their text books, where they need to find equivalent fractions.

We next work on ordering fractions and then on adding and subtracting fractions, following similar procedure to the above.

Intermittently, and as I see necessary, during this learning time I ask questions to the whole group and will ask some children to come up to the interactive whiteboard to answer some problems. I also encourage questions by responding positively to any that are asked.

At the end of this teaching the children are assessed with a written test, which is later marked by me.

An overview of the three main theories of learning

There are three main perspectives on knowing and learning (Green, Collins, Resnick, 1996):

a) Behaviourist

b) Cognitive

c) Situative

All of these perspectives have contributed to our understanding of cognition and learning, and have all had and continue to have an influence on educational practice. According to Greeno, they are not mutually exclusive and can be considered to be complementary in the same way that biology, physics and chemistry are complementary when studying some processes, like genetic replication. Therefore, each perspective has something to bring to teaching, and a complementary mixture of methods is possible when teaching. For example, fractions could be introduced using the situative theory, which will be discussed later, then practice in the use of fractions could be considered to make use of the behaviourist approach, whereby correct answers produce positive feedback and incorrect answers negative feedback.

I will examine this idea further as I give an overview of these three views, and analyse how my own teaching methods fit in with these theories.

a) The behaviourist perspective is about making an association between a stimulus and a response; what someone knows is a result of that person’s experience. Knowledge becomes an “assembly of specific responses” (Green, Collins, Resnick, 1996, p.17).

This perspective on learning encompasses the transmission or mechanistic theory of teaching, where the information to be known is given by the teacher to the pupil, either verbally or in written form, or both. What is actually absorbed and/or assimilated by the child is only really known when a test is given. The questioning after the information is given then forms the associations between stimulus and response; the correct responses receiving positive feedback. The number of correct responses could be increased by giving easy, simply-put questions, at least to start with. As the child starts to score 100% on these questions, then gradually more complex questions could be introduced. Given enough time and feedback, the number of errors a child makes should decrease, while the number of correct responses should increase. Indeed, in order to facilitate the learning of a complex skill the “sequence of instruction should proceed from simpler components to the more complex component” (Green, Collins, Resnick, 1996, p. 27).

Taking this perspective a learning environment would have to be very well organised, with routines that the children know and follow. Explicit instructions would need to specify the procedures and information that is to be learned, and the learning materials would need to be organised so that the children have learned the prerequisites for each new concept. Opportunities would then need to be provided for the children to be able to respond correctly. For example, easy questions to start with, where they are likely to give the correct response, and where direct positive reinforcement for correct answers is given by the teacher, in the way of encouragement, such as, “well done” or “great, you’re doing really well”. Alternative forms of positive reinforcement could be provided, such as gold stars, or treats.

b) The cognitive perspective views knowing as concepts and cognitive abilities(Green, Collins, Resnick, 1996).

The cognitive theory of learning encompasses constructivism, “the assumption that understanding is gained by an active process of construction rather than by passive assimilation of information or rote memorisation (Confrey, 1990).” (Green, Collins, Resnick, 1996, p. 22) Constructivism theory has been greatly influenced by Piaget’s theories about cognitive development. Piaget carried out decades of work on children’s cognitive development, and he developed a constructivist theory that students do not absorb or copy from their teachers, but need to construct their concepts through observation and experimentation. He formulated a theory of development of logical structures, stating that a child’s capacity to understand certain concepts is limited by their level of general logicodeductive development. He emphasised that this is not biologically determined, but that their intuitive conceptual understanding changes as they grow older. Studies of cognitive development have shown that significant conceptual growth in children’s informal understanding of numerical, biological and psychological concepts occurs over time (Green, Collins, Resnick, 1996).

This would mean that a mechanistic approach would be inappropriate, as the child needs to actively construct, and thereby comprehend the concept. Also, what if the information given in a declarative form to the child was beyond their level of general logicodeductive development? The information could appear meaningless or confusing to the child. I think this does happen in classrooms; the information presented in the declarative form means little to the child, and the teacher can see the child “zoning out”. I have sometimes found, to my disappointment, that some children haven’t really understood what I’ve just been talking about when I present the information in a declarative form. This could be that they are not ‘ready’ to understand the concept yet, or that they have not been given the opportunity to construct the concept themselves through observation or exploration, or both. In this way the behaviourist and cognitive perspectives are not complementary. It is not enough to simply present the material in a declarative form.

c)Finally we have the situative perspective, where the environment contributes to the learning process. It focuses on the way knowledge is distributed in the world and the practices used. “Thinking is situated in a particular context of intentions, social patterns and tools.” (Green, Collins, Resnick, 1996, p.20). This view on learning has been encapsulated by sociocultural theory, which states that, “children’s minds develop as a result of constant interactions with the social world – the world of people who do things with and for each other, who learn from each other and use the experiences of previous generations to successfully meet the demands of life. These experiences are crystallized in ‘cultural tools’ and children have to master these tools in order to develop specifically human ways of doing things and thus become competent members of a human community.” (Stetsenko and Arievitch, 2002,p.87)

Vygotsky was the main advocate of sociocultural theory (Steiner and Mahn, 2003). He placed culture, context and system at the centre of inquiry. He emphasised the importance of the role of the individual and the social in the learning process. By social he meant everything that included social life and activity, of which culture plays a big part. The transformation of social processes into individual ones is central in sociocultural theory and contributes to its interdisciplinary nature (Steiner and Mahn, 2003, p.127). He argued that learning leads development, which is in contrast to Piaget’s theory of learning where development precedes learning. Also in contrast is the fact that Piaget generally ignored the role of history and culture in learning, but based his on universal models of human behaviour. Vygotsky, on the other hand, used pedagogical methods that took into account human diversity and placed great importance on social and historical contexts. Vygotsky saw learning and development as interrelated and argued against using maturation as the essential element in development. “Vygotsky views psychological functions and the means of mediating them as emerging out of the child’s social interaction with adults and peers” (Haenen, 2001, p. 159).

So if it is the social environment which is the most important instrument in the education process, then it is up to the teacher to use it appropriately, and so provide the right conditions for learning. Context is all important, and teachers need to find and include the contexts of students’ experiences and their local communities’ points of view, and then put the new academic learning in that context. Vygotsky argued that people use specific features of their environment to structure and support mental activity, and so teachers need to pay careful attention to the context in which the pupils’ thoughts occur.

Therefore knowing how to participate in both classroom activities and classroom discourse both play a crucial part in children’s learning.

Identifying the different learning theories behind my teaching

It is clear that in my teaching I tend towards the behavioural perspective. I present the concept to be acquired in a declarative form, though I do attempt to elicit ideas from the children as an introduction to the subject. But when doing this I am talking to the class as a whole, thereby making myself the overseer, i.e. the one who possesses the knowledge and whose job it is to pass it onto the uninformed child.

When they are copying the diagrams of fractions into their books they are presenting the concept in a declarative form. Then when they answer the questions from the text book they are forming associations. Behaviourists would have children getting a maximum of correct responses, which would be more likely if the situation does not include irrelevant stimuli that could distract the child. This is exactly what happens with the text book; the first questions are easy, then gradually become more difficult, and extra information or distractions are kept to a minimum. Once these pages of questions have been finished then the children may be exposed to word problems, which may contain features of everyday life situations. Homework that is given after is a means of forming further associations.

I do also encourage classroom discourse by welcoming and responding to questions posed by the children. I have a small class size (<18), and a culturally diverse class; I find that for the most part the children feel free to express their thinking, and different methods of working through maths problems without fear of feeling different or wrong. This part of my teaching would correspond to the sociocultural model of teaching where discourse is considered to be all important (Green, Collins, Resnick, 1996).

When teaching equivalent fractions the children have the opportunity to use the magnetic manipulative strips. Is this a constructivist approach? (Green, Collins, Resnick, 1996, p. 29) “The activities of constructing understanding have two main aspects: interactions with material systems and concept in the domain that understanding is about, such as interacting with concrete manipulative materials that exemplify mathematical concepts such as place value or fractional parts, and social interactions in which learners discuss their understanding of those systems and concepts. To be successful, a learning environment must be productive in both of these aspects.” I really don’t think that introducing these manipulative strips goes very far into the constructivist approach to learning. It is more of a superficial gesture, for a start they are introduced at a point where the children have already been introduced to the concept of equivalent fractions, so they are not necessarily constructing any ideas themselves; they are merely demonstrating what they have already been told, also there is little discussion around this activity. It could be of more use in a constructivist perspective for children who have not been paying attention, and who then need to construct their own concept of equivalent fractions, possibly questioning their neighbours to fill in the gaps. But this was not my objective for the lesson!

Evaluating the different learning theories behind my teaching of fractions

Although it is clear that the behaviourist theory of learning has some direct implications for teaching, like having students produce correct responses many times in order to reinforce the stimulus-response reaction, I think it is very limited in its scope with regard to conceptual learning, and as such it only covers one aspect of learning; this aspect being that of rote learning and stimulus-response reactions. This type of learning is more typical of traditional education, and psychologists and educators have questioned this kind of learning. It is possible that results can be achieved more systematically, and with very large class sizes, where controlled interaction is more difficult, it could be said that it is an easier option for the teacher.

Since the work carried out on behaviourism there has been a wealth of research on knowledge and learning, and I find it surprising that the text book I use for teaching maths hasn’t taken into account different theories of learning. But maybe I am expecting too much from a text book, and need to think about developing my own teaching methods in light of research into learning and teaching. This is what I shall now endeavour to do.

I am particularly interested in the sociocultural model of learning since it makes learning a more personal and relevant experience. Also, it would appear that there is some research that supports the idea that learning precedes development. Steiner and Mahn (2003) state how neuroscience has provided evidence that “learning changes the physical structure of the brain, and with it, the functional organisation of the brain.” (NRC,1999, mentioned in Steiner and Mahn, 2003, p.132). This would support Vygotsky’s view that learning leads development, rather than the cognitive view that development precedes learning. In fact Vygotsky believed that learning is the pathway through which the mind develops (Stetsenko and Arievitch, 2002).

Additionally, Alexander(2004) discusses neuroscientific research, stating that this research demonstrates that talk is not necessary only for learning, but also for the physical building of the brain itself. He mentions the period which corresponds to the primary school years as being the one where the brain actually restructures itself, builds cells and makes new connections; and talk actively aids this process, but then this falls off quickly after the primary years. What he means by talk is a two-way discussion, and not the teacher talking to the student in a declarative form.

Following on from this I will look at the sociocultural model of learning, and how I can use this with regard to my teaching.

Implications of the sociocultural theory for the teaching of fractions

(Stetsenko and Arievitch, 2002)Many innovative ideas with regard to education have come from research into the Vygotskian approach to the role of learning in development. Key to Vygotsky’s theory was the concept of internalisation, but one of the most radical approaches to learning comes from the work of Piotr Gal’perin, who was a close colleague of Vygotsky. He stated that “mental processes should be understood as transformed and internalised material actions that involve cultural tools” (Stetsenko and Arievitch, 2002, p.88). After looking at institutional practices he came to the conclusion that, “school children are often faced with fragmented, poorly generalised phenomena that are supposed to be learned by simply memorising them.” (Stetsenko and Arievitch, 2002, p.89) Typically, this form is the way I teach fractions at the moment, i.e. First teacher presents the task (division of circle into fraction parts), then teacher gives explanation of rule (fraction names), then pupils learn rule, and finally they practice solving typical tasks (exercises from the text book). The main problem with this type of teaching is that, “it does not encourage children to build the actions in a way that would allow them to meaningfully generalise these actions, and hence to internalise them”(Stetsenko and Arievitch, 2002, p.89).

(Arievitch and Haenen, 2005)Gal’perin stated that three stages were needed for mental processes to be truly acquired; progressing from physical actions to audible verbalisation and finally to ‘internal speech’.

The first level is the material level, where actions are based on physical objects or their material representation, like looking at or imitating. This would correspond to the stage in my teaching where I would use manipulatives for teaching fractions, or the demonstration using the circle, which is divided into parts. The children then need to imitate the actions I have shown them using the manipulatives and drawing diagrams themselves.

The second level is the verbal level, where actions are based on overt or covert speech, and tangible objects are replaced by word concepts or speech. The actions are executed verbally. This would mean that the children would explain what they are doing, we would have discussions, they would express their ideas, etc. In my teaching this stage is rather neglected, therefore the children are not beginning to internalise the concept.

The third level is the mental level, where actions are based on pure thought (conceptual thinking). This means they can manipulate concepts, generate hypotheses, pose and solve mental problems and plan and monitor cognitively. This stage is also neglected in my teaching. Once I think the children have mastered the procedure, as in the first level, then I tend to press on ahead to the next topic, so I am again moving on before the children have had much of a chance to internalise the concept, and without having given them the cultural tools necessary to help them in the process.

One result of this type of learning is that children have possibly not mastered the concept, as they have not actively built the action; instead they have been presented with the concept in a declarative form. They then follow the taught procedure, possibly getting some questions wrong and some right, and as they receive feedback from previous questions, they form an idea of what is correct procedure. As they answer more questions, they will be able to apply the procedure more accurately, but this is really little more that ‘trial and error’. Most of the children can follow procedure, and so perform reasonably well on the tests given soon after. However, since their actions have not been internalised, they have not become the “tools of their minds” (Stetsenko and Arievitch, 2002, p.89). This could explain why they have such poor retention of the procedures over longer periods of time.

(Stetsenko and Arievitch, 2002)Gal’perin tried to develop a form of teaching that would provide children with more psychologically and developmentally efficient cultural tools. He defined these as “learning materials that present in a generalised or schematic form the essential features of a given class of phenomena.” (Stetsenko and Arievitch, 2002, p90) These features relate to how the phenomena evolved in the social world, and the cultural tools are to be found in the historically evolved knowledge. This knowledge would be formed from the evolution of previous generations’ methods for dealing with the particular phenomena. Gal’perin and his colleagues developed a new type of teaching based on such cultural tools.

This kind of teaching is called systemic-theoretical, and involves showing the origin of the practices one is teaching. This is neglected in my teaching of fractions; I tend to introduce fractions as discrete, single objects, paying practically no regard to the logic and function, or their evolution in our social world.

(Schmittau, 2003) Vygotskian cultural–historical psychology takes a very clear approach to the genesis of both number, and fundamental mathematical actions, such as multiplication. It states that number developed out of the action of measurement rather than counting.

However, for children number usually comes from counting. (Davydov, 1991, cited by Schmittau, 2003) states that, “since number traditionally becomes identified for children with the action of counting, this only generates the positive integers, and formalist mathematics generates real numbers from these as well, a rational number (and hence a fraction) is defined as a quotient of two integers a/b such that b cannot= 0. (This allows, for example, for 2/3, and 5/4, while properly excluding 2/0 from the realm of number.)” This is a formalist definition, and dividing the circle into parts to illustrate fractions, as I do, is merely a visual interpretation of a formal definition. (Schmittau, 2003) Davydov criticises this as it separates fractions from their historical origin in measurement. Historically fractions could not have been developed as quotients of integers. Historically and socially the rules, or notation of a concept, come after the concept has naturally occurred in a society. Why decide on a set of rules or notation for something that we have not yet encountered?

(Schmittau, 2003) This formalization of mathematics occurred in the 19th and early 20th centuries, and was an attempt to make mathematics purely deductive. This meant that it required cognitive reflection that was based on a body of knowledge that was different to the body of knowledge that had developed in our social history over thousands of years. They assumed that the formalist definitions could be learned directly, without passing by the development of concepts as they had naturally occurred. It was rather like learning maths backwards; starting at the conclusion and working back to the hypothesis or questions. But ordinary students had problems learning mathematics in this way. “Rigorous deduction and formal logic were not the paths of conceptual genesis.”(Schimmtau, 2003, p.227) Indeed it has been shown through clinical interviewing, “that the direct transmission of mathematical understanding from teacher to student was not occurring despite clear explanations of mathematical content.”(Schimmtau, 2003, p.226)

However, I am expecting my pupils to learn these formalist definitions directly through a mechanistic approach to learning, having skipped the development of the concepts as they occurred naturally, and if I follow the sociocultural model I need to reintroduce this when teaching fractions.

Research (Schmittau, 1994, cited by Schmittau, 2003) indicates that when the concept of number is allowed to develop from the action of counting, then the entire category of real numbers may be interpreted by students in terms of the counting numbers, and the smaller the numbers, the better. This means that mathematical operations may be understood for small, whole numbers, but what happens when you reach fractions and irrational numbers? These cannot be generated through counting, and as a consequence many students, and even adults fail to see fractions and irrationals as numbers (Skemp, 1987;Schmittau,1994, cited by Schmittau, 2003), and as such they may inadequately conceptualize the fundamental operations (i.e., addition, subtraction, multiplication, and division) on these numbers as well. This could help explain why some children have a fear of maths, and appear to a have a mental block when it comes to the stage of working with numbers which may not be small, whole, or may even be negative! I have experienced this with children when they get to the age of about nine; this would correspond to the point in time where they are expected to work with fractions and larger numbers.

Assuming then, that numbers evolved first of all as a form of measurement, children need to be introduced to this idea first of all. They could be presented with various practical tasks for which measurement is needed, whether that measurement takes the form of tokens, footsteps, rulers, scales, litre measures or money. This technique means that the concept of number is not taught through separate objects, but through reconstructing the problem as it emerged, and the resulting practice as it evolved in our world. The tools used for measurement would be the cultural tools that Gal’perin mentions.

When I compare this approach to my typically behaviourist approach to teaching fractions, it is clear that I am only teaching the mechanics and formal definitions of fractions, hardly addressing the sociocultural side. Many of the children in my class have hardly come across fractions before I introduce the concept; some understand what a half represents, and possibly a quarter, but not much more. As a result the whole concept means little to them and they have difficulty applying it to any real life situations, and indeed after a holiday of two months have totally forgotten the whole concept. Whereas if I had applied the socio-cultural model they would have understood the need for fractions before they were introduced formally.

To take a systemic-theoretical approach I would need to find a way to present a problem where the children would need to use parts of a whole in order to solve it. This is how the concept of fractions would have evolved naturally. For example I could reconstruct a problem where whole numbers are not sufficient to solve it, this would push the children forwards to develop another practice in order to solve it. E.g. I could ask them to measure the size of a basin using cups as a measure of volume. I would make sure that the basin had a volume involving a half cup measure. I would expect some children just to ignore the half cup when finding the answer, and some to say ‘nearly’ x number of cups, or a ‘bit more’ than x number. Some might come up with a half. When representing their answer in term of counters they would need to break a counter in half. Then they would need to devise a method for recording their results using numbers. This is exactly where they would have to develop the notation we use to represent fractions; it would be very interesting to see what they come up with here. Then I could introduce the vocabulary we use, such as denominator and numerator, thereby providing them with the cultural tools.

From here I would need to make the tasks progressively more difficult. Vygotsky and Luria (1993), cited by Schmittau (2003) carried out an extensive investigation of the development of primates, traditional peoples, and children and concluded that cognitive development occurs only when members of these groups are confronted with a problem for which previous solution methods are inadequate. As a teacher I need to create situations for which the children have to come up with new ways to solve a problem. During their attempts to solve the problem I could provide them with cultural tools, such as a litre jug or a measuring tape. This idea fits in with the cognitive perspective, whereby children need to construct their concepts through observation or experimentation, rather than through passive assimulation.

Conclusion

In conclusion, I think I need to work on the children in my class internalising the concept of fractions by having more discourse in class, and where the children have to verbalise what they are doing, explaining why they are taking the steps they are. I also need to have a more practical approach to teaching where I use activities to introduce a concept instead of merely declaring it to them. This would involve more planning and thought, but could produce more satisfactory results for me as a teacher.

Given the importance of measurement, it is also something which needs to be given more time in the curriculum. This point was brought home to me when after recently teaching fractions to a 3^rd grade class, I asked them to measure something in order to draw a table in another subject. They asked me what the little lines between the numbers were (the mm), I explained by saying they were tenths of the cm; this really seemed to baffle them, and they had a difficult time relating what we had learned about fractions to this real life situation, where a measurement was needed. I find it logical that we need to bring more aspects of measurement into the curriculum, from an early age.

The important thing is to bridge the gap between purely academic, mechanical learning and everyday applicable learning. Getting children to solve problems that they actually have a genuine interest in solving through their own cultural background could help to bridge this gap. I think it is up to the individual teacher to find problems for their own class which are of personal significance to the students, and which will also challenge them, and so help them to grow cognitively. As Vygotsky states, learning leads development, and so the teaching must be ahead of development to be truly effective.

For this to happen the teacher will need to familiarise him/herself with the students. Students should also be encouraged to bring their own experiences into the classroom, in a safe and secure class environment, so that they are free to take intellectual risks, and move forwards in their cognitive development. As the sociocultural model states: the context of students’ experiences is all important and classroom discourse plays a vital role.

References

Alexander, Robin (2004) Towards Dialogic Teaching: Rethinking Classroom Talk. Cambridge: Dialogos.

Arievitch, I.M.,and Haenen, J.P.P.(2005).Connecting Sociocultural Theory and Educational Practice: Galperin's Approach, Educational psychologist,40,(pp.155-165)

Greeno, J., Collins, A., Resnick, L. (1996). Cognition and Learning. In D.C.Berliner and R.C.Calfree, Handbook of Educational Psychology. New York: Simon and Schuster Macmillan (pp. 15-46)

Haenen J. Outlining the teaching-learning process: Piotr Gal’perin’s contribution: Learning and Instruction II (2001) pp. 157-170

Schmittau, J (2003). Cultural Historical Theory and Mathematics Education. In Kozulin, A., Gindis, B., Ageev, V. S., and Miller, S.M. (Eds.). (2003). Vygotsky’s Educational Theory in Cultural Context. Cambridge: Cambridge University Press, pp 225-246.

Steiner and Mahn (2003). Sociocultural contexts for teaching and learning. Handbook of psychology, vol.7:educational psychology (pp. 125-151)

Stetsenko A. and Arievitch I. (2002). Teaching, Learning, and Development: A Post-Vygotskian Perspective. In G. Wells and G.Claxton, Ed. Learning for Life in the 21^st Century:sociocultural perspectives on the future of education. Blackwell Publishers Ltd.

(pp.82-96).

Voice	Fluency	Actions
Automated, no attempt to emphasize any words	Frequently stumbles over words	No actions
Some attempt to put emphasis on key words	Stumbles over some words	A few actions attempted
Emphasis on key words, begins to sound like character.	Stumbles only occasionally	Some actions are made which fit the speech
Really sounds as one would imagine the character	Totally fluent, and at ease with the words	More actions, which all fit perfectly with speech

Ruth Druart's educational portfolio

Libellés

jeudi 6 octobre 2011

lundi 23 mai 2011

Personal goals for students

Rubric for acting scene from Holes

Effective Communication

MA unit on teaching fractions to 3rd grade students

mardi 3 mai 2011

Debating

lundi 2 mai 2011

Power point presentations by students on home country

Using technology to teach

News items looked at during the year

Acting out scene from Holes

vendredi 29 avril 2011

Test on Fractions (no words)

Treasure Hunt using points of the compass

Libellés

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