Why and how do students attend the math help centre and what sort of learning and teaching takes place there?  This question guided the research that is to be discussed in this paper.  The math help centre served as the focal point for the research.  The setting is a room at a university campus in western New York.  Its principal role is to serve the student population of three first year mathematics courses.  These courses are designed for students who require some form of basic skills development in mathematics or, alternatively, precalculus preparation.  Students in other courses are welcome to make use of the services offered.  However, priority is given to students in any of the three courses.

 The help centre is staffed from 10 a.m. to 4 p.m. (Monday - Friday) by tutors.  The tutors include graduate students who serve as instructors for the three aforementioned courses as well as undergraduate students.  The instructors are present in the math help centre two hours weekly.  Most undergraduate tutors spend anywhere from three to five hours weekly in the math help centre.

 Initially, the research was restricted to participant observation and informal conversations with some students and tutors.  The observations allowed me to develop a sense of the help centre as an environment. Paraphrasing Taylor and Bogdan (1984), as an observer my intent was to establish open relationships with informants.  "Working with informants is the hallmark of ethnographic fieldwork.  It involves an ongoing relationship" (Spradley & McCurdy, 1972).  The desire for such a relationship led me to visit the help centre regularly (about twice weekly for 1-2 hours on average per visit) over a six week period.

 A total of 6 in-depth interviews were conducted.  Five students and a tutor were interviewed.  These students (Ann, Cliff, Ellen, Pam, and Shelley) all visited the math help centre 3 or 4 times weekly.  The tutor, Carla, spends 10 hours weekly in the help centre.  The transcripts of these interviews combine with my field notes from observations and informal conversations to provide the data for this research.  It is this data that lays the foundation from which themes may develop.  The spirit of the research experience is captured by the following quotation:  "Our advice is to not hold too tightly to any theoretical interest, but to explore phenomena as they emerge during observations (Taylor & Bogdan, 1984)."

 This spirit was exemplified by an early experience in the course of the study.  While exploring the possibility of doing research at the help centre, I engaged in conversations with some tutors and the coordinator of the centre. It was suggested by them that a core group of students visited at regular hours because they had developed bonds with specific tutors.  The tutors adhere to a weekly schedule that remains constant throughout the semester, thus making it feasible for such routines to establish themselves.  In fact, I expected to be observing such relationships.

 However, this expectation was contradicted by my early experiences in the context of the study.  It appears that students have preferences but it is not so common for strictly one-to-one relationships to develop.  Quoting Heidi, a tutor at the help centre:
 

 There are some people I may see more of because they drop in when I'm here but it's not specifically to see me.

 The matching seems to be more random than I had initially anticipated.  The following excerpt from my field notes echoes this sentiment.  The conversation was between a student named Bob (B) and me (J):

 J: Do you use the Math Place much?

 B: Quite a bit.

 J: Do you work with a specific tutor?

 B: No, whoever is here but some are better.

 Let us return to the umbrella question:  "Why and how do students attend a math help centre and what sort of learning and teaching takes place there?"  Themes have been extracted from the data in an effort to address this question.

 Three themes are discussed in this paper.  The first of these concerns the random matching of students and tutors.  The second deals with the routine nature of attendance.  It is to be argued that these two themes are overshadowed by a notion of convenience.  By this, I mean that what is convenient to the student takes precedence over their desires to work with particular tutors or to be present at specific times.

 The crux of the paper rests with the third theme:  the help centre as a crutch.  We shall examine this theme in greater detail than the others.  Data will be presented that suggests that students become dependent upon the help centre as a means of coping with mathematics.

 Let us begin to address the research question through the medium of the data.  The idea of random matching provides a starting point for our discussion.  The following conversation with Pam, a student, suggests that preferences are tempered by convenience.  That is, the timing of the visit to the math help centre takes precedence over the desire to work with particular tutors:
 

 J: Do you find yourself drawn to particular tutors or particular people that you try to work with when you are there?

 P: Yes. I work better with some than others.

 J: Does that in any way affect the timing - the times that you come to the help centre?

 P: Oh that I come at certain times.

 J: Knowing that certain people will be there.

 P: Yeah I mean I come when it's good for me but you know yeah I like to look for certain people.

 J: So you wouldn't say that it influences the time.  It's more that when you're there.

 P: Yeah (as I speak).

 J: You sort of will look for certain people.

 P: Yeah but I realize that certain people I work better with but it's just basically the one-on-one.  It could be anyone.

 A similar story is narrated by Ellen:

 J: Do you find yourself bonding with any particular tutors?

 E: Yeah - a couple of them that I know that they just help me more than the others do.

 J: In what way?

 E: Well two of them - their explanations, just the way they explain the problem to me - just it comes out a lot better.  It almost seems like they know math a little bit more than the other ones, in my opinion.  I don't really know if they do or not, but.

 J: So, now with these tutors has the bond developed a bit randomly also?

 E: Probably, yeah.  I think so.  It's just something that I notice just in that I mean I don't think it's a mutual one.  You know what I mean.  I'll notice that I'll be looking for a specific one and I'll wait for her if she is with someone else versus asking someone who I don't think really explains it as well.

 J: Would you say that you attend the help centre at certain times because these people are there?

 E: No, only when it's convenient for me.  It just so happens that they're usually there - like I know one isn't there on Monday, Wednesday and Friday when I'm there but then two times I've been there on Tuesday she's been there.

 The voices of students indicated that they indeed exhibited preferences.  However, these preferences were secondary to their desire to be present in the help centre at times which were convenient to them.  The following excerpts from interviews with two students, Shelley and Cliff, lend further support to this idea:
 

 Excerpt 1

 J: Have you been developing a bond with particular tutors?

 S: Going to certain ones?

 J: Uh-huh.

 S: Yeah, I guess so.  I think that some do explain things better.  They just are better teachers.  People get things across easier than other people do.  Yeah there is a difference but I don't say get away if they come up or scram if I don't like the way they explain something.

 J: You don't fix your schedule based upon who will be there.

 S: No.

 J: You work with whoever is there.

 S: (laughing) I'm not that organized to fix my schedule like that.

 Excerpt 2

 J: Have you found that in going to the help centre that you have developed any sort of special bonds with particular tutors?

 C: Yeah.  Sometimes you know you find certain tutors can explain pretty good and certain tutors can relate to you better than other ones, you know, which is common.

 J: How do you attend the help centre?  Do you attend pretty randomly or do you tend to have a routine that you follow?

 C: Mainly I'd say in between routine and random.  Usually I come whenever like after class, like after my math class, or early in the morning.  Like if I have an hour break I'll come in between.  Or sometimes I'll just come if I get the chance to come.

 J: So when you come to the help centre it's not really determined then by who the tutor is - or do you find yourself coming because so and so will be there?

 C: No, I just come because I have a break or if I am available to come but I'm under no obligations.  Or if I really just need to learn a problem, I'll come.  So it depends on the person.  [OC:  Cliff meant that the timing of the visit would determine the person with whom he'd work.]

 Recall that one element of the research question concerned itself with "how" students attend the math help centre.  That is, do students attend in some random manner or do they integrate regular visits into their schedules in some form of routine?  Again, the bells of convenience rang loud and clear through the data.  The convenience that affected the nature of student-tutor relationships also exhibited itself through the students' descriptions of routine visiting patterns.

 In the preceding conversation with Cliff, he described his somewhat routine attendance.  In doing so, he clearly stated "I'm under no obligations." The emphasis was on convenience.  Consider the following excerpts from conversations with two other students, Ellen and Shelley respectively:
 

 Excerpt 1

 J: How do you attend the help centre?  By that I mean do you make it part of a routine for you or is it some place that you just go to randomly?

 E: It's a routine according to my time schedule.  I commute so I don't want to come up here unless I absolutely have to.  So when I have free time usually 11-12 or whatever Mondays, Wednesdays, and Fridays.  That's usually when I come.  Only once in awhile if I'm really having trouble or if we're having a quiz or a test coming up, then I'll come in specially.

 Excerpt 2

 J: How do you attend the help centre?  By that I mean do you attend it in a sort of routine as part of your schedule or is it pretty random?

 S: I'd say it's more routine now.  Well I don't have a set schedule.  I'm trying to do that but I can't say I do.  It's just try to get in a couple of days a week.  Probably I've been in more now than I ever have because it gets harder and harder.

 Another student, Ann, explained that she attended the help centre in a routine manner:
 

 J: How often do you tend to use the help centre?

 A: Every day or sometimes I'll skip a day if I really understand the assignment well.

 J: Do you use it at a particular time each day?

 A: Usually at the end of the day when my classes are over.  I'll spend maybe a half hour to an hour there.

 As a tutor, Carla observed the preferences of students.  She describes  her observations:
 

 J: Is there generally consistent use of the help centre Monday to Friday?

 C: It seems like Mondays, Wednesdays, and Fridays are more busy.

 J: Is that do you think because they have math on those days?

 C: Yeah.  It's all to do with their schedules.

 My own observations did not pick up on the strong bias towards routine that has been expressed through the comments.  Although the observation times varied somewhat, I did not tend to see the same people each week on a Monday morning between 10:30 and 11:30 or on a Wednesday afternoon between 2 and 3 o'clock, for example.  I was usually present at those times during the course of the study.  In fact, four students failed to show up for interviews at agreed upon times.  (One of these interviews was conducted when we met another day at the help centre).  These students selected times at which they would meet me in the help centre.  Quoting one student:
 

 Let's meet at the help centre because then if I forget about the interview, I'll be there anyhow.  I'm usually there at that time.

 Why were these people unreliable?  I can only conjecture that they planned to be there but something else came up that was more important to them.

 A self-centredness expressed itself through convenient selection.  It is like having a routine but...or wanting to work with a particular tutor but... The help centre certainly played an important role in the day to day academic life of many students.  Some spent as many hours in the centre as they did in class (three and a half hours weekly).  The question "What brings you to the help centre?" produced responses such as:
 

 Shelley:  Well I need extra help.  It's hard to do it on my own and I think it's just easier when you know you have somebody there to work with.  It sort of disciplines.  For myself it's hard for me to just do it at home and it's better if I come into a separate place - I don't know how to explain it but a place where it's quiet and everyone is doing the same thing more or less and obviously if I have a question, I can have it answered. I can't answer my own question at home.

 Ellen:  Basically to help me with my homework because there is no point in me sitting at home you know wasting time for like 2 or 3 hours or whatever when there's people there who are qualified to help me work through the problems.

 Jeanette:  I don't get stuck as much.

 The comments of Shelley and Ellen reflect a dependency of sorts.  In reviewing my field notes, I came across an informal conversation between Carla and myself.  This took place at the outset of the study.  The following few lines are quite telling:
 

 C: People who come by regularly tend to do less work.

 J: Do they become dependent on you?

 C: Yes.  I'm interested to see what you find.

 Could it be that students utilize the math help centre as a crutch? Consider the following scenario.  Two students, Patsy and Lloyd, are both visiting the help centre for the first time.  There is a copy of a take home test on the bulletin board.  An attached note informs tutors that they may assist students with the test.  A conversation transpired among the three of us:
 

 J: Why did you come to the help centre today?

 P: We had a take home test. I have some questions.  I want to get the correct answers but I also want to understand how to do them.  They will be tested again in the final.

 J: Is that why you're here, Lloyd?

 L: Yes.  The take home test.

 P: I usually go to my teacher for help.  But I didn't think it was fair to ask her lots of questions about the take home test.

 Philip regularly visited the help centre.  As he was preparing to leave one morning, he shared these comments:
 

 J: You use the help centre a lot.

 P: Me and math don't get along.  I work better here.

 J: Do you come here as a form of discipline - so that you'll work more effectively?

 P: No.  I can't do the math on my own.  I can do it here but when tests come, I can't do it.

 My final interview was with Carla.  At the time of the interview, I had no  recollection of her earlier comment about regular students not working as hard.  However, the issue of dependency surfaced.  She identified students' need for confirmation as a reason for coming to the help centre.  The issue of self esteem was raised:
 

 J: What's your perspective on the students that use the help centre in terms of their backgrounds or what's bringing them here?

 C: Well it seems like lots of different people come in here but a lot of the people who come in regularly have lots of trouble with math - like it really scares the heck out of them. They are the ones who show up all of the time and they are the ones that don't have so much problems with the math. Just their self esteem I think.  They just need to be told, yeah you're doing it right.  That's what I think.

 J: How would you describe the learning that takes place in the help centre?

 C: Learning to trust themselves.  I mean there's personal things like trusting you're going to get the right answer.  Or that when the answer in the back of the book is wrong often, to be able to trust yourself that you did it right...

 Further along in the interview...
 

 J: How many students would you say, in the afternoons, that you see, come in here 3 or 4 days a week?

 C: I'd say about 12 that come in a lot.  I'd say half of them don't really need to be in here.  I'm glad they are but it's not for math.  It's just for getting their confidence up.

 J: Yeah.  If you were able to change something about the set up here, in terms of the way students interact with tutors, is there something that you'd like to change/see changed?

 C: I'd like to see more, as I was talking about, more interaction of the students instead of just talking to them.  I would like them to get more involved in the process of what they're doing.  That's hard because it would be so easy for us to sit down and just do one of these problems and say here's the answer but then it does absolutely nothing for them.  So I'd like to see more of that, I think.  But some of it is going on so I don't know what I would change exactly.

 Carla's depiction of students as passive learners seems to be reasonable.  Ann used the phrase "they'll show you how to do it" in an interview.  When asked to explain what she meant, Ann replied:
 

 They'll actually sit down with a piece of paper and look at the problem you're doing and tell you exactly what you're doing wrong for each individual problem which the teacher obviously doesn't have time to do in a classroom situation.

 One day I found myself observing a student, Barbara, and a tutor, Marsha, who happened to also be Barbara's instructor.  Barbara seemed confused.  The following dialogue ensued:
 

 M: If you believe me that this is standard form, you would erase everything you wrote.

 B: (no response)

 M: Erase everything on the page.  [OC:  Barbara erases the work and Marsha proceeds to instruct her on how to do the question.]

 B: I see now.

 M: Is that completely factored?

 B: Yes.

 M: Set it equal to 0.  Is it fully factored?

 B: Yes.

 M: No, it isn't.  [OC:  Barbara smirks and completes the factoring.]

 M: Are you trying to do things too fast.  People that take more time and write neatly tend to make less errors.

 It seemed like the help centre offered a reliable source of support to these students.  However, its real function may be to act as a coping mechanism - a crutch on which one could rest.  With respect to tutors, Ellen had this to say:
 

 ...you know they're not the replacement of a teacher over there but I mean it's a lot better than struggling by myself.

 When Ellen was invited to add any final comments at the conclusion of her interview, this is what she said about the help centre:
 

 They've been doing their own surveys I guess about having it continue and I think it definitely should.  It definitely has helped me because there have been some homeworks (sic) that I mean I've had no clue as to what to do.  Then I'll go in and they'll help me through it and then I'll see how it's done and then I can do it myself and then you know it's done.

 Carla spoke about the learning objectives of students who used the help centre:
 

 C: Other people they seem like they want it as a crutch.  There are a lot of people who do their homework in here.  They want to be able to have it checked in case they come up with problems.  I'd say most of them are that kind.  They have a difficult subject to get through and they just want someone here.

 J: Do many of the students come in here with the intent of saying "Look at I don't understand a topic (e.g., inequalities).  Can you help me with inequalities?" or is the help they want generally geared to specific question?

 C: Most want help with a question in the book but sometimes it will turn out that they actually do want help with a subject but they'll never come out and say it - hardly ever.

 J: So that you're saying as the tutor you would pick up that they're looking for help beyond that question.

 C: Right.

 Here we have evidence that places the responsibility on the tutor to root out the question that the student may really want to ask.  The student is playing a passive role in his/her own learning process.  The metaphor of the passive student leaning on a crutch seems to categorize much of the learning that is taking place in the help centre.
 

 Initially I set out to shed insight on the following question:  "Why and how do students attend the math help centre and what sort of learning takes place there?"  In developing the question, it was the learning and teaching aspects which interested me most.  However, this paper may not reflect that. Why?

 Insight into the nature of learning and teaching has been gained through the discussion of each of the themes; however, the paper has taken a different flavour the one I might have anticipated before delving into the data. The dependent nature of the student population raises concerns about mathematics education.  My experiences as a mathematics educator have led me to believe that the teaching of mathematics as a product oriented subject leads to increased levels of dependency.  In contrast, teaching which places greater emphasis on process provides students with greater potential to adapt their knowledge.  This conceptual basis reduces the dependency upon others for ideas and insight.

 What are the implications for the help centre?  If dependency upon the centre is perceived to be undesirable, then tutors and instructors may consider shifting the emphasis of teaching and testing from product towards process.  I have seen various examples of tests.  In my opinion, these tests have been extremely product oriented.  The name of the game appears to be getting the answer through the use of algorithmic procedures.  If this is the gist of the game, then students have seemingly learned a strategy that allows them to work effectively within the rules.

 While chatting with Cliff about the nature of questions and learning in the help centre, he provided further insight into the role of the help centre in his own academic pursuits.  His assessment of the situation indicates that his personal strategy is in place:
 

 ...O.K. when I'm going for a test or a test is coming around, and I realize a certain section I was weak in, 'cause a lot of times you try 'cause we get a lot of homework and it's like you got to keep up with the homework trying the homework you get, you know.  I tend to worry more about the homework and the grade.  It's like I have to finish my homework.  But when it comes test time and she, the teacher, kind of slows down on the homework you know you have to think about what subject, you know what chapter you were weak on and then you go back and tell them "Could you teach, you know help me with this chapter all over because I think a lot of things I didn't understand but I had to go by it to keep up you know?"...

 It is not my desire, nor is it my place, to judge the math help centre.  Though I must confess that it disappoints me to see more students who perceive mathematics as a discipline defined by right and wrong answers.  The need to be right brings out a body of students who rely heavily upon the help centre.

 I wonder if the instructors would be open to placing greater emphasis on process in their teaching?  Or are they people who excelled in the same game?  Are mathematics teachers open to exposing their weaknesses? Excellent teaching of mathematics requires a strong conceptual basis. Outstanding performance on product oriented tests commonly does not demand such understanding.  The dependency level of the students suggests to me that they have not been encouraged to develop a conceptual knowledge in their mathematical experiences at university or other levels of education.

 I would like to close with a challenge to take risks and experiment with a process oriented emphasis.  When that "I can't do this" becomes "Wow!  I got it!", students feel proud of their accomplishment.  That is how self confidence can grow! 

 Spradley, James P. and McCurdy, David W. (1972).  The Cultural Experience:  Ethnography in Complex Society.  Chicago:  Science Research Associates.

 Taylor, Steven J. and Bogdan, Robert (1984).  Introduction to Qualitative Research Methods.  New York:  John Wiley and Sons.