# Impact of Online Discussion on Elementary Teacher Candidates’ Anxiety Towards Teaching Mathematics1

By Liu, Fuchang

This study investigated the impact of online discussion of anxiety towards teaching mathematics (ATTM) on elementary teacher candidates’ ATTM. Participants (N = 39) in elementary mathematics methods classes completed Anxiety Towards Teaching Mathematics Questionnaire immediately before and after 8 weeks of online discussion of ATTM. It was found that online discussion of ATTM significantly reduced participants’ self reported anxiety caused by the conception that mathematics is more difficult, anxiety towards other people’s perception of one’s teaching of mathematics, and anxiety towards teaching in general. The reduction of anxiety towards other people’s perception was more prominent in participants without experience than those with experience. It is suggested that elements aimed at reducing ATTM be built into methods courses for elementary teacher candidates. Mathematics anxiety is a well documented phenomenon and has been a popular research topic for the past several decades (see Hembree, 1990; Ma, 1999 for meta-analyses of this topic). The primary reason for this extensive attention is that mathematics anxiety is prevalent among students of all levels and among elementary teachers as well (Martinez & Martinez, 1996). Additionally, mathematics anxiety not only directly affects the teaching and learning of mathematics but also affects one’s professional and personal opportunities (Tobias, 1993; Trujillo & Hadfield, 1999).

When mathematics anxiety affects elementary teachers, it will ultimately affect their students as well, as success in teaching mathematics is substantially conditioned by the teacher’s attitudes and beliefs (Cornell, 1999). However, even though mathematics anxiety has been identified as an important component of a teacher’s attitude system (for example, Sandman (1980) identified mathematics anxiety as one of six constructs of mathematics attitude in a large- scale study), elementary teachers’ beliefs concerning mathematics or mathematics anxiety have not been investigated sufficiently (Thompson, 1992).

Mathematics anxiety is learned (Austin, Wadlington, & Bitner, 2001; Martinez & Martinez, 1996; Tobias, 1993). Like anything that is acquired or learned, mathematics anxiety is contagious. At the elementary school level, mathematics-anxious teachers, often unwittingly, pass this anxiety to some of their students (Austin et al.; Vinson, Haynes, Sloan, & Gresham, 1997), either through a weak understanding of or a negative attitude towards mathematics on the part of the teacher, or through negative experiences inflicted on the part of the student (Harper & Daane, 1998; Martinez & Martinez; Trujillo & Hadfield, 1999). After students get it, such anxiety increases across the school years (Townsend, Lai, Lavery, Sutherland, & Wilton, 1999). By high school, many students have developed severe mathematics anxiety. It is not uncommon that such mathematics-anxious students, as a result, either hate or avoid mathematics.

The problem is that mathematics anxiety does not end when students graduate from high school. It has been recognized that many elementary teacher candidates begin their college studies with anxiety towards mathematics (Harper & Daane, 1998). When such candidates finish college and start teaching, they will take their anxiety to their classrooms. Recent research revealed a high level of mathematics anxiety in elementary teachers (Austin et al., 2001). These teachers then transmit this anxiety to their own students. This vicious cycle goes on and on.

Researchers who study mathematics anxiety usually take either of two different positions: those that seek to formulate theoretical models to explain the relationship between mathematics anxiety and other variables and related issues, and those that use intervention to reduce mathematics anxiety. Studies of both positions have made contributions to the advancement of understandings of this important subject. Although the search for causes of mathematics anxiety has not been fruitful, researchers who take the first position have been successful in identifying some detrimental consequences of having anxiety towards mathematics. It is widely recognized that mathematics anxiety is negatively associated with mathematics achievement among students of all age levels and among students from different countries (Hembree, 1990; Ho et al., 2000; Ma, 1999). Researchers of this position have also attempted to include a number of mediating variables such as gender, grade level, and race- ethnicity into the theoretical models of the relationship. Nevertheless, results about the roles played by such variables have been mixed. For example, Hembree analyzed 151 studies and found that females displayed higher levels of mathematics anxiety than males, especially in college. Also, levels of mathematics anxiety increased through junior high school, peaked near grades 9-10, and leveled off in upper high school and college. Despite such differences, Ma (1999), based on the meta-analysis of 26 studies of mathematics anxiety and mathematics achievement among elementary and secondary students, found that gender and grade level accounted for only a small, though statistically significant, percentage of the total variance. Sloan, Daane and Giesen (2002) found only a small correlation between mathematics anxiety and learning styles.

Researchers who assume the intervention position have employed a variety of techniques to reduce mathematics anxiety in participants from a variety of populations. Such research is based on the premise that mathematics anxiety is learned and can be unlearned. Martinez & Martine/ (1996), for example, offered a series of diagnosing and treating strategies. Hembree (1990) listed four kinds of such techniques: classroom, behavioral, cognitive, and cognitive- behavioral interventions. Of these techniques, systematic desensiti/ ation, which was behavioral in nature, was found to be highly successful when used with anxiety management training and conditioned inhibition. Similarly, Foss and Hadfield (1993) reported mathematics anxiety reduction clinics as successful.

Also, mathematics methods classes employing some particular elements have been found to be effective in reducing elementary teacher candidates’ mathematics anxiety. For example, participants in Levine’s (1996) study wrote weekly journal entries about their thoughts and feelings, though not necessarily anxiety-related, and the study found that when those reporting high initial anxiety for teaching mathematics described interest in developing creative strategies for teaching mathematics, their anxiety was reduced. Vmson et al. (1997) found that their participants’ overall mathematics anxiety was significantly reduced after a methods class emphasizing manipulatives.

The present investigation, of an intervention nature, focused on a form of instruction that had not been studied in relation with mathematics anxiety before: online discussion. Before any analysis of the topic is embarked upon, a distinction between two types of mathematics anxiety in elementary teacher candidates needs to be made. Anxiety in such candidates may display itself in two different but closely related ways. Like students in any other age group or majoring in any other field, such candidates may experience mathematics anxiety in their own studies, such as anxiety towards taking a mathematics test. The other form of anxiety is shown towards their future teaching of mathematics. Levine (1996) used “anxiety for teaching mathematics” to refer to this form of anxiety. It is this second kind of anxiety that this study was concerned with and it is referred to as “anxiety towards teaching mathematics” (ATTM) in this article. The author hoped that by engaging the targeted candidates in in-depth online discussion about some important aspects of anxiety towards their future teaching of mathematics, their anxiety could be reduced so that their students would be able to handle their mathematics studies with a higher level of confidence and better conceptual understanding and not develop the same anxiety as suffered by their teachers.

The purpose of this study was to answer two research questions: 1) Will there be significant differences in elementary teacher candidates’ level of ATTM before and after online discussion of ATTM? 2) Will age, gender, race, and teaching experience play a role in the reduction of AlTM, if any, through online discussion of ATTM? An additional goal of this study was to analyze the participants’ responses generated during their online discussion of ATTM in order to gain an in-depth understanding of their mindset, which, in turn, may help those in a similar situation fight against their own anxiety.

METHOD

Participants

The participants in this study were 39 elementary teacher candidates taking a mathematics methods course at a midwestern university. They were enrolled in two classes, 19 of one and 20 of the other. The majority of the participants were female, Caucasian, and in their early 20s. Slightly less than half of them had prior part-time teaching experience (see Table 1).

The two classes met three times a week for the first 4 weeks of the semester. Starting from the 5th week, the participants went to an elementary school for pre-student teaching practicum for 2 full days a week in place of the first two class meetings of the week. They still had their third weekly class meeting on campus. This pre- student teaching practicum lasted for 8 weeks, during which time the intervention was administered. Intervention

The intervention utilized in this investigation was online discussion of AlTM. The author, as instructor for both classes, posted weekly discussion topics on “Blackboard,” an online system that all faculty and students had access to for academic uses. The participants engaged themselves in the discussion and shared their opinions. For each topic, every participant was required to post a minimum of two posts (it was specified that short responses to other participants’ posts, such as “I agree,” would not count). Seven topics were given (see “Analysis of Online Discussion Responses” below). Some of these topics were based on research involving mathematics anxiety in relation with such variables as gender and conceptual understanding (see Hembree, 1990; Ma, 1999). Some other topics were based on conceptions the participants expressed in their earlier posts. For example, some participants believed that mathematics was more difficult to teach than the other school subjects.

Instrument

To measure the impact of the online discussion on the participants’ level of ATTM, the author developed a 15-item Anxiety Towards Teaching Mathematics Questionnaire (ATTMQ) for this study. The responses were on a 0-4 scale (0-strongly disagree, !-disagree, 2-not sure, 3-agree, 4-strongly agree), with higher scores indicating higher levels of ATTM.

In developing ATTMQ, the author considered several questions involving ATTM, such as: Could a participant with AlTM also have anxiety towards teaching in general? Could a participant’s anxiety just be a result of anxiety towards the content knowledge of mathematics or a result of worrying about other people’s perception of his or her teaching of mathematics? The final version of AiTMQ sought to measure five constructs: anxiety caused by the conception that mathematics is more difficult than the other school subjects (Items 1, 2 and 12), anxiety towards others people’s perception of one’s teaching of mathematics (Items 5,6,7 and 13), anxiety towards one’s content knowledge of mathematics (Items 10,11 and 14), anxiety towards teaching mathematics in general (Items 4, 8 and 15), and anxiety towards teaching in general (Items 3 and 9. See Table 2).

Procedure

A written consent was obtained from all the participants, who completed ATTMQ as pretest prior to going to their pre-student teaching practicum. During their practicum, they were divided into groups of four or five, according to the alphabetical order of their last names, and engaged themselves in the online discussion based on the topic given, within their assigned groups. At the end of their practicum, they took ATTMQ again as posttest.

RESULTS

Cronbach’s alpha was conducted on both the pretest and posttest data. The coefficient alpha index of 0.85 for pretest items and 0.88 for posttest items indicated a high estimated internal reliability.

To answer research question 1, each participant’s pretest and posttest responses on the five constructs were first summed up, respectively, and subjected to a pairedsamples Mest. Because of an inflated Type I error resulting from the use of multiple tests, a Bonferroni adjustment was performed and the alpha level was established at .01 (.05 / 5). On the average, there was a significant difference between a participant’s level of ATTM before and after online discussion on three constructs: anxiety caused by the conception that mathematics is more difficult, anxiety towards other people’s perception of one’s teaching of mathematics, and anxiety towards teaching in general. The strengths of the relationship between online discussion and ATTM with respect to these three constructs, as indexed by eta2, were . 18, .17, and .26, respectively. Such results indicate that online discussion can reduce elementary teacher candidates’ ATTM in the three constructs. The differences on the other two constructs (anxiety towards one’s content knowledge of mathematics and anxiety towards teaching mathematics in general), on the other hand, were not significant (see Table 3).

Even though the participants were representative of elementary teacher candidates of a mid-western university (for example, the majority being female), the markedly different cell sizes and some possible empty cells in age, gender and race would violate the homogeneity of variance assumptions should these variables be used in analysis of variance tests. Thus, no ANOVA tests were conducted on these variables. However, the two subgroups under experience (those with experience and those without) were rather balanced and, therefore, were compared in an independent-samples f-test with respect to the net change between pretest and posttest scores on the above-mentioned five constructs of ATTM. Again, a Bonferroni adjustment was made and the alpha level was set at .01. Results show that the mean net change for those without experience (2.90) was significantly more prominent than those with experience (-.06) on the construct of anxiety towards other people’s perception of one’s teaching of mathematics, t (37) = 2.787, p

A closer look at the differences between the total pretest and posttest scores for each participant revealed that 31 participants (79.5%) had a lower posttest score, suggesting that online discussion of ATTM had a positive impact on most participants. However, seven (17.9%) participants had an increased posttest score while one participant’s scores remained unchanged.

Table 4 shows the mean pretest and posttest scores and the net change between the two scores for each of the 15 items of ATTMQ. An item-by-item examination showed that for all but two items, the participants had a lower mean posttest score, indicating that the majority of the items reflected a decrease in the participants’ overall levels of ATTM. The two items that ran the opposite direction were Items 14 and 15. While the net change in Item 14 was minor, the change in Item 15 was more obvious.

ANALYSIS OF ONLINE DISCUSSION RESPONSES

1. Why are some of us anxious about teaching mathematics?

Prompt: Mathematics anxiety is a common phenomenon. For those of us who will be elementary school teachers, teaching mathematics will be an integral part of our career, and some people may worry about that. What do you think might be some of the reasons why some of us are anxious about our future teaching of mathematics?

For this question, a sizable number of participants mentioned lack of conceptual understanding of mathematics as a reason for ATTM. Several participants further related this lack of understanding to their own schooling when they were taught how to do problems, but not why they should be done that way. One participant talked about how her elementary school teacher had students follow exact procedures, and problems done in a different way, even if correctly, would be counted wrong. These participants believed that teachers who lack a good understanding will not be able to generate a good understanding in their students, and when such students later become teachers, they will feel anxious about teaching mathematics.

In talking about their own lack of understanding of mathematics, some participants recalled the many mechanical exercises they were required to do, such as “Math Mad Minutes.”"Every problem had to be done at warp speed AND correctly,” one participant commented. “That is a lot of pressure! Pressure leads to anxiety and before you know it, you have anxiety just thinking about math.”

A few participants approached the topic from the characteristics of mathematics and maintained that mathematics is a series of elements all linked together. If one element is messed up, a child’s learning could be put on hold. Not wanting to mess up a student’s learning of mathematics might be another reason why some teachers have ATTM.

2. Can anxiety towards teaching mathematics be overcome?

Prompt: Starting with an analogy, a few of us are shy. Some people may argue that being shy is an innate temperament and will stay with us for a long time, if not a lifetime. Others may argue that with conscious effort and proper training it can be overcome. In your opinion, can anxiety towards teaching mathematics be overcome? Why or why not?

Although a few participants sounded cautious, saying that ATTM could only be “lessened,” the overwhelming majority agreed that ATTM could be overcome. Some participants gave examples of either themselves or people they knew that overcame severe shyness as support. Some participants pointed out that the underlying reason for a person’s ATTM had to be addressed first before it could be overcome. They further discussed ways of overcoming it. As discussion in this respect overlapped with Topic 6, it will be further analyzed under that topic.

3. Is mathematics more difficult than the other subjects?

Prompt: Several people mentioned that some people are anxious about their future teaching of mathematics because mathematics is more difficult to teach than the other subjects. Is math really more difficult to teach?

It is interesting that two contradictory patterns repeatedly surfaced during the discussion of this topic. While most participants did not believe that mathematics is more difficult to teach than any other subject, quite some nevertheless said that in reality, many “other” people believe so. One of the common reasons they listed was that how mathematics should be taught had always been changing. Another reason was that most mathematical concepts were links of a coherent whole, and when students missed a link, they tended to struggle with other concepts. These participants believed that this was where “other” people got this concept. The other contradictory pattern was that some participants said that teaching mathematics was not necessarily more difficult, but yet used some expressions, such as “intimidating” and “requires a different type of thinking,” that suggested that they more or less had the belief that mathematics is more difficult to teach.

A few participants commented that whether mathematics is difficult to teach differed from person to person. Every subject had its own characteristics and may be easy for some people but difficult for others. Thus, they maintained, it was more a matter of personal feelings than of the content. Also, such personal feelings had a lot to do with the way the people holding such feelings learned their own mathematics. Some people had teachers who made mathematics fun and enjoyable while others had teachers that made it boring and dry. That, they believed, contributed to how teaching mathematics was perceived.

Although in the minority, a few participants did believe that mathematics was more difficult. The reason, they argued, was that mathematics is “abstract,”"strictly rule-governed,” or “requires a higher-order thinking skill.” Furthermore, some participants talked about this difficulty from the procedural point of view. Mathematics problems, one argued, “require a lot of steps for almost everything, and if a step is left out the whole problem is wrong.”

4. Which should be more emphasized: Understanding or memorizing mathematics facts?

Prompt: It has been mentioned that when we were going to school, we were not taught the conceptual understanding of some mathematical concepts, while other people believe that memorizing math facts is a very important part of learning mathematics. Which do you think should be more emphasized, conceptual understanding or memorizing mathematics facts?

Basically, a participant took either of two positions: that conceptual understanding should be “definitely” more emphasized, or that both understanding and memorization of mathematics facts should be emphasized.

Participants of the first position maintained that if students have understanding, memorization of mathematics facts will come along, and the information will be retained in the long run. Some went a step further and pointed out that most teachers opt to teach memorization of mathematics facts because teaching for understanding is more difficult. A participant commented, “I hated math in high school because my teacher would always explain things with ‘because that is the way it is done’. Just because students have memorized the facts does not mean that they have actually learned them.”

Participants who held the second position agreed that conceptual understanding is important, but they believed that memorizing certain mathematics facts is equally important. The example most often cited was the multiplication table. “If students use their fingers when they get into upper grades, it is just going to slow them down.” Another participant mentioned that it is important for students to retrieve their mathematics facts quickly because “we still require them to take timed tests on math facts.”

5. Is gender a factor?

Prompt: As we know, a few students may feel anxious about their future teaching of mathematics. We also know that most elementary school teacher candidates are female. Is there a relation? Put another way, does gender play a role in such students’ anxiety? If the trend were reversed and most candidates were male, would, in your opinion, the anxiety level be higher, lower, or about the same?

This topic generated an almost complete consensus: gender did not have anything to do with ATTM. Instead, participants listed some factors that they thought would affect it. The greatest impact would be teachers’ attitude towards mathematics and their own school experience with mathematics.

There was a prevailing perception among the participants that men are better in mathematics than women. However, these participants promptly went on to say that even though men may perform better in mathematics, it does not necessarily lead to the conclusion that men are better in teaching mathematics. Here many participants became conscious of the distinction between anxiety towards mathematics and ATTM. “It is possible to have a good experience with mathematics but still not feeling comfortable with teaching it,” one said.

A few participants believed that men can “cover up their emotions” and do not reveal any weaknesses. Thus, they are perceived to be more confident with teaching mathematics and usually taken more seriously by their students.

6. Ways to overcome anxiety towards teaching mathematics

Prompt: A few of us may feel anxious about their future teaching of mathematics. We agree, from a previous topic, that such anxiety can be overcome. What are some of the ways that you can suggest to overcome such anxiety?

Although answers were varied, the ways suggested typically fell under four categories: content knowledge, practice/experience, preparation, and help from others.

1. Understand the mathematics one is teaching. As repeatedly pointed out, those who have ATTM usually do not have a profound understanding of mathematics. Spending extra time working on fundamental mathematical concepts would be a good way to overcome ATTM. Concrete suggestions include reading books, taking classes, and staying current with research-based strategies.

2. Practice. Many participants believed that with practice and experience, ATTM could be effectively overcome. Before each lesson, enough time should be set aside for practice. “Practice in front of friends, family, a mirror, even your dog,” one participant said.

3. Make detailed preparations. This entails thinking about and studying thoroughly the lesson to be taught and writing a detailed lesson plan. Many participants mentioned thinking about possible questions students could ask. “I often find myself putting potential questions or answers into my lesson plan,” one said. Another suggested a “dry run” before delivering a lesson.

4. Learn from mentor teachers and colleagues. Some participants with teaching experience said that they particularly appreciated the help they got from others, and such help greatly reduced their ATTM.

7. How not to instill mathematics anxiety in your own students?

Prompt: By the time students start high school, some of them have developed math anxiety. Now that you know that it is an acquired psychological state and it is detrimental to their academic development, how can you, as a future elementary school teacher, try NOT to instill mathematics anxiety in your own students?

Most participants agreed that they need to do some fundamental things, such as making mathematics fun and pleasant, encouraging different learning styles and different ways to solve a problem, and fostering a pressure-free classroom environment. An implicit emphasis that many participants considered central to this topic was conceptual understanding. As one participant mentioned, “Teaching students why and how mathematics works will give them confidence.” Another participant mentioned that she enjoyed the topics that she understood but felt worrisome about those that she did not.

Even if teachers may not have a firm grasp of some concepts they are teaching, a participant contended, it is important not to let this anxiety show in front of students: “Fake it until we get it.” Another participant supported this claim by saying, “If a teacher tells her kids she hates math, why should they want to enjoy it?” A teacher’s anxiety can, as one participant said, easily “rub off on” her students, and it is crucial that teachers maintain a positive attitude and show enthusiasm towards mathematics.

Some participants mentioned that there are always a few students who do not get a concept immediately. Teachers should show patience and provide help and not pressure. If students get an unpleasant experience from such a situation, they are prone to mathematics anxiety.

It is also important to have students talk about how they feel about learning mathematics. One participant admitted that she suffered from mathematics anxiety at elementary school but basically kept it to herself. She thought she was the only one not understanding. If she had talked about it in class, she said, she would have known that there were others also having trouble with mathematics and that could have prevented her anxiety.

Some other elements were also put forth as important in how not to instill anxiety in students, and such ideas were generally offered by those participants with teaching experience. For example, manipulatives and hands-on activities can get students involved, and involved students tend to be less likely to develop mathematics anxiety. Tying mathematics to real life experience can make the learning of mathematics meaningful. Also, teachers should avoid assigning mathematics as a form of punishment for behavioral problems, especially during recess time.

DISCUSSION

In line with other studies on the impact of different components of mathematics methods classes on elementary teacher candidates’ ATTM (e.g., Levine 1996; Vinson et al., 1997), the present investigation found that engaging participants in online discussion of ATTM could significantly reduce some aspects of their ATTM. This has important instructional implications.

As elementary teacher candidates demonstrate a very high level of mathematics anxiety (Hembree, 1990; Trujillo & Hadfield, 1999), it is of great importance that such anxiety be reduced before they become teachers and unwittingly transmit this anxiety to their students. Also, teacher candidates may be the crucial link where it makes greatest sense to break the vicious cycle of mathematics anxiety. For, although elementary school teachers also possess a high level of mathematics anxiety (Austin et al., 2001), reducing anxiety in such teachers lacks practicality in that most of them have a busy daily schedule and, except for a few sporadic staff development workshops scattered throughout the year, their professional growth depends largely on their own conscientious effort. Thus, it is necessary to backtrack one step and address this problem while they are still at college taking core education courses on a fulltime basis. It may be a great advantage to elementary teacher candidates if an element addressing ATTM could be built into the methods course. Why would discussing ATTM reduce ATTM? One explanation may be that having a good understanding of a phenomenon is the very first step in learning how to handle it, and discussing ATTM gives participants a chance to reveal, share and understand the many different facets of this complex psychological phenomenon.

Another explanation may be that the form of online discussion allowed participants sufficient time to engage in an increased personal reflection about ATTM than in-class discussion or other spontaneous responses. As Trujillo and Hadfield (1999) commented, an in-depth look at one’s own negative experiences can often help to set a more positive direction for future encounters. Also, knowing that some other people also suffer from ATTM may help alleviate one’s own ATTM.

Most important of all may be the healing effect of disclosure. A central tenet of most psychotherapies is that talking about traumatic experiences is beneficial (Pennebaker, 1995, 1997). The disclosure process, where individuals translate their experience into words, may be as important as any feedback the client receives from the therapist. Indeed, investigators have found that talking about a trauma helps cure the trauma (Pennebaker) and that speaking about psychological distress such as anxiety helps relieve it by catharsis and by self-understanding (Stiles, 1995). In a similar vein, participants in the current study wrote about their own personal feelings and opinions about ATTM and this sharing of their personal feelings and opinions achieved the effect of reducing some aspects of their ATTM.

It is interesting to note that while participants’ scores decreased with respect to anxiety caused by the conception that mathematics is more difficult and anxiety towards other people’s perception of one’s teaching of mathematics, this pattern did not hold true for anxiety towards teaching mathematics in general. The reason is probably that the former constructs were concrete and participants could somehow pinpoint their anxiety while the latter may be a little too vague and sweeping and thus not sensitive enough to gauge any change.

Another interesting pattern is that the construct of anxiety towards teaching in general had a stronger effect than the two constructs concerning specific areas of teaching mathematics. This suggests that elementary teacher candidates’ ATTM might actually be a part of their anxiety towards teaching in general. In other words, they could at the same time have anxiety towards teaching language arts, science, and so on. Further studies are suggested as to whether reducing anxiety towards teaching in general will simultaneously reduce ATTM.

The online discussion of ATTM had a much greater impact on those participants without experience than those with experience on the construct of anxiety towards other people’s perception of one’s teaching of mathematics. It may be the case that when teacher candidates have not had any teaching experience, they tend to worry about how other people might perceive their future teaching of mathematics. But those that have had teaching experience may no longer be as self conscious and may no longer worry about how other people would perceive them teaching mathematics.

Of particular interest was Item 15 of the instrument, for which the participants’ average scores noticeably increased from pretest to posttest. One possible explanation may be offered with respect to the current curricular structure for most elementary teacher candidates. Although they will teach several different subjects on their future job, such as mathematics, language arts, science and social studies, they are not specially trained in any of them. Several weeks of field experience in a real classroom may have given the participants a sense of need for training in specific areas.

An apparent limitation of this study was the 8-week span of the intervention, during which time the participants had their practicum as well as a weekly on-campus class meeting. As all these events occurred simultaneously, it is somewhat difficult to attribute the decrease of scores in three ATTM constructs solely to the online discussion. To address this issue, the author applied the same research design to those who took the same course during the following semester. The participants went through the same instruction, practicum, and online discussion, and took the same ATTMQ before and after online discussion. The only difference was the topics used, which were seven topics on issues other than ATTM. They were: departmentalization of elementary schools, gender issues concerning elementary school teachers, the metric system, English number words, order of core subjects in practicum, field experience in general, and advice to the next group of students. Results from a paired-samples t-test indicate that online discussion without the element of ATTM did not produce a significant change in any of the five constructs of ATTM from pretest to posttest (t (26) = 0.67, 0.22,-0.17,1.99, 1.91, p = 0.51, 0.83, 0.87, 0.06, 0.07, respectively).

Although the results were not directly comparable (two different groups of participants, during two different semesters), the relatively stable levels of ATTM in the second group of participants suggest that online discussion with ATTM built in may have played a major role in decreasing AlTM in the participants of the first group. Such observations lend support to the suggestion that some elements aimed at reducing elementary teacher candidates’ ATTM be built into their methods courses. Caution has to be exercised, however, because results from the present study show that seven participants (17.9%) had a higher level of ATTM after the intervention. While it may be argued that not everything will work for everybody, an element formally built into a course should have the power of appealing to an overwhelming majority of students.

1 Part of this manuscript was presented at the annual conference of the Association of Teacher Educators, San Diego, CA, in February 2007.

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FUCHANG LIU

Wichita State University

Copyright Project Innovation Summer 2008

(c) 2008 Education. Provided by ProQuest Information and Learning. All rights Reserved.

**Topics:**Education, Elementary mathematics, Mathematics education, Symptoms, teacher, online discussion, 0.999..., Mathematical anxiety, Shyness, Anxiety, Mathematics, Educational psychology, elementary school