autobiographical stories from preservice elementary mathematics and science students: implications...

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Volume 100(7), November 2000 355 I never cared much for either subject [mathematics or science]....It took me many years to overcome my feelings of being inadequate, and sometimes I still have some trouble. I discovered a love for geology I never suspected I had until then. Up until this point I had failed to see the real value of mathematics in my life. For the first time I enjoyed math. It was real. ~ Preservice students’ autobiographical comments Attitudes can affect the way students view their abilities in mathematics and science and the choices they make (National Council of Teachers of Mathemat- ics [NCTM], 1989; National Research Council [NRC], 1996; Tobias, 1993). Students’ autobiographical sto- ries reveal, however, that these attitudes are not static and can be influenced by experiences and interactions at different points in time, both in and out of school. Autobiographies are an effective tool for assessing students’ predispositions toward content areas and iden- tifying any changes in attitude over time, for identify- ing general attitudes toward learning, and for encouraging students to share joys and fears in relation to these experiences. Autobiographies provide insights into students’ mathematics and science experiences and help students make connections to feelings they currently hold about these subjects (Koch, 1990; Shaw & Chessin, 1996). It can be argued that students’ memories of a particular classroom, teacher, or experi- ence may not always be precise and, therefore, autobio- graphical accounts might not be completely accurate. What students remember, however, and the way they remember it are primary influences on their thinking as they describe attitudes and perceptions (Cole & Knowles, 2000; Meyer, 1993; Thompson, 1992; Yager & Penick, 1984). Meyer (1993) described a conversation with preservice students discussing the nature of evidence presented in an autobiography. While students felt that autobiographical recollections could be biased, they also saw the validity of such recollections, because if “we recall something a certain way, that is the way that it influences our present belief system” (p. 8). And as stated in an autobiographical excerpt reported by Cole and Knowles (2000), “My story is my reality. My story communicates my experience, and it is this experience that shapes my practice” (p. 45). Many studies of preservice elementary teachers’ mathematics attitudes have focused on anxiety and sources of these negative feelings (e.g., Hembree, 1990). These studies have used a variety of instruments iden- tifying levels of confidence or levels of anxiety about mathematics, including rating scales (e.g., Brush, 1981; Bulmahn & Young, 1982; Kelly & Tomhave, 1985), open-ended question responses or oral interviews (e.g., Jackson & Leffingwell, 1999; Meyer, 1980; Trujillo & Hadfield, 1999) and, less often, autobiographies (e.g., Autobiographical Stories from Preservice Elementary Mathematics and Science Students: Implications for K-16 Teaching Judith Z. Ellsworth and Alan Buss University of Wyoming Autobiographies are an effective tool for assessing students’ predispositions toward science and mathematics content and identifying any changes in attitude over time. The purpose of this study was to analyze autobiographies of students enrolled in elementary education methods classes to determine the kinds of K-12 and college content course experiences affecting their perceptions of mathematics or science. Special attention was given to recollections of events that had positive or negative effects on students’ interest in and attitudes toward science or mathematics, their confidence in these areas, and transitions in attitude throughout their experiences. Ninety-eight autobiographies were collected and analyzed, revealing attitudes that were generally more positive than expected, five major emergent themes, and important information about when and why transitions in attitudes occurred.

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Page 1: Autobiographical Stories from Preservice Elementary Mathematics and Science Students: Implications for K-16 Teaching

Volume 100(7), November 2000

355

I never cared much for either subject [mathematicsor science]....It took me many years to overcomemy feelings of being inadequate, and sometimes Istill have some trouble.

I discovered a love for geology I never suspected Ihad until then.

Up until this point I had failed to see the real valueof mathematics in my life. For the first time Ienjoyed math. It was real.

~ Preservice students’ autobiographical comments

Attitudes can affect the way students view theirabilities in mathematics and science and the choicesthey make (National Council of Teachers of Mathemat-ics [NCTM], 1989; National Research Council [NRC],1996; Tobias, 1993). Students’ autobiographical sto-ries reveal, however, that these attitudes are not staticand can be influenced by experiences and interactionsat different points in time, both in and out of school.

Autobiographies are an effective tool for assessingstudents’ predispositions toward content areas and iden-tifying any changes in attitude over time, for identify-ing general attitudes toward learning, and forencouraging students to share joys and fears in relationto these experiences. Autobiographies provide insightsinto students’ mathematics and science experiencesand help students make connections to feelings they

currently hold about these subjects (Koch, 1990; Shaw& Chessin, 1996). It can be argued that students’memories of a particular classroom, teacher, or experi-ence may not always be precise and, therefore, autobio-graphical accounts might not be completely accurate.What students remember, however, and the way theyremember it are primary influences on their thinking asthey describe attitudes and perceptions (Cole & Knowles,2000; Meyer, 1993; Thompson, 1992; Yager & Penick,1984). Meyer (1993) described a conversation withpreservice students discussing the nature of evidencepresented in an autobiography. While students felt thatautobiographical recollections could be biased, theyalso saw the validity of such recollections, because if“we recall something a certain way, that is the way thatit influences our present belief system” (p. 8). And asstated in an autobiographical excerpt reported by Coleand Knowles (2000), “My story is my reality. My storycommunicates my experience, and it is this experiencethat shapes my practice” (p. 45).

Many studies of preservice elementary teachers’mathematics attitudes have focused on anxiety andsources of these negative feelings (e.g., Hembree, 1990).These studies have used a variety of instruments iden-tifying levels of confidence or levels of anxiety aboutmathematics, including rating scales (e.g., Brush, 1981;Bulmahn & Young, 1982; Kelly & Tomhave, 1985),open-ended question responses or oral interviews (e.g.,Jackson & Leffingwell, 1999; Meyer, 1980; Trujillo &Hadfield, 1999) and, less often, autobiographies (e.g.,

Autobiographical Stories from Preservice ElementaryMathematics and Science Students:

Implications for K-16 Teaching

Judith Z. Ellsworth and Alan BussUniversity of Wyoming

Autobiographies are an effective tool for assessing students’ predispositions toward science andmathematics content and identifying any changes in attitude over time. The purpose of this study wasto analyze autobiographies of students enrolled in elementary education methods classes to determinethe kinds of K-12 and college content course experiences affecting their perceptions of mathematics orscience. Special attention was given to recollections of events that had positive or negative effects onstudents’ interest in and attitudes toward science or mathematics, their confidence in these areas, andtransitions in attitude throughout their experiences. Ninety-eight autobiographies were collected andanalyzed, revealing attitudes that were generally more positive than expected, five major emergentthemes, and important information about when and why transitions in attitudes occurred.

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Bulmahn & Young, 1982; Tobias, 1993). Commonfindings described as affecting students’ attitudes nega-tively are teacher behaviors, an emphasis on correctprocedures and answers, difficult content, testing, alack of comprehension, perceived irrelevance of con-tent, family attitudes, and peer attitudes (e.g., Bulmahn& Young, 1982; Hembree, 1990; Jackson & Leffingwell,1999; Kelly & Tomhave, 1985; Meyer, 1980). Studiesof students’ attitudes in science reinforce many of thesesame findings when describing negative attitudes to-ward that subject (e.g., Atwater, 1994; Ebenezer &Zoller, 1993). Studies of anxiety issues using open-ended questions or autobiographical prompts have alsoincluded, to varying extents, descriptions of positiveinfluences toward science and mathematics revealed inthe data (e.g. Ebenezer & Zoller, 1993; Meyer, 1980;Trujillo & Hadfield, 1999).

Areas of transition, changes in attitudes, and ef-fects on those changes in mathematics and scienceattitudes are not as clear in the literature. Autobiogra-phies in which students reflect on their learning expe-riences are well suited to reveal these positive ornegative transitions.

Through the autobiographical writing process, edu-cation students can see influences and experiences thataffected their view at different points in time. Thisperspective helps them focus on what it means to teachand learn by considering the implications of theirreflections to issues of pedagogy and content for theirown future teaching (Brookfield, 1995; Cole & Knowles,2000). Brookfield (1995) stated,

The influences that shape teachers’ lives and thatmove teachers’ actions are rarely found in researchstudies, policy reform proposals, or institutionalmission statements. They are more likely to befound in a complex web of formative memories andexperiences....We may espouse philosophies ofteaching that we have learned from formal study,but the most significant and most deeply embeddedinfluences that operate on us are the images, mod-els, and conceptions of teaching derived from ourown experiences as learners....Our autobiographiesas learners in childhood, adolescence, and youngadulthood frame our approach to teaching at thestart of our careers, and they frequently exert aninfluence that lasts a lifetime (pp. 49-50).

Purpose

The purpose of this study was to analyze autobiog-raphies of students enrolled in elementary educationmethods classes to determine the kinds of K-12 and

college content course experiences affecting their per-ceptions of mathematics or science. Special attentionwas given to recollections of events that had positive ornegative effects on students’ interest in and attitudestoward science or mathematics, their confidence inthese areas, and transitions in their attitudes throughouttheir experiences.

Methods

The participants in this study were 98 elementaryeducation majors, 82 females and 16 males, enrolled ina 6-hour integrated mathematics and science methodscourse during the semester before student teaching.Although demographic data were not collected in thestudents’ autobiographies, the typical populations ofmethods classes include a majority of students fromWyoming and other rural western states, with someurban representation mainly from Colorado and Cali-fornia (based on the university Office of InstitutionalAnalysis data). The participants were from five sec-tions, taught by three different instructors over a foursemester period from fall 1997 to spring 1999. Prior toenrolling in this course the students, as part of theeducation program, had already taken 9 hours of math-ematics and 12 hours of science content. On the first dayof the methods course, participants were asked to writea mathematics or science autobiography based on theirexperiences from elementary school to the present. Theassignment was intentionally given early to eliminateinfluences of methods’ teachers or methods coursediscussions on the student autobiographies. As part ofthe assignment explanation, question prompts (adaptedfrom Koch, 1990, p. 42) were provided to help studentsfocus:

When you look at your education through the lensof “mathematics or science” (pick one), what doyou see? Did you like it? Hate it? Did you ever eventhink about it? What was your background? Who orwhat influenced you? In what ways? Do you seeplaces where your experience affected life choices?Are there differences between in-school and out-of-school memories? What have you grown tobelieve about mathematics/science? What has in-fluenced your attitudes toward the teaching andlearning of mathematics/science? At the end ofyour autobiography, please explain why you choseto reflect on this subject over the other.The assignment was presented as an open-ended

task, in which students were to move in any directiontheir memories took them. Students were not requiredto answer all of the prompts as presented, but they were

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asked to provide examples within their descriptions andto provide the specific reason(s) they chose to writeabout either science or mathematics as an additionalway for the researchers to view attitudes. All instructorspresented the assignment in this manner.

The autobiographies were then collected, coded,and analyzed for general attitudes and emergent themes(Miles & Huberman, 1984). To increase the internalvalidity of the analysis, the researchers used a multistepprocess to discuss, develop, and refine emerging atti-tudes and themes. Through these discussions, the re-searchers were able to establish common understandingsin the coding and analysis process.

First, the researchers randomly selected three auto-biographies from one section and analyzed each auto-biography together to identify the student’s generalattitudes and to begin to identify attitude transitionpoints. Key words (e.g., “scares,” “great,” “hate,”“loved,” “setback,” “until”) associated with attitudeswere initially identified and discussed. Second, theresearchers individually analyzed seven additional ran-domly selected autobiographies to define attitude codesand to identify emergent themes. Additional attitudekey words were identified through this process. Theseseven autobiographies were then analyzedcollaboratively to compare individual ratings and dis-cuss the emergent themes. The attitudes were coded asbeing positive overall, negative overall, changing frompositive to negative over time, or changing from nega-tive to positive over time (see Appendix A). In order toavoid attitude codes that were unnecessarily complex,the researchers defined only the two transition codeswhere a transition represented a significant change inthe direction of the description. Responses that wereneutral overall were coded as negative; e.g., “I neverreally thought one way or the other about mathematics[or science]. It was just there and something to getthrough.” Third, attitude codes and emergent themeswere cross-checked with two outside coders and dis-cussed. Both outside coders were university educators;one brought the expertise of early childhood educationand developmental appropriateness, and the secondprovided expertise in the content and issues of criticalthinking. The remaining data were then analyzed ac-cording to the attitude codes and themes.

Results

Out of the 98 autobiographies collected, 61 werewritten on mathematics and 37 were written on science.Autobiographies were written by students from differ-ent backgrounds, communities, and schools over differ-

ent semesters, yet they revealed similar attitudes andthemes. Beyond these attitudes and themes were fourfindings that provided further insights from students’science and mathematics experiences.

AttitudesSurprisingly, this study revealed attitudes that were

generally more positive than expected, based on resultsof previous studies of elementary preservice teachers(Hembree, 1990). Fifty-one percent of the 61 math-ematics autobiographies and 81% of the 37 scienceautobiographies were coded as being positive or changedfrom negative to positive (see Figure 1). While math-ematics was viewed more negatively than science, evena balance of attitudes was represented for mathematics.Two factors specific to this study may have influencedthis higher positive result. The first may be the use of theautobiography itself. As a tool, autobiographies allow abroader opportunity for description of experiences andan ongoing record of transitions in attitude based onfurther experiences. The stories demonstrate that it ispossible to go through a variety of short-term transitionsin attitude and still retain a positive view over time. Thesecond may be a reflection of the choice students weregiven to write about either mathematics or science.While choice provides one more view of students’attitudes when they explain their selection, it does notthen provide a complete view of the whole studypopulation in either content area.

ThemesFive major themes emerged from the autobiogra-

phies:1. The powerful effect of teachers, both positive

and negative.2. The impact of family members on attitudes

toward mathematics and science.3. The importance of content being relevant to real-

life situations.4. The problem of comprehension versus coverage

of content.5. The effects of classroom emphasis on skills and

memorization, predominately in mathematics (see Ap-pendix B).

Teacher effect. The strongest theme concernedteacher effect. Over three fourths of the autobiogra-phies described teachers as playing a significant role inthe attitudes of students, both from positive and nega-tive experiences. Results showed that students per-ceived teachers in two ways: (a) teacher as authorityand (b) teacher as facilitator. The major influences onstudents’ positive or negative attitudes were comments

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(supportive or demeaning) made by teachers to stu-dents, students’ perception of the teacher’s competencein and/or attitude toward the subject, and the instruc-tional strategies teachers used. Student accounts wereoften not limited to one perspective or the other, butrather described both at different points in time. Theseaccounts indicated that a singular experience couldaffect a student’s attitude.

From the perspective of teacher as authority, stu-dents viewed teachers as having the authority andpower to dictate their success or failure. These students

viewed themselves as powerless in those classrooms,e.g., the teacher “made me absolutely despise science”or “gave me a love for learning math”(italics added).The responsibility for learning and the accountabilityfor success or failure rested entirely on the teacher, asseen in the following example quote:

The one superior reason that lies forefront in mymind (for disliking math) is the fact that not onemath teacher I had growing up had the desire orthe skills to succeed in treating or relating mathto my life or as an important part of my learningexperience.Another student said,Throughout my school career, I found one thing tobe true. Science can either be a great deal of fun orin many ways a tortuous experience. This is alldependent on the teacher’s enthusiasm and desireto make the subject enjoyable.From the perspective of teacher as facilitator, teach-

ers were viewed as guides in the learning process.Students viewed themselves as having an active roleand a responsibility in their learning. These teacherswere described as “encouraging,” “enthusiastic,” “in-fluential,” “motivational,” or having the ability to helpstudents succeed in learning. One student wrote aboutchemistry,

I was actively involved in my learning. We workedin groups, pairs and individually on fun experi-ments. I knew the material because I was notmemorizing it from a book. I took ownership of mylearning, and I gained confidence in sharing andcontributing my knowledge within the groups.Another wrote, “My high school Calculus AP

teacher had the greatest influence on me. He was alwaysthere to help and encourage me, even when I thought Iwould never understand.”

Family. Statements regarding the impact of par-ents, siblings, spouses, and children on students’ atti-tudes were combined into a single theme of familyinfluences and, as combined, were described in themajority of autobiographies. Students commented onexperiences, both positive and negative, with parentsand homework, trips to museums and zoos, relation-ships with siblings, connections between their parents’vocations and their own experiences and attitudes, anddiscussions with a spouse that helped students under-stand a concept or appreciate a content area. Thefollowing two student quotes exemplify statements inthis category: “The influence of my dad being anaccountant pushed me to be better. . . .I always tried toimpress my dad with the things that I could do.” “Theonly person that really helped me to enjoy science more

Figure 1. Overall attitudes of student autobiographies.

Science (n = 37)

54%

27%

11%

8%

Math (n = 61)

25%

26%

33%

16%

PosNeg-PosNegPos-Neg

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was my husband. He is constantly explaining scienceconcepts to me.”

Data showed that family members’ influence car-ried powerful messages throughout the student’s entirelearning career. When students felt successful, theyoften described the support and encouragement of afamily member as one aspect of their feelings of successand/or confidence. Vice versa, negative family pressurewas frequently cited as contributing to stress if a studentdescribed feelings of frustration or lack of confidence.

The descriptions of the influences of peers weresimilar to those of family and were both positive andnegative, as in the following statements: “I enjoyedworking with a peer. It helped me a lot that year to haveTom re-explain things that we had learned in class, touse our words, not mathematician words, so I couldunderstand the concepts.”

In elementary school I went out to what we referredto as “the trailer” for math and reading. The namesI was called by classmates, including “stupid,” stillring in my ears. Ever since, I have shied away frommath.Relevance. Approximately half of the students’

stories revealed a strong desire for course content to berelated to real-life contexts. They either felt frustrationwhen unable to see the connection between the contentand its practical applications or satisfaction when theconnections were evident. Students indicated that theunderstanding of the concepts and their desire to learnthem increased when they could apply the learning(e.g., “Relating science to everyday activities helpedme understand the importance of how things worked,why they worked that way, and many other unfamiliarquestions that I asked and answered myself”). Whenstudents did not have experiences that linked content toapplications, they felt discouraged, sensed a lack ofdirection, or could not understand where the informa-tion was leading. (“Math class was predictable andboring. I saw no relevance. By the time I was a freshmanin high school, I knew math was awful.”)

Comprehension vs. Coverage. Comprehension ver-sus coverage has been and remains a point of contentionand debate in the educational community (Beaton, etal., 1996). Over one third of the autobiographies re-flected the impact of this issue on students’ attitudes.Students expressed frustration about moving on too fastand not spending enough time on concepts to gain acomfortable understanding. The following commentabout a sixth grade science class typifies this theme:

I remember copying notes from the chalkboardevery day. I am positive that I never really under-stood what I was copying down in my notebook. I

just wrote as fast as I could just to get through withit and on to the next thing. The information that Iwas supposed to be getting by copying those notesnever sunk in. I believe this is why I was so unsuc-cessful in this class.Another wrote, “Classes were a whirlwind and I

never felt as though I could keep up with the conceptswe were learning.”

Emphasis on Skills and Memorization. Twentystudents (one third) who chose to write about theirmathematics education described positive or negativeexperiences related to skills. The data indicated thatstudents who were adept at memorizing felt successfulin situations requiring speed and recall, such as timedtests and competitive games like “Around the World.”Generally, they remembered these experiences as beingpleasurable, as in the following two statements: “Theonly thing I found fun while in math class was the ‘speedquiz.’ I could memorize anything, so it was really fun todo my quizzes when all I had to do was recall theanswer.” “I remember always winning the games andalways finishing the timed tests. I have such greatmemories of math because I was ‘good’ at it.”

In contrast, those students who struggled with memo-rization activities described those same experiences ascritical events where they felt like failures. Thesedescriptions reflected a remembered sense of threat,inadequacy, and embarrassment because the experi-ences were so public. “What I can remember,” wroteone student, “is timed-tests on multiplication. I remem-ber never finishing one of these tests, while my class-mates were getting perfect scores. I know this is when Ibegan to think that I could never understand math.”Another stated, “Math in school was very competitive.We had timed tests and relay races. This pressurefrustrated me even more and made it hard to concen-trate on learning the facts.”

Further InsightsBeyond the general attitudes and themes, the auto-

biographies revealed important information about whenand why transitions in attitudes occurred, societal mes-sages about gender, how much students rememberedfrom early school experiences, and why the studentschose to write about mathematics or science.

Transitions. Transitions in students’ attitudes weremost often associated with individual teachers or stu-dents’ confidence to successfully learn a specific con-cept within mathematics or science, such as geometry orphysics. For example, at the high school and collegelevel, in particular, some students would describe theirfeelings of dread at having to take a specific course —

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not thinking they would do well — only to be surprisedat how successful they felt and crediting that feeling tothe environment created by the teacher.

I hated math until I was in 10th grade. Then I hadan amazing teacher for geometry. He made it somuch fun to learn all of the things he taught and healmost changed my view of math completely.Students who felt unsuccessful and lacked confi-

dence one year could have completely opposite experi-ences the following year, and vice versa: “Everything wasgreat until I got Mr. X in seventh grade,” said one student.Another student described her experience as follows:

As I began the Theory of Arithmetic I class [incollege], I was pretty skeptical about my ability tohandle math at this level. My instructor, however,was very good to explain the things that I did notunderstand. I felt that she believed in me and myability to do the math. Small successes in her classbuilt up to larger successes, and I finished the classwith flying colors. This led to success in the othermath classes that I needed to take for my degree.Societal messages about gender. Issues of gender

bias were identified by a smaller percentage of thestudents than expected by the researchers. Out of allautobiographies, 11 statements were made by femalestudents (13.5% of the females in the study) and nonewere made by male students. These statements, how-ever, show the power of negative messages to stronglyaffect learning choices and careers of some students, asin the following example:

I feel that I was placed under a stereotype from thebeginning of school. Girls were not supposed to beinterested in science. . . .This train of thought didn’tchange for me until I had a teacher point out howridiculous this stereotype was.Another student said,I have grown and believed for many years thatmales were always better at math and science andthey would obtain careers that dealt in mathematicsand science. Many of my teachers throughout el-ementary and high school confirmed this assump-tion by praising and giving much attention to themales in these classes.Student comments regarding gender, both positive

and negative, focused on family and teacher influences,as well as other, less context specific, societal influ-ences: “My family did not raise me to believe that girlscould not do math, science, or even history. My sisterand I were always encouraged to work to the best of ourability and be successful students.”

If I am to be really honest, I do not think my dislikefor mathematics began in school, but rather with my

mother. My mother is a teacher and she has alwaysbeen willing to help me with my homework. Yet, asfar back as I can remember, I can hear her telling mehow much she disliked math – not only from astudent’s point of view, but also from a teacher’spoint of view. I think her comments have trained meto think I do not like math as well.Early memories of content. A most surprising

finding from this study was that 18 students commenteddirectly that they did not remember much from theirelementary school years. Four of the 61 mathematicsautobiographies contained statements that they remem-bered few, if any, early mathematics experiences. Incontrast, 14 of the 37 students who wrote scienceautobiographies mentioned that they remembered fewscience experiences in grades K-6.

Students’ comments often indicated that there wasgreater emphasis on mathematics than science in theelementary grades. Several stated that they felt sciencewas not valued by their elementary teachers, as in thefollowing two examples: “In elementary school sciencewas fun, but none of my teachers thought it was ex-tremely important.” “During elementary school I didnot have a teacher who was passionate about teachingscience concepts. It seemed like they were ‘just doingtheir job’ when it came to science.”

It was not always clear in the results whetherstudents actually had science in the elementary gradesand did not find it memorable, whether they did nothave science often enough to see it as a content area, orwhether the teacher presented science embedded inother contexts and never described it directly as sci-ence. A few students did make this distinction, withstatements such as, “I don’t remember any science ingrade school. I know I had it, but there aren’t anymemories strong enough to remember.”

Student choice. Student perceptions of less sciencebeing taught in elementary school is reinforced in thereasons given for selecting to write about mathematicsor science. Of those who chose to write about mathemat-ics, 21% chose this area because they had few memoriesof science. In contrast, none of the students who choseto write about science said that they chose it becausethey did not remember any mathematics.

The largest reason given (43% in science; 41% inmathematics) for choosing one content over the otherwas a like or dislike of the subject. Science was largelyselected because it was liked (35% versus 8% respond-ing for this reason). Mathematics selection reflected amore even division of like and dislike (16% versus 25%of those responding for this reason). This breakdownappears to support the attitudes reflected in Figure 1, in

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which the positive attitudes outweighed the negative inscience and balanced in mathematics.

The next most frequently cited reason for selectionwas the desire to provide better instructional opportuni-ties for developing understanding than these studentsfelt they had received in their own school experiences.

Discussion

Study findings support and extend themes in theliterature described and cited earlier in this paper.Student autobiographical accounts speak of anxietiesand internalized messages (positive and negative) af-fecting their attitudes and confidence to do mathemat-ics and science, developed through influences ofteachers, classmates, and family (see, for example,Hembree, 1990; Tobias, 1993). They also describe theimpact of perceived relevance of content, how contentwas presented, how content was valued by adults, andhow they were treated as learners as affecting theirattitudes and success with these subjects (see, for ex-ample, Bulmahn & Young, 1982; Jackson &Leffingwell, 1999).

The value of this study is in the richness of theautobiographical data and the depth and clarity theyprovide. These results not only identify attitudes butthey also provide in-depth reasons for these attitudesand for transitions in attitudes and confidence, asdescribed by some students. The depth and clarity alsoprovide critical insights into the influences that impactthe shaping of future educators. “We teach who we are”(Cole & Knowles, 2000, p. 27).

Study findings demonstrate that students’ attitudesand confidence are being affected at all levels, fromelementary to college, and that praise or blame forstudent attitudes cannot be placed at the doorstep of anyone level of education. It is quite clear from theautobiographical accounts that an individual teacherhas the opportunity to change student perceptions aboutand confidence in learning mathematics or science. It isalso clear that students can carry attitudes over timeand, in the case of negative attitudes, can make learningchoices based solely on avoidance of a particular subject,unless that attitude or confidence level is affected by asuccessful experience. It is the responsibility of educatorsat all levels to assess their practice in order to providean environment that challenges and nurtures the learner.As stated in the National Science Education Standards(NRC, 1996),

The decisions about content and activities that teach-ers make, their interaction with students, the selectionof assessments, the habits of mind that teachers

demonstrate and nurture among their students, andthe attitudes conveyed wittingly and unwittinglyall affect the knowledge, understanding, abilities,and attitudes that students develop. (p. 28)The implications for teachers can be drawn directly

from the students’ autobiographical accounts. Students’responses indicated that they felt most successful andpositive toward mathematics or science when they werein learning environments where they were

• Respected; placed in situations which were notembarrassing, degrading, or a judgment of theirabilities based on particular situation (e.g. “Youdon’t do problem solving well, do you?”).

• Encouraged and challenged.• Treated as capable learners, regardless of gender.• Provided a structure in which they could explore

ideas and build understandings.• Afforded opportunities to apply their learning to

real situations and contexts.• Offered opportunities outside of class time to

receive assistance.These conditions suggest that students felt more

positive and confident in their abilities when they hadsome role in and responsibility for their own learning. It is,therefore, important for teachers to create discussion andapplication opportunities in which students can seetheir role and responsibilities in the learning process.

Instructional strategies that were most often de-scribed by students as facilitating their success (K-16)were those that

• Fostered student understanding of concepts ratherthan those which focused on coverage.

• Included less straight lecture, “talking to thechalkboard,” and more actual student-centered,minds-on experiences.

• Included problems and situations that encouragedapplications of learning.

• Demonstrated a valuing of class time fordiscussion of ideas rather than a valuing of classtime for taking notes, answering recall questions,and working on text exercises.

The finding of this study that students often do nothave specific memories of science in the early yearssuggests that it would be important for teachers toexhibit a positive attitude toward science and math-ematics and to implement these strategies consistentlyfrom the earliest school years.

These messages provided by students, through theirstories on both the classroom environment and instruc-tional strategies, suggest that teachers need carefully toconsider the effect of their choices and actions on thelearning process. For example, timed and competitive

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activities prompted descriptions of either enjoyment oranxiety. These findings imply that the use of theseactivities should be considered carefully and presentedwith understanding of the potential effect on somelearners. This is particularly important if the classroomteacher is one who found the competition enjoyable andsuccessful as an elementary school student.

The influence of family was a primary consider-ation in students’ attitudes about and confidence intheir ability to do mathematics or science. This wouldpoint to a real value in more deliberately involvingfamily in what is happening in the classroom andidentifying quality ways that family members can beinvolved with the content and processes promoted inscience and mathematics classrooms. One key is delib-erately to invite family members to be involved inspecific aspects of the science and mathematics pro-grams. Some suggestions for involving family membersare as follows:

• Develop Family Math (Stenmark, Thompson, &Cossey, 1986) and Family Science (Heil,Amorose, & Harrison, 1999) sessions.

• Invite direct classroom involvement with studentsin the classroom learning activities (as is donewith reading at the elementary and middle schoollevel), in fieldtrips, and in special projects, suchas Science Oympiad or Odyssey of the Mind.

• Use regular newsletters and/or e-mailcommunications to inform parents about whattheir child is learning, how the content is beingused, why teaching strategies may differ fromprevious strategies, and ways to support andencourage their child’s interests in these contentareas.

• Invite family members into the classroom todiscuss their careers in mathematics or science,or how they use mathematics or science in theircareers. This is also an opportunity for students tosee family members as role models for learningscience and mathematics.

• Invite participation as mentors or tutors toindividual students.

National mathematics, science, and staff develop-ment standards and professional development litera-ture speak to the importance of teachers reflecting onpractice in order to thoughtfully examine teaching andlearning and to identify necessary structures to supportgood practice (e.g., collaborative planning and identi-fying resources). This includes reflection on what isbeing taught, how it should be taught, and teacherattitudes and beliefs toward teaching (NCTM, 1991;NRC, 1996; National Staff Development Council,1995;

Schön, 1983; Schmoker, 1996; Sparks & Hirsh, 1997;Wiggins, 1998). The findings of this study support theimportance of providing these professional develop-ment opportunities.

In the methods classrooms involved in this study,the autobiographies were used for both individual andgroup reflection. Students shared in small groups thoseparts of their autobiography that they were comfortablesharing. Small groups then shared their insights with thewhole class which, in turn, led to discussions of theimplications to their own future teaching. These in-sights were referred to throughout the semester asstudents were comparing current insights to their auto-biographical reflections.

Thinking about what we do in light of what weknow from research and daily experience helps usdistinguish between what is important and what issimply habit. As Wiggins (1998) stated, “We cannotever be truly effective teachers until and unless eachone of us is more flinty-eyed and skeptical about his orher own effect. We must become good assessors, inother words, of our own performance” (p. 292). This isreinforced in the National Science Education Stan-dards (NRC, 1996), ”Teachers can be effective guidesfor students learning science only if they have theopportunity to examine their own beliefs…” (p. 28).Autobiographies are one effective tool in this reflectiveprocess. Through mathematics and science autobiogra-phies, teachers can begin to identify common threads instudents’ stories and consider those “commons” as theyreflect on their practice.

References

Atwater, M. M. (1994). Research on culturaldiversity in the classroom. In D. L. Gabel (Ed.),Handbook of research on science teaching andlearning (pp. 558-576). New York: Macmillan.

Beaton, A. E., Mullis, I. V. S., Martin, M. O.,Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1996).Mathematics achievement in the middle school years:IEA’s Third International Mathematics and ScienceStudy (TIMSS). Chestnut Hill, MA: TIMSS InternationalStudy Center, Boston College.

Brookfield, S. D. (1995). Becoming a criticallyreflective teacher. San Francisco: Jossey-BassPublishers.

Brush, L. R. (1981). Some thoughts for teachers onmathematics anxiety. Arithmetic Teacher, 29(4), 37-39.

Bulmahn, B. J., & Young, D. M. (1982). On thetransmission of mathematics anxiety. ArithmeticTeacher, 30(3), 55-56.

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Cole, A. L., & Knowles, J. G. (2000). Researchingteaching: Exploring teacher development throughreflexive inquiry. Boston: Allyn and Bacon.

Ebenezer, J. V., & Zoller, U. (1993). Grade 10students’ perceptions of and attitudes toward scienceteaching and school science. Journal of Research inScience Teaching, 30(2), 175-186.

Heil, D., Amorose, G, Gurnee, A., & Harrison, A.(Eds.). (1999). Family science. Portland, OR: PortlandState University.

Hembree, R. (1990). The nature, effects, and reliefof mathematics anxiety. Journal for Research inMathematics Education, 21(1), 33-46.

Jackson, C. D., & Leffingwell, R. J. (1999). Therole of instructors in creating math anxiety in studentsfrom kindergarten through college. MathematicsTeacher, 92(7), pp. 583-586.

Kelly, W. P., & Tomhave, W. K. (1985). A studyof math anxiety/math avoidance in preservice elementaryteachers. Arithmetic Teacher, 32(5), 51-53.

Koch, J. (1990). The science autobiography. Scienceand Children, 28(3), 42-43.

Meyer, R. A. (1980). Attitudes of elementaryteachers toward mathematics. (ERIC DocumentReproduction Service No. ED 190 388)

Meyer, R. J. (1993, December). Preserviceteachers’ literacy autobiographies and teacherdevelopment. Paper presented at the annual meeting ofthe National Reading Conference, Charleston, SC. (ERICDocument Reproduction Service No. ED 367 620)

Miles, M.B., & Huberman, A. M. (1984).Qualitative data analysis: A sourcebook of newmethods. Newbury Park, CA: Sage Publications.

National Council of Teachers of Mathematics.(1989). Curriculum and evaluation standards forschool mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics.(1991). Professional standards for teachingmathematics. Reston, VA: Author.

National Research Council. (1996). Nationalscience education standards. Washington, DC:National Academy Press.

National Staff Development Council. (1995).Standards for staff development: Elementary schooledition. Oxford, OH: Author.

Schmoker, M. (1996). Results. Alexandria, VA:Association for Supervision and CurriculumDevelopment.

Schön, D. A. (1983). The reflective practitioner.New York: Basic Books, Inc.

Shaw, J. M., & Chessin, D. A. (1996). Usingpreservice teachers’ mathematics autobiographies to

promote learning. Teaching Children Mathematics,2(8), 486-488.

Sparks, D., & Hirsh, S. (1997). A new vision forstaff development. Alexandria, VA: Association forSupervision and Curriculum Development.

Stenmark, J. K., Thompson, V., & Cossey, R.(1986). Family math. Berkeley, CA: Lawrence Hall ofScience, University of California.

Thompson, A. G. (1992). Teachers’ beliefs andconceptions: A synthesis of the research. In D. A.Grouws (Ed.), Handbook of research on mathematicsteaching and learning (pp. 127-146). New York:Macmillan.

Tobias, S. (1993). Overcoming math anxiety (Rev.ed.). New York: Norton & Co.

Trujillo, K. M., & Hadfield, O. D. (1999). Tracingthe roots of mathematics anxiety through in-depthinterviews with preservice elementary teachers. CollegeStudent Journal, 33(2), 219-232.

Wiggins, G. (1998). Educative assessment:Designing assessments to inform and improve studentperformance. San Francisco: Jossey-Bass.

Yager, R. E., & Penick, J.E. (1984). What studentssay about science teaching and science teachers. ScienceEducation, 68(2), 143-152.

Editor’s Note: Correspondence concerning thisarticle should be addressed to Judith Z. Ellsworth,College of Education, P. O. Box 3374, University ofWyoming, Laramie, WY 82071-3374.

Electronic mail may be sent via Internet [email protected]

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Appendix AAttitude Codes and Their Definitions.

PositiveAutobiographies reflected a moderate to strong favorable student reaction to mathematics/science educationexperiences throughout the description.

NegativeAutobiographies reflected an indifferent to strong unfavorable student reaction to mathematics/scienceeducation experiences throughout the description.

Negative to Positive or Positive to NegativeAutobiographies reflected a definite transition in attitude from the beginning to the end of the description.

Appendix BEmergent Theme Definitions

Teacher EffectTeacher as authority

The teacher is perceived by students as having the power to determine the student’s success or failureand is acknowledged accordingly. Students see themselves as not in control of their own success orfailure.

Teacher as facilitatorThe teacher is perceived by students as helping them to be empowered. The teacher facilitates theprocess of student learning.

FamilyStudents describe the influence of family members, positive or negative, on their attitudes.

RelevanceStudents describe the value, positive or negative, of mathematics/science in relation to seeing or notseeing its application in real life.

Comprehension vs. CoverageStudents describe experiences which reflect feelings about understanding content; either expressingthe desire to spend more time on understanding concepts rather than simply covering content, ordescribing instances in which they felt successful because they understood.

Emphasis on Skills and MemorizationStudents describe direct relationships between proficiency in procedural skills and memorization andfeelings of success or vice versa.