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This article was downloaded by: [University of North Texas] On: 23 November 2014, At: 19:49 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK The Journal of Experimental Education Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/vjxe20 Can a Teacher Intervention Improve Classroom Practices and Student Motivation in Mathematics? Deborah Stipek a , Karen B. Givvin a , Julie M. Salmon a & Valanne L. Macgyvers b a University of California , Los Angeles b Southwestern Louisiana State University Published online: 01 Apr 2010. To cite this article: Deborah Stipek , Karen B. Givvin , Julie M. Salmon & Valanne L. Macgyvers (1998) Can a Teacher Intervention Improve Classroom Practices and Student Motivation in Mathematics?, The Journal of Experimental Education, 66:4, 319-337, DOI: 10.1080/00220979809601404 To link to this article: http://dx.doi.org/10.1080/00220979809601404 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the

Can a Teacher Intervention Improve Classroom Practices and Student Motivation in Mathematics?

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Page 1: Can a Teacher Intervention Improve Classroom Practices and Student Motivation in Mathematics?

This article was downloaded by: [University of North Texas]On: 23 November 2014, At: 19:49Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK

The Journal of ExperimentalEducationPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/vjxe20

Can a Teacher InterventionImprove Classroom Practicesand Student Motivation inMathematics?Deborah Stipek a , Karen B. Givvin a , Julie M.Salmon a & Valanne L. Macgyvers ba University of California , Los Angelesb Southwestern Louisiana State UniversityPublished online: 01 Apr 2010.

To cite this article: Deborah Stipek , Karen B. Givvin , Julie M. Salmon & Valanne L.Macgyvers (1998) Can a Teacher Intervention Improve Classroom Practices and StudentMotivation in Mathematics?, The Journal of Experimental Education, 66:4, 319-337,DOI: 10.1080/00220979809601404

To link to this article: http://dx.doi.org/10.1080/00220979809601404

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all theinformation (the “Content”) contained in the publications on our platform.However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness,or suitability for any purpose of the Content. Any opinions and viewsexpressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the

Page 2: Can a Teacher Intervention Improve Classroom Practices and Student Motivation in Mathematics?

Content should not be relied upon and should be independently verified withprimary sources of information. Taylor and Francis shall not be liable for anylosses, actions, claims, proceedings, demands, costs, expenses, damages,and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of theContent.

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The Journal of Experimental Education, 1998,66(4), 3 19-337

Can a Teacher Intervention Improve Classroom Practices and Student Motivation in Mathematics?

DEBORAH STIPEK KAREN B. GIVVIN JULIE M. SALMON University of California, Los Angeles

VALANNE L. MACGYVERS Southwestern Louisiana State University

ABSTRACT. Classroom practices believed to affect student motivation were assessed for 24 upper elementary school teachers during a unit on fractions. Two groups of mathematics “reform-minded” teachers participated in professional devel- opment programs-in either an intensive intervention or an intervention involving primarily teacher support. A 3rd group of teachers implemented traditional, text- based instruction and was not involved in any intervention. For most practices assessed, the 2 reform-minded groups of teachers did not differ significantly from each other, but both differed from the traditional teachers. The reform-minded teachers emphasized effort, mastery, and understanding more; encouraged student autonomy more; and created a psychologically safer environment than the tradi- tional teachers did. The teachers in the intensive intervention, which included train- ing in motivation, made more accurate judgments of students’ motivation than the other reform-minded teachers did. There was modest evidence that the teachers who had had only minimal training in reform-minded practices had negative effects on students’ motivation (e.g., lower self-confidence and increased concerns about per- formance).

REFORM-MINDED MATHEMATICS EDUCATION is designed to increase children’s conceptual understanding of mathematics. It also is designed to max- imize students’ motivation-to foster in students a desire to develop mastery and understanding, to develop their sense of autonomy and personal responsibility, and to increase their intrinsic interest in math and pride in developing math com- petencies. Mathematics education reform is designed to increase students’ appre-

319

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320 The Journal Of‘Experirnental Education

ciation of the value of mathematical understanding in everyday life, their self- confidence as autonomous math learners, and their willingness to take risks and approach challenging tasks (California State Department of Education, 1992; National Council of Teachers of Mathematics, 1989, 1991).

Research on motivation suggests that the instructional strategies promoted by mathematics reformers should have these positive motivational effects (see Pin- trich & Schunk, 1996; Stipek, 1993, 1996). The greater emphasis on process and on seeking alternative solutions rather than on finding the one correct solution should help children focus on developing mastery and understanding rather than on performance (getting it right), social approval (pleasing the teacher), or grades. It should also foster the belief that effort will lead to success and increased student willingness to take risks and approach challenging tasks (Ames & Archer, 1988; Dweck, 1986; Nicholls, Cobb, Wood, Yackel, & Patashnick, 1990; Nicholls, Cobb, Yackel, Wood, & Wheatley, 1990). Relative to the more traditional authoritative and directive role teachers have played, teachers’ support of students’ active engagement with mathematical ideas and personal construc- tion of math concepts should encourage more autonomy and independence in students, as well as greater intrinsic interest in math (Deci, Spiegel, Ryan, Koest- ner, & Kauffman, 1982).

The greater diversity of tasks and modes of working should render relative per- formance less stable across tasks; more children should have an opportunity to demonstrate skills than is true when all children are assigned the same type of task (e.g., paper-and-pencil problems sets) every day (Rosenholtz & Rosenholtz, 198 1; Rosenholtz & Simpson, 1984). Reform-minded mathematics instruction should, therefore, also foster both teachers’ and students’ perceptions of mathe- matics as a domain in which competency and success are achievable through practice and effort, rather than as an ability tqat some people have and others lack (what Dweck, 1986, and her colleagues refer to as an entity concept ofability). Finally, pride and other positive affective experiences should be enhanced by increased feelings of competence and by opportunities to complete multidimen- sional products that require sustained effort.

This kind of reform-minded teaching of mathematics promoted by the Nation- al Council of Teachers of Mathematics (1989, 1991) and other organizations and experts, however, is currently implemented in few U.S. classrooms. It requires fundamental changes in the way teachers think about mathematics and about teaching; it is different from the way most teachers were taught mathematics and were taught to teach mathematics. The challenge is to design professional pro- grams that provide teachers with opportunities to reflect on their existing under- standing of mathematics, teaching, and learning and to develop practices that are consistent with reform.

The study reported here is embedded in a larger study designed to compare different approaches to helping elementary teachers teach mathematics accord-

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Stipek, Givvin, Salmon, & MacGyvers 32 1

ing to current reform principles. (The larger study was supported by Grant MDR 9154512 from the National Science Foundation to Mary1 Gearhart, Geoffrey Saxe, and Deborah Stipek.) In the larger study, teaching practices and student learning and motivation were compared in three groups of teachers; two of the groups participated in professional development programs designed specifically for the study, and a control group of traditional teachers received no intervention. Motivation was a significant component of the intervention.

The effects of the intervention on student learning were reported in a separate article (Saxe & Gearhart, 1997). Students’ understanding of fractions was assessed before and after the fractions unit was implemented in the classroom. Two different kinds of problems were given: (a) procedurally oriented problems, which assessed computation (adding and subtracting fractions), fraction equiva- lences, computing and expressing values in a pie chart, and missing value-equiv- alence problems), and (b) conceptually oriented problems, which involved con- structing fractions for unequal parts of wholes, estimating fractional parts of areas, and fair-share problems. The results indicated that student gains in achievement related to fractions vaned by teacher group. On the procedurally oriented problems, the students in the traditional classrooms gained significantly more than the students in the support classrooms did, but not significantly more than the students in IMA classrooms. Thus, despite the greater emphasis on com- putation in the traditional classrooms, these students did not show greater gains on computational problems than the students in the IMA classrooms did. On the conceptual problems, the students in the IMA classrooms gained significantly more than the students in both the traditional and the support classrooms did. Despite the support teachers’ commitment to emphasizing conceptual under- standing, their students did not gain more on the conceptual problems than the students in the traditional classrooms did.

In the present article, we discuss the intervention’s effect, related to motiva- tion, on teacher practices and student motivation.

,

Method

Study Design

We matched the applicants selected for the intervention study as well as pos- sible for years of experience, advanced degreeskertificates, and student charac- teristics and placed them into one of three study groups (see Tables 1 and 2). The teachers in the two reform groups were clearly committed to teaching according to reform principles. All had taken at least one 1-2-day training session and had previously taught one, and usually both, of the California Framework replace- ment units Seeing Fractions and M y Travels With Gulliver: They agreed to teach the units again during the year of the intervention. These teachers were also will-

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TABLE 1 Study Design: Groups Participating

Group name n Curriculum Staff development

Integrating mathematics assessment

support

Traditional

9 Reform Knowledge. instruction, assessment, and motivation

8 Reform Collegial support only

7 Traditional None

TABLE 2 Teachers’ Experience and Education, by Group

IMA teachers Support teachers Traditional teachers Years Years Years

Teacher teaching Degree teaching Degree teaching Degree

1 2 3 4 5 6 7 8 9

M SD

1 7

12 14 17 22 24 24 25

16.22 8.45

BA 3 BA 5 MA 12 BA 13 MA 17 MA 17 MA 18 MA 22 MA

13.38 6.57

BA BA MA BA MA MA BA MA

4 MA 23 MA 25 BA 26 MA 29 MA 30 BA 34 MS

24.43 9.7 1

Note. IMA = integrating mathematics assessment. I

ing to participate in a professional development program focused on reform- minded mathematics teaching that would require time outside of their regular workday. The two groups of teachers were matched for the extent of their partic- ipation in mathematics reform workshops.

One of the reform groups, referred to henceforth as the support group, was provided with opportunities for collegial support and collaboration during the year of the study. The second reform group, the integrating mathematics assess- ment (IMA) group, participated in a fairly intensive intervention focused on assessment of students’ mathematics understanding and motivation. A compari- son of these two groups provides information on the added value of an intensive intervention that includes motivation as a specific focus over the kind of profes- sional development that is typically available to teachers.

The third group of teachers, the traditional group, taught fractions and meas- urement with their school-approved textbook and workbook materials; these

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Stipek, Givvin, Salmon, & MacGyvers 323

teachers did not participate in a professional development program and expressed no interest in teaching according to mathematics-education-reform principles. A comparison of the first two groups and the third group provided evidence on dif- ferences in the practices of teachers who are committed to implementing reform- minded practices and teachers who are not.

The Intervention

The IMA group participated in a 1-week summer workshop followed by biweekly evening meetings with the study researchers and participating graduate students. The meetings were informal and involved activities, videotapes, pre- sentations, discussions, and analyses of student work. There were four compo- nents to the intervention:

1. Teachers ’ mathematics-The teachers participated in activities designed to enhance the teachers’ knowledge of the mathematical concepts they taught and to model reform-type instructional and assessment strategies.

2. Children’s mathematics-The teachers participated in activities designed to develop the teachers’ knowledge of children’s “sense-making” efforts to con- struct mathematical understandings and strategies.

3. Assessment-The teachers were encouraged and given assistance in assess- ing students’ mathematical understanding and using their reflections on chil- dren’s understanding to guide instruction.

4. Motivation-Motivational constructs were discussed, and the teachers were asked to apply them in analyses of their own students.

Throughout the intervention, the teachers in the IMA group were introduced to motivation issues; the motivation issues, including children’s (a) beliefs about ability (e.g., as stable and uncontrollable vs. flexible and influenced by effort), (b) perceptions of competence and self-efficacy in math, (c) goals (e.g., to develop understanding vs. to perform), (d) perceptions of the usefulness of mathematics outside of the classroom, (e) interest in and enjoyment of math activities, and (Q emotions associated with mathematics (e.g., shame, fear, anx- iety, pride).

Considerable emphasis was given to assessing student motivation. We helped the teachers identify behaviors that reveal students’ beliefs, values, and interest in mathematics and suggested strategies for seeking additional infor- mation to help interpret the meaning of observed behavior. The teachers were given examples of self-reflective exercises that they could use to involve stu- dents in their own assessments. The self-reflective exercises asked the stu- dents-usually through brief questionnaires-to report on their own beliefs, goals, values, and feelings about themselves as math learners. The teachers were given some assistance in interpreting students’ responses and in consid-

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324 The Journal c f E.rperitnmfol Educntioti

ering possible interventions to address any problems revealed. The teachers also analyzed videotape snippets that revealed students’ motivational beliefs and dispositions and discussed observations of their own students. Role play- ing and discussions supported the teachers’ strategies for addressing the moti- vation problems they identified and for maximizing students’ positive motiva- tional orientations.

In the initial 1-week workshop, approximately 1 day was devoted specifically to motivation. A total of approximately 10 hr of the biweekly meetings over the course of the year focused on motivation issues; motivation was also occasional- ly addressed in the context of activities or discussions related to the other three components.

The support group received the kind of exposure to reform-minded mathe- matics instruction that most teachers in California receive (if they are exposed at all). The intervention began with a 2-day group meeting, and the group met monthly thereafter with one of the principal investigators. The teachers in this group shared strategies, assessment challenges, and homework and discussed the use of supplementary resources (e.g., manipulatives) and the role of the textbook. The teachers discussed problems that they had in implementing reform strategies-some very general, such as lack of parent support for reform practices, and some very specific, concerning teaching particular concepts. The teachers shared and critiqued specific teaching strategies and assessment tech- niques that they used.

There was no explicit effort to introduce motivation into the support-group dis- cussions, but motivation often entered into the conversation. For example, the teachers described students’ becoming frustrated and expressing preferences for textbook mathematics (with clear right-and-wrong answers) and students’ want- ing a grade on portfolios that the teachers promoted for the students to chart their progress in understanding. They also rkported motivational successes-for example, children who became engaged in mathematics for the first time. The teachers claimed that the support-group meetings helped them anticipate prob- lems and provided moral support when they encountered them; the teachers also claimed that the support-group meetings made them more conscious and reflec- tive in making myriad decisions while teaching.

Student Population

All teachers taught fourth, fifth, or sixth grade in schools serving predomi- nantly low-income children. Some data were collected on all of the children in the participating teachers’ classrooms who were present on the day of the student assessment. There were 624 students-274 boys, 27 1 girls, and 79 students for whom we did not have information on gender. The participants represented diverse ethnic backgrounds; 46 were African American; 358, Latino; 49, Asian;

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Stipek, Givvin, Salmon, & MacGyvers 325

92, White; and 26 were from other ethnic groups. We did not have ethnicity data on the remaining 53 participants. There was a substantial number (over 20%) of limited-English-proficiency students (predominantly Spanish speaking) in one IMA, three support, and two traditional teachers’ classrooms. Average class sizes were high and similar across the three groups of teachers (3 1, IMA; 34, support; 32, traditional).

We selected 6 target children in each classroom for some analyses on the basis of a fractions test given at the beginning of the year; 2 children ( 1 girl and 1 boy) in the top third, 2 in the middle third, and 2 in the bottom third of the distribu- tion of scores within each classroom were randomly selected.

We analyzed the data reported here to assess the impact of the intervention on teacher practices and on student motivation. In other reports, we discussed the effects of teacher practices (regardless of the teachers’ experimental-group assignment) on student motivation and associations between student motivation and student learning (see Stipek et al., in press).

Research Assessments

Teacher Practices

Videotapes. The first source of information on teacher practices was a series of videotapes of at least two instructional periods. For the teachers implementing Seeing Fractions, videotaping was done during the addition of fractions or dur- ing the peer problem-solving lessons. Videotaping in the traditional teachers’ classrooms was done when the teachers were covering the addition of fractions.

We developed a coding system to characterize the teacher practices, as described above. Reliable codes were developed for nine dimensions:

i

1 . The degree to which the teacher emphasized student effort and conveyed the message that effort will eventually pay off, such as by praising effort or encouraging students to keep trying;

2. The degree to which the teacher emphasized and encouraged students to focus on learning, understanding, and mastery such as by encouraging them to try alternative strategies, asking them to explain their strategies, asking them to apply concepts in new contexts, and using inadequate solutions in instruction;

3. The degree to which the teacher emphasized pe~ormance (e.g., getting answers right, high grades), such as by praising or criticizing performance (e.g., correctness), referring to grades, or recommending that students avoid problems that they might not be able to do;

4. The degree to which the teacher encouraged and gave opportunities for stu- dents to work autonomously, such as by pointing out resources in the room, encouraging children to engage in self-evaluation, giving students choices in how to solve problems, and refraining from offering unnecessary help;

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Page 10: Can a Teacher Intervention Improve Classroom Practices and Student Motivation in Mathematics?

5. Whether the teacher displayed more negative (e.g., anger, sarcasm, gruffness, dissatisfaction, aloofness) versus positive (e.g., sensitivity, respect, interest) afect;

6. The level of the teacher’s enthusiasm and interest in mathematics; 7. Whether the teacher fostered a threatening (ignoring wrong answers and

asking another child, threatening tests, tolerating put-downs by students) versus a psychologically safe environment (e.g., conveying that mistakes are OK, “scaf- folding” a child having difficulty, not tolerating students putting each other down); and

8. The degree to which the teachers emphasized speed in completing tasks.

We created a detailed description of the practices associated with each dimension and rated each dimension on a scale ranging from 1 (not at all like this teacher) to 5 (very much like this teacher).

Videotapes were coded by graduate students who were familiar with the study design and could distinguish between the teachers who were using the replace- ment units and the traditional teachers. We used undergraduate students who were not knowledgeable in mathematics reform or motivation literature to assess reliability.

The raters observed videotapes as many times as they believed necessary to make reliable ratings. Each lesson was given two sets of ratings, one that reflect- ed all of the time in which the teacher was involved in instruction with the whole class and one for the periods in which the children worked on activities or prob- lems in small groups or individually. These two parts of the instructional period were coded separately because the teachers might behave differently along the dimensions assessed when they were directing whole-class lessons than when they were supervising student work. For most teachers, these two classroom seg- ments were clearly distinguished. A common format was for the teacher to pre- sent a lesson or work with the whole class at the beginning of the time set aside for math and for students subsequently to work collaboratively or independently on problems or activities. In some classrooms, the teacher returned to a whole- class format at the end of the math period. A few of the teachers moved back and forth from a more teacher-dominated, whole-class format to an individual or small-group student-work format.

Two raters independently rated 12 of the math lessons, including at least 3 teachers from each group. Table 3 contains the reliabilities (percentage of exact matches or ratings within I point) and the correlations between the whole-class and student-activity segments. As can be seen from the correlations, the teachers’ instructional styles were fairly consistent across the two settings. We therefore used an average in further analyses of teacher practices.

Field notes. Teacher practices were also observed on at least 2 separate days while the teachers taught fractions (not the same days that the videotaping was done). The field notes from the graduate students constituted an additional source

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Stipek, Givvin, Salmon, & MacCyvers 327

TABLE 3 Teacher Practices, Based on Videotapes

Group IW IMAd Support Traditional

Dimension a, P (n = 6 ) (n = 8) ( n = 6) F( I . 20)

Emphasis on learning/ mastery

Emphasis on performance

Encourage student autonomy

Emphasis on effort

Teaching affect

Teacher enthusiasm

Safe environment

Emphasis on speed

92/100

83/70

92/80

92/90

75/100

92/100

83/80

92/90

.82***

.76***

.82***

.69***

.92***

.82***

.88***

.62**

3.85, (.79)

2.93, (.87)

(.71)

3.80a (.go)

3.46 (1.12)

3.49 (.65)

3.61 (.93)

(.79)

3.53,

1.60

3.31L (.72)

3.06& ( I .00)

3.09* ( 1.04)

3.3 I (.95)

2.87 ( 1.20)

3.22 (.81)

2.97 ( I .OO)

1.69 (58)

1.97, ( S 2 )

4.52, (.45)

I .so, (.32)

2.3 1 , (.73)

2.60 (1.31)

2.72 (.48)

2.39 (1.10)

2.25 (.82)

13.05***

7.50**

12.82***

5.72**

1.12

2.36

2.77

I .58

"Whole-classlstudent-work. 'Correlation coefficient between whole-class and student-work ratings. 'Standard deviations are in parentheses. dIMA = integrating mathematics assessment. **p < .01. ***p < ,001. Different subscripts indicate significantly different means, p < .05.

of information on teacher practices that could be used to assess the validity of the scores based on the videotapes. Some of the graduate-student observers had backgrounds in mathematics education; others worked in the area of motivation. The observers primarily sat in the back of the classroom, but they were free to move around and observe teacher-to-student and student-to-student interactions more closely.

We developed a coding system for the field notes that was patterned after the videotape coding system. Because of the variability in the quality and detail in the notes, as well as in attention to teacher practices related to the motivation dimensions of interest, global ratings based on the corpus of notes was the most reliable coding strategy.

Raters blind to the teachers' identities read all of the field notes of a given teacher and made ratings using the same 5-point scale and the same protocol that were used for coding the videos. Although an attempt was made to apply all eight videotape codes, only four of the eight dimensions were rated reliably (by two

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328 The Jounial of Experiniental Educution

raters) from the field notes: (a) emphasis on learning and mastery (95% agree- ment), (b) emphasis on performance (95%), (c) encouragement of student auton- omy (95%), and (d) creating a safe environment (86%).

Teacher evaluation practices. A third source of information about the teachers’ practices came from a questionnaire they completed on their strategies for eval- uating students. They were asked how often (nevel; occasionally, or often) they gave the following kinds of evaluative feedback to students: (a) letter grades, (b) number of errors or number correct, (c) substantive written feedback, (d) sym- bols (e.g., stars, happy faces), and (e) check marks for completion.

Teachers ’ Assessments of Students’ Beliefs, Values, and Goals

The teachers were asked to rate the six target children in their class four times: (a) at the beginning of the school year, (b) after completing the fractions unit, (c) after completing the measurement unit, and (d) at the end of the school year. The fust and last questionnaires referred to math tasks in general; the second and third questionnaires referred specifically to fractions and measurement, respectively.

Items were measured on a Likert-type scale ( 1 = not at alVnot mucwalmost never; 6 = veryh great deaValmost always). The average alpha over the four administrations of the survey for the subscales created are indicated in parenthe- ses below. The teachers rated the target children’s (a) effodmastery orientation (6 items, e.g., “How concerned about really understanding math concepts is she? Does s h e prefer easy or challenging math taskdactivities?”; .93); (b) perform- ance orientation (2 items, e.g., “How concerned about others’ views is she?’ [e.g., teachedparental approval]; .48); (c) persistence (4 items; e.g., “How does s h e react when s h e encounters difficulty in math?’ [e.g., tries new strategies, persists on own]; 3 3 ) ; (d) help-seeking (2 itdms, e.g., “Does s h e seek help when s h e encounters difficulty in math?”; .61); (e) positive emotions (3 items, e.g., “How much does s h e enjoy math work? How much does s h e evidence joy/pride while working on math tasks?’; .92); (f) negative emotions (5 items, e.g., “How much does s h e evidence confusion/distress/embarrassment/frustration while working on math tasks?’; 39); and (g) self-perceptions of ability (1 item, “How confident is the child in hisher math ability?’). The teachers also rated target stu- dents’ math competence (3 items, e.g., “How easily does s h e master new math concepts?’; .92).

Students ’ Self-Reported Motivation

All students completed a questionnaire about their own beliefs, values, goals, and feelings associated with mathematics. The student questionnaires were given at the same four times that teacher ratings of the target students were done. Table

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Stipek, Givvin, Salmon, & MacGyvers 329

TABLE 4 Measure of Students' Beliefs, Values, and Goals

Subscale Average d No. items Sample items

Mastery orientation

Performance orientation

Help-seeking

Positive emotions

Negative emotions

Perceived ability

Persistence

.67 5 How much did you care about really under-

. 4 4 b

standing mathlfractionslmeasurement'?

When you want to know how well you are doing in math, which of these are important to you? (get more right or wrong than other kids)'

What do you do when you are having trouble with mathlfractions/measurement work'? (ask my teacher for help)c

How did you feel when you were doing math/ fractions/measurement work'? (interested, proud)c

. I2 5 How do/did you feel when you [were doing] mathlfractionslmeasurement work'? (embar- rassed, frustrated. upset, worried)c

urement?d

What do you do when you are having trouble with math work'? (keep trying on my own)'

2

.45b 2

.63 3

.62 3 How good are you at mathlfractiondmeas

.25b 2

'Average of four assessments. hCorrelation. 'Rating of response in parentheses was included in this suhscale. dAsked only on the questionnaire given at the beginning and the end of the school year.

4 contains a summary of the subscales created from the student questionnaires. The student subscales were conceptually matcped to the teacher scales.

Students Behavior

Students' behavior was coded, from the same videotaped lessons from which teacher practices were coded, during times when the students were working on math activities or problems either independently or in cooperative groups. To ensure that student-behavior ratings included students' performing at all skill levels, we focused the camera primarily on students selected as tar- get children.

Raters coded all children who were clearly visible and could be heard for at least 3 consecutive min of tape. A new set of ratings was made every 6 min, for up to 24 min (or 4 intervals). Ratings were made on 4-point scales (1 = low, 4 = high) for the child(ren) in view who met the 3-min criterion. When the camera moved to another child or group of children, a new set of ratings was made.

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330 The Journal of’E.rper.ittieittci1 Educurion

We assessed reliability by computing correlations (indicated in parentheses, below) between two independent coders who coded half of the teachers’ class- rooms (12 out of 24). All correlations had a p value of less than ,001. Ratings were made of (a) how eagerly the children got to work after being given direc- tions ( r = .73), (b) the children’s engagement (how on task they were; r = .78), and (c) how emotionally engaged (enthusiastic) they were ( r = S4). If more than one child was in view (which was usually true), the mean rating, averaged across children, on these three dimensions was recorded. If the children were supposed to be working cooperatively, ratings also were made of (d) how much discussion there was among members of the group ( r = .82), (e) how broad participation was ( r = .83), (f) how focused the discussion was on mathematics (I = .85), and (8) the level of interpersonal conflict ( r = .75).

Results

Coherence of Teacher Practices

The high correlations between ratings on the dimensions of teacher practices made during whole-class instruction and those made during independent student work suggest some coherence in teacher practices. The correlation coefficients between ratings of teacher practices from the videotapes and those (on different days) from the field notes were also high: (a) emphasis on learning and mastery, r = .74, p < .001; (b) emphasis on performance, r = .67, p < .001; (c) encourage- ment of autonomy, r = .60, p < .01; and (d) safe environment, r = .5 1, p < .01.

Effect of Intervention I

Teacher Practices

We computed a series of analyses of variance (ANOVAs), with teachers’ group placement as the independent variable and each of the teachers’ ratings from the videotapes and from the field notes as the dependent variables. Compared with the traditional teachers, the IMA and support teachers were more focused on mas- tery and learning, less focused on performance, and more supportive of student autonomy (see Table 3). The support teachers fell in between on this variable. In no case did the IMA teachers differ significantly from the support teachers.

The ANOVAs also revealed significant differences in teacher practices assessed from the field notes (see Table 5) . The traditional teachers emphasized mastery and learning less than the IMA teachers did and emphasized perform- ance significantly more than the support teachers did. They encouraged student autonomy less and had a less safe environment than both the IMA and support teachers did.

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Stipek, Givvin, Salmon, & MacGyvers 33 1

TABLE 5 Mean Differences in Field-Note Ratings, by Group

Rating IMA support Traditional F(2. 20)

Emphasis on learning/mastery 3.04, 2.88 (.82) (1.13)

Emphasis on performance 3.02 2.84a ( I .02) (.SO)

Encourage student autonomy 2.96, 2.99, (1.04) (.64)

Safe environment 3.15. 3.09;1 (52) (33)

I .74, 4.57* ( 3 2 )

4.0, 4.56* (.4@

1.78, 4.92* (.S 1 )

(.47) 2.08, 6.00**

Nofe. Standard deviations are in parentheses. Means with different subscripts are significantly different from each other. p < .05. IMA = integrating mathematics assessment. * p < .05. **p < . O l .

Evaluation Practices

Analyses of group differences in the teachers’ evaluation practices (how often they gave letter grades, number of errors, substantive written feedback, symbols, and check marks for completion) revealed only one marginally significant group difference. The IMA teachers (M = 1.04, SD = .36) were more likely than the support teachers ( M = .79, SD = .21) or the traditional teachers ( M = S7, SD = .42) to claim to give substantive written comments to students, F(2, 17) = 3.29, p < .06.

Student Beliefs, Values, Goals, and Emotions I

We assessed the effect of teacher group on students’ beliefs, values, goals, and emotions by first regressing student end-of-the-year motivation scores on equiv- alent beginning-of-the-year scores and then computing one-way ANOVAs on the residuals. There was one significant and one marginally significant finding. The IMA teachers’ students were the least concerned about performance (residual M = -.22, SD = 1.23), and the support teachers’ students were the most concerned about performance ( M = .29, SD = 1.38); the traditional teachers’students were in between (M = -.06, SD = 1.40), F(2,434) = 5.86, p < .01. The IMA teachers’ stu- dents also showed the highest degree of mastery orientation (residual M = .09, SD = .85), and the traditional teachers’ students showed the lowest degree of mas- tery orientation (residual M = -.12, SD = .85), with the support teachers’ students in between (residual M = -.01, SD = .85), F(2,434) = 2.48, p < .08.

We also assessed student scores for fractions and measurement, again using

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332 The Journal of Exuc~riitienrtil Educatioti

TABLE 6 Adjusted Mean Scores for Student Beliefs, Goals, and Emotions

Fractions Measurement Variable IMA Support Traditional F(2, 448) IMA Support Traditional F(2, 358)

Mastery .04 orientation (.62)

Performance -.2Sa orientation (1.28)

Help- .o I seeking ( I . 18)

Positive .12 emotions (37)

-.01 (.74)

.2 I , ( 1.47)

. I7= (1.15)

-.08 (I .07)

-.06 (.85)

.13, ( 1 .52)

-.23, (1.09)

-.08 (.94)

.75 .06 ~ 7 1 )

5.59** -.06 (1.31)

4.30* .1za (1.12)

2.70t -.o I (1.03)

Negative .01 .09 -.13 2.17 -.06 emotions (37) (.84) (.99) ~ 9 0 )

Perceived .09a -.16, .06 4.58** .06 ability (32) ( 3 1 ) (.92) (.83)

Persistence .04 -.09 .06 .89 .05;, (1.04) (1.10) (1.05) (1.02)

-.04 ( .93

.20 ( I .47)

(1.14)

.I2 ( I .08)

.I0 I .03)

.02 (.96)

. lga I .20)

.ISa

-.07 .76 ( 9 5 )

-.I4 1.81 ( I .28)

-.48, 9.96*** (1.14)

-.I2 1.22 (1.17)

-.Ol .98 (.97)

-.I5 1.62 (.82)

-33, 5.51** ( 1 . 1 1 )

Nore. Standard deviations are in parentheses. Means with different subscripts are significantly different from each other, p < .05. IMA = integrating mathematics assessment. I-p < .lo. * p < .05. **p < .01. ***p < .001.

residual scores after regressing them on equivalent beginning-of-the-year scores. Table 6 contains several significant teacher-group effects. Scores for perceptions of ability in fractions were significantly lower for the support teachers’ students than for the IMA teachers’ students. The traditional teachers’ students reported less help seeking in both fractions and measurement, and the IMA teachers’ stu- dents reported more positive emotions in fractions compared with the students in the other two groups.

Students’ Behavior

We computed a multivariate analysis of variance (MANOVA) to assess the effects of teacher group on the students’ behavior while working on tasks. A teacher’s score on each student-behavior variable was the average of all intervals rated for the students in the teacher’s class. We included all of the student-behav- ior ratings from videotapes as dependent variables. The teacher-group difference was significant, F(6, 16) = 7.21, p < .05. Univariate ANOVAs revealed two stu- dent behaviors that were significantly associated with the teacher groups. The IMA teachers’ students were more emotionally engaged (enthusiastic) in their

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Stipek, Givvin, Salmon, & MacGyvers 333

math work (M = I .6 1, SD = .40) than were the traditional teachers’ students (M = 1.08, SD = .15), with the support teachers’ students ( M = 1.32, SD = .32) in between. The IMA teachers’ students were also more likely to be observed dis- cussing mathematics (M = 2.96, SD = S O ) than were the traditional teachers’ stu- dents (M = 1.61, SD = .69), again with the support teachers’ students falling in between (M = 2.58, SD = .69).

Teachers ’ Knowledge of Student Motivation

We calculated correlation coefficients between teachers’ ratings of students and students’ ratings of themselves on each motivation dimension, within each teacher group, for ratings made at the beginning and at the end of the year. Cor- relations between teachers’ ratings of students and students’ ratings of them- selves on the motivation dimensions were weak at the beginning of the year, with only 2 of 21 significant correlations (for perceptions of ability for the support group, r = .41, p < .05, and for mastery orientation for the traditional group, r = .48, p < .05).

The pattern of correlations shown in Table 7 provides modest support for the IMA teachers’ having a more accurate (in the sense of agreeing with students’ perceptions of themselves) assessment of their students’ motivation by the end of the year. The IMA teachers’ ratings were significantly correlated with their stu- dents’ ratings for 5 of 7 motivation dimensions. For the support teachers, only I of the correlations was significant, and for the traditional teachers, none were

TABLE 7 Correlations Between Teachers’ Ratings of Students and Students’ Own Motivation Ratings at the End of the Year L

Motivation dimension IMA support Traditional

(n = 23) (n = 24) (11 = 15)

Mastery orientation

Performance orientation

Help seeking

Positive emotions

Negative emotions

Perceived ability

Persistence

.46* . I7 .48t

.05 -.I8 30

.20 .38t .35

.58** .03 .21

.51* .43* . I 1

.44* .02 .45t

.43* .05 .3 I

Nore. IMA = integrating mathematics assessment. tp<.1O.*p<.O5.**p<.O1.

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(although it is noteworthy that the sample size was particularly small for this group). At the end of the year, the correlations for the IMA and support teachers were significantly different 0, < .05) from each other for positive emotions; the correlations for the IMA and support teachers were marginally significantly dif- ferent 0, < .lo) from each other for perceived ability and persistence; and the cor- relations for the IMA and traditional teachers were marginally significantly dif- ferent 0, < .lo) from each other for positive emotions.

Discussion

The data provide clear and consistent evidence that teachers who have volun- teered for and have experienced some kind of training related to reform-minded mathematics teach in ways that are more consistent with practices being pro- moted by mathematics reform experts as well as with practices promoted by motivation experts (see Stipek, 1993, 1996). For example, the field-note data indicated that relative to the traditional teachers, both the IMA and support teach- ers encouraged student autonomy more and provided a psychologically safer context in which the students felt comfortable taking risks. Relative to the tradi- tional teachers, the IMA and support teachers also were rated as emphasizing mastery and learning more, or emphasizing performance less. The consistency in the teachers’ practices over days (correlations between videotape and field-note ratings) and in different instructional organizations (correlations between ratings for whole-group instruction and student-work time) suggest, moreover, that our sampling of mathematics lessons reliably reflected the teachers’ typical practices.

The evidence for the effect of our own (IMA) training on teacher practices is weaker, although the pattern of the results of the videotape analyses suggests a modest effect. Analyses of the teachers’ practices in their classroom revealed that the IMA teachers scored the highest of the‘,three groups on their emphasis on effort, their emphasis on learning and mastery, and their encouragement of stu- dent autonomy; they received the lowest scores for their emphasis on perform- ance. The IMA teachers also claimed to provide more substantive feedback on the students’ work than both the support and traditional teachers did. All of these practices are consistent with reform-minded mathematics teaching and with what was being encouraged in our professional development program. The IMA teach- ers’ scores on these dimensions were not, however, significantly different from the support group teachers’ scores (although the difference for substantive feed- back was marginally significant).

Stronger evidence for the effectiveness of the IMA intervention comes indi- rectly, from the student data. The findings suggest that the IMA intervention low- ered the students’ concerns about their performance over the course of the year, and, after completing the unit on fractions (which was the primary focus of the teacher intervention), the IMA intervention had the most positive impact on the

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Stipek, Givvin, Salmon, & MacGyvers 335

students’ self-confidence in their ability to do mathematics and on their emo- tions. In contrast, relative to the IMA teachers’ students, the support teachers’ students became more concerned about their performance, became less self-con- fident in their ability to do fractions, and reported somewhat less positive emo- tions.

Although we do not have systematic evidence, we are willing to speculate that the maladaptive motivational trajectory of the students in the classrooms of the teachers who had minimal training in reform practices emerged from problems with the teachers’ instructional approaches that were not picked up in our global ratings. The students in the support and IMA teachers’ classrooms were accus- tomed to more traditional instruction that emphasized correct answers. The sup- port teachers may have removed the clear criteria for evaluation that the students were used to without moving them toward a focus on understanding and mastery as fully as was done by the IMA teachers who had experienced the more inten- sive training program. The ambiguity might have created anxiety about perform- ance. Perhaps the additional training the IMA teachers received helped them to encourage student autonomy and focus on effort, mastery, and learning S U E - ciently to maintain their students’ relatively high perceptions of ability and low concern about performance and external evaluation.

The student behavior data provide further indirect evidence for an effect of our intensive intervention on instructional practices. The IMA teachers’ students classrooms were the most emotionally engaged in their math work and the most likely to be observed discussing mathematics. These findings again suggest that, relative to the support teachers, the IMA teachers might have implemented more effective teaching practices that our classroom observation measures did not identify.

Finally, the evidence suggests that the IMA teachers were a little more in tune with their students. The sample size was small, but the pattern of correlations sug- gests that the IMA teachers were more knowledgeable of their students’ self-con- fidence as math learners, concerns about mastery and learning, positive emotions, and persistence in the face of difficulty. The emphasis on assessment of student motivation in the professional development program seemed to have some payoff. The IMA teachers’ attention to individual students’ beliefs and feelings may have helped them provide an educational experience that supported the students’ self- confidence, enthusiasm, and relative lack of concern for performance.

In summary, the results of our study provide compelling evidence that reform- minded teachers and traditional teachers teach mathematics differently. Our results also provide support, primarily in the form of student motivation effects, for the value of professional development programs like the one we developed. Some of the evidence suggests that the kind of modest exposure to math-reform principles that most teachers receive might actually have, at least in the short term, negative consequences for student motivation.

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336 The Journal of Experiniental Educariou

We cannot generalize to other areas of instruction. But the results of this study indicate to us that professional development designed to improve the way teach- ers teach mathematics must be intensive and of long duration. The teachers in our support group were highly committed to implementing practices promoted in the mathematics education reform literature. Before becoming involved in our study, they had all voluntarily attended workshops designed to teach them how to implement the California framework-based curriculum units, and they were will- ing to continue to spend time, after school, to work with other teachers endeav- oring to improve their mathematics teaching. Our findings suggest that the train- ing they received, which was substantially more than most teachers receive, was insufficient and may have even caused some modest harm in student motivation. We are not willing to conclude that if you can’t do it well, don’t do it at all. We are willing to join with others (e.g., Little, 1993) who have raised concerns about the value of modest interventions, such as the kind of 2-day workshops that our support teachers experienced.

One cannot assume, however, that even our more intense intervention would have the same positive effects for all teachers in all contexts. First, particular qualities of the teachers may explain some of the findings. For example, our intervention might have had less positive effects on teachers who were required to participate or who felt coerced. In addition, particular qualities of the IMA intervention may limit its generalizability. It was, for example, planned and implemented by university faculty who had considerable expertise in children’s mathematical thinking, teacher practices, and achievement motivation. The moti- vation findings in particular may have been due, in part, to the unusual emphasis put on motivation in the professional development program. The intervention also involved a relatively small group of teachers who developed supportive rela- tionships with each other. What we have shown in this study, therefore, is what can, under some circumstances, be accompltshed in professional development. I

NOTE

This study was supported by Grant MDR 9 I545 12 from the National Science Foundation. Address correspondence to Deborah Stipek, Graduate School of Education & Infomation Studies,

UCLA, Los Angeles, CA 90095- 16 19.

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