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Annual Report Overviews

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Annual Overview

submitter: Austin Collaborative for Mathematics Education
published: 12/17/1998
posted to site: 12/17/1998

Results and Discussion

The findings presented in this section integrate different perspectives on the ACME project, including the viewpoints of teachers, principals, and central office staff. This section includes data on the district’s mathematics curriculum and instruction in the ACME project’s baseline year, the quality of professional development provided, and the supports for sustaining the project.

In general, the data from teacher questionnaires were taken from the responses of the 289 mathematics teachers because in many cases their responses were not different from those of the 39 special education teachers who completed questionnaires. Where the differences in the responses of these two teacher samples were statistically significant, the discrepancies were noted.

Teachers’ Attitudes Toward and Preparation for Mathematics Reforms

 

Figure 1. A Comparison of the Percentage of Teachers Who Responded

Very Important and Very Well Prepared for Use of Specific Instructional Strategies

not available on the LSC-Net at this time

Source: Teacher questionnaires

Attitudes Toward and Preparation in Instructional Strategies

Many of the teachers who responded to the questionnaire highly endorsed investigative strategies in mathematics instruction. They rated a variety of these strategies as very important for effective mathematics instruction (see Figure 1). Over 80% of the teachers placed high importance on hands-on activities, providing concrete experiences before abstract concepts, making connections between mathematics and other disciplines, and applying mathematics in a variety of contexts. More than 60% of these teachers reported that they found cooperative learning and inquiry-oriented activities very important to effective mathematics instruction. Over half of the teachers valued highly the use of computers in mathematics instruction.

Although many teachers endorsed instructional strategies that characterize standards-based mathematics, fewer teachers felt highly prepared to use these strategies (see Figure 1). Less than half of the teachers reported feeling very well prepared to direct students in hands-on activities and cooperative learning, for example. Moreover, less than one-third of these teachers reportedly felt very well prepared to facilitate inquiry-oriented activities or to use computers in their mathematics lessons. Thus, according to teachers’ reports of their teaching preparation, many lack preparation to teach children successfully through the instructional strategies of standards-based mathematics.

Preparation in Mathematics Content

In general, many of the mathematics teachers reported feeling well prepared to teach mathematics, including the mathematics content traditionally taught in U.S. elementary and middle schools. Many of these teachers (58%) reported feeling very well prepared to teach mathematics compared with few (27%) who felt very well prepared to teach science. As a majority of these teachers (82%) taught in elementary schools, the mathematics content that they felt comfortable with reflects their work experience (see Table 1). More than half of the mathematics teachers reportedly felt very well prepared to teach computation, patterns and relationships, measurement, numeration and number theory, and estimation. Small proportions of these teachers felt very well prepared to teach subjects such as probability and pre-algebra, which broaden the mathematical knowledge of elementary students in accordance with current standards. Thus, a minority of the mathematics teachers who responded felt well prepared to teach mathematics content that traditionally has received little attention.

Fewer special education teachers than mathematics teachers reported feeling well prepared to teach mathematics and mathematics content that U.S. elementary and middle schools have traditionally overlooked. One-quarter (26%) of the special education teachers reported feeling very well prepared to teach mathematics, whereas less than one-tenth (8%) of these teachers felt very well prepared to teach science. Although more than half (56%) of the special education teachers felt very well prepared to teach traditional mathematics content, such as computation, approximately one-third of these teachers felt very well prepared to teach patterns and relationships, measurement, numeration and number theory, and estimation. Similarly, less than one-fourth of the special education teachers felt very well prepared to teach topics traditionally overlooked such as geometry and data collection, and one-tenth of these teachers felt very well prepared to teach probability and use calculators and computers in mathematics classes. In sum, a small majority of these special education teachers feel comfortable teaching computation and some felt comfortable with some traditional content. For the most part, these special education teachers do not report feeling prepared to teach any other areas of mathematics, especially areas that expand the curriculum beyond traditional content areas.

Table 1. Percentage of K-8 Mathematics Teachers Prepared in Mathematics Topics


Mathematics Topics

% Not adequately prepared

% Somewhat prepared

% Fairly well prepared

% Very well prepared

Computation

0

6

28

66

Patterns and relationships

0

4

35

61

Measurement

1

9

35

55

Numeration and number theory

0

11

34

54

Estimation

2

8

38

52

         

Geometry and spatial sense

2

11

42

45

Data collection and analysis

7

16

38

40

Probability

6

27

35

33

Pre-algebra

16

28

30

26

Calculators or computers in mathematics

13

30

37

21

Algebra

29

30

24

16

Source: Teacher questionnaires

Relationship Between Teachers’ Attitudes and Preparation

Teachers’ endorsement of standards-based instructional strategies could be interpreted in different ways. One hypothesis is that many teachers who have not yet participated in training highly value investigative instructional strategies and would like to use them in their classrooms. Perhaps, these teachers will welcome the new curriculum and instruction. On the other hand, the findings that many teachers are not well prepared to carry out these activities imply that many will require some professional development to be able to implement them in their classrooms. Teachers’ endorsement of these instructional strategies in combination with their lack of preparation may suggest that many are eager to learn these types of instructional strategies.

Supporting evidence for the eagerness to learn how to implement standards-based instructional strategies comes from informal conversations with teachers and school administrators. When observing teachers’ classrooms, the evaluator learned that kindergarten through fourth grade teachers who were scheduled to participate in ACME professional development in subsequent years of the project were anxiously awaiting the opportunity. One fourth grade teacher said that she had seen what a trained fifth grade teacher had been doing in her mathematics classroom and looked forward to learning more about the new curriculum and instruction herself. A first grade teacher was disappointed to find out that she would have to wait two years before participating in ACME professional development.

Similarly, some schools are not waiting for the planned grade-by-grade implementation to reach all of their teachers. Although the district is committed to buying curriculum materials for all campuses before each grade level begins professional development, ACME program staff reported that some schools have bought the materials with campus funds for all grade levels in advance. Because on some campuses all of the teachers wanted to participate, not just the fifth and sixth grade teachers who were scheduled, schools requested professional development for teachers in other grade levels. ACME program staff decided that they could not include extra participants, and some school staffs were disappointed. On at least one campus, the administrator hired outside staff developers to teach their teachers, who were not yet targeted for ACME professional development, how to implement investigative mathematics curriculum and instruction.

Thus, it appears that some teachers’ eagerness to learn how to implement the standards-based curriculum and instruction may explain, in part, the high level of endorsement of these strategies coupled with their reported lack of preparation to use these strategies. Moreover, the eagerness of some teachers who must wait for professional development suggests that a momentum may build as some motivated teachers anxiously anticipate their turn to participate and to try out standards-based curriculum and instruction.

Another hypothesis is that teachers’ endorsement of the standards-based curriculum may reflect familiarity with the language of new trends in mathematics education, but teachers may lack a clear understanding of the implications of these strategies for classroom activities and children’s learning. These data were gathered through teachers’ responses to questionnaire items. Many teachers may be familiar with phrases like "hands-on activities" or "cooperative learning" and readily rate these items as very important. Cohen (1990) found that although teachers may be able to communicate in the language of mathematics reforms, their classroom instruction may be dominated by traditional strategies. Thus, the findings that teachers highly endorse standards-based strategies may be misleading because the data are self-report. Teachers’ endorsement does not necessarily imply that these strategies will be evident in their teaching practice.

Other evidence from teachers’ questionnaires points to their lack of information about mathematics reforms. Before participating in the ACME project, some teachers in the district were not familiar with NCTM standards. Twenty-two percent of the mathematics teachers and 29% of the special education teachers did not consider themselves well-informed about the NCTM Standards for the grades they teach, and 21% and 32%, respectively, had no opinion. Consequently, 43% of the mathematics teachers and 61% of the special education teachers who responded did not assert that they knew the standards well. Although some teachers who have not participated in the project endorse the language of standards-based instructional strategies, they may not know the philosophy behind the strategies nor how to use the techniques effectively to help children reason mathematically. This finding supports the hypothesis that teachers may be familiar with the language of standards-based strategies, but not understand the implications of these strategies for teaching and learning.

Project staff discerned this lack of knowledge about standards-based mathematics education during the first year of the project. One staff member said,

We had to examine where our teachers are. Our teachers didn’t know NCTM standards or understand problem-solving. When we launched the professional development, we assumed that teachers knew why "drill and kill" was not O.K. We had to go back and talk about it, go back to the foundations.

Source: Project staff interviews

Through interaction with teachers in ACME professional development, the mathematics team learned the limits to teachers’ knowledge about the NCTM standards and its philosophy and decided to address the lack of knowledge. However, this lack of knowledge supports the supposition that some untrained teachers do not have a comprehensive understanding of the standards-based teaching practice. Again, teachers’ endorsement of standards-based instructional strategies may reflect familiarity with the terms rather than a deep understanding of the implications for teaching practices and children’s learning.

Similar to some teachers’ lack of knowledge of NCTM standards, during the first year of the project, the team recognized limits to teachers’ mathematics content knowledge. In teachers’ evaluations of how their mathematics content was enhanced by the summer institute of 1998, some acknowledged that they made improvements in this strand over the course of the institute. For example, teachers stated that they gained a "better understanding of math," became "more confident with my own understanding of math," and "learned different ways to approach problems." On the other hand, other teachers stated that they did not gain content knowledge, but described instructional strategies that they gained instead. Thus, in evaluating what teachers learned in professional development, some acknowledged gaining a deeper understanding of mathematics than they had before ACME professional development, but other teachers seemed to emphasize developing new strategies and approaches to solve mathematics problems.

Interviews with the ACME project staff and observations of teachers at professional development suggest that teachers’ attitudes toward standards-based instructional strategies are more complex than the responses to questionnaires imply. When the project began in the summer of 1997, one staff member described teachers’ attitudes as anxious, apprehensive, and cautious. These attitudes are supported by the observations of hesitance in some fourth grade teachers at the beginning of their first summer institute. Moreover, teachers’ attitudes ranged from opposition to the district’s approach to curriculum and instruction to interest and desire for support. Thus, behind teachers’ endorsement of standards-based instructional strategies, there may be a mixture of anxiety and interest.

Over the course of the first year, the same staff member who noted a range of attitudes also observed a great deal of change in teachers’ attitudes toward the new curriculum. At the end of the first year of the project and the second summer institute, fifth grade teachers who attended training showed more confidence and interest in the curriculum and instructional strategies. Additionally, a higher proportion of the teachers were enthusiastic about the project than were the previous summer. Consequently, through professional development, facilitators may have helped teachers become more prepared to teach standards-based mathematics by supporting and addressing their concerns as they tried out the new materials and strategies in their classrooms.

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