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Creating Advocates: Building Preservice Teachers'Confidence Using an Integrated, Spiral-Based,Inquiry Approach in Mathematics and ScienceMethods InstructionCatherine Kelly aa University of Colorado, Colorado Springs, USAPublished online: 04 Jan 2012.

To cite this article: Catherine Kelly (2001) Creating Advocates: Building Preservice Teachers' Confidence Usingan Integrated, Spiral-Based, Inquiry Approach in Mathematics and Science Methods Instruction, Action in TeacherEducation, 23:3, 75-83, DOI: 10.1080/01626620.2001.10463077

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Creating Advocates: Building Preservice Teachers' Confidence Using an Integrated, Spiral-Based, Inquiry Approach in Mathematics and Science Methods Instruction

Catherine Kelly Universsiiy of Colorado, Colomib Springs

Abstract

This stu& compared elementary level preservice teachers' beliefs about mathematics and science teaching prior to and following their immersion in an integrated, spiral-based, inquiry approach in a mathematics and science methoak course. Eighty-three teachers, including 12 males and 71 females, participated. The primary measure was a 20-item pre- and posttest which focused on a number of teaching factors; in &ition, teachers were interviewed and observed in classroom settings. Using a paired samples t-test statistical analysis, results revealed several areas of statistical signi$cance, including the importance of the teacher's role; use of methaki, strategies, and styles; use of manijndatives and materials; integration of disciplines; and overall confidence levels in teaching mathematics and science classes.

This research sought to examine the effects of an integrated, spiral-based, inquiry approach on preservice teachers' beliefs about teaching mathematics and science. This approach builds on the work of Piaget (Santrock, 1993) and Vygotsky (Eggen & Kauchak, 1994) whose theories ground current conceptions of learning. First, it addresses Piaget's beliefs of constructivism whereby learning is viewed as a process in which the learner constructs his or her own representation of what is known (Martin, 2000). Second, it uses Vygotsky's concepts of scaflolding in the zone ofproximal development as a means of "holding up" or s tabl i ig learners during the learning process. In addition, it builds specifically on Brunefs (1965) work regarding discovery learning in the science curriculum. That is, Bruner's beliefs focused on experiential learning in which the teacher operates as facilitator rather than as dominator as in the more traditional expository approach. He believed that the learner should not be passive but active and that the knowledge itself should be dynamic rather than inert (Martin, 2000). As part of experiential learning, Bruner supported active discussion, guided inquiry, and problem solving since he believes that these are the paving stones leading the way to meaningful learning.

In this study, preservice teachers enrolled in a methods course for mathematics and science teaching that built upon these concepts of learning. Two research objectives were:

1. What impact do prior beliefs and concepts about doing mathematics and science have on preservice teachers' teaching of these subjects?

2. If preservice teachers' perceptions of their own mathematics and science ability affect their teaching, will an integrated, spiral-based, inquiry approach significantly raise their confidence in teaching these subjects?

Review of Literature

Exemplary teaching of math and science must incorporate an undmtanding of how learning occurs in order to foster success for all students (MCREL, 1999). The integrated, spiral model of inquiry used in this study was designed to facilitate the use of knowledge that creates opportunities for success and growth for all teachers and, subsequently, their students. This approach was created to guide and facilitate beginning teachers as they work through u n d m d i n g and analyzing how problem posing and problem solving occur in the human thought process, although it is hoped that the findings from this research can be beneficial to all teachers, novice and veteran.

Sp i r a l -M i n q w was founded on the premise that all teachem must be advocates for all leamm and that all leamers can learn math and science. Consequently, preservice teachers given the opportunity to learn, understand, and implement this approach using an integrakd format might be more able to promote the development of all students' dispositions to be able to successfully do math and science. Additionally, they would be able to create and maintain an environment that is physically and emotionally safe for asking math and science questions, posing and solving math and science problems, and conducting mathematical and scientific inquiries (MCREL, 1999).

Having positive attitudes toward learning, such as seeing the value of learning something; acquiring and integrating declarative knowledge (knowing what) and procedural. knowledge (knowing how); refining and extending knowledge, such as finding analogies; using knowledge for meaningful purposes, such as solving problem; and developing productive habits of mind, such as thinking creatively have been described as dimensions of thinking by Marzano and pickering (1997). Each of these is closely related to effective teaching methods not only in mathematics and science but also in all discipline areas. Key aspects of both math and science teaching relate to procedural and declarative knowledge, analyzing data and

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relationships, problem solving, and embracing multiple solutions to problems (creative thinking). Thinking about one's own thinking or metucognition has been a common topic of conversation in circles of educators

for more than a decade. Teachers are continuously reflecting, rethinking, and reformulating their ideas and strategies; it is large portion of their job on a minute-by-minute basis. Caine and Caine (1997) suggested that such thinking processes encourage a greater use of reflective thought and that the human reflexive system is triggered by a strong emotional impulse that is not always rational, a term labeled "downshifting." These tenets coincide with the belief that learning is enhanced by challenge and inhibited by threat and give some credence to the term "math anxiety." Metacognitive skills are essential for effective teaching and learning of mathematics and science since many of the tasks involved in these disciplines are inherently reflective and require pondering and posing of fiuther questions.

Current results of the Third International Mathematics and Science Study (TIMSS-R) (Wang-Iverson & Jackson, 2000) have once again shown Singapore at first place in mathematics and second place in science. With the United States reporting in at 19th place in mathematics and at 18th place in science worldwide, it is important to consider the linkage of factors deemed to help Singapore maintain such high rankings. Factors considered to be heavily influential in this high ranking include students displaying very positive attitudes about mathematics and science and articulating that doing well in these areas is very important; strong support at home including high access to computers (80%); committed teachers, principals, and school systems; a rigorous curriculum with access to instructional technology; and, in comparison to other countries, fewer schools reporting serious absenteeism, tardiness, and discipline problems ( Wang-Iverson & Jackson, 2000).

Singapore's high rankings in both the 1995 and 1999 TIMSS assessments also establish its sustainability, especially when data on specific students are analyzed. In mathematics, Singapore students from the same cohort (Primary Four for the TIMSS 1995 and in Secondary Two or Eighth Grade for the TIMSS 1999) who were at the top in TIMSS 1995 maintained the top position in TIMSS 1999. In science, Singapore Primary Four students who were ranked seventh in the TIMSS 1995 jumped to a position of second at Secondary Two or Eighth Grade in the TIMSS 1999 (Wang-Iverson & Jackson, 2000).

Research also has shown the emergence of three clusters of grade levels within which students recalled having serious difficulty in mathematics: (a) grades 3 and 4 (a time when Singapore students seem to excel); (b) grades 9 and 12; and (c) freshman year of college (Jackson & Leffingwell, 1999). Some reasons for this difficulty were attributed to increased difficulty of material; communication and language barriers; and inappropriate, non-authentic assessments or not testing what was taught. Specific factors relating to the role of instructor included gender bias (e.g., girls really don't need mathematics); uncaring, insensitive, angry teachers; insensitivity to communication and language barriers; being embarrassed in front of peers; unrealistic expectations; poor quality instructiodexplanation; and disrespect for the student.

Other researchers also have shown that a negative experience with a mathematics teacher may cause math anxiety, and, more seriously, that the math anxiety probably is more the result of the method or way math is presented rather than the subject matter itself (Crawford & Witte, 1999; Greenwood, 1984). Clearly, the academic material and curriculum are not the sole problem in developing confidence in mathematics and science. The role of instructors, at any level, seems to be significant in developing and sustaining confidence and positive regard in their students. Williams (1 988) found that teacher's beliefs and attitudes about mathematics significantly affected the ways in which they projected a like or dislike for mathematics and subsequently taught mathematics.

Some believe that when students are faced with real problems about their world, they will derive accurate, logical, and creative solutions that naturally integrate with many subjects (Krynock & Robb, 1999). Activities or ideas that elicit strong emotion, disgust, excitement, or accomplishment tend to form lasting memories; therefore, the ways in which mathematics and science are taught must have a significant effect on how students perceive these subjects as disciplines and as necessary in their lives. These findings seem to bring support to why Singapore students' value and belief in mathematics and science in their lives may have impacted current TIMSS (Wang-Iverson & Jackson, 2000) results. Additionally, Sherman and Christian (1999) found that preservice teachers attitudes, in general, toward mathematics improved as they experienced welldesigned, theoretically sound mathematics education methods courses while global self-concepts remained constant.

Learning how to work with all students and all learning styles and needs remains essential for effective teaching. Realizing how to prevent and overcome math anxiety is grounded in the teacher's ability to understand and implement effective strategies that will foster positive and realistic self-esteem in preservice teachers while facilitating their conceptual grasp of mathematics. Using multi-modality materials that will encourage extended mathematical discourse and communication, and multi-faceted, interdisciplinary problem solving opportunities may be pivotal in alleviating some of the anxiety and developing confident beginning mathematics and science teachers.

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Methodology

Eighty-three preservice teacher candidates, including 12 males and 71 females, from two consecutive semesters were studied and compared. Students were enrolled at a large, urban campus in the western United States where they were required to take an academic major and minor to graduate plus a fifth year of teacher licensure instruction. Others attended teacher licensure classes as post-baccalaureate students. Twenty-eight percent held baccalaureate degrees while 72% were seeking degrees and licensure. The ages of respondents ranged from 22 to 52 with a mean age of 30. Thirty-seven percent were identified as minority.

Data were collected using a variety of measures, including informal classroom observation, individual interviews, review of student-generated work, professor observations of student's lessons, and pre- and posttest attitude surveys. For the purposes of this paper, survey results provide the primary data source. This measure included 20 questions; 11 particularly concerned attitudes and confidence levels about using and teaching mathematics and science and were the focus for this research (see Table 1).

At the beginning of the semester, the students completed the pretest measure. Following, the surveys were placed in a manila envelope and sealed until the end of the semester when the posttest measure was given. During the semester, the students were immersed in the study of inquiry-based teaching via a nine-step spiral approach (see Table 2). This approach took the students from reading and research and defining inquiry to developing inquiry questions and strategies, selecting appropriate materials, and standards-driven instruction.

The focus of the course was discipline integration. First, students wrote a one-page, reflective paper on how mathematics might be integrated or connected with other disciplines taught in the elementary classroom. Then they read at least three current, practical selections from journals such as Teaching Children Mathematics or Science and Children and discussed them in large and small groups in class. Each small group, based on their readings and discussions, developed a definition of the following terms: discipline integration and inquiry. These definitions and brief summaries of the discipline integration papers were written on poster sheets and shared with the class as a whole. Following this process, students were asked to look at their text's definition of the scientific process and determine how this might connect to integration and inquiry or "integrated inquiry."

Since the content discipline focus covered both mathematics and science, discipline integration was imperative. Based on the student generated poster data sheets, discipline integration had been identified. At this point, the professor modeled an integrated, inquiry-based mathematics and science lesson showing students how and why it would be useful and appropriate. Techniques for enhancing higher level thinking, observation skills, questioning skills, and strategies for developing authentic, performance-based assessments were emphasized. Finally, methods for sustaining standards-based instruction, reflective practice and integrated inquiry learning in mathematics and science were discussed and evaluated.

During the fifth and sixth weeks of the semester, each student presented an integrated, inquiry-based mathematics and science lesson to a small group of peers in class. As a part of the assignment, students selected an article, similar to the ones they had read and discussed in class, to use as springboards for their lessons. Imperative in the lesson requirements was the conceptualization of a true inquiry-based question that would drive the overall lesson, such as.. ."How do bridges hold up hundreds of cars without breaking?" A true inquiry question was defined as "a question to which the outcome or answer is unknown to the researcher."

As each lesson was presented, the professor/researcher observed and recorded data using a rubric-based assessment that students had been given with the assignment criteria. This assignment was done in a non-threatening manner as students were given the grading rubric as a part of the project requirement criteria in order to plan the lesson, teach the lesson to a small group of peers in class, and, finally, reflect on and use the peer feedback and the professor's comments to revise the lesson prior to receiving a final grade. Since they had the opportunity to revise and edit their lessons using this input, it was hoped that students would be willing to assume more risk by using integration and inquiry.

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Table 1. Survey of Teaching Mathematics and Science

Mathematics Survey

In answering the following items, circle only one choice for each question using the following rubric criteria: l=Extremely Confidentnmportant; 3=Somewhat Confidentnmportant; +Not Confidentnmportant

From your perspective.. . . . . 1. How confident do you feel about teaching and using mathematics?

1 2 3 4 5 2. How confident do you feel about teaching and using science?

1 2 3 4 5 3. How important do you feel using inquiry in your teaching is?

1 2 3 4 5 4. How important is the teacher in a math class?

1 2 3 4 5 5. How important are the teacher's methods and styles of teaching in a math class?

1 2 3 4 5 6. How important are manipulative, hands-on activities in a math class?

1 2 3 4 5 7. How important is an integrated, interdisciplinary teaching approach in a math class?

1 2 3 4 5 8. How important is lecture and direct instruction by the teacher in a math class?

2 3 4 5 9. How confident are you about teaching in your own elementary classroom?

1 2 3 4 5 10. How important do you think training in mathematics and science is for girls?

1 2 3 4 5 11. How important do you think training in mathematics and science is for boys?

1 2 3 4 5 In answering the following items, circle only one choice for each question.

12. Circle the year in which you feel you had the best math class.

13. List three reasons why this was the best year. P-K 1 2 3 4 5 6 7 8 9 10 11 12 13(CollegeF)

14. Circle the year in which you feel you had the worst math class.

15. List three reasons why this was the worst year. P-K 1 2 3 4 5 6 7 8 9 10 11 12 13(CollegeF)

16. Circle the year in which you feel you learned the most in math class.

17. Circle the year in which you feel you learned the least in math class.

18. Do you have anxiety about doing math? (Circle one)

19. Do you have anxiety about teaching math? (Circle one)

P-K 1 2 3 4 5 6 7 8 9 10 11 12 13(CollegeF)

P-K 1 2 3 4 5 6 7 8 9 10 11 12 13(CollegeF)

Yes No Sometimes

Yes No Sometimes

1 I . (College S) 1 (College J)

14 (College S) 15 (College J)

14 (College S) 15 (College J)

14 (College S) 15 (College J)

20. What is your learning preference or style? NOTE: If you believe that your preference is a combination, please write in the combination on the line provided.Classify your learning preference using the following catetegories:

Auditory Kinesthetic/Tactile Visual Combination of

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Following this activity and maintaining the spiral-based inquiry approach, numerous manipulative-based, hands- on integrated mathematics and science activities and lessons were modeled in the class and students actively participated, usually in small groups. The role of the teacher in facilitating and managing hands-on inquiry was also emphasized and using differing strategies and methods for enhancing integrated, inquiry-based mathematics and science lessons was evaluated. Students were asked to critically analyze the National Council of Teachers of Mathematics Curriculum Standardsfor School Mathematics and Assessment Standards for School Mathematics (NCTM, 1989; 1995) and the National Science Education Standards (1996) while determining appropriate teaching strategies and methods for most effectively meeting these standards. At the end of the 16-week semester and following the intervention technique, students completed the posttest measure of attitudes and perceptions about teaching and using mathematics and science.

Based on the pre- and posttest model, a paired samples t-test statistic was used to calculate the data. From analyzing the descriptive statistics, 9 out of 11 pre- and posttest pairs were identified. SPSS 8.0 was used to compile and compute the data.

Results

In an analysis of the data derived from the nine paired samples, statistically significant results surfaced (see Table 3). Survey items 1 and 2 addressed confidence levels in teaching mathematics and science, respectively. Results showed significant differences between pre- and posttest means at the 99% confidence level for both items. These findings revealed a marked change between pre- and posttest, with greater confidence on the posttest (item 1, changF1.18; item 2, change=1.26). Although both items showed high change differences, of special significance is the large change in beliefs about confidence in science teaching, indicating a strong connection between using inquiry-based science approaches as springboards for building confidence in mathematics integration for pre-service teachers.

Other areas of significance at the 99% level included item 3: use of inquiry as a method of teaching (change =2.25); item 4: the role of the teacher (change=.77); item 5 : methods and styles of teaching (change=.66); item 6, the use of manipulatives (change2.12); item 7, the use of discipline integration (changF1.22; item 8, use of lecture and direct instruction (change=l.O4); and item 9, overall confidence in teaching mathematics and science (changpl.36).

In addition, item 5 was of interest, showing that preservice teachers felt strongly about the importance of the teacher and the methods and styles of teaching in both the pre- and posttests with a t-test score of -6.603 at the 99% confidence level. The largest numerical span was shown in item 6 that asked preservice teachers to rate how important manipulative hands-on activities were in a mathematics or science class. The pretest mean for this item was 2.6867 (low) and the post-test mean was 4.8072 (high) with a t of -15.068 at the 99% confidence level. These findings could signifj. students' general understanding of mathematics courses -- lecture-based rather than manipulative-based instruction--based on personal experience in mathematics classrooms.

The pretest of item 8 (lecture/direct instruction) revealed a mean score of 3.5783 while the posttest mean score was 2.5301 indicating that initially preservice teachers felt that a lecture-based, direct instruction approach was important. This item was the only one on the survey that decreased in importance rather than increased; however, it remained significant at the 99% level with a t score of 7.262.

Other areas of interest surfaced in items 10 (importance of math for girls) and 11 (importance of math for boys). Although gender issues were not the thrust of the current research, these items showed that in this group of participants some of the equity gap for girls may be narrowing. In the pretest, a mean of 3.61 was reported for item 10 (math for girls) and a mean of 4.54 surfaced for item 1 1 (math for boys) that is not as broad of a difference as reported in previous research. Posttest means showed a marked rise for item 10 (math for girls) with a mean of 4.94 and a moderate rise for item 11 (math for boys) with a mean of 4.96.

Finally, items 1 8 and 19 dealt with anxiety about doing and teaching mathematics. In the pretest, for item 18 (doing mathematics) the mean was 2.19 and for item 19 (teaching math) the mean was 1.89 which may indicate that prior to a mathematics methods course these participants felt somewhat challenged by doing mathematics themselves and even more challenged by teaching mathematics. The posttest revealed somewhat higher means for items 18 and 19 with means of 2.37 and 2.39, respectively, which indicates that some confidence in doing and teaching mathematics was acquired following methods instruction.

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Table 3. Paired Samples T-Test of Pre- and Posttest Survey Results Based on Statistical Significance

Pair #

1. Confidence in Teaching Math Pretest Posttest

Pretest Posttest

2. Confidence in Teaching Science

3. Importance of Inquiry in Teaching Math/Science Pretest Posttest

Posttest Pretest

Pretest Posttest

Pretest Posttest

Pretest Posttest

Pretest Posttest

Pretest Posttest

4. Importance of Teacher in Teaching Mawscience

5. Importance of Methods/ Styles of Teaching

6. Importance of Manipulatives/Hands-on MethodsMaterials

7. Importance of Integration/ Inter-disciplinary Teaching

8. Importance of Lecture/ Direct Instruction in Teaching

9. Confidence in Teaching in Own Class

Mean T Sie. (two tailed)

3.0843 4.265 1 - 14.637 .ooo

2.8434 4.1446 -13.920

2.4337 4.6867 -20.565

4.2530 4.95 18 -6.467

4.3012 4.9639 -6.603

2.6867 4.8072 -15.068

.OW

.ooo

.ooo

.ooo

.ooo

3.5783 4.7229 -20.889 .ooo

3.5783 2.5301 7.262 .ooo

3.0241 4.3855 -14.362 .OOO

Discussion

In reviewing the purpose of this research--to determine if prior beliefs and self-concept about doing mathematics and science and immersion into a spiral-based inquiry method will affect pre-service teachers abilities to teach mathematics and science in the elementary school--it appears that some degree of success has been reached by the current research. The earlier work of Williams (1988) and Greenwood (1984) showed that beliefs and attitudes about mathematics significantly affected how mathematics was taught. Taking this a step further, the current study looked at using a spiral-based, inquiry approach to teaching preservice teachers mathematics and science methods and heavily immersing pre-service teachers into the study and implementation of inquiry in the classroom.

Since two consecutive semesters of pre-service teachers enrolled in methods classes were surveyed and the pre- and posttest means remained significant, there appears to be some amount of consistency in using this approach. However, a limitation of this study may be the inability to control the individual teaching style and background knowledge of the methods professor. Clearly, the methods instruction between the pre- and posttests administered during this research involved a strong inquiry-based, problem solving approach.

Interestingly, preservice teachers felt that the role of the teacher and the methods and styles used by the teacher were important in the both the pre- (teacher mean4.2530) (methods mean4.3012) and posttest (teacher mean4.9518) (methods mean=4.9639). This finding would substantiate the premise that teacher educators would like to believe--that these preservice teachers value the role of the teacher and the activities that make teachers "good." They seem to have not only maintained a belief in teaching as a profession but, based on the pre- and posttest means, strengthened it over the course of a semester of spiral-based inquiry.

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In examining items 1 and 2 (confidence in teaching math; confidence in teaching science) it should be noted that the respondents showed stronger confidence in teaching math than science in the pretest but that this difference diminished remarkably in the posttest results. This could be related to item 3 (using inquiry in teaching) that revealed a large difference in means between the pre- and posttests (pr~2.4337; post-4.6867) and individual knowledge levels at the beginning of the semester. Using manipulative activities (item 6) may also relate to items 1,2, and 3 since both science and mathematics are manipulative- and/or materials-based disciplines and these respondents were exposed to a great deal of manipulative-based methods instruction between the pre- and the posttests.

Since the science curriculum has historically been more inquiry-oriented than the mathematics curriculum, it may make sense that students had had less interaction with inquiry and science in general. It could also be that preservice teachers enrolled in this particular program received little or no instruction about the inquiry method of teaching prior to this methods course. At the onset of the methods course, they may not have known enough about inquiry to find it valuable as a teaching method. However, by the end of the semester after the intense involvement with spiral-based inquiry they seem to have attributed more value to the inquiry method of teaching.

With the semester focusing on integration and interdisciplinary approaches, it is not surprising to see the item 7 (using integration and interdisciplinary teaching) moving fiom a pretest mean of 3.5783 to a posttest mean of 4.7229. It is interesting, however, to ponder why, with the current universal use of integrated, interdisciplinary teaching strategies, these respondents would find this style only moderately important at the first rating. It could be related to the nature of the teacher education program in which these preservice teachers were enrolled or to their prior perceptions of mathematics and/or science as an integrated subject. Most of these preservice teachers were likely to have only had mathematics andor science taught to them in a single-subject format. And during the semester of integrated, spiral-based inquiry, they were required and encouraged to integrate as much as reasonably possible.

Another interesting finding was the plunge of the mean in item 8 (using lecture and direct instruction) from 3.5783 to 2.5301 at the 99% confidence level in the posttest results. The respondents pretest means indicated a relatively strong (over 3.5) belief in the lecture or direct instruction style of teaching while, after a semester of intense spiral-based inquiry, they held less esteem for this method. This could possibly be attributed to a lack of experience with other methods of instruction until this time and the commonly known belief that "teachers teach as they were taught" that was most likely a direct instruction or lecture format. Additionally, respondents were asked to indicate a learning style or preference on the survey. Thirty-six of the 83 respondents indicated auditory as their primary learning style, 37 selected auditory combined with another learning style or preference, and 10 indicated visual as their primary learning style or preference. Since the majority of the population believed their learning preference to be auditory or combined auditory, the responses to item 8 seem credible.

Finally, the integrated, spiral-based inquiry approach studied in this research appeared to offer preservice teachers some concrete strategies for approaching mathematics and science teaching based on the pre- and posttest attitudinal meas- ures of how students felt coming in prior to this approach and after having participated in the approach for one semester. Further study concerning preservice teacher beliefs and confidence levels in teaching mathematics and science should be completed using different methods professors and varying approaches to inquiry-based teaching. Also of grave importance is the sustainability of confidence in mathematics and science teaching in elementary teachers and their ongoing use of a spiral-based, inquiry approach.

Catherine A. Kelly is Assistant Professor in Mathematics Education at the University of Colorado at Colorado Springs. She is Editor of the Colorado Mathematics Teacher and conducts research in the field of mathematics education.

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