Development and factorial structure of students

Cypriot Journal of Educational Sciences Volume 7, Issue 1 (2012) 33-44 www.world-education-center.org/index.php/cjes

Development and factorial structure of students’ evaluation of teaching effectiveness scale in mathematics Adeneye Olarewaju Awofala a * a

Dr., Department of Science and Technology Education, University of Lagos, Nigeria

Received August 22, 2011; revised November 06, 2011; accepted November 20, 2011

Abstract This study dealt with the development and factorial validation of a students’ evaluation of teaching effectiveness scale in mathematics (SETES-M) which could be used to evaluate Nigerian Secondary Schools mathematics teachers’ teaching effectiveness. The effect of SETES-M on achievement in mathematics was also considered. In its final form, the 60-item SETESM is a 4-point Likert rating scale containing seven sub-scales. The construct validity of SETES-M was assessed and judged as adequate using factor analysis. Item loadings of 0.36 or above on seven principal factors were recorded. The internal consistency estimate of the sub-scales using Cronbach coefficient α ranged from 0.70 to 0.84 while the overall internal consistency estimate for SETES-M was 0.77. Students’ evaluation of teaching effectiveness factors accounted for 49.4% of the variance in mathematics achievement. The seven factors made significant relative contributions to the variance of students’ achievement in mathematics and were found to be good predictors of achievement in mathematics. Keywords: Factorial structure; students’ evaluation of teaching effectiveness; mathematics achievement; ©2012 Academic World Education & Research Center. All rights reserved.

1. INTRODUCTION Generally, the consensus in recent times in Nigeria is that there is considerable fall in the standard of education as observed in the poor performances in senior secondary school certificate examination (SSSCE). Various causes of the poor performance in secondary schools among others include: quality and quantity of teachers available; attitude of teachers to work; learning resources available; individual unrests and class size (Bassey, 2002; Nwosu, 1995). It is no doubt that the quality of the teachers at any level of education represents a crucial factor in determining the quality of education at that level. This is further affirmed by the National Policy on Education (2004), which clearly states that no educational system can rise above the quality of its teachers.

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Adeneye Olarewaju Awofala. E-mail address: [email protected]

Adeneye Olarewaju Awofala / Cypriot Journal of Educational Sciences. 7,1 (2012) 33-44

Common approaches to assessing the quality of teachers include the performance of students in the various subjects and teachers’ self-assessment. These assessment procedures had been adjudged ineffective (Ogomaka & Harbor- Peters, 1993), in that many factors have been found to characterize the effectiveness of a teacher and consequently his teaching (Ogomaka & Harbor- Peters, 1993; Imhanlahimi & Aguele, 2006). Teaching is a complex and demanding activity that embodies provision of experiences, guidance and materials designed to enhance meaningful learning in knowledge, skill and attitude on the part of the learners. Effectiveness in general refers to producing the result that is wanted or intended; producing a successful result. If we apply this to the education situation, then we may define effectiveness as producing those results that reflect the teacher and objective of education in the context of observable changes in students’ learning. The notion of ‘teaching effectiveness’ as an ideal is multifaceted and controversial. This is because it is partly difficult to give a list of commonly agreed qualities of teaching effectiveness, which are functionally non-overlapping. Also, there are varied teaching effectiveness models as there are definitions of teaching effectiveness. Sometimes, teaching effectiveness is incorrectly used synonymously as “teacher effectiveness.” While the latter refers to individual instructor performance, the former implies effectiveness of teaching within the unit. Teaching effectiveness can be said to encompass teacher effectiveness. Wheeler and Knoop (1982) remarked that teacher effectiveness is exhibited in; giving instructions, teacher-students relations, provision of leaning climate, curriculum matters, maintaining expected relations with peers and principal, professional tasks/qualities, and expected/desired personality qualities. These categorizations according to (Ogomaka & Harbor- Peters, 1993) are very elucidating but functionally overlapping. Slavin (1994) equates teaching effectiveness with what he calls “quality of instruction.” To him, high quality of instruction is that which is sensible, interesting and easy to remember and apply information presented to students. This definition is deficient considering the measures of overall teaching effectiveness (Boex, 2000; Decanio, 1986; Manson, Steagall & Fabritius, 1995). The most commonly employed measures of overall teaching effectiveness are student perceptions of: the overall quality of teacher’s teaching; the general quality of lectures/teaching; and • the overall value of the course/subject. Teaching is considered effective only if student performance improves after a period of instruction in a manner consistent with the goals of that instruction (Stringer & Irwing, 1998). The importance of effective teaching is further affirmed by Palmer (1998) when he states that: reduce teaching to intellect and it becomes a cold abstraction; reduce it to the spiritual and it loses its anchor to the world…Good teaching cannot be reduced to technique; good teaching comes from the identity and integrity of the teacher (P.4, 10). As stated earlier that no educational system can rise above the quality of its teachers, so the evaluation of an educational system must include the evaluation of the teacher and his/her teaching. This is paramount at a time in which argument over the falling standard of education in Nigeria is linked to teaching ineffectiveness. The question is: are Nigerian teachers not effective in their teaching? Answering this question may entail a comprehensive evaluation of teachers’ teaching effectiveness in the context of a conceptualized model. One important agent in evaluation of teaching/instruction is students. This is because students are consumers of teaching/instruction. Student evaluation of instruction entails that students are made to express their opinion and feeling concerning the effectiveness of the teacher’s instructional process (Joshua, Joshua & Kritsonis, 2006). An effective teaching is predicated on four characteristics namely: presage, context, process and product variables (Biddle & Dunkin, 1987) involved in a lesson. Adetula (1993) sees these variables as synonymous to extraneous, intervening, independent and dependent variables respectively. Conceptually, most studies that examine the determinants of student evaluation 34


of teacher have modelled the evaluation rating as an output of a teacher production function (Harris 2001). The production function expresses teaching effectiveness as an output determined by three primary inputs: student characteristics, course characteristics and teacher characteristics. The model is expressed as follows: Eval = f (T, C, S)……………… (1) Where Eval = evaluation measure of effectiveness T = vector of teacher characteristics C = vector of course characteristics S = vector of student characteristics Mathematically, the marginal effect of any one input on teacher evaluation is simply the partial derivative of equation (1) with respect to that input. For instance, the marginal effect of a particular teacher characteristic at time t is given by Eval = δf/δt (T,C,S). Investigation into students’ evaluation of teaching effectiveness has been the subject of considerable research in developed countries (Marsh & Dikin, 1992; Aubrecht, Hanna & Hoyt, 1986) and a number of instruments that have well defined factor structures and provide measures of distinct components of teaching effectiveness have been developed (Aubrecht, Hanna & Hoyt, 1986; Ogunniyi, 2004). Beside the robust psychometric properties of the student evaluation of teaching effectiveness scales (SETS) (Marsh, 1984; 1983; 1982) they are often criticized as lacking validity. This criticism is based on the possible existence of the culture of specific aspects of teaching effectiveness which have no universal criteria for effective teaching. Factors, which may appear to be very vital in developed countries, may not be appropriate in developing world. While discrediting the use of foreign instruments on indigenous sample, Nnachi (2005) in a review of literature states that standardized scales of indigenous character are more appropriate in probing the activities we value in developing countries than the foreign imported instruments. He argued that locally constructed and validated instruments are preferred and more useful because they provide more valid information when used on indigenous subjects than the foreign instruments. In Nigeria, education literature shows that efforts at developing and validating scales for measuring teaching effectiveness have not been properly harnessed (Ogomaka & Harbor- Peters, 1993; Ogomaka, 1984). Ogomaka (1984) devised a Students, Evaluation of Teacher Effectiveness Scale. Few documented studies on teaching effectiveness and related behaviours most often used data based on ordinarily facevalidated instruments (Ogomaka & Harbor- Peters, 1993) and this gives only mere speculation of the extent of manifestation of teaching effectiveness among the subjects. In such situations where the factorial structures of the face-validated instruments are not ascertained, it is no doubt that whatever data collected with such instruments and the conclusions derived from them may not be immune to bias and as such questionable. Although, SETS were specifically developed for university education to improve instruction, enhance the professional growth of the academic staff and used as a measure of observed instructional performance of the instruction teacher from the student standpoint (Joshua, 1998a; 1998b), it is evident that findings from them could be generalized to all levels of education. While Fox, Deck & Blattstein (1983) remarked that the SETS by sixth grade pupils “appear to be reliable, valid, useful measure of teacher behaviour” (p.21), Aubrecht, Hanna & Hoyt (1986) provided support for the validity of high school student ratings of instruction and predicted that SETS would be of immense benefit to high school merit pay systems and professional development activities as obtainable at university level. Questions about the validity, reliability, generalisability, utility, interpretability and acceptability of students’ ratings as measures of evaluating teachers on their jobs, especially when the results of such evaluation exercises are to serve some summative purposes have been raised (Aubrecht, Hanna & Hoyt, 35


1986) and studies that focused on correcting the flaws associated with the use of students to evaluate teachers conducted (Joshua, 1998b; Marsh, 1983). More recent studies have attested to the usefulness and accuracy of students’ evaluation and their positive relationship to teaching effectiveness in comparison with other measures such as students’ achievement and attitude (Cohen, 1981; Feldman, 1989; Mckeachie, 1983; Mckeachie, 1999). This positive attitude has been found among the lecturers/teachers in Nigeria (Joshua & Joshua, 2000). Relationship have also been detected between students’ evaluation of teaching effectiveness factors and interest in schooling (Orji, 2004) and school factors such as school type and class size have also been speculated to influence students’ evaluation of teaching effectiveness (Ogunniyi, 2004). The factorial structure of SETES has been examined and a good number of studies and arguments have been put forward in support of a number of more or less isolated independent subscales (Marsh & Hocevar, 1991; Marsh, 1983; 1982; Marsh & Dinkin, 1992). These and other findings suggest that (Ogunniyi, 2004) students’ evaluation of teaching effectiveness may best be regarded as multidimensional in nature. Supporting this suggestion, Boex (2000) and Centra (1979) devised a students’ evaluation of teaching effectiveness scale and a number of indices measuring different relatively mutually exclusive dimensions provided. The identified indices include: good organization of subject matter and course, effective communication, knowledge of and enthusiasm for subject-matter and teacher positive attitude towards students, fairness in examination and grading and flexibility in approaches to teaching. Preliminary validation of SETES was reported by (Ogunniyi, 2004), who suggested that it was school type-and gender- related. 1.1. Purpose of the study This study aimed at developing and validating a reliable and valid students’ evaluation of teaching effectiveness scale in mathematics. Specifically, the study: (a)constructed and trial tested a students’ evaluation of teaching effectiveness scale in mathematics for secondary school students. (b)examined the construct validity of the students’ evaluation of teaching effectiveness scale in mathematics. (c)established the internal consistency of the students’ evaluation of teaching effectiveness scale in mathematics. (d)determined the composite and relative contributions of students’ evaluation of teaching effectiveness factors to the prediction of achievement in mathematics. 1.2. Research Questions (1) How construct valid are the items of the students’ evaluation of teaching effectiveness scale in mathematics? (2)What is the internal consistency estimate of the students’ evaluation of teaching effectiveness scale in mathematics? (3) To what extent will the identified variables of teaching effectiveness when taken together predict students’ achievement in mathematics? (4) What is the relative contribution of each of the identified variables of teaching effectiveness to the prediction of students’ achievement in mathematics?

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2. METHOD 2.1. Design of the study This study is an instrumentation study. An instrumentation research is the type of research that focuses on introduction of new or modified content, procedure, technologies or instruments of educational practice (Ogomaka, 1984; Ogunniyi, 2004). 2.2. Population of the study The population for the study consisted of all the secondary school students in Kwali and Gwagwalada Area Council of FCT Abuja. The population of the study were made of up 10,488 (6667 males, 3821 females) students (Table 1). These statistics of students’ numbers in secondary schools in the two area councils were taken from the State of Education in F.C.T. for 2003. The average teacher-student ratio for the Kwali School is about 1 teacher to 33 students while the average teacher-student ratio for the Gwagwalada School is about 1teacher to 60 students. Table 1: Population of Students by Gender per Area Council Area Council Gwagwalada Kwali

No. of Schools 5 4

Male 4,087 2,580

Female 2,811 1,010

Total 6,898 3,590

2.3. Sampling and Sampling Procedure A total of one thousand and forty secondary school students were used for the study. In each of the two Area Councils, two secondary schools were drawn for the study through a non-proportionate stratified random sampling to make a total of four schools. In each of the four schools 260 SSII and 260 SS III students were randomly selected, to make a total 1,040 students. 2.4. Construction of the Students’ Evaluation of Teaching Effectiveness Scale in Mathematics (SETES-M) The construction of this scale was based on the theoretical formulation on teaching effectiveness. The component parts are the teaching skills, personality attributes, teaching principles, knowledge of learners, interpersonal relations, mastery of content and impact on learning. The researcher adopted both the rational and the empirical approaches in writing the items of the SETES-M for this study. A pool of relevant items on students’ evaluation of teaching effectiveness was written out. This was achieved partially by requesting sixty senior secondary school students randomly selected outside the sample study to write down their experiences, reactions or feelings they notice about their mathematics teachers in relation to the aforementioned components of teaching effectiveness. From the students’ pool of items, an initial teaching effectiveness related statements were selected, restructured, organized and incorporated with the pool of items derived from literature on teaching effectiveness. A pool of 100 items represented the first draft of the SETES-M. 2.4.1. Face Validation of the SETES-M The draft copy of the SETES-M items was first face validated by specialists in measurement and evaluation in terms of clarity, relevance and structure. 2.5. Initial Trail Testing of the SETES-M (Preliminary Factorial Validation) The face-validated SETES-M was administered to a sample of thirty senior secondary school students in Kwali and Gwagwalada Area Council (15 students each). The students’ responses were scored and subjected to factor analysis. Out of the 100 items that were subjected to factorial validation, ten items 37


were not loaded on any factor based on accepted range of 0.35 and above. These factors were dropped. Also eighteen items were loaded on more than one factor and were considered factorially complex and dropped leaving behind 72-item. The 72-item SETES-M was used in the main field work. 2.6. Mathematics Achievement Test (MAT) The MAT had 40 multiple-choice objective test items with one key and three distractors. It covered the major concepts around the Senior Secondary Mathematics Curriculum often considered difficult (WAEC, 2005). As shown in Table 2, test content covered the concepts of trigonometry, latitudes and longitudes and bearings and distances in the three levels of cognitive domain of remembering, understanding and thinking. After establishing content and construct validity, MAT was administered to thirty (30) senior secondary students that were not part of the main study. Their responses were used to compute the average item difficulty which yielded 0.45 and discriminating power of more than 0.40 was recorded for each of the items. A reliability coefficient of 0.85 was also obtained using Kuder-Richardson’s formula 20. Table 2: Test Items Specifications Content area The sine and cosine rules Angles of elevation and depression Height and distances Bearing and distances Angles between two places on the Earth’s surface Shortest distance between two points Total

Remembering 2 3 2 2 2

Understanding 2 3 3 1 2

Thinking 1 2 3 2 2

Total 5 8 8 5 6

3 14

3 14

2 12

8 40

2.7. Method of Data Collection The 72-item SETES-M that emerged after the preliminary factorial validation was used for data collection. Copies of the 72-item SETES-M were administered to the sample drawn for the study. Thereafter, the MAT was administered to collect data on the dependent measure. The data collection was carried out with the help of the mathematics teachers in the selected schools. The total period of the data collection spanned six weeks. 2.8. Data Analysis Research question 1 was answered using factor analysis with varimax rotation. Question 2 was answered using Cronbach coefficient alpha while questions 3 and 4 were answered using multiple regression analysis. 3. RESULTS Factor analysis (Principal components with varimax rotation) was performed on the responses to the SETES-M, treating males and females separately. Since both male and female teaching effectiveness rating profiles showed pattern and magnitude similarities, the data were combined. The subsequent factor analysis produced seven meaningful factors with eigen values greater than unity, which accounted for a total of 56.7% of variance. These factors had interpretable structures with factor loadings ranged from 0.36 to 0.58. 38


Table 3: Item Loadings of 0.36 or above on principal factors: Factors 1 to 7 Factor Name Teaching Skills

Personal Attributes

Teaching Principles

Knowledge of the Students

Interpersonal Relations

Mastery of Content

Loading 0.38 0.42 0.36 0.37 0.39 0.41 0.40 0.43 0.55 0.41 0.52 0.47 0.56 0.39 0.42 0.58 0.48 0.49 0.93 0.41 0.52 0.54 0.49 0.50 0.53 0.36 0.51 0.47 0.42 0.56 0.47 0.38 0.56 0.55 0.38 0.41 0.42 0.49 0.43 0.51 0.47 0.53 0.49 0.52

Scale Item Arrange his/her work clearly on the chalkboard Use instructional aids such as charts, posters to make lesson enjoyable Use class time effectively Write legibly on the chalkboard Speak audibly and communicate mathematical information effectively Explain clearly and give notes Distribute questions evenly to all members of the class Use body movements to demonstrate lessons Ask questions always and Listen well to students’ questions Be jovier, crack jokes and have a good sense of humour Dress well and neatly Be regular and punctual to class Be diligent and hardworking Always consider the views of others Not easily get provoked over any error made by students Not give up easily while solving a problem Be dynamic and energetic person Treat students with courtesy and respect State objectives for each class session Present lessons logically and sequentially Display an interesting style of presentation Start lesson from simple and known aspects to complex and unknown aspects Be good at facilitating group discussion among students Examine students on what is emphasized in class Praise good work Give students adequate assignments after each lesson Be concerned about students’ individual differences Not fail to detect indisciplinary acts of students Identify difficult areas for students and take care of them Identify students’ learning problems and errors and give remedies Posses solutions to individual student and group problems Be able to match students’ personality traits with teaching methods during teaching Be able to provide adequate information on students’ learning behaviour Keep continuous assessment records of all students Relate to students as individuals Invite students to share their knowledge and experience Encourage students to help one another Feel concerned over students’ failure to perform well Be very approachable and not strict Have a cordial relationship with all students Be able to share his/her wealth of experience with students on both academic and nonacademic matters Treat every student in the class equally Present origin of ideas and concepts Present current developments and applications relevant to the content of the lesson 39


0.58 0.57 0.52 0.49 0.41 0.51 0.39 Impact on Learning

0.39 0.41 0.45 0.51 0.39 0.38 0.39 0.46 0.52

Show a thorough knowledge of the subject matter Be confident in teaching and handling many topics in mathematics Relate and associate ideas and concepts in mathematics to ideas and concepts in other related subject areas Be able to give practical example to most problems Summarize major points Encourage intelligent and independent thought Teach without sticking to only one method in solving problem Discuss the topics reasonably and confidently with colleagues Transfer skills, concepts, rules and principles gained in the topics to solving true life problems Make up my own notes on the topics Solve most problems set on the topics during examination Score high marks on problems set on the topics during class test Recall most of the facts/concepts taught Do the assignment given on the topics taught See that mathematics is very useful in life Being to have interest in pursuing mathematics to the tertiary level

The significantly loading items are presented in Table 3. Loadings ranging from 0.30 to 0.39 may be considered significant; loadings ranging from 0.40 to 0.49 may be considered more significant and loadings over 0.50 may be considered very significant. The terminal solution of orthogonally rotated factors showed that twelve items had no significant correlation with any of the 7 identified factors thereby making the identification and naming of factors simple. Each of the 7 factors cluster of items were analysed and this resulted in factor’s name being assigned, which best conceptualized each factor’s high loading items. The items identified that loaded significantly on Factors 1 to 7 were tested for internal reliability. Cronbach’s alpha coefficients of 0.70, 0.83, 0.81, 0.84, 0.79, 0.72 and 0.70 were found for Factors 1, 2, 3, 4, 5, 6 and 7 items for both males and females respectively (p < 0.05 in all cases). Since the SETES-M scale separated into seven latent factors identified to possess minimum of 1.0 eigen values, statistically significantly liable and non-overlapping subscales based on these seven factors were used in subsequent data analyses. The following models were obtained: f1 = 0.38d11 + 0.42 d12 + 0.36 d13 + 0.37d14 + 0.39d15 + 0.41d16 + 0.40d17 + 0.43d18 + 0.55d19 f2 = 0.41d21 + 0.52d22 + 0.47 d23 + 0.56d24 + 0.39d25 + 0.42d26 + 0.58d27 + 0.48d28 + 0.49 d29 f3 = 0.39d31 + 0.41d32 + 0.52d33 + 0.54d34 + 0.49 d35 + 0.50 d36 + 0.53 d37 + 0.36 d38 f4 = 0.51d41 + 0.47d42 + 0.42d43 + 0.56d44 + 0.47 d45 + 0.38 d46 + 0.56 d47 + 0.55 d48 f5 = 0.38d51 + 0.41d52 + 0.42d53 + 0.49d54 + 0.43 d55 + 0.51 d56 + 0.47d57 +0.53 d58 f6 = 0.49d61 + 0.52d62 +0.58d63 +0.57d64 + 0.52d65 + 0.49d66 + 0.41d67 + 0.51d68 +0.39 d69 f7 = 0.39d71 +0.41d72 +0.45d73 + 0.51d74 + 0.39d75 +0.38d76 +0.39 d77 + 0.46 d78 + 0.52 d79

Where dij are the items that loaded significantly high on factor i, i and j are unique for each model because no item indicates a factorial complexity of two or more. The factors fi were than regressed on the students’ mathematics scores. Table 4: Summary of Regression Analysis on Students’ Evaluation of Teaching Effectiveness Factors combined Multiple R 0.705

2

R 0.497

2

Adjusted R 0.494

Std error of estimate 1.898 40


Table 4 showed that the seven factors of students’ evaluation of teaching effectiveness jointly correlate positively with achievement in Mathematics (R = 0.705). This shows that the factors were quite relevant towards the determination of achievement in Mathematics. The table also revealed an adjusted R2 value of 0.494 which indicates that 49.4% of the total variance in student achievement in Mathematics is accounted for by the seven factors of students’ evaluation of teaching effectiveness, taken together. The remaining 50.6% could be due to the residuals and other factors not included in this study. The significance or otherwise of the R value is tested on Table 5. Table 5: Analysis of Variance of Regression on Students’ Evaluation of Teaching Effectiveness Source of Sum of Squares Df Mean Square F Sig Variance Regression 1130.482 7 161.50 64.86 .000* Residual 2561.342 1,030 2.49 Total 3691.824 1,037 *Significant at p < 0.05

From Table 5, the R value obtained in the regression analysis is significant (F (7, 1030) = 64.86; p < 0.05). This implies that the R value of 0.705 is not due to chance. Hence, it is found that there is a significant composite effect of the students’ evaluation of teaching effectiveness factors on students’ achievement in Mathematics. Table 6. Coefficients of the Regression Models of the Relative Effects of Students’ Evaluation of Teaching Effectiveness Factors on Achievement in Mathematics. Model (Constant) FACTOR 1 FACTOR 2 FACTOR 3 FACTOR 4 FACTOR 5 FACTOR 6 FACTOR 7 *Significant at p < 0.05

Unstandardized coefficients ß 2.351 0.653 0.831 0.746 -0.568 -0.467 0.378 -0.984

Std error 0.372 0.081 0.074 0.078 0.091 0.110 0.072 0.326

Standardized coefficients Beta 6.320 0.121 0.314 0.083 -0.068 -0.051 0.094 -0.052

Rank

T

Sig

2nd 1st th 4 th 7 5th 3rd 6th

8.021 11.17 9.24 -6.31 -4.21 5.32 -3.24

0.000 0.000* 0.000* 0.000* 0.002* 0.012* 0.005* 0.024*

Table 6 showed that of the seven factors of students’ evaluation of teaching effectiveness, Factor 2 (personal attributes) made the greatest contribution (ß = 0.314; p < 0.05) followed by Factor 1 (Teaching Skill) (ß = 0.121; p < 0.05). The third, fourth and fifth on the ranking of the contributions are made by Factor 6 (Mastery of Content) (ß = 0.094; p < 0.05), Factor 3 (Teaching Principle) (ß = 0.083; p < 0.05) and Factor 5 (Interpersonal relation) (ß = -0.051; p < 0.05). Factor 7 (Impact on Learning) (ß = -0.062; p < 0.05) and Factor 4 (Knowledge of Student) (ß = -0.068; p < 0.05) made the least contributions to achievement in Mathematics in that order. Thus, each of the seven factors of students’ evaluation of teaching effectiveness could predict achievement in Mathematics. These include Teaching skill (ß = 0.653; t = 8.021; p < 0.05), Personal attribute (ß = 0.831; t = 11.17; p < 0.05), Teaching principle (ß = 0.746; t = 9.24; p < 0.05), Knowledge of student (ß = -0.568; t = -6.31; p < 0.05), Interpersonal relation (ß = -0.467; t = -4.21; p < 0.05), Mastery of content (ß = 0.378; t = 5.32; p < 0.05) and Impact on learning (ß = -0.984; t = -3.24; p < 0.05). However, Factors 4, 5 and 7 have inverse relationship on the achievement score in Mathematics. The model obtained is: Score = 2.351 + 0.653f1 + 0.831f2 + 0.746f3 – 0.568f4 – 0.467f5 + 0.378f6 – 0.984f7 41


Where fi is the factor, i = 1…7 4. DISCUSSION Factor analysis of SETES-M scale produced seven interpretable principal factors that are functionally non-overlapping or mutually exclusive. Factor 1 items appeared to be concerned with teacher’s ability to teach well, e.g. ‘Mathematics teacher in his/her teaching should arrange his/her work clearly on the chalkboard’ or ‘…ask questions always and listen well to students’ questions.’ This factor was, therefore, labelled ‘Teaching skill.’ Factor 2 appeared to be concerned with the personal features of the teacher which may influence his/her teaching, e.g. ‘…be jovier, crack jokes and have a good sense of humour’ or ‘…treat students with courtesy and respect.’ This factor was, however, labelled ‘Personal attributes.’ Factor 3 items were concerned with the basic laws, rules or theories that teaching is based on, e.g. ‘…state objectives for each class session’ or ‘…start lesson from simple and known aspects to complex and unknown aspects.’ This factor was, therefore, labelled ‘Teaching principle.’ Factor 4 appeared to be concerned with the teacher knowing about the students, e.g. ‘…be concerned about students’ individual differences’ or ‘…keep continuous assessment records of all students’. This factor was, however, labelled ‘knowledge of student.’ Items of Factor 5 seemed to be concerned with the relationship existing between a teacher and his/her students on academic and non-academic matters, e.g. ‘… relate to students as individuals’ or ‘…make students feel free to question and express their ideas.’ This factor was, therefore, labelled ‘interpersonal relation.’ Factor 6 items appeared to be concerned with the teacher knowing the content of the lesson, e.g. ‘…present current developments and applications relevant to the content of the lesson’ or ‘…be confident in teaching and handling many topics in mathematics.’ This factor was, however, tagged ‘Mastery of content.’ Items of the last factor, Factor 7 seemed to be connected with effect of the interaction between a teacher and his/her students on learning, e.g. ‘After our Mathematics teacher’s teaching of topics, I am able to transfer skills, concepts, rules and principles gained in the topics to solving true life problems’ or ‘…begin to have interest in pursuing Mathematics to the tertiary level.’ This factor was, therefore, tagged ‘Impact on learning.’ In considering evidence of statistically significant influence(s) which some independent factors/variables could exert on a dependent measure it is vital to examine the nature of such effect(s). However, while there are theoretical bases for causal effects to exist between certain factors/variables, some effects may either be function of or predicted by other factors/variables commonly related to both, and yet others may be due to error. The study showed that about half of the total variance in students’ achievement in Mathematics is accounted for by the seven factors of students’ evaluation of teaching effectiveness. This indicates that students’ performance in Mathematics is a function of students’ evaluation of teaching effectiveness factors in mathematics. Thus, in spite of the other conditions of teaching and learning, the students’ evaluation of teaching effectiveness factors in Mathematics may create a wedge between what students were taught and what they learnt in Mathematics. It is evidently clear that each of the seven factors of students’ evaluation of teaching effectiveness (teaching skill, personal attributes, teaching principle, knowledge of student, interpersonal relation, mastery of content and impact on learning) made significant contributions to and could also predict students’ achievement in Mathematics. The implication of this is that possession of teaching skill enhances effective teaching and learning of Mathematics. Good personal attributes are more likely to arouse students’ interest in the learning of Mathematics. Adhering to teaching principle is most likely to make students’ learning enjoyable and permanent. Good interpersonal relation between the teacher and his/her students creates an enabling environment for result oriented teaching and learning. Also, without teacher’s possession of mastery of content, students are less likely to learn 42


Mathematics effectively. While knowledge of students helps teacher in detecting learning problems, errors and students’ indisciplinary acts in the classrooms, positive teacher’s impact on learning is a sign of successful teaching. 5. CONCLUSIONS Four important conclusions would appear to become known from the present investigation. These are (1) that the concept of ‘students’ evaluation of teaching effectiveness’ should be regarded as multidimensional in nature; (2) that the seven dimensions identified here jointly made significant contributions to the determination of student achievement in Mathematics; (3) that each of the seven dimensions identified made significant relative contributions to the variance of student achievement in Mathematics; and (4) that the seven dimensions of students’ evaluation of teaching effectiveness were found to be good predictors of students’ achievement in Mathematics. The results of the factor analyses, coupled with evidence of statistically significant high internal reliabilities of the emergent nonoverlapping factors point (i) to the stability of using the SETES-M as a single scale, and (ii) to a factorial structure for the scale that is similar to those of Wheeler and Knoop (1982) and Ogomaka and HarborPeters (1993). REFERENCES Adetula, L.O. (1993). Different faces of research on effective teaching, Journal of Studies in Curriculum. Academic Publications Associations of Nigeria, Lagos, 4 (1&2), 123-134. Aleamoni, L.M. (1978). Development and factorial validation of the Arizona course/Instructor. evaluation questionnaire. Educational and Psychological Measurement, 38 (4), 1063-1067. Aleamoni, L.M., & Pamela, Z.H. (1980).A Review of the Research on Student Evaluation and Report of the Effect of Different SETS of Instructions on Student Course and Instructor Evaluation”. Journal of Instructional Science, 9, 67-84. Aubrecht , J.D. Hanna, G.S., & Hoyt, D.P. (1986). A comparison of high school Student Ratings of Teaching Effectiveness with Teacher Self ratings: Factor Analysis and Multitrait-Multimethod Analyses. Educational and Psychological Measurement, 46(1), 233-31. Bassey, B.A. (2002). Students’ evaluation of instruction, attitude toward mathematics and mathematics achievement of SS3 students in Southern Cross River State of Nigeria.Unpublished Masters’ thesis, University of Calabar, Calabar, Nigeria, Biddle, B.,& Dunkin, M. (1987) Effects of Teaching. In Dunkin, M. J. (Ed) The International Encyclopedia of Teaching and Teacher Education, pp. 119-124 Oxford: Pergamon Press. Boex, L.F.J. (2000). Attributes of Effective Economics Instructors: An Analysis of Student Evaluations. Journal of Economic Education, 31, 211-227. Centra, J.A. (1979). Determining faculty effectiveness: Assessing teaching, research, and service for personnel decisions and improvement. San Francisco: Jossey-Bass. Cohen, P.A. (1981). Student Ratings of Instruction and Student Achievement: A Metal Analysis of Multi Section Validity Studies. Review of Educational Research, 51(3), 281-309. Decanio, S.J. (1986). Student Evaluations of Teaching: A Multinominal Logic Approach. Journal of Economic Education, 17, 165-176. Federal Republic of Nigeria (2004). National Policy on Education. Lagos: Federal Ministry of Education. Feldman, K.A. (1989).The Association between Students’ Ratings of specific instructional dimensions and student achievement: Refining and extending the synthesis of data from multi section validity studies. Research in higher Education, 30(6), 583-645. Fox, R. Deck, R.F., & Blattstein, D. (1983). Student evaluation of teacher as a measure of Teacher Behaviour and Teacher Impact on Students. Journal of Educational Research, 77 (1), 1621. Harris, B.D. (2001). An Aggregate Approach to Measuring Teaching Performance. Unpublished doctoral dissertation, San Diego State University. Imhanlahimi, E.O., & Aguele, L.L. (2006). Comparing Three Instruments for Assessing Biology Teachers’ Effectiveness in the Instructional Process in Edo State, Nigeria. Journal of Social Science, 13(1), 67-70. 43


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