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Inclusive and Supportive Education Congress 1st - 4th August 2005. Glasgow, Scotland |
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Donna McGhie-Richmond, Ph.D.
Kathryn Underwood, Ph. D.
Anne Jordan, Ph. D.
Ontario Institute for Studies in Education/University of Toronto
Melissa McGee, Ph. D.
University of Texas
For correspondence please contact Anne Jordan: ajordan@oise.utoronto.ca
Abstract
In this study we investigated the sequence of skill development for effective teaching behaviors in inclusive classrooms, and the kinds of instruction provided to students with identified disabilities and those considered to be at risk in those classrooms. According to “constructivist” pedagogy (Brophy, 2004), effective teachers are presumed not to “transmit” knowledge, but to elicit it through dialogical interaction with students. Even so, students who have disabilities benefit from “direct instruction” in which teachers transmit skills and knowledge (Swanson, 1999). We were interested in determining whether 'constructivist' skills, such as engaging students in cognitively extending dialogues, and student-teacher interactions that elicit higher-order thinking, follow the mastery of teaching behaviors that are more transmissive in nature.
The Classroom Observation Scale (COS) developed by Stanovich (1994) and Stanovich & Jordan (1998) provided the data from 63 half-day observations of elementary teachers in general education classrooms in which students with disabilities were included. The COS contains items which span the spectrum of teaching behaviors from classroom organization and time management to engaging students in one-to-one dialogical interactions. We investigated whether a set of COS items distinguishes effective teaching skills. A canonical discriminant functions analysis identified items accounting for differences between the teacher groups. The results suggest that the sequence of instructional practices is cumulative rather than differentiated, and results in a wide repertoire of teaching behaviors consisting of both transmissive and constructivist elements. Although there was some evidence that the students who were considered to be academically ‘at risk’ may have received differential attention and instruction that was less responsive to their levels of knowledge, t eachers’ teaching style was consistent across the range of students in the classroom, including those students who have identified disabilities. The results are discussed with respect to the debate concerning constructivist and transmissive teaching practices as well as teaching diverse students in inclusive classrooms.
Introduction
Inclusion is now the preferred service delivery model in most educational jurisdictions in Canada. Furthermore, a growing body of research evidence speaks in favour of an inclusive approach to the education of students with learning difficulties (Ainscow, 1999; Salend & Duhaney, 1999; Villa & Thousand, 2000). The heterogeneous nature of today’s classrooms means that the responsibility for teaching an increasingly diverse group of students falls largely to the general education classroom teacher. Teachers are not only required to meet rigorous curriculum standards, but to also respond to the individual needs of the students in their classrooms. While many teachers support the philosophy of inclusion and believe it is both academically and socially beneficial to students with special needs, as well as their peers, (Bunch, Lupart, & Brown, 1997), others have expressed skepticism and mixed opinions about the potential benefits, as well as an expectation of the problems inherent in inclusion, particularly when it comes to implementing it in the classroom (D’Alonzo, Giordano, & Vanleuven, 1997). Indeed, only about 10% of elementary teachers are willing and able to adapt their instructional practices to include the breadth of learner differences in their classrooms, for example by including students with disabilities (Jordan, Lindsay & Stanovich, 1997; Jordan & Stanovich, 2001; Schumm, Vaughn, Haager, McDowell, Rothlein, & Saumell, 1995) . One possible reason for this is that skills that are needed to calibrate to instruction to individual differences in students' knowledge and skill, let alone engage students in dialogical interaction are complex and difficult for teachers to implement. It may be the case that teachers learn to develop such skills as a result of considerable classroom experience and only after mastery of other skills, and that only the most proficient teachers reach this level of development.
The study reported here lies at the intersection of two areas of research: effective instruction in elementary regular education classrooms, in general, and the nature of instruction provided to students with disabilities in inclusive classrooms. The past three decades have witnessed a growing body of research identifying specific teacher behaviours as predictors of student achievement (Brophy & Good, 1986; Englert, Tarrant, & Mariage, 1992). In addition to macro-level classroom and time management elements, much of this research examines the micro-level of teaching: how teachers actually teach; that is, how they structure their lessons, ask questions, and provide feedback to students (Brophy & Good, 1986; Rosenshine & Stevens, 1986). Research in advanced placement classrooms (Henderson, Winitzky, & Kauchak, 1996), in mathematics (Reynolds & Muijs, 1999; Muijs & Reynolds, 2000), in science (Lapadat, 2000; Roth, Anderson, & Smith, 1987) as well as in reading (Mariage, 1995; Pressley, Hogan, Wharton-McDonald, & Mistretta, 1996) all substantiate a social constructivist view of learning primarily evidenced in teacher student interaction through dialogue. Based on Vygotsky’s (1978) concept of the “zone of proximal development”, teacher student dialogue is at the heart of knowledge building in the classroom. Teachers who are considered to be effective, “apprentice students in the language, dialogue, and actions of the skilled problem solver” (Englert, Tarrant, and Mariage, 1992, p. 72). Wells (1998) refers to this mediating role of dialogue in building knowledge as ‘dialogic responsivity’. Through dialogue, effective teachers are able to calibrate their instruction according to their students’ responses and thereby meet the range of learner needs inherent in today’s classrooms. According to "constructivist pedagogy" (Brophy, 2004), effective teachers are presumed not to "transmit" knowledge but to co-construct it through dialogical interaction with their students. Yet, students with disabilities are known to benefit from "direct instruction" in which teachers transmit skills and knowledge (Swanson, 1999). Swanson, Hoskyn and Lee (1999) highlight the significance of direct instruction that includes small-step, sequenced transmission of content and strategies for students with learning disabilities.
In the literature on instructional characteristics in the general education classroom, there seems to be a prevalent assumption that teachers who assist their students to construct knowledge are more effective than those who transmit it. The more extreme of these claims hold that the two styles of teaching are mutually exclusive, derived from fundamentally different sets of epistemological beliefs. It is claimed that teachers who are constructivist in their teaching style view learning as centered in the development of skills and knowledge in the child, while those who are transmissive are focused on the delivery of curriculum and on the efficiency of information flow to the learner (Torff, 1999, 2003; Torff & Sternberg, 2001). It also seems that curriculum-centered, transmissive techniques of instruction that maximize the flow of knowledge to the learner is a negative instructional attribute derived from an erroneous view of learning based in trait psychology (Olson & Katz, 2001).
Torff (2003) claims that novice teachers engage in direct instruction by transmitting content knowledge "based on the belief that learning is tantamount to memorization" (p.563). As teachers develop expertise, their skills increase for promoting higher order thinking with a simultaneous decrease in quantity of content knowledge covered. Experienced teachers do not automatically develop such expertise, however. Torff claims that their instruction tends to show a decrease in content knowledge while failing to increase techniques that promote higher order thinking skills.
In this paper we examine the evidence for such claims using an empirical database of classroom observations conducted with 63 general education elementary classroom teachers. Part of the Classroom Observation Scale (COS) (Stanovich, 1994; Stanovich & Jordan, 1998) is comprised of instructional skills and techniques derived from the literature on effective teaching (Englert, Tarrant & Mariage, 1992). The COS contains constructivist and teacher-directed elements as well as a broad array of classroom and time management, and lesson presentation skills. If the claims described above are accurate, there will be different patterns in the instructional techniques that high-scoring and, by definition, effective teachers predominantly use in their elementary classrooms compared to lower-scoring, less effective and novice teachers. These should emerge as distinct clusters of COS items, some relating to constructivist skills which promote higher-order thinking, and others to transmissive elements in which the teacher manages the flow of information. Teachers with high scores on the COS should show a predominance of constructivist elements and very little transmissive elements in their teaching repertoire compared to lower scoring teachers, and vice versa for lower scoring teachers. The differences in predominant instructional patterns should also differentiate the teacher candidates and novice teachers from those with longer teaching experience. If this proves to be the case, it would suggest that teachers acquire instructional skills along a developmental sequence that is not simply cumulative, but represents a switch in emphasis from transmission to constructivist techniques at some point along the career span of those who excel.
We also examined the consistency of instructional patterns for students with disabilities and who are academically at risk in the class. By specifically monitoring the quantity and type of instruction received by two such students in each class, we investigated whether the instructional style that each teacher customarily used with the students in the class as a whole is also used with students with disabilities, or whether such students received a different instructional treatment. We speculated that novice and less effective teachers, with their focus on delivering curriculum, might direct their instruction to the overall class and pay little attention to the students at the low end of the range of achievement in the class. However, effective teachers, who presumably subscribe to a social constructivist view of learning, would be more likely to adapt their instruction to meet the academic needs of the range of students in their class, as indicated by the instruction received by the two monitored students. Thus the rating of instruction received by two specific students can inform us about the breadth of instructional adaptations of teachers, and whether there are differences between teachers in relation to their predominant teaching patterns with the class overall.
Research Questions
Our research questions are three-fold. We asked:
1. Is there evidence that effective teachers (as indicated by those who score high on the COS) use instructional techniques that are constructivist and that these techniques discriminate them from less effective teachers? Conversely, does a predominance of transmissive instructional techniques discriminate the teaching practices of less effective teachers (as indicated by those who score lower on the COS) from those of more effective teachers?
2. Is length of teaching experience related to differences in styles of teaching practice? That is, do effective teachers and mid-career, less effective teachers differ from novice teachers on the types of instructional techniques they use?
3. Are there differences in the type of instruction received by students with disabilities and by those designated as being academically at-risk, compared to the class as a whole? Do any differences relate to the teachers' scores on the COS, or to differences in their predominant instructional patterns?
Method
Instruments
Classroom Observation Scale (COS) (Stanovich, 1994; Stanovich & Jordan, 1998) was used to measure teachers’ instructional behaviours. The COS was developed from a synthesis of effective teaching skills that had been operationalized in 1992 by Englert, Tarrant, and Mariage as a series of teacher self-rating checklists. It is based upon a synthesis of the research conducted from 1970 to 1990 on teaching factors known to be effective, both in terms of student achievement (Brophy & Good, 1986; Gage and Needels, 1989; Rosenshine & Stevens, 1986), as well as the more recent ‘social constructivist’ factors (Marshall, 1992; Hogan & Pressley, 1997).
The COS is comprised of 27 observation items and three rating scales which span the spectrum of teaching behaviours from classroom organization and time management to engaging students in one-to-one dialogical interactions, such as responsive questioning and elaborating student responses. The items cover common indicators of teaching effectiveness along three dimensions: (a) classroom management, (b) time management, and (c) lesson presentation. For example, the items include: citing rules for instructional and non-instructional events (classroom management), gaining and maintaining student attention and allocating generous amounts of time for instruction (time management), actively modeling and demonstrating concepts, learning strategies, and procedures required for effective problem-solving and scaffolding, elaborating student responses and eliciting higher-order thinking skills (lesson presentation). The scale contains four sections:
Rating Scales of Classroom Practices .
The first section contains 27 items in three blocks that are rated on a three-point scale: Not in evidence (0), Inconsistent (1), Consistent (2). Eight items rate classroom management (e.g. Item A6 'scans class frequently', Item A8 'administers praise contingently and uses specific praise statements'). Eight items code time management (e.g. Item B1 'allocates generous amounts of time for instruction', Item B3 'establishes clear lesson routines that signal a beginning and an end'). Eleven items gauge lesson presentation. These include items that are linked a priori to the claims of those who subscribe to “constructivist pedagogy” (Table 1).
Predominant Teaching Style.
The second section of the COS contains a 7-point rating scale on which the observer records the teacher's predominant teaching style with the total class during lessons. This scale is a gauge of teaching style with the total class, and provides a measure of concurrent validity of the analysis of the items in the first section of the observation scale. The following 7-point scale was used:
0: No interaction with students on lesson content during seatwork. If any interactions occurred, they were non-academic in nature, concerning organization or classroom procedures, behavior management, status of the task at hand, and affective or personal (Jordan, et al., 1997).
1: Teacher circulates infrequently (one or two times) checks the students’ work and moves on.
2: Teacher frequently (three or more times) checks the students’ work and moves on.
3: Teacher occasionally (one or two times) transmits information related to the lesson to the students (e.g., tells students what to work on, how to correct it) and moves on.
4: Teacher consistently (three or more times) transmits information related to the lesson to the students (e.g., tells students what to work on, how to correct it) and moves on.
5: Teacher occasionally (one or two times) elaborates student responses (e.g., asks students questions about the lesson material concepts that require responses; interaction requiring student participation).
6: Teacher consistently (three or more times) elaborates student responses (e.g., asks students questions about the lesson material concepts that require responses; interaction requiring student participation).
Teaching Style with Two Included Students .
We examined the third question by coding on a 7-point scale the teacher-student instructional interactions received individually by two students who had been designated by the teacher, as exceptional or as academically at risk. The two students were selected from a class list on which the teacher had previously ranked every student's standing in relation to the class average in achievement, behavior and need for accommodations. The teacher was not told which two students were being monitored during the observation. The same 7-point rating scale used to rate the teacher's predominant teaching style with the whole class was used to rate the teaching style with each student. This rating provides an index of the breadth of instructional adaptations that the teacher uses to accommodate the diverse needs of students in the class.
The COS therefore provided a measure of effective teaching behaviour at both the macro- and micro-levels of teaching in inclusive classrooms. The COS items and three scales resulted in 30 measures in total.
As part of a larger series of studies, half-day classroom observations were conducted in 63 inclusive elementary classrooms. These grades 2 to 8 classrooms were in public, Catholic and private Canadian schools. For the observation, the teacher was asked to conduct at least two expository lessons in core areas of the curriculum (e.g., language arts, mathematics or science). The observations consisted of anywhere between one and four lessons that took place during a three-hour period of time, or half day of instruction. Two trained researchers independently conducted the COS by observing and coding the teachers' practices, and simultaneously monitoring the specific instructional opportunities received by two students in each class. A total of 63 students, one per class, were designated as having a disability, and a further 63 students, one per class were deemed by their teachers to be at risk for academic failure. In order to select the students for observation, the teachers were asked to rank all the students in the class on three dimensions; academic progress made, behavioral difficulties and extent of accommodations and/or modified curriculum required. The observers randomly selected the students from those ranked by their teacher as low on these criteria. The teacher was not aware which students were the focus of the observation. The inter-rater reliability, following extensive observation training, was 94% agreement. The 63 teacher observation results used in this analysis are the mean ratings of the two observers.
Discriminant Functions .
To examine the first two research questions, an a priori analysis of the items in the COS was conducted. The items were designated as fitting a curriculum-centered, transmissive conception of teaching, or a student-centered, constructivist conception (Table 1). Items were assigned to the constructivist category if they featured teacher-student dialogical interaction, such as activating students' prior knowledge relevant to the topics and skills to be learned, and providing frequent questions to evaluate students' mastery of lesson concepts. Assigning items that were transmissive posed a greater challenge. The literature that criticizes this style of teaching does not distinguish between the transmission of learning skills and strategies as distinct from facts and content knowledge. Elements claimed to be part of scaffolding instruction such as modeling, self talk and think-alouds were designated as transmission (Englert et al, 1992), although some authors claim them to be elements of constructivist techniques. It should be noted that direct instruction of learning skills and strategies is also a debatable characteristic of transmissive teaching.
The purpose was to see if the sets of items classified as characterizing transmissive compared to constructivist instruction would emerge as discriminating high- from low-scoring teachers using step-wise canonical Discriminant Functions Analysis (SPSS, 2004). The range of total scores on the COS was divided into eighths, and the 63 teachers were assigned to the group in which their total score fell. These groups were entered into the analysis to see which COS items emerged as accounting for differences between groups.
Using discriminant function analysis the contribution of each item to the overall scores on the COS was estimated and the clusters of discriminating items were determined. Based on overall scores, the teachers were divided into 4 groups, from lowest- to highest-scoring quartile. We hypothesized that items in the Lesson Presentation section of the COS that relate to teacher-student dialogues and the extension of students' thinking would discriminate the highest scoring quartile of teachers from the rest of the sample. We also anticipated that skills relating to student engagement in the lesson, and classroom management skills would add to the discriminant functions for mid-scoring quartiles, indicating a possible developmental sequence of skills mastery.
b) Years of Teaching.
A score was generated for each teacher on the 5 items that emerged as Function 1. This score and the total COS score were correlated with number of years of teaching experience.
c) Teaching Style with Included Students with Special Needs.
The two scale scores for each of the two students, designated as exceptional and as academically at risk, were compared with the teachers' total COS score.
The COS items on the function that discriminated the rank ordered teacher groups were used to create a subscale score that represented each teacher's relative standing on this function. This score was correlated with the teacher style ratings for each of the two included students.
Results
One significant function emerged from the discriminant functions analysis, accounting for 95% of the variance: student engagement (Table 2). This function reflected the teachers’ efficient use of time to engage students in learning and to maintain their attention in the instructional component of the lesson by for example, informing students of the expectations and time frames for lessons, and maintaining a high degree of student attention during large-group activities and during seatwork. Function 1 significantly discriminated the eight groups of teachers as shown in the relationship of the function to group centroids (Table 3). Further functions had eigenvalues of less than 1.
A comparison of the items derived from the a priori division of items into transmissive vs. constructivist groups (Table 1) with those items that contributed to the subscale for student engagement resulting from the discriminant function analysis (Table 2), suggests that there is little correspondence.
Number of years of teaching had no relationship with either the COS total score nor the subscale score for student engagement.
The predominant teaching style rating with the class as a whole was correlated with the COS scale total score (n = 32, r = .66, p < .001) and with the subscale score for student engagement (n=33, r = .599, p<.001). These provided evidence of the concurrent validity of the COS-derived and rating scale measure of teaching style.
The relationship of the rating of teaching style for each of the two included students with the COS measures and the predominant teaching style rating provides a more complex picture. The teaching style received by student 1, who was designated as exceptional, was similar to the style used by teachers overall. That is, the teaching style received by student 1 correlated with the teachers' COS total score, (n=24, r = .55, p < .001); with the predominant teaching style rating (n = 25, r = .69, p < .001); and with the subscale score for student engagement (n = 24, r = .42, p<.01). On the other hand, the correlation between the teaching style received by student 2, who was designated as academically at-risk, with the predominant teaching style and student engagement measures failed to reach significance.
The results of the analysis indicate that the highest scoring teachers in our observation using the COS used a skillful blend of instruction involving classroom management, modeling, scaffolding, as well as questioning routines. However, the elements that were common in this function were the provision of organizational frameworks for lesson delivery and the effective use of instructional time. These teaching behaviors were related to high levels of student engagement.
A set of elements defined as constructivist did not emerge as a distinctive feature of the teaching repertoire of the high-scoring teachers, if by these we mean the flow of information was generated primarily in dialogical interactions between students and teacher or in student peer groupings. That is not to say that there were no instances of instruction that promoted higher-order thinking, as there were many. Some of these, however, stemmed from teachers directly describing and modeling the component strategies and skills of the lesson, a set of techniques classified by Englert et al. (1992) as transmissive. Student-led procedures did not discriminate the higher from the lower scoring teachers. On the other hand, there was ample evidence of teaching techniques that were responsive to student-initiated ideas, or which resulted from questioning routines that featured "what, how", and "why" questions. It appears that the highest scoring teachers had mastered techniques that included both maximizing instructional time by keeping students aware of lesson parameters, and by conducting teacher-led explanations of concepts and learning strategies.
Thus, rather than discriminating the highest scoring quartile of teachers from the rest on the basis of items that exclusively target teachers’ use of constructivist skills to engage students in cognitively extending dialogues, the highly predictive items in function 1 suggested a broader set of skills. This set marks the ability of teachers to engage their students in the lesson and to maintain student engagement by such techniques as gaining and maintaining their attention, moving the lesson along at a brisk pace and involving students in anticipating how the lesson material will relate to future lessons. Although this set of skills was the least mastered in our sample, it characterized the group of teachers who scored highest on the COS overall. Moreover, when practiced, this set of skills typically follows mastery of the skills characterized by classroom and time management skills, dimensions of effective teaching that have been criticized by some authors as mechanistic and transmissive, and detracting from social constructivist principles. Thus, teachers appear to master and use certain mechanical and transmission teaching practices in order to be able to engage students in the lesson. The results suggest that a part of the skill of fostering extended dialogues that lead to higher-order thinking in their students is the ability to gain and hold students' attention. And gaining and holding students’ attention is achieved through effective classroom organization and management skills.
The results also reveal that teaching style was consistent across the range of students in the class, except for some evidence that the students deemed to be academically at risk may have received less frequent attention and instruction that was less responsive to their levels of knowledge than did other students in the class who were designated as either having or as not having a disability.
Of particular interest is the finding that length of teaching experience was not a predictor of teaching style. Indeed some teachers with less that 5 years of teaching experience scored high on the COS, while some teachers with more than 5 years of teaching experience scored low.
A fractious debate exists today about the development of teaching quality. Brophy (2004) warns about the dangers of extremism associated with polarizations such as transmission vs. construction. Borko (2004) cautions against the dangers of over-generalizing prescriptions for practice from a single conceptual framework. Others have questioned the relevance of importing socio-cultural theories of learning as knowledge construction into prescriptions for teaching (Wells, 2004). Three of Heward’s (2003) faulty notions that hinder the effectiveness of special education concern the direct instruction vs. constructivism debate; that structured curricula impede true learning, that drill and practice limit students’ deep understanding and dulls their creativity, and that teaching discrete skills ignores the whole child. The claim prevails that direct instruction is undesirable, not student-centered and antithetical to the development of higher order thinking skills in students, if not potentially damaging to them.
Our results indicate that the range of skills used by the higher scoring teachers were broad and often innovative, and defy a simple classification as constructing vs. transmitting knowledge. Moreover, these skills were made possible in the context of classroom and time management practices that ensured that maximum time was devoted to instruction, with little time spent on managerial and procedural routines.
Three main conclusions can be drawn from this research study.
1. There seems to be a sequence of instructional practices that may reflect the development of teaching skills in elementary teachers. This sequence of instructional practices is cumulative rather than differentiated, and results in a wide repertoire that consist of both transmissive and constructivist elements.
This finding throws into question recent criticisms of process-product skills in teacher development as well as the current educational theory that students learn effectively exclusively through teachers’ use of constructivist pedagogical techniques. The emphasis on the benefits of student-centered learning and constructivist pedagogy (Torff, 2003) are not supported by these data. The findings also affirm the importance of direct instruction as a set of teacher-led skills that engage students in learning.
2. Teachers may need to master the fundamental mechanics of classroom management and maximizing instructional time as a pre-requisite to developing skills of student engagement.
3. The skills that teachers use with their students in general are used for students with disabilities in inclusive classrooms. Effective teaching practices that can benefit all students focus on high levels of student engagement, together with excellent managerial and time management skills, in order to maximize the instructional time which teachers are able to provide to individuals and groups during lessons. Indeed, the findings of this research study further validate what has been posited by others (Englert, et al, 1992; Larrivee, 1986; McGee, 2001) suggesting that teachers who are generally effective are also effective with students who have special learning needs. Teachers’ classroom organizational and management skills appear to play an important role in their ability to maximize their time spent in elaborative individual student-teacher instructional interactions. Teachers who are effective at including students with disabilities in their classrooms free up instructional time for targeting instruction “without sacrificing the instructional quality for their other students” (Stanovich & Jordan, in press). They use their classroom organizational and management skills to maximize their time spent in are able to manage their instructional time that allows them to allocate generous amounts of time for teaching and learning in their classrooms. They are then able to adapt and modify their instruction for individual students.
It is estimated that classroom teachers account for 30% of the variance in students’ achievement (Hattie, 2002). As Hattie states, “It is what teachers know, do, and care about which is very powerful in this learning equation.” (p. 2). The findings of this study contribute to the growing body of knowledge about what teachers know and do in inclusive classrooms (Jordan & Stanovich, 2001, 2003; Stanovich & Jordan, 1998), as well as the use of classroom observation as a means of inquiry into teaching practices (Brophy & Good, 1986; Good & Brophy, 2000; Hattie, 2003). Given the significant and direct role of teaching behaviors on student learning outcomes, our lens should remain focussed on both the macro and micro levels of teaching practices in inclusive classrooms to determine in what ways teachers address diverse learner needs, the factors that influence their teaching practices, as well as how teaching practices evolve over time.
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Table 1. Items that were a priorily assigned to the categories of "Transmissive" and "Constructivist".
Transmissive |
Constructivist |
A4. Consequates rule compliance quickly; cites rule or procedure in responding to disruptive behavior B2. States expectations for seatwork in advance B4. Gains students' attention at the beginning of the lesson and maintains it during instruction at 90% level C3. Actively models and demonstrates concepts, learning strategies and procedures C7 Maintains high accurate responding rate in teacher-led activities: - repeats practice opportunities until students not making errors - delivers instructional cues and prompts - provides error correction procedures - uses prompting and modeling following errors. C8. Provides error drills on missed concepts and reviews difficult concepts C9 Gives summary of lesson content and integrates lesson content with other lessons and experiences. |
C1. Provides review of previous day's concepts at beginning; actively tests students' understanding and retention of previous lesson concepts C2. Provides a clear overview of the lesson: States the purpose and objectives of the lesson. Explains in terms of teachers' and students' actions. Tells students what they will be accountable for doing C5. Provides frequent questions to evaluate students' mastery of lesson concepts C6. Evaluates students' understanding of seatwork tasks and cognitive processes by asking "what, how, when, why" questions. |
Table 2. COS Items in Discriminant Function 1: Student Engagement.
Function 1 - Accounts for 95% of variance N=63, eigenvalue = 6.93 |
B2 States expectations for seatwork in advance B3 Establishes clear lesson routines that signal a beginning and an end B4 Gains students' attention at the beginning of the lesson and maintains it during instruction at 90% level B5 Monitors transitions by scanning and circulating among students C7 Maintains high accurate responding rate in teacher-led activities: - repeats practice opportunities until students not making errors - delivers instructional cues and prompts - provides error correction procedures - uses prompting and modeling following errors. |
Table 3: Functions at group centroids
(Teachers grouped by COS score)
Teachers grouped by COS score |
N |
Function |
Lowest 1-12.5% |
8 |
- 5.46 |
13 – 25% |
8 |
- 3.93 |
25-37.5% |
8 |
- 2.78 |
38 - 50% |
7 |
- 1.39 |
50- 62.5% |
8 |
.49 |
63 – 75% |
8 |
1.57 |
75- 82.5% |
8 |
2.39 |
Highest 83 – 100% |
8 |
2.88 |
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