EARCOME 7 The 7th ICMI-‐East Asia Conference on Mathema8cs Educa8on In Pursuit of Quality Mathema8cs Educa8on for All Cebu City, Philippines 11 – 15 May 2015
Identifying The Pedagogical Features Influencing The Quality Of Mathematics Classroom Practice Masitah Shahrill
Sultan Hassanal Bolkiah Institute of Education Universiti Brunei Darussalam Brunei Darussalam
David J. Clarke Melbourne Graduate School of Education University of Melbourne Australia
Introduc)on In order to inform the mathema.cs classroom prac.ces in Brunei Darussalam, lesson sequences of four Year 8 mathema.cs classrooms were video recorded and analysed (Shahrill, 2009).
This study drew upon the coding scheme that was used in the TIMSS 1999 Video Study (Hiebert et al., 2003).
Among the many TIMSS codes were five codes specifically iden.fying the pedagogical features that influenced the lesson clarity and flow of the mathema.cs lesson sequences. 2
Pedagogical Features that Influence Lesson Clarity and Flow
• Goal statements • Lesson Summary Statements • Outside Interruptions • Non-‐Mathematical Segments • Public Announcements that were unrelated to the current Mathematics assignment
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Enhances clarity of key points given to the students May break the flow of the mathema8cs lessons
Review of the Literature Literature
Topic
Their Bindings
Relevance
Brophy Use of goal • Students should be (1999); Furner statements motivated to acquire and Gonzalez-‐ in lessons knowledge with DeHass (2011) learning goals. • Students with learning goals deJine individual improvement as success.
Goal statements contribute to long-‐ term effective learning.
Murrell and Surber (1987); Kintsch and van Dijk (1978)
Processes involved in sumarisation improve students’ high order skills.
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Use of • Effort to identify main summary points helps students statements remember the ideas. in lessons • Making a summary involves deletion, generalisation and construction of data.
Review of the Literature Literature National Center for Education Statistics, (1993); Ranallo (1997)
Topic
Their Bindings
Instructional • Effective use of Events that time in the instructional time has a reduce classroom great inJluence on instructional time
student learning opportunities and outcomes. • However, only a portion of allotted time was effectively used for instructional purposes
Leonard, (2003); Outside • Distract students from Foerde, interruptions the class activity Knowlton and • Decrease overall Poldrack (2006)
learning process
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Relevance
could be either within or beyond the teacher’s control.
Outside interruptions break the the Jlow of the lesson.
Methodology • Sample used in this study were four Year 8 Mathematics classes. • Data was collected by video recording the lessons. • In total, 20 sets of video recorded lessons were coded. • To interpret the four Brunei classrooms and connect them to the TIMSS-‐99 Video Study data, the codes used in the TIMSS-‐99 Video Study were adapted and applied to the Brunei video data. 6
Methodology • In the TIMSS-‐99 Video Study, the videotaping was carried out for each teacher only once, capturing only a single classroom lesson (Hiebert et al., 2003). That would not provide us with an adequate representation of the practices of the four mathematics classrooms for meaningful comparison to be undertaken with the diversity of activity types documented in the national data sets generated for the TIMSS-‐99 Video Study.
• Therefore, we have used an adaptation of the data generation methods used in the Learner’s Perspective Study (henceforth, referred to as the LPS Project, see Clarke, Keitel & Shimizu, 2006) to give us a more substantial body of data, so we can characterise the practices of each of the four Brunei classrooms in sufficient detail in order to make comparison with the large data set of TIMSS-‐99 Video Study possible. 7
Limita)on One of the limitations in this study is the restrictive use of the term ‘the Brunei data’. Because this study included only four mathematics teachers in Brunei in comparison to the 50-‐140 teachers documented in each of the countries in the TIMSS-‐99 Video Study, the extent to which a connection can be constructed between the two studies has to be argued carefully.
Therefore, when reporting on the data obtained in Brunei, the term ‘the Brunei data’ have been used consistently instead of ‘Brunei’. It is important to note that the use of the term ‘the Brunei data’ should not be interpreted as the data representing the whole of Brunei. Rather, the term ‘the Brunei data’ was used to represent the data from all four of the Brunei teachers only. 8
Goal Statements
FINDINGS
Goal statements were defined as explicit written or verbal statements by the teacher about the specific mathematical topic(s) that would be covered during the lesson. To count as a goal statement, the statement had to preview the mathematics that students encountered during at least one-‐third of the lesson time (Hiebert et al., 2003, pp. 59-‐60).
80% of eighth-‐grade mathematics lessons in the Brunei data contained at least one goal statement. 9
Lesson Summary Statements
FINDINGS
Summary statements highlight points that have just been studied in the lesson. They were defined as statements that occurred near the end of the public portions of the lesson and described the mathematical point(s) of the lesson (Hiebert et al., 2003, p. 60).
Data showed that lesson summaries given in the Brunei data were less common than goal statements. At least 10% of lessons contained at least one summary statement. 10
Outside Interrup)ons
FINDINGS
One kind of interruption comes from outside the classroom. Examples of outside interruptions include announcements over the intercom, individuals from outside the class requiring the teacher’s attention, and talking to a student who has arrived late (Hiebert et al., 2003, p. 61).
It was found that 55% of lessons in the Brunei data were interrupted. This is significantly higher than the TIMSS-‐countries. 11
Outside Interrup)ons
FINDINGS
Examples of interrup1ons recorded in the Brunei lessons were: § the teacher remarking on the student(s) late arrival into class; § school bell ringing over the intercom with the teacher commen1ng about it; § individuals from outside the class requiring the teacher’s aAen1on, an announcement over the intercom that caused an abrupt end to the class; § and some sort of interrup1on from outside the classroom (noises coming from the roof) that disrupted the classroom ac1vi1es (students stopped working while the teacher commented about it). It was found that 55% of lessons in the Brunei data were interrupted. This is significantly higher than the TIMSS-‐countries. 12
Non-‐Mathema)cal Segments
FINDINGS
Another type of potential interruption to the flow of lessons occurred when the class engaged in non-‐mathematical activities after the mathematics portion of the lesson had begun. By definition, a non-‐mathematical segment was any activity unrelated to the teaching and learning of mathematics that lasted for at least 30 seconds. When these segments occurred at the beginning of the lesson (e.g., when teachers and students attended to such things as greetings, checking attendance, or discussing the videotaping procedure) or at the end of lesson (e.g., when teachers and students talked socially, or discussed when and where future lessons would be held), they did not interrupt the flow of the lesson. So, the segments of interest here were those that occurred within the mathematics portion of the lesson (Hiebert et al., 2003, p. 62).
The result obtained for the Brunei data is 15%, which is not as significant is the data for outside interruptions (55%). 13
Unrelated Public Announcements
FINDINGS
A second way in which teachers’ actions might affect the flow of the lesson and potentially interrupt students’ work occurred when teachers made an off-‐topic announcement during private work time. This type of announcement was defined as one containing either no mathematical information (for example, the teacher might have addressed a disciplinary problem) or mathematical information that appeared to be unrelated to the assignment at hand. There was no minimum time length for this code, so a public announcement of this sort could be of varying length (Hiebert et al., 2003, p. 63).
The graph shows that 45% of lessons in the Brunei data were interrupted by unrelated public announcements. This is a percentage higher than the other TIMSS-‐countries except The Netherlands. 14
FINDINGS
Unrelated Public Announcements
• Further inves1ga1ons revealed 3 of the 4 Brunei teachers made several off-‐topic announcements completely unrelated to the current mathema1cs assignment during the lessons’ private work 1me. • In total, there were 29 instances recorded for all three teachers. • Only T4 made no off-‐topic announcements in any of her videotaped lessons. • Therefore, this type of unrelated announcements could poten1ally interrupt the students’ concentra1on whilst they are working on the current mathema1cs assignment during the private work 1me. The graph shows that 45% of lessons in the Brunei data were interrupted by unrelated public announcements. This is a percentage higher than the other TIMSS-‐countries except The Netherlands. 15
Summary • A signiJicantly higher percentage of lessons in the Brunei data (55%) were interrupted from outside the classroom, in comparison to the TIMSS-‐countries (between 8% and 32%). And, based on the results obtained, the interruptions recorded from the Brunei lessons mostly occurred outside the mathematics portion of the lesson.
• The proportion of Year 8 mathematics lessons that contained public announcements unrelated to the current mathematics assignment was greater in the Brunei data (45%) and the Netherlands (64%), in comparison to the other TIMSS-‐countries.
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Conclusions All these kinds of interruptions suggest that there may be frequent instances of uneven 9low within the entire length of the mathematics lessons taught by the four teachers involved in this study. The time spent in learning mathematics may be affected because these ‘interrupted’ lesson times could have been used effectively for instructional purposes.
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References Brophy, J. (1999). Toward a model of the value aspects of motivation in education: Developing appreciation for particular learning domains and activities. Educational Psychologist, 34(2), 75-‐85. Clarke, D. J., Keitel, C., & Shimizu, Y. (Eds.). (2006a). Mathematics classrooms in twelve countries: The insider’s perspective. Rotterdam: Sense Publications. Foerde, K., Knowlton, B.J., & Poldrack, R.A.(2006). Modulation of competing memory systems by distraction. Proceedings of the National Academy of Sciences, 103(31), 11778–11783. Furner, J.M. and Gonzalez-‐DeHass, A. (2011). How do Students’ Mastery and Performance Goals Relate to Math Anxiety? Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 227-‐242 Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., Chui, A., Wearne, D., Smith, M., Kersting, N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, C., Gonzales, P., & Stigler, J. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study. Washington, DC: U.S. Department of Education, National Center for Education Statistics. Kintsch, W., & van Dijk, T. A. (1978). Toward a model of text comprehension and production. Psychological Review, 85(5), 363-‐394. Leonard, L. J. (2003). Optimising by minimising: Interruptions and the erosion of teaching time. Journal of Educational Enquiry, 4(2), 15–29. Murrell, P. C., Jr., & J.R. Surher (1987). Constructing macrostructure: The Effect of Generative Summarization on the Comprehension of Main Ideas from Lengthy Expository Text. Paper presented at the annual meeting of the American Educational Research Association, Washington, DC. Ranallo, J., Bareham, S., & Chandler, M. (1997). Student conduct management: The passionate side of teaching. Vancouver, BC: Eduserv. Shahrill, M. (2009). From the general to the particular: Connecting international classroom research to four classrooms in Brunei Darussalam. Unpublished doctoral dissertation, University of Melbourne, Melbourne, Australia. 13
THANK YOU
Acknowledgment Appreciation Ms Cheryl Lee (MTeach Sec Ed Maths TC from cohort January 2015) in assisting with the preparation.
Masitah Shahrill (
[email protected]) David J. Clarke (
[email protected]) 19
