Can High Achievement be Attributed to Better Teaching? - Results of the TIMSS Video Study Bogota, Columbia, November 2006 Frederick K.S. Leung The University of Hong Kong Introduction East Asian students have consistently out-performed their counterparts around the world in international comparisons of mathematics achievement. Can the high achievement be explained by better teaching in the East Asian classroom? This presentation reports some of the results of the TIMSS Video Study in an attempt to portray the mathematics teaching in the East Asian classroom Implications of the findings will also be discussed TIMSS 1999 Video Study (Math) Goal: Describe and compare eighth-grade mathematics teaching across seven countries (Australia, Czech Republic, Hong Kong SAR, Japan*, Netherlands, Switzerland, United States) * The 1995 Japanese data were re-analyzed using the 1999 methodology in some of the analysis Sampling and Data Collection National probability sample of 8th-grade math lessons: a Video Survey One lesson per teacher Sampled across the school year Standardized camera procedures 638 lessons, from 50 (Japan) – 140 (Switzerland) Data Coding and Analysis An international team developed codes to apply to the video data. Fluently bilingual coders in the international video coding team applied 45 codes in seven coding passes to each of the videotaped lessons. Three marks (i.e., the in-point, out-point, and category) were evaluated and included in the measures of reliability. If, after numerous attempts, reliability measures fell below the minimum acceptable standard, the code was dropped from the study. The Mathematics Quality Analysis Group A specialist group in mathematics and teaching mathematics at the post-secondary level reviewed a randomly selected subset of 120 lessons (20 lessons from each country except Japan). The international video coding team created expanded lesson tables for each lesson in this subset. The tables included details about the classroom interaction, the nature of the math problems worked on, mathematical generalizations, and other relevant information. The tables were “country-blind,” with all indicators that might reveal the country removed. Instructional Practices in East Asia as Portrayed by the Analysis of the Codes 1. Dominance of teacher talk In all countries in the study, the teachers did a lot of talking, and considerably more than their students Hong Kong and Japan differ considerably in the amount of teacher talk Average Number of Teacher and Student Words Per Lesson 7000 6000 5536 5452 5902 5798 5148 5360 5000 4000 3000 2000 1000 810 824 640 766 1016 1018 0 AU CZ HK Average number of teacher words JP NL US Average number of student words Ratio of teacher and student talk Hong Kong and Japanese teachers spoke much more relative to their students “Hong Kong SAR eighth-grade mathematics teachers spoke significantly more words relative to their students (16:1) than did teachers in Australia (9:1), the Czech Republic (9:1), and the United States (8:1).” (p. 109, Chapter 5) When we factor in the relatively large class size (about 40), the reticence of East Asian students is striking Number of Teacher Words Per 1 Student Word Average Number of Teacher Words to Every One Student Word Per Lesson 20 16 16 13 12 9 9 AU CZ 10 8 8 4 0 HK JP NL US 2. More opportunities to learn new content 75% of lesson time in the East Asian classroom spent on dealing with new content Corresponding figures for other countries ranged between 42% (Czech Republic) and 63% (Switzerland) Inference: East Asian students learn more mathematics than students in other countries? Average percentage of lesson time devoted to various purposes 3. Mathematics problems worked on more complex Procedural complexity of problems: “the number of steps it takes to solve a problem using a common solution method” (p.70) Japanese students worked on procedurally more complex problems Problems Hong Kong students worked on not particularly complex, although the percentage (63%) of low complexity problems is relatively small Average percentage of problems at each level of procedural complexity Percent of Problems 100 80 8 11 8 25 29 16 6 39 25 12 22 6 27 60 40 45 77 64 63 69 65 67 20 17 0 AU CZ HK JP NL SW US Low C omple xity Mode rate C omple xity High C omple xity Problem complexity (cont’d) Another measure of problem complexity: length of time students spent working on the problem (more or less than 45 seconds) Conclusion: East Asian students have more opportunities to work on procedurally more complex problems which required a longer duration to solve Average percentage of problems that were worked on longer more than 45 s 4. Problems unrelated to real-life Majority of problems in the East Asian classroom were expressed in mathematical language and symbols, and set in contexts unrelated to real life Similar to classrooms in Czech Republic, and differ markedly from classrooms in the Netherlands Average Percentage of Problems Per Lesson Set Up With a Real Life Connection or With Mathematical Language or Symbols Only 5. More proof Problems East Asian students worked on involved more proof The emphasis is particularly marked in Japan The practice in Hong Kong more in line with Switzerland Percentage of problems that contained at least one proof Instructional practices as portrayed by the analysis of the codes • Dominance of teacher talk • Students have more opportunities to learn new content • Students solve problems that are more complex and are unrelated to real-life • More proof Quality of Content as judged by the Math Quality Analysis Group (based on the same data set) Japanese not in the analysis “Readers are urged to be cautious in their interpretations of these results because the subsample, due to its relatively small size, might not be representative of the entire sample or of eighth-grade mathematics lessons in each country.” (p. 190, Appendix D) 1. Relatively advanced content “the ratings for countries with the most advanced (5) to the most elementary (1) content in the subsample of lessons, were the Czech Republic and Hong Kong SAR (3.7), Switzerland (3.0), the Netherlands (2.9), the United States (2.7), and Australia (2.5)” (p. 191, Appendix D) Percent of Sub-sampled Lessons Percentage of Lessons in Sub-sample at each Content Level 100 15 0 0 20 20 80 5 0 20 30 35 30 60 35 45 40 40 40 30 45 20 20 0 10 15 AU CZ 40 0 5 0 HK 25 20 15 10 15 15 NL SW US Advanced Moderate/Advanced Moderate Elementary/Moderate Elementary 2. More deductive reasoning Deduction reasoning = “deriving conclusions from stated assumptions using a logical chain of inferences.” The reasoning did not need to include a formal proof, only a logical chain of inferences with some explanation. Percent of Sub-sampled Lessons Percentage of Lessons in Sub-sample that Contained Deductive Reasoning 100 80 60 40 15 20 0 0 AU 5 CZ 10 10 SW US 5 HK NL 3. More coherent Coherence was defined by the group as the (implicit and explicit) interrelation of all mathematical components of the lesson. Percent of Sub-sampled Lessons Percentage of Lessons in Sub-sample Rated at Each Level of Coherence 100 30 80 30 55 60 60 20 40 15 20 15 0 AU Mixed 5 CZ 15 Moderately fragmented 5 20 0 Moderately thematic 20 10 10 15 65 90 30 Thematic 0 10 0 0 HK 10 5 NL 20 Fragmented 35 10 0 SW 0 US 4. More fully developed presentation Presentation = “the extent to which the lesson included some development of the mathematical concepts or procedures”. Development required that mathematical reasons or justifications were given for the mathematical results presented or used. Presentation ratings took into account the quality of mathematical arguments. Higher ratings meant that sound mathematical reasons were provided by the teacher (or students) for concepts and procedures. Mathematical errors made by the teacher reduced the ratings. Percent of Sub-sampled Lessons Percentage of Lessons in Sub-sample Rated at Each Level of Presentation 100 80 0 40 5 10 20 15 20 30 45 55 30 0 AU 10 Substantially developed 20 Moderately developed Partially developed 20 10 Fully developed 40 35 20 25 30 60 40 5 15 20 0 CZ 10 0 HK 20 5 10 15 NL SW 40 US Undeveloped 5. Students more likely to be engaged Student engagement = “the likelihood that students would be actively engaged in meaningful mathematics during the lesson”. A rating of very unlikely (1) indicated a lesson in which students were asked to work on few of the problems and those problems did not appear to stimulate reflection on math concepts or procedures. A rating of very likely (5) indicated a lesson in which students were expected to work actively on, and make progress solving, problems that appeared to raise interesting mathematical questions for them and then to discuss their solutions with the class. Percent of Sub-sampled Lessons Percentage of Lessons in Sub-sample Rated at Each Level of Student Engagement 100 80 10 10 35 15 20 10 15 25 Probable 55 30 30 30 Possible 30 20 30 0 0 AU 10 5 CZ 30 5 0 HK 0 Very likely 20 40 60 40 10 45 30 Doubtful Very unlikely 10 10 10 15 NL SW US 6. Overall quality Overall quality judgment: “the opportunities that the lesson provided for students to construct important mathematical understandings” (p. 199, Appendix D) “the relative standing of Hong Kong SAR was consistently high ….” (p. 200, Appendix D) Percent of Sub-sampled Lessons Percentage of Lessons in Sub-sample Rated at Each Level of Overall Quality 100 80 5 30 30 15 20 0 25 High 35 40 60 20 35 30 40 20 5 15 45 20 15 15 15 5 0 AU CZ 15 25 10 0 HK 15 40 10 NL SW Moderate Moderately low 25 20 20 Moderately high US Low General Ratings for Each Overall Dimension of Content Quality of Lessons 5.0 4.0 3.0 HK SW AU NL CZ US HK SW CZ AU NL US HK CZ SW AU NL US 2.0 HK CZ SW AU NL US 1.0 0.0 Coherence Presentation Student engagement Overall quality AU CZ HK NL SW US Quality of the Content as judged by the Math Quality Analysis Group Relatively advanced content More deductive reasoning More coherent More fully developed presentation Students are more engaged, and Overall quality is high Discussion Some characteristics of the East Asian classroom found in this study (large class size, dominance of teacher talk, reticence of students, abstract problems unrelated to real-life) seem to be at odds with modern theories of learning Despite the rhetoric of constructivism and studentcentred learning to the contrary, the findings show that meaningful learning can still take place in a teacher directed classroom with a large class size Teacher dominance with a lot of teacher talk does not necessarily lead to passive, receptive learning Much depends on the content of the teacher talk and how it is delivered, and whether the talk can stimulate students to be engaged in mathematics The data in this study suggest that the kind of teacher talk in the East Asian classroom was able to direct students to be engaged in the lesson Indeed, a well-taught teacher-dominated lesson may better provide the mathematical coherence which students need in their construction of mathematical knowledge rather more effectively than many student-led approaches. Mathematics content covered in East Asian classrooms East Asian students learned more new content than their counterparts in the West The content was more complex and advanced There were more proofs and more use of mathematical language Proof and the use of maths language In many countries, mathematical language is considered too alien and proof too abstract for school students Both are deemed to be too difficult for school students and are thus excluded from the curricula However, both have traditionally been regarded as distinctive features of mathematics, and it seems that they are still judged to be so in the East Asian classroom Neither was stressed in TIMSS and PISA A firm foundation in mathematics laid for East Asian students through emphasis on mathematical language and proof that enables these students to do well in the less abstract tasks in the international tests? “In a milieu which seems to believe that the most effective way to enhance understanding and raise attainment levels is through an improved pedagogy, the clear indication that the high achievement of East Asian students is related to the high quality of the mathematics content to which they are exposed, should act as a sharp reminder that without quality content, quality learning will not take place - no matter how ingenious the teaching method.” Expectation on students East Asian teachers have higher expectations of their students on the kind of mathematics to be learned The level of expected mathematics achievement in many Western countries seems to be declining Mathematics is considered by students and teachers alike as a difficult subject Majority of student population not expected to learn more advanced mathematics, and are not even expected to do well in elementary mathematics The low student achievement becomes a selffulfilling prophecy Teacher competence East Asia teachers are sufficiently competent in mathematics to deliver complex and advanced content (Ma, 1999, Leung and Park, 2002)? More coherent and better developed presentation may be attributed to the mathematical and pedagogical competence of the teachers Ma (1999): competence in mathematics and pedagogy are intrinsically related: without a profound understanding of mathematics, it is not possible to invoke the appropriate pedagogy. Scholar teacher In East Asian or “Confucian Heritage” Culture (Biggs, 1996), the ideal of the “scholar teacher” is that of an expert or a learned figure in the subject matter Teaching skills are also important, but teachers will not be respected if they are not expert in the area they teach This image of the scholar-teacher may provide incentives for East Asian teachers to strive to attain high levels of competence in the subject matter as well as in pedagogy Conclusion No simple casual relation between classroom teaching and student achievement can be drawn, but East Asian teachers did teach differently from their counterparts in the West Classroom practices are deeply rooted in the underlying cultural values of the classroom and the wider society Simple transplant of educational practice from high achieving countries to low achieving ones would not work One cannot transplant the practice without transplanting the culture as well Conclusion (cont’d) We should identify not only the superficial differences in educational practice, but the intricate relationship between the educational practice and the underlying culture of other countries Through identifying the commonality and differences of both the educational practices and the underlying cultures, we may then determine how much can or cannot be borrowed from another culture. 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