Chapter 7: Classroom Characteristics And Instruction
Chapter 7Classroom Characteristics and InstructionTo place students’ mathematics achievement results in instructional contexts,this chapter begins by providing information about class size and thecharacteristics of students in mathematics classes. The focus of the rest ofthe chapter is on the instructional activities used in teaching and learningmathematics and how these activities are supported with technology use,homework, and assessment.How Do the Characteristics of Mathematics ClassroomsImpact Instruction?Because having larger or smaller classes can impact instructional choices,TIMSS asked teachers about the size of their mathematics classes. The classsize data are shown in Exhibits 7.1 and 7.2. Exhibit 7.1 presents trends inaverage class sizes back to 1995, and across the distribution of different classsizes. Exhibit 7.2 presents the TIMSS 2007 distribution of students in differentsizes of classes in relation to their mathematics achievement.As presented in Exhibit 7.1, in TIMSS 2007 across participating countriesat the fourth grade, the average size of mathematics classes was 26. Thisrepresented a decrease in class size in eight of the participating countries. Twoof the benchmarking provinces, Ontario and Quebec, also had decreases.At the eighth grade, the average class size of 29 represented a decrease inclass size in 19 countries. Also among the benchmarking participants,the Basque country in Spain and the Canadian province of Ontario hadsmaller average class sizes in TIMSS 2007 than in previous assessments.
chapter 7: classroom characteristics and instruction268Overall Average Class SizeCountryDifferencefrom 2003Differencefrom 199528 (0.8)31 (1.6)24 (0.4)20 (0.3)31 (0.3)32 (1.0)22 (0.4)21 (0.3)30 (0.7)28 (0.5)22 (0.6)22 (0.2)35 (0.4)22 (0.4)24 (0.5)20 (0.2)31 (0.4)22 (0.5)25 (0.5)22 (0.8)20 (0.3)29 (0.8)22 (0.4)26 (0.4)21 (0.5)28 (0.0)21 (0.4)25 (0.4)38 (0.2)21 (0.3)19 (0.3)22 (0.5)25 (0.4)23 (0.4)23 (0.4)46 (1.7)26 (0.1) 2 (2.2)–1 (0.7) –1 (0.4) 0 (0.9) 1 (0.6)–2 (0.6)–3 (0.8)0 (0.4)–1 (0.5) 0 (0.9)–1 (0.5)–––1 (0.6)–1 (0.5)0 (0.6) 0 (0.5)–1 (0.6)0 (0.3) 0 (0.5) –6 (0.6) 0 (0.5) –1 (0.6)0 (0.6) 0 (0.7) –1 (0.7) –1 (0.7)0 (0.7)–7 (1.4)–––2 (0.6) ––1 (1.1) –1 (0.9)–3 (0.7)2 (0.8) –1 (0.6)–1 (0.3) –3 (0.5) –1 (0.7) 22 (0.5)22 (0.5)––21 (0.5)24 (0.7)23 (0.4)24 (0.3) –2 (0.6)–2 (0.4)2007AlgeriaArmeniaAustraliaAustriaChinese TaipeiColombiaCzech RepublicDenmarkEl SalvadorEnglandGeorgiaGermanyHong Kong SARHungaryIran, Islamic Rep. NetherlandsNew ZealandNorwayQatarRussian FederationScotlandSingaporeSlovak RepublicSloveniaSwedenTunisiaUkraineUnited StatesYemenInternational Avg.Benchmarking ParticipantsAlberta, CanadaBritish Columbia, CanadaDubai, UAEMassachusetts, USMinnesota, USOntario, CanadaQuebec, Canadarsrssrsrsrrrrriiiiiiii0 (1.2) –––2 (0.7)–1 (0.7)1-19 Students2007Percentof Studentsiiiihii20-32 StudentsDifferencein Percentfrom 2003Differencein Percentfrom 199511 (2.8)24 (3.3)19 (3.0)37 (2.9)3 (1.2)19 (3.3)31 (3.5)34 (3.9)20 (2.7)8 (1.9)37 (3.8)21 (2.4)1 (0.7)33 (3.7)25 (2.7)44 (2.6)7 (1.5)30 (4.5)7 (2.8)44 (2.4)37 (3.0)17 (3.3)27 (3.3)13 (2.1)42 (3.3)8 (0.1)33 (2.7)16 (2.8)0 (0.0)34 (2.5)46 (2.9)36 (3.4)20 (2.8)30 (3.3)26 (2.6)9 (2.1)24 (0.5) 2 (5.3)2 (4.3) 2 (1.4) –3 (3.3) –1 (1.1)14 (4.7)9 (3.8)–1 (4.3)3 (1.7) 12 (4.6)8 (4.2)––3 (4.8)4 (2.6)4 (4.6) 0 (4.2)–1 (4.4)0 (0.1) 1 (5.1) 15 (3.2) 3 (3.6) 6 (3.9)–4 (6.2) 7 (5.2) 1 (2.9) 1 (0.7)1 (6.0)10 (4.6)––6 (1.6) ––2 (6.3) 0 (5.4)2 (3.5)–9 (6.3) 2 (3.6)0 (0.0) 20 (5.3) 8 (4.1) 25 (2.9)29 (3.7)––24 (5.6)16 (4.2)18 (3.5)16 (2.5) 7 (4.5)11 (2.9)hhhhh0 (8.7) ––2 (5.2)8 (5.5)2007Percentof StudentshhhDifferencein Percentfrom 200360 (4.3)50 (3.8)80 (3.0)63 (2.9)45 (3.7)24 (4.7)69 (3.5)66 (3.9)37 (4.1)80 (3.0)50 (4.5)79 (2.4)25 (3.3)67 (3.7)59 (3.8)56 (2.6)47 (2.9)68 (4.6)88 (3.4)49 (3.0)63 (3.0)42 (4.3)71 (3.5)81 (2.4)53 (3.6)75 (0.2)67 (2.7)79 (3.0)6 (1.3)65 (2.6)53 (3.0)60 (3.6)69 (3.8)65 (3.5)69 (2.8)17 (4.0)58 (0.6) –2 (6.3)–2 (4.4) 1 (5.3) 12 (5.6) –9 (5.4)–13 (4.8)5 (5.8)1 (4.3)6 (4.2) –12 (5.2)–7 (4.2)–––3 (5.1)0 (3.5)–7 (5.0) 2 (4.2)3 (5.1)1 (1.8) –2 (5.1) 12 (5.8) –5 (3.9) 70 (3.4)69 (3.8)––76 (5.6)83 (4.3)78 (3.9)83 (2.5) –8 (5.2)–11 (3.0)Differencein Percentfrom 1995hiihi –4 (4.3)4 (6.2) –6 (5.2) 2 (5.2) 5 (6.6)1 (6.0)19 (6.8)–––2 (5.4) –––8 (6.5) 10 (5.6)27 (5.0)4 (6.5) –2 (4.3)2 (1.6) –21 (5.3) –8 (4.3) –4 (8.9) –––2 (5.5)–8 (5.5)h 2007 significantly higheri 2007 significantly lowerBackground data provided by teachers.( ) Standard errors appear in parentheses. Because results are rounded to the nearestwhole number, some totals may appear inconsistent.A dash (–) indicates comparable data are not available.An “r” indicates data are available for at least 70 but less than 85% of the students. An “s”indicates data are available for at least 50 but less than 70% of the students.A diamond ( ) indicates the country did not participate in the assessment.hhiSOURCE: IEA’s Trends in International Mathematics and Science Study (TIMSS) 2007Exhibit7.1:7.1 bitSizeforforMathematicsInstructionwithTrends
chapter 7: classroom characteristics and instruction26933 or More se TaipeiColombiaCzech RepublicDenmarkEl SalvadorEnglandGeorgiaGermanyHong Kong SARHungaryIran, Islamic Rep. NetherlandsNew ZealandNorwayQatarRussian FederationScotlandSingaporeSlovak RepublicSloveniaSwedenTunisiaUkraineUnited StatesYemenInternational Avg.Benchmarking ParticipantsAlberta, CanadaBritish Columbia, CanadaDubai, UAEMassachusetts, USMinnesota, USOntario, CanadaQuebec, Canada2007Percentof StudentsrsrssrsrsrrrrrDifferencein Percentfrom 200329 (4.0)26 (3.6)2 (1.2)0 (0.0)51 (3.4)57 (4.4)0 (0.0)0 (0.0)43 (3.8)12 (2.4)13 (2.2)0 (0.0)74 (3.4)0 (0.0)16 (2.9)0 (0.0)45 (3.2)3 (1.2)5 (1.9)6 (2.0)0 (0.0)41 (3.9)2 (1.3)6 (1.7)5 (1.9)17 (0.2)0 (0.3)5 (1.6)94 (1.3)1 (0.6)1 (0.6)4 (1.6)11 (2.7)5 (1.4)5 (1.3)74 (4.1)18 (0.4) 0 (6.0)0 (2.0) –3 (5.1) –8 (5.0) 10 (5.5)–1 (0.9)–14 (4.9)0 (0.0)–10 (4.3) –1 (3.3)0 (0.3)––0 (1.9)–4 (2.8)3 (2.3) –1 (0.9)–2 (3.0)–1 (1.8) 1 (0.6) –27 (5.1) 2 (1.7) 4 (1.8)1 (0.8)––0 (0.0)1 (1.2)4 (1.4)1 (0.2) 1 (2.1)1 (0.2)Differencein Percentfrom 1995iii –2 (2.3)0 (0.0) –1 (0.1) –3 (4.6) –5 (6.6)–1 (1.0)–30 (7.1)–––3 (5.6) ––6 (2.0) –10 (3.5)–29 (4.7)5 (1.9) 0 (2.8)–2 (1.7) 1 (0.6) 0 (2.2) 4 (1.8) ––0 (2.4)1 (0.2)iSOURCE: IEA’s Trends in International Mathematics and Science Study (TIMSS) 2007Exhibit7.1:7.1 Trends(Continued)hiihhh 2007 significantly higheri 2007 significantly lower
chapter 7: classroom characteristics and instruction270Overall Average Class a and HerzegovinaBotswanaBulgariaChinese TaipeiColombiaCyprusCzech RepublicEgyptEl SalvadorEnglandGeorgiaGhanaHong Kong SARHungaryIndonesiaIran, Islamic Rep. ofIsraelItalyJapanJordanKorea, Rep. estinian Nat'l Auth.QatarRomaniaRussian FederationSaudi ArabiaScotlandSerbiaSingaporeSloveniaSwedenSyrian Arab RepublicThailandTunisiaTurkeyUkraineUnited States¶ MoroccoInternational Avg.Benchmarking ParticipantsBasque Country, SpainBritish Columbia, CanadaDubai, UAEMassachusetts, USMinnesota, USOntario, CanadaQuebec, CanadarrrsrrsrrsssrrrrsrsrsrrrDifferencefrom 200337 (0.7)25 (0.4)26 (0.3)31 (0.1)24 (0.4)38 (0.4)22 (0.3)35 (0.5)35 (0.6)24 (0.2)24 (0.3)39 (0.6)29 (0.8)26 (0.6)23 (0.6)46 (1.9)37 (0.5)21 (0.5)38 (0.9)26 (0.5)33 (0.4)22 (0.2)34 (0.5)35 (0.7)37 (0.4)30 (0.5)26 (0.6)25 (0.3)36 (0.4)22 (0.0)25 (0.4)32 (0.4)38 (0.5)27 (0.0)21 (0.3)21 (0.3)30 (0.8)25 (0.5)24 (0.4)38 (0.2)16 (0.2)23 (0.5)31 (0.6)38 (0.6)32 (0.4)33 (0.7)25 (0.4)24 (0.4)34 (0.8)29 (0.1) –2 (1.0)–1 (0.5)–1 (0.2) 0 (0.5)–1 (0.6)–2 (0.7) –2 (0.2) 1 (0.8) 0 (0.7) 9 (2.1)–2 (0.6)–1 (0.6)–1 (1.0)–3 (0.7)0 (0.6)0 (0.3)–2 (0.6)1 (1.0)0 (0.5) –2 (1.1)0 (0.4)–1 (0.5) –1 (0.5) –1 (0.7) –3 (0.6)–2 (0.6)–––2 (0.7)–2 (0.5)0 (0.3)–5 (0.4)2 (0.6) –2 (0.4) 0 (0.6)––22 (0.3)26 (0.5)27 (0.7)22 (0.6)27 (1.3)26 (0.4)29 (0.4)–2 (0.5) 0 (0.6)0 (0.5)Differencefrom 1999iiiihiiiiiiiihii –– –1 (0.6)–4 (0.7) –4 (0.3)0 (0.5) –– 0 (0.8)0 (0.7)–16 (3.2)–7 (0.8)7 (0.8)2 (0.4)–2 (0.6)–1 (1.0)–7 (0.9) 2 (0.5)–3 (1.0) –3 (0.6)–3 (0.6) 1 (0.4)–– –8 (1.8)–2 (0.5)–– –7 (1.5)–– –1 (0.8) –2 (1.5) –1 (0.7)0 (0.6)1-24 Students2007Percentof StudentsDifferencefrom 1995iiiihhiihiiihiii 0 (0.5) –4 (1.6)–7 (0.5)–1 (0.6) 1 (0.8) –2 (0.8)–1 (0.7) –10 (1.3)–––––3 (0.6) –21 (3.0)–– 4 (0.6) 1 (0.7) –5 (0.9)–4 (0.5) –1 (0.6) 2 (0.4)–9 (0.4)3 (0.8) –– –4 (1.1)–– –––2 (0.9)1 (1.1)iiiiiihiihihiiDifferencein Percentfrom 20035 (2.1)40 (4.0)30 (2.8)6 (0.7)48 (3.6)1 (0.6)59 (3.5)4 (1.8)13 (2.5)54 (2.7)49 (4.3)4 (1.5)35 (3.7)30 (3.8)52 (5.2)13 (2.4)10 (1.9)72 (3.4)6 (1.8)35 (3.2)5 (1.2)73 (2.9)10 (2.1)13 (2.5)4 (1.4)12 (3.3)38 (4.3)35 (3.2)1 (0.8)71 (0.2)47 (3.9)10 (2.2)8 (1.6)20 (0.1)76 (2.9)63 (2.8)28 (3.6)43 (3.2)53 (3.9)2 (0.6)94 (1.0)63 (3.6)24 (3.6)11 (2.4)3 (1.2)18 (3.4)36 (3.2)57 (2.3)6 (3.3)30 (0.4) 0 (6.0)–1 (5.1)1 (1.0) 0 (0.9)–5 (5.5)0 (2.3) 33 (3.3) 1 (1.9) –4 (6.4) –3 (3.6)7 (2.2)8 (5.2)3 (2.5)13 (4.3)–5 (2.5)–5 (4.3)7 (2.5)–1 (3.8)3 (1.7) 7 (5.8)–4 (4.6)0 (1.0) 13 (5.4) 1 (2.6) 25 (5.3)16 (5.0)––10 (5.0)15 (5.3)–1 (0.9)25 (4.2)–8 (5.1) 1 (1.6) 2 (3.7)––68 (2.7)30 (4.0)34 (3.2)65 (6.0)32 (5.6)36 (4.0)20 (3.4)19 (4.5) 5 (5.6)6 (4.4)Differencein Percentfrom 1999hhhihhhhhhhh –– –2 (6.7)3 (2.1) 44 (3.7)–4 (7.1) –– 1 (2.9)1 (5.0)5 (1.8)24 (3.9)–36 (3.7)–14 (4.0)9 (2.1)5 (3.2)4 (1.4) –22 (5.1)0 (1.1) 27 (4.9)23 (4.7) –2 (1.4)–– 5 (2.7)–1 (2.0)–– 10 (4.2)–– 11 (7.5) 3 (8.9) 9 (6.2)6 (5.7)Differencein Percentfrom 1995hhhiihhihhh 0 (4.5) –– –5 (5.2)51 (3.2)10 (6.7) –3 (5.6) 4 (3.2)5 (5.3) 27 (4.1)––––8 (2.3) 2 (1.9)–– –50 (4.7) 6 (6.7) 36 (5.9)19 (4.6) 17 (4.9) –2 (1.6)54 (4.5)–11 (7.3) –– 11 (5.4)–– ––13 (6.5)6 (6.1)h 2007 significantly higheri 2007 significantly lowerBackground data provided by teachers.¶ Did not satisfy guidelines for sample participation rates (see Appendix A).( ) Standard errors appear in parentheses. Because results are rounded to the nearestwhole number, some totals may appear inconsistent.A dash (–) indicates comparable data are not available.An “r” indicates data are available for at least 70 but less than 85% of the students. An “s”indicates data are available for at least 50 but less than 70% of the students.A diamond ( ) indicates the country did not participate in the assessment.hhhihhhhhhSOURCE: IEA’s Trends in International Mathematics and Science Study (TIMSS) 2007Exhibit7.1:7.1 Trends(Continued)
chapter 7: classroom characteristics and instruction27125-40 a and HerzegovinaBotswanaBulgariaChinese TaipeiColombiaCyprusCzech RepublicEgyptEl SalvadorEnglandGeorgiaGhanaHong Kong SARHungaryIndonesiaIran, Islamic Rep. ofIsraelItalyJapanJordanKorea, Rep. estinian Nat'l Auth.QatarRomaniaRussian FederationSaudi ArabiaScotlandSerbiaSingaporeSloveniaSwedenSyrian Arab RepublicThailandTunisiaTurkeyUkraineUnited States¶ MoroccoInternational Avg.Benchmarking ParticipantsBasque Country, SpainBritish Columbia, CanadaDubai, UAEMassachusetts, USMinnesota, USOntario, CanadaQuebec, Canada2007Percentof StudentsrrrsrrsrrsssrrrrsrsrsrrrDifferencein Percentfrom 200364 (4.2)60 (3.9)70 (2.9)94 (0.7)52 (3.6)73 (3.8)41 (3.5)85 (3.3)66 (4.6)45 (2.7)51 (4.3)53 (3.6)51 (4.0)69 (3.7)47 (5.3)40 (4.2)44 (4.3)27 (3.3)62 (4.7)64 (3.3)92 (2.2)27 (2.9)85 (2.7)58 (4.4)78 (2.6)87 (3.2)58 (4.5)65 (3.2)80 (3.2)29 (0.2)51 (4.0)90 (2.2)51 (4.0)77 (0.2)24 (2.9)37 (2.8)61 (4.0)56 (3.1)47 (3.9)76 (2.5)6 (1.0)35 (3.4)65 (4.2)47 (3.7)96 (1.6)61 (3.9)63 (3.1)41 (2.3)79 (5.3)59 (0.5) 10 (5.9)2 (5.1)2 (1.0) –1 (5.6)5 (5.5)6 (4.8) –34 (3.3) –17 (5.3) 2 (6.3) –7 (5.9)–10 (5.9)–9 (5.1)13 (6.4)–11 (4.6)5 (3.5)5 (4.3)–11 (3.1)0 (6.3)1 (4.4) –2 (6.3)4 (4.6)6 (4.8) –14 (5.5) 7 (5.6) –25 (5.4)–16 (5.0)–––11 (5.0)–15 (5.3)5 (3.6)–25 (4.2)6 (5.0) –1 (2.2) –2 (3.6)––32 (2.7)68 (4.2)64 (3.2)34 (5.5)64 (6.8)63 (4.0)80 (3.4)–19 (4.5) –6 (5.6)–6 (4.4)41 or More StudentsDifferencein Percentfrom 1999hiihiiiiiiiii –– 4 (7.1)17 (4.9) –44 (3.6)4 (7.1) –– –8 (5.6)–2 (5.0)35 (5.9)–19 (4.4)36 (4.1)14 (4.0)–11 (3.4)–3 (6.0)37 (4.2) 22 (5.1)15 (5.2) –27 (4.9)–23 (4.7) 0 (4.7)–– 9 (5.4)–1 (2.3)–– –4 (4.4)–– –13 (7.6) –1 (8.4) –6 (6.4)–6 (5.7)Differencein Percentfrom 1995hihihhihhhii –1 (4.6) –– 29 (7.3)–51 (3.1)–10 (6.7) 2 (5.5) –13 (7.3)–6 (5.3) –9 (6.3)–––––6 (4.1) 73 (3.2)–– 50 (4.7) –6 (6.7) –34 (5.8)–19 (4.6) –18 (4.9) –3 (4.6)–54 (4.5)9 (7.2) –– –9 (5.6)–– –––13 (6.5)–7 (6.0)2007Percentof StudentshihhiiiiDifferencein Percentfrom 200331 (3.9)0 (0.0)0 (0.1)0 (0.0)0 (0.0)26 (3.7)0 (0.0)11 (2.7)21 (3.9)1 (0.0)0 (0.0)43 (3.7)14 (3.2)1 (1.0)1 (0.6)47 (4.3)46 (4.1)1 (0.9)32 (4.8)1 (1.1)3 (1.8)0 (0.0)5 (1.6)29 (4.1)18 (2.3)1 (0.0)4 (1.2)0 (0.0)19 (3.1)0 (0.0)1 (1.0)0 (0.0)41 (3.6)2 (0.0)0 (0.0)0 (0.0)11 (2.6)1 (0.8)0 (0.0)22 (2.5)0 (0.0)2 (1.1)11 (2.6)42 (3.1)1 (1.0)20 (2.7)1 (0.8)2 (0.9)15 (4.5)11 (0.3) –10 (2.8)0 (0.4)–2 (0.1) 1 (5.5)–1 (0.0)–7 (4.2) 1 (0.0) 16 (5.3) 1 (1.0) 10 (6.4)3 (5.8)1 (0.9)–16 (6.4)–2 (1.8)0 (2.5)0 (0.0)5 (1.9)1 (5.5)–4 (4.1) –4 (3.3)0 (0.0)–6 (4.6) 1 (1.2) –9 (5.2) –1 (0.0)0 (0.0)––0 (1.1)0 (0.0)–4 (3.5)0 (0.0)2 (1.2) 0 (1.5) 0 (1.2)––0 (0.0)1 (1.3)2 (0.5)1 (1.3)4 (3.6)1 (0.8)0 (0.0)0 (0.0) 1 (0.8)0 (0.0)h 2007 significantly higheri 2007 significantly lowerDifferencein Percentfrom 1999iihih –– –2 (1.3)–20 (4.6) 1 (0.0)0 (0.0) –– 7 (5.5)1 (0.9)–40 (5.9)–5 (2.4)0 (2.5)0 (0.0)2 (2.5)–2 (5.6)–40 (3.9) 0 (0.0)–15 (5.2) 0 (0.0)0 (0.0) 2 (4.6)–– –14 (5.0)1 (1.0)–– –6 (2.1)–– 1 (1.3) –2 (2.2) –2 (2.3)0 (0.0)Differencein Percentfrom 1995iiiiiii 0 (0.1) –– –23 (7.2)1 (0.0)0 (0.0) 1 (1.0) 9 (6.9)1 (0.9) –18 (5.2)–––––3 (3.4) –75 (3.2)–– 0 (0.0) 1 (1.0) –2 (1.2)0 (0.0) 1 (0.8) 4 (4.3)0 (0.0)2 (1.1) –– –2 (1.9)–– –––1 (1.4)0 (0.0)iiihSOURCE: IEA’s Trends in International Mathematics and Science Study (TIMSS) 2007Exhibit7.1:7.1 Trends(Continued)
272chapter 7: classroom characteristics and instructionHowever, some countries averaged larger mathematics classes (usually amodest increase, but not always), including Ghana, Israel, Italy, Lithuania,Singapore, and Sweden.The results in Exhibit 7.2 show that the majority of students arein medium-sized mathematics classes. At the fourth grade, on averageinternationally, 24 percent of the students were in classes with fewer than20 students, 58 percent were in classes of 20 to 32 students, and 18 percentwere in classes with 33 or more students. Notable exceptions includedSingapore with almost all students (94%) in large classes, Hong Kong SARand Yemen with about three-fourths in large classes, and Chinese Taipei,Colombia, and Japan with approximately half in large classes. In general,class sizes were larger at the eighth grade, 30 percent were in classes of1 to 24 students, 59 percent in classes of 25 to 40 students, and 11 percentwere in classes of 41 or more students. The largest percentages of studentsin large classes, from 41 to 47 percent, were in Egypt, Ghana, Hong KongSAR, the Palestinian National Authority, and Thailand. The countries withmore than half of their eighth grade students in small classes were Bulgaria(59%), Cyprus (54%), Georgia (52%), Hungary (72%), Italy (73%), Malta (71%),Romania (76%), the Russian Federation (63%), Serbia (53%), Slovenia (94%),Sweden (63%), and the United States (57%), as well as the benchmarking stateof Massachusetts (65%) and the Basque country in Spain (68%).Because countries have a variety of policies, practices, and realitiesdetermining class sizes, the relationship between class size and achievementis extremely difficult to disentangle. For example, in some countries thesmaller classes tend to be in rural areas with fewer resource and the largerclasses in urban areas with more resources. Also, countries and schoolscannot always control class size. Because of this, the ability to cap classsizes can indicate the availability of more resources in general. As anothercomplicating factor, smaller classes can be used for advanced or practicalclasses such as computer laboratories on one hand, and for remedial learningor students with special needs on the other. Finally, TIMSS data repeatedlyshow, contrary to what might be anticipated, that the high-achieving Asian
chapter 7: classroom characteristics and instructioncountries have some of the largest class sizes. The complexity of this issue isevidenced in the TIMSS 2007 results showing a curvilinear relationship, onaverage, between class size and mathematics achievement at both the eighthand fourth grades.Mathematics teachers were asked about the instructional impact offive characteristics of their students—differing academic abilities, a widerange in backgrounds, students with special needs, uninterested students,and disruptive students. Responses were given on a four-point scale; not atall, a little, some, and a lot. TIMSS used the teachers’ responses to constructan Index of Teachers’ Reports on Teaching Mathematics Classes withFew or No Limitations on Instruction due to Student Factors (MCFL) andthe results are presented in Exhibit 7.3. Students were placed in the highcategory, if, on average, teachers reported their classrooms were impactedonly a little (if at all), and in the low category, if, on average, these factorsimpacted instruction at least somewhat. The remaining students fell in themedium category. The results show that at both grades average mathematicsachievement was related to the diversity of the students in the class andthe instructional challenges involved. At the fourth and eighth grades,45 and 38 percent of the students, respectively, were in classes where teachersreported the composition had little, if any impact on instruction, and thesestudents had the highest achievement internationally. At the eighth grade,the 23 percent of students in classes with adversely impacted instruction,had noticeably lower average achievement. In general, between 2003 and2007, teachers in eight countries and one benchmarking participant reportedincreases in these more challenging types of classes whereas teachers in onlythree countries reported decreases.273
chapter 7: classroom characteristics and instruction2741–19 se TaipeiColombiaCzech RepublicDenmarkEl SalvadorEnglandGeorgiaGermanyHong Kong SARHungaryIran, Islamic Rep. NetherlandsNew ZealandNorwayQatarRussian FederationScotlandSingaporeSlovak RepublicSloveniaSwedenTunisiaUkraineUnited StatesYemenInternational Avg.Benchmarking ParticipantsAlberta, CanadaBritish Columbia, CanadaDubai, UAEMassachusetts, USMinnesota, USOntario, CanadaQuebec, Canadarssrsrrrrr20–32 Students33 or More StudentsPercentof StudentsAverageAchievementPercentof StudentsAverageAchievementPercentof StudentsAverageAchievement11 (2.8)24 (3.3)19 (3
Exhibit 7.2 presents the TIMSS 2007 distribution of students in different sizes of classes in relation to their mathematics achievement. As presented in Exhibit 7.1, in TIMSS 2007 across participating countries at the fourth gr
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
classroom classroom 30 31 classroom 32 classroom 33 classroom 35 classroom 36 classroom 37 classroom 38 classroom 39 classroom 40 classroom 41 classroom 42 classroom 43
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
About the husband’s secret. Dedication Epigraph Pandora Monday Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Tuesday Chapter Six Chapter Seven. Chapter Eight Chapter Nine Chapter Ten Chapter Eleven Chapter Twelve Chapter Thirteen Chapter Fourteen Chapter Fifteen Chapter Sixteen Chapter Seventeen Chapter Eighteen
18.4 35 18.5 35 I Solutions to Applying the Concepts Questions II Answers to End-of-chapter Conceptual Questions Chapter 1 37 Chapter 2 38 Chapter 3 39 Chapter 4 40 Chapter 5 43 Chapter 6 45 Chapter 7 46 Chapter 8 47 Chapter 9 50 Chapter 10 52 Chapter 11 55 Chapter 12 56 Chapter 13 57 Chapter 14 61 Chapter 15 62 Chapter 16 63 Chapter 17 65 .
HUNTER. Special thanks to Kate Cary. Contents Cover Title Page Prologue Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter
Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 . Within was a room as familiar to her as her home back in Oparium. A large desk was situated i
