Following is a complete list of the resources for each lesson in this guide, organized by country.
Australia
Australia does not have a national mathematics curriculum. Each state and territory have their own curriculum, typically consisting of five content strands: space, number, measurement, chance and data, and algebra. Some states also distinguish separate affective and process strands, such as 'appreciating mathematics' and 'working mathematically.'
The majority of Australian schools are co-educational, although A2, an advanced class about a topic normally taught in grade 9, was filmed at a girl's school. Graphing calculators are commonly used in grades 11 and 12; their use is increasing in middle school. No mention is made on the CD about different tracks.
| A1 |
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| A2 |
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| A3 |
- Focus: studying simulation and data collection
- Mathematical topics: statistics
- Lesson graph
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| A4 |
- Focus: developing student understanding of ratios
- Mathematical topics: Statistics
- Lesson graph
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Czech Republic
It is customary for students to stand up to greet the teacher at the beginning of the class. It also is common practice for teachers to call students to the board to solve a problem—explaining orally what they are doing at each step—and to be graded publicly for their work. Czech teachers emphasize the use of proper mathematical language. Students tend to work individually, and work is discussed as a whole class. They also are discussed from using calculators unless it helps to save time in solvingcomplicated problems. Students copy everything written on the board and tend to study from their notebooks rather than the texts. The national research coordinator makes no mention of different tracks.
| C1 |
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| C2 |
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| C3 |
- Focus: raising numbers and algebraic expressions to certain powers, and adding and subtracting numbers raised to certain powers
- Mathematical topics: Algebra: exponents
- Pedagogical topics: Assessment, asking for show of hands, 34:35; Peer assessment, 34:47—38:54
- Lesson graph
- New translation of lesson transcript
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| C4 |
- Focus: operating with numbers raised to certain powers, and calculating the area of a triangle and a trapezoid
- Mathematical topics: Algebra: exponents; Geometry: Pythagorean theorem—applications of (38:00—49:00), in three dimensions (38:00—49:00)
- Lesson graph
- New translation of lesson transcript
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Hong Kong
It is common practice for Hong Kong students to show their work on the board. Mathematics classes can be taught in Chinese (Cantonese) or English. Of the four public release lessons, three (HK1, HK3 and HK4) are conducted in English, which is not the students' native language. Thus, the mathematics teacher needs to teach them every aspect of the English term: the spelling, the pronunciation, and the meaning. In HK2, which is taught in Cantonese, the teacher introduces technical terms in English. (The TIMSS assessments are presented in both Chinese and English, and students can choose which language to use). In HK4 the teacher asks the students not to use calculators; the national research coordinator comments that calculators "are not forbidden in grade 8." He makes no mention of different tracks.
| HK1 |
- Focus: reviewing square numbers and square roots
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| HK2 |
- Focus: using the elimination method to solve simultaneous equations
- Mathematical topics: Algebra: equations, linear, systems; Proof
- Relevant pedagogical topics: Connections with work in earlier grades (9:46—15:31)
- Lesson graph
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| HK3 |
- Focus: deriving the sum of the interior angles of a polygon
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| HK4 |
- Focus: studying equations that are identities
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
- Susanna Epps' Report on the Use of HK4
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Japan
In Japanese junior high schools, mathematics is a mandatory subject and all students are supposed to study the same content. This content is regulated by the Guidelines for the Course of Study issued by the Ministry of Education, Culture, Sports, Science and Technology. In the curriculum designed by the Ministry, there are no additional math courses where students might be grouped in accordance with their abilities (at the time of filming of these lessons in 1995), nor on their orientation towards their future academic majors, such as can be found in other countries. Since 2002, there has been an increase in the number of ability-grouped classrooms. Ninety-four percent of Japanese students attend public school. The other six percent attend a private or a National school.
It is common to review the previous lesson in order to make a bridge between the previous and the current lesson. This is due to the fact that the teachers recognize the value in the idea that "coming to understand the meaning of a problem takes time". It is also common for teachers not to provide the answer but rather to use students' opinions. One characteristic of Japanese lessons is to let the students themselves articulate the important points.
In Japan, the ratio of mathematics teachers who received their teaching certificates in mathematics or mathematics education is very high, and 93% of the students are instructed by such teachers (as compared with the international average, which is 73% (TIMSS 1999 International Mathematics Report)).
| J1 |
- Focus: studying two-dimensional geometry, especially parallel lines and angles.
- Mathematical and pedagogical topics
- Lesson graph
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| J2 |
- Focus: studying two-dimensional geometry, especially the areas of triangles between parallel lines
- Mathematical and pedagogical topics
- Lesson graph
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| J3 |
- Focus: studying linear inequalities in one variable
- Mathematical and pedagogical topics
- Lesson graph
- Lesson plan
- Detailed description and commentary
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| J4 |
- Focus: studying inequalities
- Mathematical and pedagogical topics
- Lesson graph
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Netherlands
In the Netherlands, secondary education consists of three main ability tracks: 1. Junior secondary or prevocational education (vmbo), preparing students for senior secondary vocational education, and the labor market. 2. Senior general secondary education (havo), preparing students for higher vocational education. 3. Pre-university education (vwo), a six-year course preparing students for university and higher vocational education. In mathematics lessons in grade eight, ability tracks use two different textbooks, either for vmbo (lower ability) or for havo/vwo students (higher ability). More than 75% of math lessons rely on the textbook.
N1 is a havo class and N2 is a vwo class. N3 ( havo/vwo) and N4 (vwo) are Dalton schools. See the national research coordinator's comments on the CD for more detail.
| N1 |
- Focus: making linear formulas
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| N2 |
- Focus: introducing the Pythagorean theorem
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| N3 |
- Focus: factoring
- Mathematical topics: Algebra: distributive law, factoring
- Lesson graph
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| N4 |
- Focus: factoring
- Mathematical topics: Algebra: factoring
- Pedagogical topics: Instructional situations: something taught (7:53—9:18) but not learned (33:03—34:01); Scaffolding
- Lesson graph
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Switzerland
Switzerland is divided into three main linguistics areas: French, Italian, and German, and is also comprised of 26 cantons. Each canton has its own educational system, with its own curriculum, and to some extent its own textbooks. In the majority of the German-speaking cantons there are three tracks at the lower secondary level. The same school usually includes classes in all three tracks: track one (basic demands), track two (extended demands), and track three (advanced, or highest demands). There are some mixed classes in which two tracks are taught.
The four public release Swiss lessons include two German lessons, S1 (track three) and S2 (track two). S3 and S4 are taught in Italian and French, respectively. No information is available on the CDs about tracks in the Italian and French educational systems in Switzerland.
| S1 |
- Focus: factoring quadratic equations
- Mathematical topics: Algebra: factoring, equations, quadratic
- Pedagogical topics: Instructional decisions: choosing and using problems (25:16—35:30); Instructional strategies: whole class; teacher describes solution method (38:20—40:37)
- Lesson graph
- Detailed description and commentary
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| S2 |
- Focus: learning terms and variables
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| S3 |
- Focus: studying geometrical solids
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| S4 |
- Focus: studying equations
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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United States
No comments are available from the national research coordinator. The United States does not have a national mathematics curriculum. There are state mathematics standards, but most individual districts (and sometimes schools and even individual teachers) determine what textbooks to use. Different tracks are common at grade 8; nationally, fewer than 30% of students are enrolled in algebra at this grade. US1 and US2 deal with algebra. US4 is an advanced class using a high school geometry text.
| US1 |
- Focus: graphing linear equations
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| US2 |
- Focus: writing variable expressions
- Mathematical and pedagogical topics
- Lesson graph
- Detailed description and commentary
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| US3 |
- Focus: calculating with exponents
- Mathematical topics: Algebra: exponents
- Pedagogical topics: Language (spoken and written): precision (7:45—9:56)
- Lesson graph
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| US4 |
- Focus: measuring angles formed by secants and tangents of a circle.
- Mathematical topics: Geometry: auxiliary line, secants and tangents; Problem solving: heuristics—auxiliary line
- Pedagogical topics: Scaffolding
- Lesson graph
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