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Following is a list of detailed mathematical and pedagogical topics organized by lesson for 18 lessons. The mathematical and/or pedagogical topics for the other 10 lessons can be found on the lessons by country page.
Australia
| A1 |
Mathematical Topics |
Pedagogical Topics |
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Geometry
Angle sum
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Geometry software, use of,
Work in pairs: 19:06–42–15
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Polygons
Angle sum
Convex
Non-convex
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Instructional strategy,
individual work
work in pairs
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Exterior angle
Polygon: 6:15–18:52
Polygon, convex: 4:52–16:07
Polygon, non-convex
Ray
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Technology, use of
Calculator use: 41:14–41:38
Computer, work in pairs
Geometry software,
work in pairs: 19:06–42–15
Overhead projector,
Preparation for class activity: 6:15–19:08
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| A2 |
Mathematical Topics |
Pedagogical Topics |
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Geometry,
Congruence
Triangle,
Congruence
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Instructional situations,
Leading a discussion after an activity: 33:00–38:00
Teacher responses to unexpected student solutions, questions, misconceptions: 29:51–31:02
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Czech Republic
| C1 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Exponents
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Assessment,
asking for show of hands, 19:29
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Geometry,
Perimeter
Polygons
Pythagorean theorem
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Technology, use of,
calculator, 4:48–5:45, 10:14–10:55, 12:03–12:59
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| C2 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Factoring: 3:28–4:20
Formulas
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Connections,
Made 04:37–26:44
With work in earlier grades: 10:37–11:32, 15:58
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Approximation |
History,
Archimedes,
van Ceulen, 20:07–22:10
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Geometry,
Archimedes’ Formula (C=2pr)
Circle
Perimeter (Circumference)
Perimeter
Polygon,
Perimeter
Pythagorean Theorem,
Applications of: 8:34–9:58
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Instructional strategies,
Students come to the board
Present idea: 5:40–6:03
Work problem: 37:49–44:17
Whole class,
Students volunteer ideas: 4:37–26:44
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“Motivating”
Different form of formula: 39:51
Formula: 0:00–26:44
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Mathematics,
Connections with previous learning: 14:58–18:47
Preserving integrity of, while maintaining appropriate level: 14:58–18:47
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Problem solving,
Using related problems 4:37–13:11
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Teacher responses to,
Unexpected student solutions, questions, misconceptions: 3:21–4:07
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Technology, use of,
Calculator use: 19:49–22:28, 26:44–27:46
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Hong Kong
| HK1 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Exponent (of degree two)
Square (of a number)
Square root
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Instructional situations,
Teacher responses to unexpected student solutions, questions, misconceptions
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Geometry,
Pythagorean Theorem,
Preparation for
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Instructional strategies,
Students come to the board to present solutions: 1:30–1:34, 2:12–2:22, 2:31–2:44, 3:05–3:12, 7:00–8:00, 20:00–20:57
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Inverse,
Square root
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Language (spoken and written),
As a second language
Precision 3:27–5:56
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| HK3 |
Mathematical Topics |
Pedagogical Topics |
| |
Geometry,
Angle sum
Area,
Polygons
Polygons,
Angle sum
Area
Convex
Non-convex
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Instructional strategies,
Students come to the board
Present example: 1:13–1:18, 2:03–2:22, 3:04–3:25, 5:39–6:40, 14:00–14:51, 16:38–16:50, 19:20–19:46
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Polygon,
convex: 0:56–6:59
equilateral but not equiangular: 6:40–21:35
non-convex: 5:39–6:40
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Language (spoken and written),
As a second language
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Proof |
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Problem solving,
Heuristics,
Auxiliary lines
Reducing to simpler problem
Reducing to previously solved problem
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| HK4 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Distributive law
Identity
Equations, linear,
Identities
interpreting 0 = 0
Solving
Variables
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Connections,
Made: 2:50–17:40
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Instructional decisions,
Introduction of new topic using old/new knowledge, etc.: 00:34-2:58, 5:52-6:29
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Counterexample, use of: 18:45 |
Instructional situations,
Leading a discussion after an activity: 00:34–2:58, 5:52–6:29
Problem solution launches the main topic of the lesson: 3:17–4:33, 5:52–7:35, 12:47–17:40
Teacher responses to unexpected student solutions, questions, misconceptions: 5:52–6:29
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Meaning of,
Identity
Variable
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Instructional strategies,
Students come to the board,
Work problem: 00:34–2:50, 24:21–27:46
Whole class,
Teacher calls on students for answers to class work: 11:18–12:31
Teacher discusses problem: 2:50–9:35, 12:31–17:40
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Motivating,
Concept: 1:00–19:27
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Language (spoken and written),
As a second language,
Modeling use of terms: 17:14–17:27, 17:56, 27:34–27:46
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Proof |
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Representations,
Illustration of meaning of expanded and factored form: 13:50–14:14
Imprecise notation: 26:33
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Japan
| J1 |
Mathematical Topics |
Pedagogical Topics |
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Geometry,
Angle sum: 6:50-8:00
Angles
Auxiliary line
Parallel lines
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Mathematics,
Problems with multiple entry points (different solution methods)
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Problem solving,
Heuristics,
Auxiliary line
Reducing to simpler problem: 4:32–10:10
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Scaffolding |
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Student-created problems |
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| J2 |
Mathematical Topics |
Pedagogical Topics |
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Geometry,
Area,
Polygon
Parallel lines
Polygons,
Area
Triangles,
Area
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Geometry software,
Use of,
Whole class, 0:27–1:27, 46:36–49:47
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Instructional strategies,
Students come to the board,
Present idea 3:19–3:33
Present solutions 19:45–21:07, 21:14–22:24, 42:14–46:00 (put up solutions on board)
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Technology use,
Geometry software,
Whole class, 0:27–1:27, 46:36–49:47
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| J3 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Inequalities
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Assessment,
Asking for show of hands
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Representations,
Relationships among quantities
Line graph: 1:25–5:01, 46:32
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Instructional decisions,
Choosing and using problems
Teacher observes students working individually, strategically selects students to present their work: 4:55–18:32
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Instructional situations,
Interactions with students as they work individually: 4:55–18:32
Presenting problems: 1:00–4:39
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Instructional strategies,
Individual work: 4:55–18:32
Students come to the board: 18:32–31:39
Present solution: 18:32–31:39
Whole class,
Teacher asks for show of hands
Teacher presents problem: 1:00–4:39
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Maintaining the challenge of the task |
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Mathematics,
Problems with multiple entry points (different solution methods) 1:00–31:39
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| J4 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Inequalities
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Assessment,
Asking for show of hands
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Motivating,
Usefulness of variables
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Instructional decisions,
Teacher observes students working privately, strategically selects students to present their work: 9:10–16:08, 17:24–33:05, 34:44-46:00
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Problem solving |
Instructional situations,
Leading a discussion after an activity: 24:54–33:05 (summary of a solution), 49:47–50:30 (synthesizing ideas)
Problem solution launches the main topic of the lesson: 17:09–21:11, 23:30–25:43
Teacher responses to unexpected student solutions, questions, misconceptions: 26:16–29:19
Teacher sees that student(s) are struggling and tries to address it: 26:16–29:19
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Instructional strategies,
Whole class,
Teacher asks for show of hands
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Representation
Notation for multiplication by constant: 0:00–7:00
Relationships among quantities
Line graph: 27:27–29:01
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Mathematics,
Multiple representations of a topic: 26:16–29:19
Problems with multiple entry points (different solution methods),
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Netherlands
| N1 |
Mathematical Topics |
Pedagogical Topics |
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Algebra
Equations, linear,
Graphing
Formulas
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Connections,
Made: 6:11–11:50
Real-world: 12:32–16:03
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Instructional situations,
Interactions with students as they work individually: 16:03–40:56
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Instructional strategies,
Whole class,
Teacher calls on students for answers to homework: 1:25–12:32
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Language (spoken and written),
Precision: 34:20–36:09
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Technology, use of,
Overhead projector,
Discussion of homework solutions: 1:25–12:32
Video,
Examples of linear and non-linear relationships: 12:32–14:36
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Wait time: 3:30–12:15 |
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| N2 |
Mathematical Topics |
Pedagogical Topics |
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Geometry
Pythagorean Theorem,
Introduction to
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Connections,
With work in earlier grades: 7:03–10:28
With work in previous lesson: 5:50–6:59
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Inverse,
Square root
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History,
Pythagoras
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Motivating,
Theorem: 5:50–6:59, 10:29–10:50
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Maintaining the challenge of the task |
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Proof |
Technology, use of,
Overhead projector,
Incomplete proof of Pythagorean Theorem: 10:29–16:01
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Switzerland
| S2 |
Mathematical Topics |
Pedagogical Topics |
| |
Algebra,
Expressions with variables
Variables
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Connections,
Possible (unmade): 15:03–16:44, 16:33–16:44, 17:07–19:39, 30:13–34:08
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Representations,
Relationships among quantities,
Bars
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Instructional situations,
Dealing with mistakes in whole-class discussion: 20:00–23:02
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Instructional strategies,
Group work (working as a group): 20:00–23:02
Peer assessment: 20:00–23:02
Students come to the board,
Present solution: 14:22–23:06, 27:35–36:27, 36:27–42:40
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| S3 |
Mathematical Topics |
Pedagogical Topics |
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Geometry,
Pythagorean Theorem,
Application of Solids
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Instructional situations,
Interactions with students as they work individually: 8:18–17:03, 23:56–30:38, 34:46–37:53, 42:02–45:00
Interactions with students as they work in groups: 9:45–11:02, 32:24–33:00
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Instructional strategies,
Students come to the board,
Present solution: 40:37–41:59
Whole class,
Teacher presents problem: 00:09-03:11
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Maintaining the challenge of the task |
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Technology, use of,
Calculator use: 2:59 through remainder of lesson
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| S4 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Equations, linear,
Interpreting –1 = 0
Graphing
Solving
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Instructional situations,
Interactions with students as they work individually
Teacher sees that students) are struggling and tries to address it: 16:54–23:49
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Representations,
Notations for multiplying equation by constant: 00:16–8:10
Set notation used to indicate solution: 3:34
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Instructional strategies,
Individual work
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Mathematics,
Multiple representations of a topic: 37:45-41:58
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Wait time: 1:27 |
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United States
| US1 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Equations, linear
graphing
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Connections,
Possible (unmade): 1:49–2:21, 20:03–20:53, 40:40– 41:15
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Instructional situations,
Interactions with students as they work in groups: 1:13–1:41, 2:54–3:25, 6:39–7:20, 11:37–13:12, 30:42–31:26
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Instructional strategies,
Group work (working as a group): 1:13–1:41, 2:54–3:25, 6:39–7:20, 11:37–13:12, 30:42–31:26
Small group: 2:35–20:03, 20:52–30:35
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Wait time: 2:00, 2:12, 7:27 (see detailed lesson description) |
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| US2 |
Mathematical Topics |
Pedagogical Topics |
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Algebra,
Expressions with variables
Variables
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Connections,
Real-world: 20:54–26:47
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Geometry,
Pythagorean theorem,
Applications of: 10:39–10:55
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Instructional situations,
Interactions with students as they work individually: 0:59–10:39
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Meaning of,
Variable
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Instructional strategies,
Students come to the board
Play game: 49:10–53:00
Whole class
Teacher calls on students for answers to homework: 13:58–20:00
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Language (spoken and written)
IRE: 12:26
Precision: 37:30, 42:32
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Technology, use of,
Overhead projector,
Display of answers to homework and answers: 13:58–20:00
Introduction of new material: 20:54–24:05
Examples: 24:05–26:47, 26:47–30:17, 37:39–40:00
Practice problems: 40:00–43:01
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