Presentatie titel

1. Geometry in the Junior Primary Presentatie titel Okahandja, June 2016 Rotterdam, 00 januari 2007

2. Geometry is everywhere ……….

3. Everywhere is geometry……….

4. Geometry in the house 120o A ceilingfanhasits 3 blades at 120oanglestomake 360owhile in motion. 30o 30o A Simple clothhangerhas 2 x 30oangles + 1 x 120o angle = 180o angle.

5. Geometry in architecture

6. Geometry in nature

7. Geometry in music

8. Geometry in handcraft

9. Geometry in cycles .Racing bikes are made using best geometry to give maximum efficiency. 

10. Geometry in sports

11. Geometry in stairs Inclined angle: 60o angle, Each stair: 90o angle. 90o 60o

12. Geometry in yoga

13. Geometry in tiling

14. Geometry in school

15. Geometry in the school.Which geometry do we want to teach? Grade 1 Geometrical figures Learners should be able to • identify and name common 2D shapes: square, circle, rectangle and triangle, • sort and classify common shapes, • draw/make shapes, • create pictures and patterns with shapes,

16. identify and name common 3D figures: sphere, cube and cone, • sort and classify common 3D objects, • describe common objects, • create own models, • find structures in the environment. Location, position and movement of objects Learners should be able to • describe the relative location of objects and people using positional and directional language, e.g. over, under, above, below, in front, behind, outside, inside, next to, between,.... [Junior Primary syllabus, Okahandja 2015]

17. Teaching geometry, how does it start? Van Hiele Levels of geometricthought: Level 0: Visualisation Studentsrecognize and name figuresbased on the globalvisualcharasteristics of the shape. It is the appearance of a shapethatdefines itfor a student. ‘A square is a square becauseitlookslike a square.’ Pierre M van Hiele [1909 – 2010]

19. The red car

22. A square?

23. ‘Identify and name common 2D shapes: square, circle, rectangle and triangle’ [Syllabus, grade 1] • A square?

24. A square? • Red, yellow, blue, … • Wood, wool, … • Small, large, … • Thin, thick, … ‘A square is a square, because it looks like a square’. ‘How can you define a thing before you know what you have to define? Most definitions are not preconceived but the finishing touch of the organizing activity. The child should not be deprived of this privilege……’ Hans Freudenthal [1905 – 1990] • A window, • A mirror, • A clock, • A biscuit, • A …..

25. A square? Not a square?

26. A square?

27. The language of geometry Talkingabout squares has itsownvocabulary: • Red, yellow, blue, purple, wood, wool, small, large, thin, thick, house, window, mirror, clock, biscuit, ….. • Side, vertex, angle, plane, shape, four, opposite, equal, lenght, right angle, point of intersection, diagonals, ….. Learninggeometry is a matter of language, soitshouldbe interactivelearning.

28. Geometry is an activity?! Learningobjectives in the syllabus: • Identify and name, • Sort and classify, • Draw/make, • Create, • Describe, • Find. The learningobjectivesgeometry are all skillsdescribedwith verbs, so, learninggeometryshouldbe ‘learningbydoing’. John Dewey [1859 – 1952]

29. Geometry in the school [2].Which geometry do we want to teach? Grade 2 Geometrical figures Learners should be able to • identify and name common 2D shapes: square, circle, rectangle, equilateral triangle and oval, • sort and classify a variety of shapes according to geometrical properties: number of sides, corners, • draw/make shapes, • create pictures and patterns with shapes,

30. identify and name common 3D figures: sphere, cube, cone, cylinder and rectangular prism (or brick), • sort and classify common 3D objects according to geometric properties: number of faces; shape of faces, • describe common objects using words such as edges, corners, faces, straight, curved, flat, round, rectangular, triangular and circular • create recognisable 3D figures, • find structures in the environment. Location, position and movement of objects Learners should be able to  • describe the position of objects drawn on informal maps, e.g.: on a map of the classroom, my desk is on the left. [Junior Primary syllabus, Okahandja 2015]

31. Teaching geometry, how does it go on? Van Hiele Levels of geometricthought: Level 1: Analysis Students are able to consider all shapeswithin a classratherthan a single shape. Byfocusingon a class of shapes, students are able to think aboutwhatmakes a rectangle a rectangle. Irrelevant features fall in the background. Students begin to appreciatethat a collection of shapes goestogetherbecause of itsproperties. Pierre M van Hiele [1909 – 2010]

32. Geometry in the school [3].Which geometry do we want to teach? Grade 3 Geometrical figures Learners should be able to • identify and name common 2D shapes: square, circle, rectangle, equilateral triangle and oval and pentagon, • sort and classify a variety of shapes according to geometrical properties: number of sides, corners, angles, right angles, • Identify right angles by use of a reference tool, • draw/make shapes, • create pictures and patterns with shapes,

33. identify and name common 3D figures: sphere, cube, cone, cylinder and rectangular prism (or brick), pyramid, • sort and classify common 3D objects according to geome- tric properties: number of faces, edges and vertices, • describe common objects using words such as edges, corners, faces, straight, curved, flat, round, rectangular, triangular and circular, • make models from paper and recycled material, • find structures in the environment, • recognise angles in everyday objects. Location, position and movement of objects Learners should be able to  • describe the relative location of objects drawn on maps of familiar settings. [Junior Primary syllabus, Okahandja 2015]

34. Teaching geometry, how does it go on? Van Hiele Levels of geometricthought: Level 2: Analysis Studentsperceiverelationshipsbetween properties and betweenfigures. Studentscancreatemeaningfuldefinitions and giveinformalarguments to justifytheirreasoning. Logicalimplications and classinclusions, such as ‘squares being a type of rectangle’ are understood. Pierre M van Hiele [1909 – 2010]

35. Implications for Geometry education • Geometryeducationshouldbeinteractive to use the language of geometry, • Learningbydoingto experience and to master the ‘geometricskills’, • Pleasure in solvingproblems, reasoning, discovering properties, seeing the aestheticaspects of geometry, • Discover the magnificientpresence of geometry in nature and dailylife. So the teacher shouldorganise a lot of interactivehands-onactivitiesforhislearners and discuss the experiencesby ‘doinggeometry’.

36. Summary:Subjects to teach in the Junior primary • Shapes • 2-D shapes, • 3-D shapes • Location

37. How to teach ‘Shapes’? • Discover shapes in everyday life, • Construct models, • Design patterns, • Design a tiled floor, • Play games, • Fill out worksheets, • Make geometric puzzles, • Read a math storybook, • ……….

38. How to teach ‘Location’? • Create a tableau, • Dance symmetric, • Play ‘hide-and-seek’, • Walk a route, • Look at the sun and the shadows, • Look at the mirror, • Fill out worksheets, • Read a math storybook, • ……….

39. Geometry education – Learning by doing

41. We get to work with geometry!