EDMA 262 - Task 1 Part 2 Week 9
- 2. Weekly Reflection From this week’s mathematical concept of geometry I had gained an in depth understanding upon the concept, skills and strategies that were specified and unpacked within this week’s lecture and tutorial. From this week, I had learnt many components and aspects to geometry as well as the individual steps that are to be taken whilst learning and teaching the concept. Throughout the lecture and tutorial I gained knowledge upon the diverse types of concrete materials that can be used for not only student development but also that of a teachers. As a pre-service teacher it is important for me to become knowledgeable upon not only the concept, skills and strategies of the concept of geometry but also to become aware of the various materials that can be utilized within the classroom. For instance, if I were to be placed within a low socio – economic educational setting I may not have access to IT programs or simply plastic or foam shapes and so by watching the lecture and attending the tutorial this week I was able to grasp ideas upon what concrete materials can be used within any environment I may be in. Furthermore, as I begin teaching I aim to ensure that all of my students understand each concept of geometry before we progress into thinking about skills and thinking strategies. By doing so, my students would have obtained a foundation of understanding upon what the concept is, why we’re doing it and why it may be important within a real-life context. From this, I would propose open-ended questions upon their thoughts and ideas and encourage students to contribute any ideas to the class discussion or activities that taking place. From this, I would then question my students upon their thoughts and why they may think that certain way and encourage other students to contribute their thoughts and ideas to other student’s perspective. Moreover, by doing so, students are actively collaborating and contributing their thoughts within a social constructivists approach. Moreover, whilst educating my students upon the concept I would continuously utilize concrete materials throughout the process to ensure that my students have a visual representation whilst listening to demonstrations and partaking within activities.
- 3. Concepts, Skills and Strategies Concept Geometry is an organized, logical and coherent system that involves the investigated study of shape, space and measurement. Skills 1. Visualizing: Recognizing and describing attributes, similarities and differences. 2. Communication: Discussing oral or written in relation to naming and describing concepts. 3. Drawing and modeling: Sketch and draw 4. Thinking and reasoning: Classifying, analyzing, reasoning, synthesizing similarities and differences. 5. Applying geometric concepts and knowledge and linking them between shape and function Thinking Strategies: ‘How will I work this out?’, From the lectures and tutorials, I had learnt that it is important to let students initially discover the formulae for concepts such as area and perimeter. ( Within later years students can compare their current formulas to their initial ones. This can be conducted through discussions with assistance from ICT integrated interactive activities and video)
- 4. Geometry in Relation to the Language Model Verbal Symbolic Concrete/Visual Children’s Language Materials Language Mathematics Language Symbolic Language Corners, edges, slanty, straight, sides, shapes, fence, outside, inside, ‘like the door or ball’ Vertices., faces, perimeter, circumference, area, volume, scalene, equilateral, isosceles, quadrilateral Toys, tables, shoes, plate, bowl, chair, wheel (Natural materials children see in everyday life) Soft shapes, geo board, paper (can gold into shapes), blocks, cardboard. Clay, pattern blocks, dime solids, play dough, tessellating shapes, computer and tablet apps/activities. ‘How many sides, edge and faces are there?’ (Relate to real-life context, e.g. a chair, ‘why do you think it is shaped that way?’ Identifying attributes of 1D, 2D and 3D shapes Within this interactive resource, students within years 2 & 3 re investigating 2D and 3D shapes, their properties and count up the corners and faces on each one and are encouraged to do the same with the objects that are around them within the classroom. http://splash.abc.net.au/home#!/media/1225670/ (mentioned within the language model) – This resource is an interactive geoboard which enables children to use rubber bands to create polygons such as a triangle, square, octagon etc.- http://www.scootle.edu.au/ec/viewing/L3 528/index.html Concept: Geometry is the exploration of shapes and their uses. Skill: Investigating the volume, capacity, degree etc of objects Thinking Strategy: ‘How will we find this out?’, ‘What will use to find the answer?’, “What will our thinking process be?’
- 5. Teaching Resources • This resource was constructed for teachers and contains lesson plans that depict detailed steps upon creating their own 3D prisms (for students within ears 3 and 4). Within the resource, students initially explore 3D shapes upon paper before progressing to ICT integrated activities. (if available, students are also encouraged to use a 3D printer to physically explore the dimensions of the shapes they have created) - https://www.makersempire.com/esa#3dshapegeometry • This resource may be useful for teachers as it provides a guide to introducing students to the concept of geometry- http://www.amsi.org.au/teacher_modules/introduction_to_plane_geometry.html • This resource may also be useful as teachers can educate their students upon the various different types of lines and angles, relating the concepts to real life experiences and knowledge - https://www.youtube.com/watch?v=THhMqLWdcV8 • This resource contains strategies and tips for teachers in educating students upon the concept of geometry. It contains strategies upon teaching plane figures, perimeter, area, geometric solids and how transformations are included. – https://education.wm.edu/centers/ttac/documents/packets/geometrystrategies.pdf • Bloom’s taxonomy may also be another useful resource to use to identify levels of student understanding in relation to geometry (as depicted within this week’s lecture and tutorial alongside Van Hilies’ model – depicted within the chapter summary)
- 6. Misconceptions • Both of these sources depicted various common misconceptions that occur within geometry and also provide a number of resolutions for each misconception. • https://geometrymodule.wikispaces.com/file/view/Misconceptions.pdf • http://www.ijtase.net/ojs/index.php/IJTASE/article/viewFile/150/186 One of the common misconceptions are as depicted below;
- 7. ACARA LINKS Earliest mention of geometry within the curriculum- ACMMG009 Foundation year – ACMMG010
- 8. ACARA LINKS Year 1 – ACMMG022 Year 2 – ACMMG042
- 9. ACARA LINKS Year 2 – ACMMG043 Year 3 – ACMMG063
- 10. ACARA LINKS Year 3 – ACMMG064 Year 4 – ACMMG067
- 11. ACARA LINKS Year 4 – ACMMG088 Year 4 – ACMMG089 Year 5- ACMMG109
- 12. ACARA LINKS Year 5 – ACMMG112 Year 5 – ACMMG111 Year 5 – ACMMG140
- 13. ACARA LINKS Year 6 – ACMMG141
- 14. Additional Teaching Strategies • This resource is a video series that is broken up into segments upon the mathematical concept of geometry. These video segments include, points, lines and planes, angle basics, angles and degrees, polygons, triangles, quadrilaterals, perimeter, area, circle and Pi, circles as well as circumference and area. • This series of video clips may become useful to use in conjunction of teaching of the concept as the clips provide visual aid and explanations of why certain things are within the concept in addition to a teacher explanation. • As a class, students can create their own shapes with assistance of teacher demonstration and video clips. • Links to video clips; 1. https://www.youtube.com/watch?v=k5etrWdIY6o&index=1&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n 2. https://www.youtube.com/watch?v=DGKwdHMiqCg&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=2 3. https://www.youtube.com/watch?v=_n3KZR1DSEo&index=3&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n 4. https://www.youtube.com/watch?v=IaoZhhx_I9s&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=4 5. https://www.youtube.com/watch?v=mLeNaZcy-hE&index=5&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n 6. https://www.youtube.com/watch?v=yiREqzDsMP8&index=6&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n 7. https://www.youtube.com/watch?v=AAY1bsazcgM&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=7 8. https://www.youtube.com/watch?v=xCdxURXMdFY&index=8&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n 9. https://www.youtube.com/watch?v=cC0fZ_lkFpQ&index=9&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n 10. https://www.youtube.com/watch?v=O-cawByg2aA&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=10
- 15. Chapter Summary What students are to be learning within each level in relation to the mathematical concept of geometry.
- 16. Chapter Summary Chapter 16 • The world we live in is surrounded with 3 dimensional objects. This is a concept students are enabled to physically interact and relate to in context of their home lives and the purpose these shapes serve. • Describing and Sorting: Children are to be able to describe the properties of a 3D shape (This helps children to develop at level 1, progressing towards level 2 – described by the Van Hiele model & is very similar to the four stage language model)
- 17. Chapter Summary • 2D Shapes – Children should begin to recognize types of shapes through examples and non example (not through formal definitions/learnt by rote) • Question them; why are wall rectangular?, Why are most button shapes circular?, why is paper rectangular? • Length of sides: Many definitions of geometric shapes, as well as classification schemes, depend on the lengths of sides • Size of angles – • The sum of the angles of a triangle is 180 degrees • The sum of the angles of a quadrilateral is 360 degrees • The base angles of an isosceles triangle is equal • Angles opposite the longest side of a scalene triangle is largest • Opposite angles of a parallelogram are equal • Regular polygons have equal sides The classification of triangles by sides and angles
- 18. Chapter Summary • Parallel and perpendicular sides – Students need to be able to Identify parallel lines and perpendicular lines in a plane and in space • Parallel – opposite sides of a book, the horizontal lines in E, and the top and bottom of the chalkboard • Perpendicular – Adjacent edges of a book, the vertical line and horizontal line E • The edge of the wall and the edge of the floor • Congruence – two shapes that have the same size and shape. - If the two shapes are line segments, they are congruent - If the 2 shapes are 2D and they are congruent, then they have the same area. (the reverse may not be true/2 shapes with the same area may not be congruent) • Visualizing Spatial reasoning and problem solving are important content and proficiency strands in the Australian Curriculum • Students can depict this by participating in activities that model number lines, coordinate grids and rectangular arrays. The number of sides upon different types of polygons
- 19. References ABC. (2016). How many corners, edges and faces?. Retrieved from, http://splash.abc.net.au/home#!/media/ 1225670/ Australian Curriculum Assessment and Reporting Authority. (2016). Curriculum. Retrieved from, http:// www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1 Armstrong, P. (2016). Bloom’s Taxonomy. Retrieved from, https://cft.vanderbilt.edu/guides-sub-pages/blooms- taxonomy/ Classroom Caboodle. (2013). Teaching Geometry – learning lines ad angles. Retrieved from, https:// www.youtube.com/watch?v=THhMqLWdcV8 Education Services Ltd. (2016). Geoboard. Retrieved from, http://www.scootle.edu.au/ec/viewing/L3528/ index.html Makers Empire. (2015). 3D Shape Geometry. Retrieved from, https://www.makersempire.com/ esa#3dshapegeometry Mathantics. (2015). Math Antics: Points, lines and Planes. Retrieved from, https://www.youtube.com/watch? v=k5etrWdIY6o&index=1&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n https://www.youtube.com/watch? Mathantics. (2015). Math Antics: Angle Basics. Retrieved form, https://www.youtube.com/watch? v=DGKwdHMiqCg&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=2
- 20. References Mathantics.(2015). Math Antics: Angles and Degrees. Retrieved from, https://www.youtube.com/watch? v=_n3KZR1DSEo&index=3&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n Mathantics. (2015). Math Antics: Polygons. Retrieved from, https://www.youtube.com/watch? v=IaoZhhx_I9s&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=4 Mathantics. (2015). Math Antics: Triangles. Retrieved from, https://www.youtube.com/watch?v=mLeNaZcy- hE&index=5&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n Mathantics. (2015). Math Antics: Quadrilaterals. Retrieved from, https://www.youtube.com/watch? v=yiREqzDsMP8&index=6&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n Mathantics. (2015). Math Antics: Perimeter. Retrieved from, https://www.youtube.com/watch? v=AAY1bsazcgM&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=7 Mathantics. (2015). Math Antics: Area. Retrieved from, https://www.youtube.com/watch? v=xCdxURXMdFY&index=8&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n Mathantics. (2015). Math Antics: Circles, What is Pi?. Retrieved from, https://www.youtube.com/watch? v=cC0fZ_lkFpQ&index=9&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n Mathantics. (2015). Math Antics: Circles, Circumference and Area. Retrieved from, https://www.youtube.com/ watch?v=O-cawByg2aA&list=PLUPEBWbAHUsx47fzhccfRSk4uNnBwtk7n&index=10
- 21. References O’Brien, E. (2004). Geometry Strategies for Middle School. Retrieved from, https://education.wm.edu/centers/ttac/documents/packets/geometrystrategies.pdf Ozerem, A. (2012). Misconceptions in Geometry and Suggested Solutions for 7th Grade Students. Retrieved from, http://www.ijtase.net/ojs/index.php/IJTASE/article/viewFile/150/186 Wikispaces. (n.d.) Misconceptions in Geometry. Retrieved from, https://geometrymodule.wikispaces.com/file/ view/Misconceptions.pdf