Lew W. S., Jul 8, 2017

GeoGebra Global Gathering 2017 Presentation Wednesday, 19 July 2017 Teacher Education - 9:45 to 11:20 - Room S2 - 3 10:35 - 10:55 Vincent Lew (Singapore) Teacher as designer of quality digital learning resources using GeoGebra.

Mathematics teachers traditionally teach efficiently from well written textbooks which are based upon well founded curriculum objectives. They engage their students through various activities like concrete manipulatives, games, activities, project work etc. But various forms of computer based learning and assessment are becoming more prevalent. These learning resources are either professionally produced by commercial publishers or specialists in instructional design, or by teachers. In this presentation I share about how teachers can play a useful role in the design of quality digital resources for teaching and learning mathematics using Geogebra.

• 1. Geometry Exercise (Basic) Problem 1 : Application of Tangent Radius Property

Strength of good teachers content knowledge, classroom teaching experience, monitors students’ understanding and understand students’ learning difficulties. Hence, a good teacher knows how to adapt standard lessons, assess student learning and adjusts pace of instruction in class to achieve optimal learning. Weakness of teachers in the digital age : no idea or have little skill in producing interactive resources, fear of failure in learning new technology, and rather spend time preparing traditional learning resources, fear wasting precious curriculum time and do not see the benefits of using ICT since students do just as well without ICT, unable to effectively harness many good digital learning and assessment resources and past project failures may demotivate them from embarking on more projects.

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Deciding on which resource is of good quality depends on several points. Is it a classroom demonstration, or self directed learning resource? How much supporting instructions are given that is not shown in the interactive resource ? Simplicity can be high quality too. Too much learning points in one activity could be hard for student. Quality also about the quality of the feedback given for wrong answers. Advantage of shared resources : - each one can modify to adapt or improve the feedback for wrong responses.

• 1. Calculation of Angle Bearings in Trigonometry
• 2. Bearings 1
• 3. Bearings
• 4. Compass and True Bearing
• 5. Bearings from A to B
• 6. Bearings : Practice with Compass Reference

Different ways of designing learning resource depending on the intended use or pedagogy adopted by the teacher. With little word, or With more words and reasoning. or Just mathematical statements

• 1. Tangent-radius
• 2. Angle between line AB and radius of circle (5 Jul Update)
• 3. External Tangents to a Circle
• 4. Basic Proofs In Plane Geometry -Example 6 (Scaffolded)
• 5. CIRCLE GEOMETRY FOR HIGH SCHOOL

How a learning resource (visual interactive) is first developed out of learning need perceived by the teacher. Students can also access the interactive to review what they have learnt. Others copy and modify to improve or to adapt the resource for their own curriculum and students.

• 1. Trigonometric Ratios and Reference Angles of General Angles
• 2. Trigonometric Ratios and Reference Angles of General Angles
• 3. Trigonometric Ratios of General Angles and Reference Angle
• 4. Trigonometric Ratios of Rotation and Reference Angles
• 5. Trigonometric ratio of general angles
• 6. The 6 Trigonometric Functions of a General Angle
• 7. Trigonometric Ratios of Rotation and Reference Angles的副本
• 8. Arc length: Quick Investigation
• 9. Relationship between Arc Length, Radius and Angle (in degrees)

Use of template MCQ quizzes for formative assessments. Providing quality feedback to students. Opportunities to deal with student's common errors or misconceptions. Opportunities for educators to share their resources, and to adapt others' to their own students' needs. Possibility of using javascript to collect quiz statistics. But teachers may not have the skill.

• 1. Trigonometric Ratios of General Angles (Self Assessment)
• 2. Design of Quiz
• 3. Self Assessment : Graphs of Quadratic Functions such as +/-(x-a)(x-b)
• 4. Self Assessment : Graphs of Quadratic Functions in Vertex Form +/- (x-h)^2 +k

Teachers of 21C deepen professional knowledge on how students learn, how ICT impacts learning, and reflect on their teaching practice constantly. collaborate in creating and/or curating sustainable quality digital learning resources, (through well thought frameworks in place that link academic researchers, curriculum planners and developers in the public or private sector) Commercial vendors focus on developing the learning analytics and adaptive learning systems, draw on the good quality content produced in creative commons, eg from Geogebra Tube, find licensing agreements with IGI to manage their costs of content development .

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Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245–274. Bu, L., & Schoen, R. C. (2011). Model-centered learning: Pathways to mathematical understanding using GeoGebra. Rotterdam,Sense Publishers Rogers, P. L. (2001). Traditions to transformations: the forced evolution of higher education. Educational Technology Review, 9(1), Available online at: http://www.aace.org/pubs/etr/issue1/rogers.cfm. Rogers, P. L. (Ed.). (2002). An Overview of Teacher-Designers : How Teachers Use Instructional Design in Real Classrooms, Designing Instruction for Technology-enhanced Learning. pp 1-18 Hershey, PA. Idea Group Publishing. The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom Drijvers, P., Doorman, M., Boon, P. et al. Educ Stud Math (2010) 75: 213. Susanne Narciss (2013). Designing and Evaluating Tutoring Feedback Strategies for digital learning environments on the basis of the Interactive Tutoring Feedback Model. Digital Education Review - Number 23, June 2013- http://greav.ub.edu/der/ Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9, 281–307.

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This chapter contains resources created or curated and modified after the July conference

• 1. Explore Golden Ratio in Real Life Objects (Full Toolbar Enabled Online)
• 2. Photosynthesis - Rate vs Light Intensity (Updated)
• 3. Comparing Fractions
• 4. Space Invasion - Negative Numbers Multiplication
• 5. Self Review : Add Subtract Negative Numbers (v.2)
• 6. Distance Time Graph For Self Directed Learning
• 7. Links to Applets on Circle Properties
• 8. Graphing of Polynomial Functions Point by Point
• 9. Speed Time Graph for Self Directed Learning (Customizable)
• 10. Relationship between Arc Length, Area of Sector, Radius and Angle (in degrees)
• 11. Graphing Linear Functions (II)
• 12. Linear Functions : Input Variable x and Output Variable y
• 13. Input and Output of Graphs of Linear Functions
• 14. Solve Simple Linear Equations (II)