TPACK Mathematics use cases
Digital technology (ICT) and its linkages with pedagogy and content
We will explore how the use of a digital technology tool like Geogebra can impact the content and pedagogy practices in teaching.We will explore the ‘Angle’ topic in Geometry with 3 different sets of activities. The activities have been written out in the note as if the teacher were transacting it in her classroom; in the workshop, the participating teachers can play the role of students.
After the activity is completed, each group will discuss the activity, the learning objectives, and the role of technology in the lesson, and its impact on the content and pedagogy used.
Activities
Topic : Angles
 Building an angle, measuring the angle
 Building complementary angles
 Verifying the angle sum property of a triangle
Workshop transaction suggestions
The participants can be divided into 3 groups. Each group can be given one of the 3 use cases discussed in this note.
If there are a sufficient number of participants in each of these 3 groups, each group could be further split into 3 subgroups, and each subgroup can work with one of the 3 activities discussed in each of the 3 use cases).
Use cases
Use Case 1 (for Group 1)  Use Case 2 (for Group 2)  Use Case 3 (for Group 3) 
The teacher introduces angles to the class through physical manipulatives like strings or sticks.
Activity 1:Either before, or after explaining, the students are asked to “Build the angle”. Students create an angle using the sticks and measure it with a protractor. Students also are given a measure and build the angle for that given measure, with a protractor. Activity 2:Students are asked to make a right angle with two complementary angles, using the sticks. Activity 3:Students build a triangle drawing on a piece of paper. Students will cut the corners of the triangle and place these adjacent to one another on a straight line to demonstrate angle sum property of a triangle (the sum of measures of all angles of a triangle = 180 °) 
Students are given an explanation of how an angle is formed.
The teacher introduces angles to the class through physical manipulatives like strings or sticks, asking them to “Build the angle”; either before or after the teacher has explained the idea of an angle. Angles are cut out after being measured through a protractor. Note  This is home work or prior work (meaning that this need not be done by the third group during the workshop). Activity 1:There is a video of a teacher which shows the explaining using manipulatives, the content of
The video could also have some multi media representation (flash animations etc) of the concept. The teacher could also have recorded herself in the video (in this case, students may have a higher familiarity with the language used) (There are two variations possible here – the manipulatives and the activity are shown in the video as an explanation and discussed. The activities are done by the students. Or the video is shown and the students watch. The teacher can either play the video in full or stop, discuss, interpret and add hands on activities). 
The teacher introduces angles to the class through physical manipulatives like strings or sticks, asking them to “Build the angle”; either before or after the teacher has explained the idea of an angle. Angles are cut out after being measured through a protractor.
Note  This is home work or prior work (meaning that this need not be done by the third group during the workshop). Activity 1:In class the students do the activities of building an angle and measuring as well as marking out a given angle using an application called “Geogebra”. (use 1. Introduction to angles.ggb and 2. Introduction to types of angles.ggb) Activity 2:The teacher animates and shows different types of angles and how they can be combined to form complementary angles. (use No 3. Complementary angles demonstration.ggb) Activity 3:Students go through the logical proof of angle sum property of a file (the teacher can also guide the students to make this file). (use 3a. Introduction to triangles.ggb and 5. Angle sum property of a triangle.ggb) 
Content

Content

Content

PedagogyTypically, the teacher will ask students to make the angles, The activity often has a single defined path and an end in mind. 
PedagogyThe pedagogy has been modified here to have a video of a lesson. The use of the video allows different ways of interacting in the classroom; can also allow for afterclass learning. 
PedagogyIn addition to the approaches followed in the previous two cases, the following pedagogies are possible: 1. The students can explore in a dynamic way how angles change (in a physical manipulative – often – there is one given angle; though it is possible to build sophisticated models also) 2. The concept of an angle as a clockwise or counter clockwise rotation is possible to build over and above the physical representation – this allows misconceptions to be clarified 3. It is possible to demonstrate how the sum of measures of angles does not change even as the type of triangle changes (by moving of vertices). 
Technology

Technology
(Need to source such a video or make it) 
Technology

Discussion questions
Read all these scenarios and discuss the following questions:
 What are the learning objectives in each use case? Are they the same? Could they be different?
 What are the different possibilities for student learning in each approach?
 What are the different possibilities for assessment of student learning
 What are the challenges / limitations that you could face in each approach?
 What is the nature of teacher preparedness that is needed for each use case?