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

1. Building an angle, measuring the angle
2. Building complementary angles
3. 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 angles, types of angles and the angle sum property of a triangle. 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 Angles Types of angles Angle sum property of triangle physical manipulatives Models depicting this content	Content Angles Types of angles Angle sum property of triangle Models depicting this content Video (can be of different kinds – a lecture, a recreation of a black board explanation, or a teacher using materials or digital representations of content). Learning the use of multi-media equipment is also content here (computer, projector)	Content Angles Types of angles Angle sum property of a triangle Models depicting this content Geogebra application and files (Geogebra is a content item) Video
Pedagogy Typically, the teacher will ask students to make the angles, The activity often has a single defined path and an end in mind.	Pedagogy The 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 after-class learning.	Pedagogy In 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 Blackboard and chalk Using physical materials /manipulatives	Technology Blackboard and chalk Using physical materials Using a video and other ICT equipment to project (Need to source such a video or make it)	Technology Technology Blackboard Using physical materials Using Geogebra (digital technology) Using a video and other ICT equipment to project

Discussion questions

Read all these scenarios and discuss the following questions:

1. What are the learning objectives in each use case? Are they the same? Could they be different?
2. What are the different possibilities for student learning in each approach?
3. What are the different possibilities for assessment of student learning
4. What are the challenges / limitations that you could face in each approach?
5. What is the nature of teacher preparedness that is needed for each use case?