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
{| class="wikitable"
 * 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.
 * 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.
 * 1) angles,
 * 2) types of angles and
 * 3) the angle sum property of a triangle.

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

 * 1) Angles
 * 2) Types of angles
 * 3) Angle sum property of triangle
 * 4) physical manipulatives
 * 5) Models depicting this content

Content

 * 1) Angles
 * 2) Types of angles
 * 3) Angle sum property of triangle
 * 4) Models depicting this content
 * 5) 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).
 * 6) Learning the use of multi-media    equipment is also content here (computer, projector)

Content

 * 1) Angles
 * 2) Types of angles
 * 3) Angle sum property of a triangle
 * 4) Models depicting this content
 * 5) Geogebra application and files (Geogebra    is a content item)
 * 6) 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

 * 1) Blackboard and chalk
 * 2) Using physical materials /manipulatives

Technology
(Need to source such a video or make it)
 * 1) Blackboard and chalk
 * 2) Using physical materials
 * 3) Using a video and other ICT equipment to    project

Technology

 * 1) Technology
 * 2) Blackboard
 * 3) Using physical materials
 * 4) Using Geogebra (digital technology)
 * 5) 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?