How a pedagogical lens can assist teachers in making ICT choices

Our teaching resources cover the topics of coordinate geometry, properties of geometric figures and probabilities in single and multi-step chance experiments from the Stage 4 and 5 New South Wales syllabus.  The syllabus outcomes, shown below, are taken from the Mathematics K-10 Draft Syllabus – Version 2  (NSW Board of Studies, 2012, p. 304):

Coordinate Geometry:

·      Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)

·      Plot linear relationships on the Cartesian plane with and without the use of digital technologies (ACMNA193)

·      Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294)

·      Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software (ACMNA214)

Properties of Geometric Figures:

·      Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)

·      Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates.  Identify line and rotational symmetries (ACMMG181)

·      Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166)

Probabilities in Single and Multi-step Chance Experiments:

·      Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167)

·      Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)

·      Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)

·      Calculate relative frequencies from given or collected data to estimate probabilities of events involving “and” or “or” (ACMSP226)

The main teaching focus used throughout this project is group work.  This approach is particularly effective in learning mathematical concepts such as coordinate geometry, properties of geometric shapes and probability, as group work requires the students to be active learners.  For this reason, Killen advocates that group work “can enhance students’ achievement and retention” (Killen, 2009, p. 188).  Furthermore, Roschelle et al. (2009) suggest that mathematical group work tasks can be enriched by incorporating technology, as we have done. 

Amosa, Ladwig, Griffiths and Gore’s (2007) research proved that the Quality Teaching Framework also greatly enhances student learning. As a consequence, we have endeavored to incorporate a high level of intellectual quality and significance into the lessons, as well as providing a quality learning environment.