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.

How the designed resource facilitates quality teaching and learning

The SMART board resource we designed facilitates quality teaching and learning in several ways.  Firstly, the deep knowledge of the lessons is presented through a range of mediums: pictures, diagrams, interactive graphs and games in addition to text.  The aim of these is to enhance the students’ deep understanding.   Killen (2005) suggests that in order for students to develop deep understanding, students must be given appropriate examples, detailed explanations, opportunities to think about what they are doing as well as testing of their understanding with appropriate feedback.  Our teaching resources abound in detailed and clear explanations with corresponding examples.  We have also inserted various questions, games and quizzes with instantaneous feedback throughout our resources in order to assess the students’ deep understanding.  We have inserted “think” boxes throughout the resource encouraging the students to develop higher-order thinking.  These questions require the students to go beyond simply remembering, understanding and applying the knowledge to analysing and reasoning further about the mathematical concepts. The interactive nature of the resource and the games that have been incorporated are designed to increase student engagement. In the second coordinate geometry lesson (Gradient), the students have to research real-life applications of the mathematical concepts they have learned, thus adding significance to the lessons.  

Justification of the intellectual rigor and engagement

This resource not only gets students to reach the syllabus outcomes, but to explore the concepts deeper through investigation, both with the interactive graphs, activities exploration tasks and the research project.  Questions are raised throughout this research to challenge the students and increase the intellectual rigor of the lessons.  The challenge activity at the end of the third coordinate geometry lesson extends the students further by requiring them to apply their knowledge of gradient and distance to a formal mathematical proof, something that is notoriously difficult for high school students.  This website takes the students step by step through it, thus scaffolding their knowledge and providing a challenge for them.  

Engagement is vitally important since Prensky (2001) points out that “if you can hold the attention of children, you can educate them” (p. 2). This resource enhances student engagement through its interactive nature.  Interactive graphs, exploration tasks and interactive activities, in which students learn through discovery, feature in the lessons. This is important as today’s students are “active participants rather than passive observers” (Prensky, 2001, p. 11).

Description of a key learning moment

I have been amazed at the interactive mathematical Flash animations and games that are available on the Internet.  The interactive graphs that I found online and incorporated into my lessons are invaluable resources that I want to incorporate into my future teaching.  I used the Download Flash and Video add-on for Firefox to download the Flash games and interactive graphs.  I also used the website www.keepvid.com to download the YouTube video demonstrating Pythagoras’ Theorem.  I was unaware that such teaching resources were available on the World Wide Web, let alone how to download these games and videos, prior to this “Project-Based Learning Project.”  The techniques I have learned I will be able to now use for further situations in my teaching. 

Discussion of insights through the experience of group work

I have learned so much about ICT through the group work in this “Project Based Learning Project.”  Benjamin, Anna and I all have busy schedules, so much of our correspondence after the initial meetings was via Google docs.  I had not used Google docs before.  I now see the advantages of this web 2.0 tool.  The three of us have worked together on other group projects before and used email as a communication tool, but Google docs proved to be a superior method of communication.  With Google docs, there is no need to CC other members as everyone has access to the information.  My inbox is not congested with multiple emails going backwards and forwards.  Instead, all communication is neatly stored in one place.  Furthermore, Google docs made it easy to share our work with each other since our SMART notebook files were massive.  

It was great working with Benjamin and Anna as I was able to glean great ideas from them that I was able to incorporate into my sections.  For example, Benjamin created most of his diagrams and even text in Microsoft PowerPoint and then copied it into the SMART notebook file, since Microsoft PowerPoint is so much more versatile than SMART notebook.  Also, Benjamin came up with the idea of “think” boxes, an idea that I really liked and incorporated throughout my sections. 

How Multiliteracies supports my TPCK

The term multiliteracies encompasses multiple “communication channels and media” to cater for today’s “cultural and linguistic diversity” (The New London Group, 1996, p. 63).   We incorporated a range of literacies into our teaching resources: text, images, flash animations, games, interactive graphs and videos.  Thus, we have provided the students with a diet of visual, audio, spatial and linguistic literacy – multiliteracies (Cole, 2010).  Messaris (1998) suggests that visual literacy should be given heightened attention in education, “not as competition to verbal language learning, but as a valuable complement to it” (p. 78). Thus, we have sought to incorporate visual literacy throughout our teaching resources. The video embedded into the Distance lesson uses visual literacy to prove Pythagoras’ Theorem.  No words are used.  Instead, the whole proof is conveyed through an animated yellow triangle, red square, blue square and green square.   Likewise, the three videos on the Monty Hall problem incorporated into the probability exploration tasks also incorporate multiliteracies, visual, audio and media literacies, as the students explore the mathematical probability behind this game show situation. Special use has also been made of colour in our resources.  Not only does it add interest, but it also has been used to convey messages, provide links between text and images and highlight things of importance, thus enhancing the visual literacy. 

Our teaching resource combines the content knowledge of coordinate geometry, with pedagogical practices such as group work, student research, the Quality Teaching Framework and technological knowledge of such technologies as SMART notebook software, the world wide web, glogster (a web 2.0 tool), Microsoft PowerPoint and Flash animations and games.   This integration of content knowledge, pedagogical knowledge and technological knowledge, referred to as TPCK, has been proven to enhance student learning (Mishra & Koehler, 2006).

The social impact of technology on teachers and students

It is claimed that using the Internet in the classroom increases students’ “awareness of the importance of the world around them, of citizenship” and the academic world around them (Pickersgill, quoted in Bingimlas, 2009, p. 237).  

Our teaching resources contain a considerable amount of group work. In this way, the students are given an opportunity to develop social skills through this project.  Different students have different strengths and weaknesses, so group work enables students to develop cooperation skills and “to learn respect for one another’s strengths and limitations”  (Killen, 2009, p. 189).  Furthermore, an early study conducted by Hawkins et al. (1982) revealed that children are more likely to collaborate together with computer activities than with non-computer activities. 

Group work is especially apparent in the lesson on Gradient, where the students are required to research a practical application of gradient and present their findings in the form of a glogster, a web 2.0 tool.  Gomez  (2012) believes that interactive web 2.0 technologies greatly enhance student collaboration and responsibility sharing. Thus, group work combined with technologies, especially web 2.0 technologies, can have a positive social impact on students.