Reflection 8: "Mathematics is not only about numbers, equations, computations or algorithms: it

What are the different shapes that can be created using the lines in the photograph? (You may connect lines)

How can these shapes be classified? (It might be analyzing attributes or properties)

Using all the lines in the above stimulus, what shape can be created? (And then name your shapeà remember a shape is named by how many sides the shape has)

Estimate what is the total length of the red (and the other colours) lines? Now using the appropriate tool, measure the line and see if your answer was close to being correct.

Which line will produce the most 4 sided shape?

“Open ended activities can be a powerful and an engaging tool” (Begg & Cavagna, 2009, p.1). As I have provided you above with an example of an engaging open-ended task for students to stimulate their thinking with, it allows them to develop different ideas and various solutions (Begg & Cavagna, 2009). Thus, offering students insights to their thinking and learning (Begg & Cavagna, 2009). Teaching ‘space’ to students allows them to develop their visual and spatial awareness and develop their creativity by creating their own geometric shapes and patterns, fitting them into the space provided to create the shape they want. The design on the photograph above allows for all sorts of shapes to be created and connected, thus, has many learning opportunities as infinite designs exist. Open- ended questions are fundamental in order to become an effective teacher hence, stimulating student’s mathematical thinking.

The photograph above allows students to demonstrate their thinking and fosters their shape awareness, spatial visualization skills and problem solving skills. As students get older they “classify shapes by their attributes and they can identify and classify most common shapes by their geometric properties” (Copley, 2010, p.105). Through the use of open ended questions and a hands on learning experience, it encourages students to be creative in their responses and consider their own thoughts and ideas, while choosing particular methods and applying their mathematical knowledge (Boaler, 1998). Geometry is important for students to develop an understand of because the world around us is built of shape and space, thus, geometry is the mathematics used. The use of hands on learning experiences allow students to learn mathematics in a more enjoyable way, making connections between the concrete and abstract (Furner & Worrell, 2017). Starting with manipulative materials students are able to gain an understanding and gain the knowledge to then be able to problem solve using representational models like pictures/ photographs, leading students learning to a more abstract level of understanding (Furner & Worrell, 2017).