Conventions
Alan J. Bishop (2008) examined the teaching and learning of mathematics in Papua New Guinea. Throughout his research, he found differences in conventions, drawings, visualization, language and cognitive characteristics between mathematics in Western and non-Western cultures, such as Papua New Guinea (Bishop, 2008). These differences result in challenges in the mathematics classroom where mathematics from different cultures is present.
Bishop (2008) discovered that many students in Papua New Guinea were unfamiliar with several of the conventions used in Western education. For example, he provided students with a 2-dimensional drawing and asked them to create a 3-dimensional object of the drawing (Bishop, 2008). Most students were unable to complete this task because they were unaware of what the conventions symbolized in the 2-dimensional, Western drawing. Different cultures choose different symbol to represent various things. If a student is unaware of these conventions, they will have trouble completing the mathematics task. Also, Bishop (2008) found that students from non-Western cultures have weak spatial skills, due to the conventions that are used. Individuals living in the Western culture are so used to and familiar with conventions that they forget that they are not universal and are not known by individuals from non-Western cultures (Bishop, 2008). It is important to remember that conventions are learnt. Bishop (2008) points out that if we were not aware of the conventions used, we would not be able to read and write. This same challenge is present when teaching and learning mathematics. Ensuring that all students understand the conventions being used, especially those from non-Western cultures, can help ensure that their spatial skills improve because they will better understand the math being presented to them.
A challenge with accuracy was also discovered by Bishop (2008). Students interpreted conventions, drawings and instruction differently, depending on their mathematics cultural background. For example, when students were asked to copy a diagram, many different levels of accuracy were produced (Bishop, 2008). To a Western culture, copy means identical (Bishop, 2008). However, this instruction was interpreted differently among various cultures because their definitions and criteria around accuracy varied (differences in scales, lines and angles) (Bishop, 2008). Therefore, these conventions and criteria must also be learnt. There is nothing obvious or universal with regards to what is expected in the mathematics classroom. Teachers must be aware of this and must take time to teach the meaning of the conventions used in Western cultures and ensure that their instructions are clear and nothing is assumed.
Bishop (2008) discovered that many students in Papua New Guinea were unfamiliar with several of the conventions used in Western education. For example, he provided students with a 2-dimensional drawing and asked them to create a 3-dimensional object of the drawing (Bishop, 2008). Most students were unable to complete this task because they were unaware of what the conventions symbolized in the 2-dimensional, Western drawing. Different cultures choose different symbol to represent various things. If a student is unaware of these conventions, they will have trouble completing the mathematics task. Also, Bishop (2008) found that students from non-Western cultures have weak spatial skills, due to the conventions that are used. Individuals living in the Western culture are so used to and familiar with conventions that they forget that they are not universal and are not known by individuals from non-Western cultures (Bishop, 2008). It is important to remember that conventions are learnt. Bishop (2008) points out that if we were not aware of the conventions used, we would not be able to read and write. This same challenge is present when teaching and learning mathematics. Ensuring that all students understand the conventions being used, especially those from non-Western cultures, can help ensure that their spatial skills improve because they will better understand the math being presented to them.
A challenge with accuracy was also discovered by Bishop (2008). Students interpreted conventions, drawings and instruction differently, depending on their mathematics cultural background. For example, when students were asked to copy a diagram, many different levels of accuracy were produced (Bishop, 2008). To a Western culture, copy means identical (Bishop, 2008). However, this instruction was interpreted differently among various cultures because their definitions and criteria around accuracy varied (differences in scales, lines and angles) (Bishop, 2008). Therefore, these conventions and criteria must also be learnt. There is nothing obvious or universal with regards to what is expected in the mathematics classroom. Teachers must be aware of this and must take time to teach the meaning of the conventions used in Western cultures and ensure that their instructions are clear and nothing is assumed.