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Both, the TED talk by Salman Khan about his own Khan academy and the article on Mathematical Ability by Daniel Willingham, raised key ideas and opinions on how mathematics is learned at taught today.
Looking at the Khan academy first their aim is to get students to do the lessons in their own time. This is so that the teacher can spend the lesson doing homework with the students. Therefore meaning the teacher is spending more time helping the students’ one on one, than they would if they were having to teach the class. I don’t believe you could rely on the students to do the lessons in detail and thoroughly enough for them to have a grounded knowledge on the topic. The way the site is designed it allows for students and teachers to track their progress. This means that when students complete tasks and questions on each topic the teacher can see what they got wrong and what needs to be worked on. However, in my opinion I can see how this tool may be useful for getting students through all the topics in a quicker time it is prone to possible cheating on the students behalf. This is because if they can’t do a specific topic for example that they need to do to be able to move on then they will cheat so as they are not left behind, rather than asking for help.
Moving on to the article by Daniel Willingham, he claims that everyone has the capabilities to learn mathematics. He says that you are born with a sense of numbers and the differences between them and also how numbers are related to space. I can agree with this statement as it is backed up with research showing how babies know the difference between one and two for example.
Another point raised in the article is that the reason feel they are not able to do mathematics is due to a lack of memory recall of basic maths. This is because all complex maths is made up of simple maths. All that is required to be able to complete the task is the ability to recall maths from our memories. The article shows that the less working we have to do and the more we can recall from memory then we are more likely to get the right answer. So are we teaching maths techniques or just testing students’ memory?
A thought-provoking quote for me personally in the article was; “For most topics, it does not make sense to teach concepts first or to teach procedures first; both should be taught in concert. Gaining knowledge and understanding of one supports comprehension of the other.” This links back to the idea of Relational and Instrumental learning that Skemp discussed in his article. I believe in the idea that we cannot do one without the other.
Overall I feel that the Khan academy is a good tool for homework based tasks as it has the infrastructure to help students if they get stuck on questions. However, it should not be used as a replacement for teaching. On the other hand, the article by Willingham raised many key points on why people feel they cannot do maths and also I feel that it showed ways helping these individuals who are struggling with maths.