Firstly, the questions in the numeracy test rely heavily on the student’s prior experiences in mathematics. So, instead of testing the mathematical understanding of the student, it tests how well the student has been taught mathematics. This became apparent to me when I was completing the test, because I found the questions that I had previously been exposed to at school a lot easier to answer. In comparison, I found the questions that I had never come across a lot more difficult, even if the actual mathematics involved was at a similar complexity level. This notion reduces the validity of NAPLAN due to the fact that it assesses how well the students have been directly taught for the test, rather than the mathematical ability of the students.
I chose this topic because it helps answer several concerns that arise at attempts to teach and to learn about proofs. Through a diagram that made the statement obvious, the result may be sensed or discovered intuitively. Hence it helps the viewer internalize the idea by gaining an insight into why the idea was correct, and it makes more discernable relationships between parts or parameters of a mathematical statement. Proof without words can be one step proof, or even a proof that does not start with fundamental axioms. It is very effective not only for learning mathematical statements, but also for developing a feeling for mathematics as a discipline.
Most assuring to me in my report was seeing mathematics as my highest interest and investigative as my predominant theme, as I feel that I am a strong student in math and a highly curious individual who likes to seek out facts. I was a bit unsatisfied with some of the other results. However, Miss Mindy told me to just use these assessment reports as a guide, as I am ultimately in control of what career path I decide to
Art is the illustration or presentation of human creative skill and imagination, usually in a visual form such as painting or sculpture. Its purpose is to produce works to be appreciated primarily for their beauty or emotional power. Art also involve geometry. Geometry is the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional element. Many people fail to realize that Art is related to Math.
For example, Sandburg describes arithmetic as where “ the answer is right and everything is nice” and “answer is wrong and you have to start all over again” The contrasting emotions Sandburg convey’s between a wrong and right answer shows how math emotionally rather than just physically affects our lives. The contrast between “everything is nice” and “have to start all over again” reveal just a portion of the emotional impact math can have on a person. Sandburg also depicts arithmetic as “where you carry a multiplication table in your head and you hope you don’t lose it.” Such an image implies that math forces people to store information in their head as if they were protecting something with dear care in order to not lose possession of it. The multiplication table, in this case, is portrayed as an object that humans genuinely care for and do not want to see get lost. Sandburg also relates arithmetic to winning and losing when he writes “Arithmetic tell you how many you lose or win.” Such a comparison once again depicts math as having a profound impact on our lives in that math is in a way a form of the struggle between winning and losing.
It might not be Pythagoras theorem or Newton’s laws of motion. Nevertheless, this theorem is applied to complex numbers mostly whenever they are used. It may appear that complex numbers do not have a very straight application in real life mathematics; however, they can always be used to model a phenomenon. If this phenomenon is periodic and it is modeled with a complex number, De Moivre’s theorem would provide the solution to change the frequency of our model. In other words, this theorem would be the key to solve an ultimate issue with models, as we would use the exponent to do so.
The equations we use every day are a part of mathematics, but they are not knowledge. They are simply tools we use to express our knowledge. For example, the Pythagorean theorem for right angle triangles has always been true, but we simply did not discover the case until Pythagoras legitimized the theory by creating the equation (Mastin, Luke). This brings light to how equations are the tools of knowledge in mathematics. Many believe that equations are knowledge in themselves, but they are merely tools to help us understand knowledge in maths, and to help us apply it.
Complex issues and ideas are those that can be argued for or against, and both arguments have their suitable and understandable points. In the film Stranger Than Fiction by Marc Forster, the complex ideas of literature making us socialise, routines isolate us, and needing people to change are lives are argued through the use of composition, long shots, and symbolism. In the text Stranger Than Fiction, complex issues have been constructed through visual techniques. Harald Crick, the protagonist, is an anti social character. The text suggests this is because of his love for maths, rather than english and literature.
How can we know that the knowledge we have is trustworthy in Natural science and mathematics? Knowledge is facts, information or skills that are acquired through experience and education, its the theoretical or practical understanding of a certain subject. Knowledge that is trustworthy is knowledge that is able to be relied upon as honest and truthful information. While looking at Natural science and mathematics we will see that mathematics isn’t necessarily more reliable but the knowledge we obtain in these subjects will be different. Mathematics can be seen as more trustworthy because it uses reasoning.