Section I: Investigating Goal The goal of my Personal Project is to create a mini album that consists of three therapeutic songs for children aging from 11 to 17 who have mental disorders: ADHD, bipolar disorder and major depression. My Personal Project focuses on the concept of well-being and aims to ameliorate others’ wellbeing by curing their mental disorders. Healthy People Government defines mental disorders as “health conditions that are characterized by alterations in thinking, mood, and/or behavior that are associated with distress and/or impaired functioning. This most malignant problem in mental health, can lead patients to disability, pain, or even death as a result. Mental disorders are usually caused by excess amounts of stress from academics and environments that are surrounding the patient, and the target does not exclude, us, students either. Therefore I have always desired to help those people who have mental disorders and did not want ourselves to have those unfavorable results due to mental disorders, and felt the need to establish my own solution to these problems. While studying music in MYP, I discovered that music can be a great help to mental health. Due to my personal reasons such as stress from academics and friendships, I was suffering a sort of depression in Grade 9. However after I composed my own music pieces and listening to them, I felt proud of the fact that I composed my own music pieces and the fact that they do not sound that bad this helped me to get myself stand up and cure my depression.
Some people can remember information better than others. Is this because of their capabilities or use of memorizing techniques? Several studies have investigated the link between schema activation and memory recall (Cohen, Bransford & Johnson, Stone). Schema is a cognitive framework of related pieces of information, knowledge or memory (Dixon).Bartlett’s Schema theory could explain the relationship between schema activation and memory recall: when people’s schema is activated, there is a link made between the schema and the new information, which makes them easier to process and recall it (Dixon). Hence the theory posits that if schema is activated, people are more likely remember information that relates to that schema. Bransford and Johnson (1972) investigated the relationship between schema activation and memory recall (Bransford and Johnson). The study’s aim was to investigate the effect of schema activation on comprehension and memory recall of new information. The participants were 52 male and female students at New York State University. The participants were randomly allocated into three conditions and told to listen to a passage. The independent variable was whether the title of the passage, “Washing Clothes”, was given before or after listening to the passage, or not given. There were two dependent variables: self-rating of comprehension out of 7 and number of details recalled out of 18.
The following pastiche, inspired by Tim O’Brien’s novel The Things They Carried (1990) fulfills Part 4: Critical Study’s learning outcome “Analyze elements such as themes and the ethical stance or moral values of literary texts.” by exploring themes of the anti-war genre. The pastiche intends to capture the theme loss of innocence by showing the backstory of a misunderstood character, Azar, revealing how Azar could transform from an innocent kid to a character desensitized to death that the audience is shown in the short story, Spin.
A fractal is an object that exhibits self-similarity (Falconer 22). Self-similarity is a property that a similar shape can be identified at different scales looking at the object (Falconer 22). The more self-similar an object is, the more complex it looks (Chaos, Fractals and Dynamics). A lot of time series data, such as which are data ordered by time, display this feature and this feature commonly correlates with real-life phenomena (Kantelhardt 4). For example, in electroencephalogram (EEG) signals, if the patient is has an epileptic seizure, his EEG signal looks more complex than a non-epileptic patient’s EEG signal(Neurocomputing). To incorporate this feature of self-similarity when modeling EEG signals, functions called fractal interpolation functions can be used. These fractal interpolation functions can convert the raw data into an analyzable function that displays self-similarity (Manousopoulos 1). Not only they can model these signals, they can also measure fractal dimension, which is a measure to quantify the level of self-similarity (Barnsley 223). By doing this, fractal interpolation functions can take data points that are not even part of the raw data points into consideration. There have been many algorithms devised in academics to measure a fractal’s fractal dimension using the raw data only, but there has not been much development in measuring the fractal dimension using fractal interpolation functions (Navascués 2).
My interest in Taylor series arose when I became curious of how our graphic display calculators actually calculate a value when we plug-in an value into a function. As a calculator would not be able to have every single value for any function, there must be an algorithm that the calculator uses to calculate functional values. I searched up what kind of calculations our graphic calculators are actually doing, and what I have found was the marvelous series – Taylor series. A Taylor series is “a series expansion of a function about a point” (Abramowitz). What our calculators do to calculate a functional value is that, they approximate a function into this Taylor series give approximate values when we input a value. I became curious of the explicit process ‘how’ this Taylor series is actually used and how reliable it is to use to calculate any functional value on the calculator. Therefore I developed my aims of this exploration: 1) Investigate in how Taylor series is used in graphic display calculators through its proof and applications and 2) investigate in the approximation error produced by Taylor series.