Prescribed Title: Are visual representations always helpful in the communication of knowledge? Discuss with reference to the human sciences and mathematics.
Word Count: 1523
Session: May 2023
Prescribed Title: Are visual representations always helpful in the communication of knowledge?
Discuss with reference to the human sciences and mathematics.
Do not judge the book by its cover.
Pictures worth a thousand words.
The first two phrases above have given us the idea of how visual representations are helpful in the communication of knowledge. However, they are not always helpful as several learning styles can be approached to one’s knowledge. Visual representation is defined to be one of the mediums in communication in the formof photos, images, or intuitive diagrams thatis easier for the knower to observe.
To the extent of its use to strengthen communication in all sorts of knowledge, using images, graphs, diagrams, or other kinds of depictions, does appear extensively helpful in many areas of knowledge
Through Mathematics and Economics, visual representations are used to simplify learning and understanding concepts when it comes to quantity, numbers, and clearly interpreting what happens in the economy. On the country, it can also be used to mislead information in both subjects given through the analogy of mathematics that conceals useful datasets.
Many people rely on visual representation in learning various difficult concepts of mathematics. Including myself, I used to be passionate about disliking the subject. Especially, dealing with numbers and heavy topics, it made me feel discouraged so many times. Despite that, I decided to seek help later throughout high school - watching YouTube® videos was one of the best decisions at that time. It was only to realize thatperspective towards mathematics changed completely knowing how quadratic formula works for the first time using visual representation of completing the squares!
Most high school students are likely to have come across the quadratic formula. Mathematics is derived from the technical terms of isolating the unknown variable �� given the expression of the form
����2 +����+�� =0 In the quadratic expression, letter ��, ��, and �� express the independent variables, in which itis added to basically make allvalues different as well as the value of x given the quadratic formula.
When I first learned the quadratic formula, I really doubted myself “Why does it matter to understand mathematics?” After all, it is believed that because of different learning styles, it might not suit all of us. For example, some people are visual learners so algebraic explanation may not work for them. Yet, I came across YouTube videos that helped people understand mathematics (1). Starting with the quadratic formula, through visual illustration, it is surprisingly helpful in the communication of knowledge, especially in mathematics and there arecouple reasons forthat. Firstly, mathematics is the subjectthat deals with the study of quantity, special pattern, and change By demonstrating them in a more commonsensible way, therefore, the concepts are appropriate to be explained along with data representations, images, and diagrams Secondly, learners of mathematics do receive the ability to see why things happen the way they are in use of the sense perceptions that we are acquainted biologically
Back to the quadratic formula, by deriving the expression ����2 +����+�� =0 Through visual approach, some people would be surprised by why it made so much sense. In the reverse, the approach can also confuse people at the same time arguably. To demonstrate this, Figure 1 depicts the rearrangement of the quadratic expression to the quadratic formula isolating unknown variable to �� = ��±√��2 4���� 2�� of which thereare series of step involves in (3). First, we divide thewhole expression by variable a to make it become
2 + ���� �� + �� �� =0 . Next, separate the values that are attached to x and the ones that are not into the different side separated by the equal sign, so we got ��2 + ���� �� = �� �� . Then, I use the concept “completing the square” learned in IB mathematics course to isolate the variable �� It becomes clear after several arrangements, from thegeneralquadraticexpression, thatwe have derived the quadraticformula! The illustration in Figure 1 shows why these stages are described using visual method. It basically converts the unknown �� value and the known numerical values ��,��,�� to a ‘square’ and complete them; that is where the term ‘completing the squares’ comes from. However, we could argue that the visual approach cannot be helpful from our
difference in learning styles. On top of that, all the visual representations cannot be understood in any way if the algebraic explanations did not appear along with it at the first place.
Visual representations are usually helpful for the knower in economics. When comparing the subject to mathematics, the concepts are intuitively and objectively explained through graphs, usually diagrams dealing with numbers. The subject relies heavily on rules, law, and theories that are understood by mathematicalfunctions, namely therelationship between two main variablesbetween priceandquantity. One example is the law of demand and supply - the economic theory between buyers and sellers about price and quantity (Tragakes, 2020, pp. 41-83). In the demand side, according to the IB Economics book, people tend to buy less when price increases and buy more when price decreases. On the other hand, the supply of goods increases as the market price goes up, and less as the price decreases. The use of visual representations helps us to understand the relationship between demand and supply clearer using simple depictions that also relate to high school mathematics class such as functions and graphs. It is also useful when it comes to calculation regarding what would benefit buyers or sellers in Microeconomics (Tragakes, 2020)
In the current topic I am learning in Economic – The International Trade, the use of diagrams is comprehensive to explain the concept of export and import in goods and commodities Also, the price changes in economy that the intuition of mathematics can also be useful. Given a scenario of trading one good in country X for instance, the effect of importing or exporting those goods (shown in Figure 2 above)
The positive straight line is known as supply - represents domestic supplier – the one produces the goods. While the negative straight line is known as demand - represents the demander - the one consumes goods domestically corresponding quantity and price. As demonstrate in Figure 2, the visual depiction not only illustrates how trade functions in various circumstances of domestic and international with multiple price ranges established for specific reasons, but also play the role in measure of the quantity of expenditures, profits, and losses in these economies (4).
However, the limitations of visual representations in economics arise when they are used to explain the knowledge without any further explanations. On top of that, without more pieces of information used to explain pictures, images, or diagrams, the knowledge will not be complete in terms of communication usingvisualrepresentationsitself.Theimplicationofthis waseventhoughtheuseofdepictionsisnecessary in economic interpretation, it is not possible to disregard the information behind rather “confusing” diagrams you have not seen before. Given the example of the diagrams to explain International Trades occur in the economy, it cannot explain descriptively why each country must produce decisions for the
commodities to be worth trading. In theory, there are two terms called “comparative advantage” and “comparative disadvantage” (Tragakes, 2020, pp. 428-442). The phrases basically describes that there are countries specialize in trading certain things to make the good worth exporting or importing which the fact alone can hardly be understood using visual representation. Moreover, without the basis of mathematics that is relevant to written words and numbers, it cannot be helpful for the knower at all.
In our mathematics class, we heard an interesting idea on the “line of best fit” namely in statistics lessons. This term refers to the correlation line on corresponding data points, and the interesting part was that it could mislead information (see Figure 3). The four sub- illustrations show one orientation of each dataset that causes the corresponding lines to appear visually identical. It is intriguing to see those points to be different hugely compared to one of the others. The implication of this was that such lies can be the analogy to mathematics and economics on how visual representation in fact matters. In mathematics, the line of best fits (shown in Figure 3) can hide necessary data given to the “visual representation” itself to be seen publicly. In Economics, as most knowledge requires diagrams or statistical data to produce helpful
interpretation and decisions, the idea of images or picture representation used to hide truth can also relate as a threat in the communication of knowledge.
In conclusion, visual representation is immensely helpful in the communication of knowledge, but it also requires other mediums to be involved. Nevertheless, through mathematics and economics, visual representation is necessary in the exchange of information in scientific or numeric-based questions and for serving intuitive representation to the knower. This draws to the interconnection between the areas of knowledge that the quantitative representation of mathematics, namely, is beneficial to explain harder knowledge commonly in natural or social sciences The two phrases that start the idea “Don’t judge the book by its cover” and “Pictures worth a thousand words” might be telling us that “What we sees require tremendous pieces of information to judge the book by its cover (1).” Nonetheless, “What we have seen could also worth a thousand words with its devious meaning
References
Gupta, S. (2020, July 27). [Importance of data visualization Anscombe’s quartet way. four datasets that fool the linear regression model if built.]. Medium. https://towardsdatascience.com/importanceof-data-visualization-anscombes-quartet-way-a325148b9fd2
Tragakes, E. (2020). Economics for the IB diploma: Coursebook (3rd ed.). Cambridge University Press.