Meaning and Application in Math
Many people wonder about the difference that exists between applied math and pure math. Some argue that pure math is more imperative than applied math because of its both applicability and aesthetic side. They argue that what is significant in math is math technique, which is taught, mostly in pure math. Applied math, on the other hand, teaches the application of math in a wider view and disciplines such as commerce, science, and even technology. Applied math is more of learning how to do and why unlike pure math which emphasizes how to do. Nevertheless, the current paper will analyze the difference between “teaching what to” and “teaching what to and why”.
Meaning and Application in Math
In mathematics, there is a difference between teaching ‘what to do’ and teaching ‘what to do and why’. Some teachers do not comprehend the difference. Indeed, Burns (2007) wonders why the practice of teaching the procedure of mathematics detached from the application, and the meaning of the procedures is so pervasive in learning institutions. According to Burns (2007), since mathematics does not exist in a vacuum, students should not be taught math as though it does not exist. The current paper will compare and contrast the context of teaching math in the context of meaning and application. Nonetheless, teaching ‘what to do and why’ is more important than ‘teaching what to do’.
According to Burns (2007), there are various reasons why most teachers teach students what to do but not why it should be done. First, to learn what to do is much easier than learning what to do and why. Second, most books of math emphasize mostly on learning procedures required in solving math. Books teach students to write the correct answers but will never explain why that was the right thing. They, therefore, do not give the students an opportunity to think or comprehend the concept.
Third, there is always pressure on students to pass tests. Math procedures are just learned for the sake of passing exams. Math is no longer applicable after passing the test. In addition, it is hard to assess if the ‘why’ of arithmetic is understood by students. Much of the learning is done on papers, and it would be difficult to analyze what the students are thinking. Lastly, some of the teachers do not know the difference between teaching student how to reason in arithmetic and the math procedures. Most of the teachers were taught the arithmetic procedures and that is what they teach the students. Otherwise, they cannot teach them what they do not know.
Nevertheless, there are various reasons why it is imperative to teach “what to do and why” rather than “what to do”. For instance, when the students understand why they are doing certain arithmetic, they can easily apply the new skills attained due to their high levels of understanding. Students should, therefore, use the concept that makes them understand calculations and be able to apply them in different situations. The idea of following rules is not the solution because it is something they cannot apply in future scenarios. Understanding why and knowing how is critical to students.
More so, when students learn the meaning in certain arithmetic procedures, it becomes easy to remember. As a result, students do not need to memorize large content of unrelated formulas and rules in the mind. All arithmetic instructions are standardized and organized in pieces. This makes arithmetic easy to understand and the goals of the curriculum become more manageable. However, it should be noted that teaching students in pieces does not add value to their learning other than teach them the bit-size skills. In fact, some students fail to connect the different bit-size pieces from one level to another. Such procedures are unnecessary and should not be used to teach math.
Learning how to do and why enables students to reason. Learning how to reason enhances continuous learning. When students learn how to reason, they get the power to learn more concepts compared to learning procedures of events, which are not connected. Reasoning makes the students want to analyze issues from a different angle, something that makes them learn.
Lastly, if students are taught what to do, they easily become incompetent and an attitude of negativity towards math crops up. They have to understand math for them to appreciate.
Therefore, I fully support Marilyn Burns’ belief that the “why” is as important as the “what to do” in mathematics. There is a need for students to comprehend that algorithms are only procedures invented to help carry out calculations, which are repetitive. Students should, therefore, understand how the algorithms are based on logic and structure of the number system. Most importantly, students should also understand that certain algorithms are not efficient than others and that all the methods, including the ones invented by students themselves, are valid.
For students to grasp concepts, it is imperative for them to think and reason out to make sense out of the arithmetic situation. According to Kleine et al., (2005), students should not focus on cramming the sequences of the steps needed in carrying out particular procedures. Students should also try to think answers out before reaching out for paper to do the calculation on their heads even if the arithmetic is simple. This makes it easy for them to even get errors on paper, and never understand that they were absurd solutions and should be avoided.
In conclusion, students should learn “how to do and why” rather that learn “how to do”. Most students get more benefits when they invent their own ways of calculating because it focuses only on the numbers involved, and connects to their way of reasoning. Making sense is core to learning math. Teachers should, therefore, challenge children to understand the techniques required in doing certain arithmetic and explain the reasoning for the procedures they invent. Conversely, students should be given a chance to interact and learn from each other.
Burns, M. (2007). About teaching mathematics: A k-8 resource. (3rd Ed.). Sausalito, CA: Math Solutions Publications
Kleine, M., Goetz, T., Pekrun, R., & Hall, N. (2005). The structure of students’ emotions experienced during a mathematical achievement test. Zdm. doi: 10.1007/s11858-005-0012-6