Pre-calc and Calculus
Anyone wanting to do pre-calc and calculus would do it successfully, depending on the previous foundation in mathematics that incorporates the basic information required. A learner should not just forget the fundamentals of calculus immediately after a test or examination as this might position a student behind most of the time. It is always important to make sense on whatever the students learn particularly in mathematics. The primary building blocks of mathematical literacy include understanding times-tables or basic arithmetic facts that serve as core for nearly all mathematics learning that follow afterwards. However, the rote learning does not link properly with the current digital technology, making learning easier by doing the grunt work for learners. This form of writing presents some pros and cons of learning to work pre-calc and Calculus problems by hand.
Pre-calc and Calculus
According to “Classroom Professor”, it is undeniable that arithmetic begins from a particular foundation, which includes principles for numeration system, operators, symbolic system and all other basic information. Utilization of the basic calculus thought remains vital for students. A number of people believe in the mathematical concept and therefore using the manual process of teaching calculus idea will result into a massive universal support. According to Orlin, “most of all, they complain that rote learning has become taboo, rather than accepted as a healthy part of a balanced scholastic diet” (Web). Additionally, using the manual way of learning calculus tends to reinforce some arithmetical processes as well as links that may perhaps not arise when the digital technology is used such as the use of 10 being the base for the numeration system in indices.
It is essential to understand that manual learning of using pre-calc and calculus by hand improves focus mental attention, focus to detail and is free from distractions thus making it an exceptional mental workout. Understanding basic ideas and arithmetical principles can never be substituted with the digital technology since the brain is more superior to the technology, unless a learner has learning or mental disability. Students who do not understand the fundamental concepts of Calculus may hardly understand numerous related topics or basic arithmetical concepts that were crucial in the primary mathematics curriculum. Mental computational abilities tend to eliminate issues of struggling to reach understanding of concepts the learners could have learnt in lower grades.
Every individual should understand mathematical function and parametric equations supported by evidence instead of basing their activities on the arithmetical functions. According to Hacker, the most important thing is the qualitative literacy of an individual as it helps in identifying and detecting ideology at work behind the numbers represented in the digital technology (Web). Memorization is very crucial in fuelling deep insights and enables students to reason critically and such kind of knowledge is very useful.
The advancement of technology is meant to improve the way of doing things including learning. Calculators and other digital technology equipment are meant to make calculation much quicker and accurate. Because of the presence of new technology, the calculators and other equipment have rendered rote system less important. Understanding concept and memorizing arithmetical concepts are therefore not that significant as it used to be. Understanding calculus concept through the manual technique is quite challenging because it strains the brain. Cramming or memorizing a concept may turn out to be a tough situation for students. The fact that mathematics concept sharpens wits cannot be proved because students with such kind of understanding have never proved themselves to be politically and socially intellectual. The current technology need to be embraced and forget about the analogue system that is time consuming yet there are other vital things that teachers and students should do. Deeper understanding of mathematical concept in the classroom is not that significant because it does involve quality reasoning. According to Hacker, “Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job” (Web). Hacker believes that high-tech technology is crucial for the industrial success and therefore the solution does not lie in academic concepts and theories as it is conventionally thought.
Memorizing mathematical concepts is very important as far as deeper understanding of an issue is concerned. It is indeed significant for learners to have an insight on what they doing and the background of the calculus ides. However, any other person who does not know the derivatives of a particular arithmetic can use application of calculators and other technologies. Memorizing and understanding fundamentals of an arithmetical concept creates a difference between a learner and a common person. Beneficial use of the calculators requires a little knowledge of what a learner does.
“Classroom Professor.” How important are Times Tables, Really? 2013. Web. 8 Dec. 2013. <http://www.classroomprofessor.com/teaching-math/times-tables-debate-should-students-learn-them-today/>.
Hacker, Andrew. Is Algebra Necessary? The New York Times, 28 July 2012. Web. 8 Dec. 2013. <http://www2.kenyon.edu/Depts/Math/Milnikel/IsAlgebraNecessary.htm>.
Orlin, Ben. When Memorization Gets in the Way of Learning. The Atlantic, 9 Sep. 2013. Web. 8 Dec. 2013. <http://www.theatlantic.com/education/archive/2013/09/when-memorization-gets-in-the-way-of-learning/279425/>.