Music and Modular Arithmetic and their Similarities

Modular Arithmetic has a connection to the history of the clock. From research, we came

One way to understand Mathematics is to look at language; mathematics is a language in itself and in some cases it can help you understand another culture, without having to live in that culture.

I have always considered myself a mathematician; however, that did not keep this subject from being difficult. Math has a glorious way of growing you up. For me, it began in the first grade where I was introduced to the multiplication table; my instructor used to test us with mental exams and I remember enjoying it like I was playing a game and winning.

Today we discussed the different ways we know numbers can be represented. Some great ideas were shared such as using drawings, people, numerals, objects and words. We then read a story called None the Number and recorded all the number words we could find. With our learning partners, we explored a circuit of physical activities and had a go at reading number words on the signs. Bouncing the ball ten times was a fun

“The system of understanding characteristics of that individual’s society, or of some subgroup within that society” (Trumbull and Pacheco 1). For example, being American could be your cultural identity, but for as long as you live in America you will be classified as an American and in that ethnic group. Being an American can be known as the main society, but an example of a subgroup could be Music and its culture within itself. Music is the society I personally belong in and is classified as my ethnic or cultural group. Music helps with my cultural identity because that is how I relate to the society that is around me and helps enhance my ethnic identity. Music also enhances my heritage because I am going to try to start a tradition of playing music in a band and try and influence the next generations of the family to play music. Music completely changes my perspective of the world and how I see others.

In the article, “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities,” the authors believe that number sense is as foundational to learning mathematical concepts as phonemic awareness is to reading. Gersten and Chard’s theory is based on “conceptualization of constructivism as a joint approach” where students learn conceptually with a focus on terminology and explore operations using a variety of methodologies. Furthermore, the authors support the merging of number sense activities with fact families’ automaticity activities.

In the film: “The Math Code: Numbers,” we start out in a creepy setting that immediately pulls the viewer in. Especially because this film is about numbers, the creepy settings gives the viewer a different impression. Professor Marcus de Sautoy explains how numbers represent the entire universe. In the film, viewers learn about many things. Marcus tells how numbers and ratios make up the Chartres Cathedral.

Number sense is a critical component of early math skills development and later math achievement (Irvrendi, 2011). Although the definitions of number sense are varied (Howell & Kemp, 2009), one of the pervasive components throughout most definitions involves the Approximate Number System (ANS), which is defined as the “foundational” system thought to underlie number sense and produce “abstract number representations” (Halberda & Feigenson, 2008, p. 1457). Students’ ANS abilities predict math achievement (Jordan, Kaplan, Locuniak, & Ramineni, 2007) and are related to their understanding of number meanings, relationships, magnitudes, and operations (Wagner & Davis, 2010). Currently, however, number sense (and specifically ANS) is studied in relative isolation from other cognitive skills. Although a few studies have examined the relationship of number sense and cognitive abilities together (Passolunghi, Lanfranchi, Altoé, & Sollazzo, 2015; Rodic et al., 2015), no

“Numeracy refers to the application of mathematical understanding in daily activities at school, at home, at work, and in the

Math, being one of the essential skills for the civil society to develop and progress, its importance does not require further explanation. As we become more technologically dependent, technical reasoning is needed for survival. Mathematics is no longer just a subject taken by the elite. Now it has rightfully become a staple in our educational systems even though many people do not appreciate it until it is needed. Throughout the course of MATH124, I have learned many skills and knowledge that helps me not only mathematically but also overall development.

While it is a much harder concept to define, it outlines the capability to choose and use mathematics in a broad range of contexts in society. Numeracy is the practice of mathematics, it outlines how we conceptualise maths and use it confidently at home, work and within the community. The term numeracy was first coined in 1959 in Britain, meaning that numeracy is quite a new concept, compared to mathematics, and it still evolving. For this reason, numeracy is hard to simply define because everyone has different interpretations of what it means and how it is used. Willis (1998) suggested that being numerate is about having the competence and disposition to meet the general demands of life at home, in paid work, and the participation in community and civil life. In this he addresses that to be numerate one must have the disposition to choose and use mathematical theories in specific contexts to solve problems. Hughes- Hallet (2001) define numeracy as recognising where maths can be used, choosing the appropriate mathematical tools, and being able to interpret the results. While the two definitions are quite different they both asses the importance of using maths in our day to day lives and choosing maths as a solution to a problem. In many professions, numeracy is relied on to be able to do a job, for example, a builder must have expert knowledge on geometry, measurement, and symmetry and have the disposition to apply this knowledge to their work. Geometry and symmetry are mathematical concepts that we see in building structures all around the world, and builders must be numerate to apply these skills to a project for it to function properly in society. The first goal set out by the Australian curriculum is to ensure ‘that every child leaving primary school should be numerate, and be able to read,

math. Thanks to the mathematicians from the past and present we are able to evolve as a society

Humans have many methods to describe large numbers mathematically. Ever since the invention of the concept of zero -- essential to the ancients in keeping good records of various transactions -- humans have been using mathematics to describe ever larger quantities of items. The ancient story of the king and the chessboard of wheat demonstrates that humans have been using large numbers since time immemorial. In the story, a king tells a

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

Ever since c. 17th century, musical compositions have manipulated the standard aspects of music, which include rhythm and melody. More importantly, many musical compositions have incorporated complex math within, for examples again, melodies and rhythms that create a uniqueness that has yet to be perfectly matched by other composers. One other key aspect of music in general, harmony, is where a fairly complex mathematical formula is involved: the harmonic mean. Because harmony is a major component of music, it is no surprise that this harmonic mean can be applied to nearly all types of music. Basically, a harmonic mean-as it applies to music-~is any possible division between an original note and the octave of that note that produces a different note.