Distance education is somewhat different from face to face learning. Student’s tend to learn more in an actual classroom since they can freely interact and ask questions if they are confused over the lesson discussed. However, this pandemic taught us to be more independent and responsible in our own learnings especially in mathematics. Learning and teaching math, although a bit complicated, is fun. Since the program is about Teaching Mathematics in Intermediate Grades, we tackle almost every basic lesson in mathematics.
First, we discussed the nature of mathematics. I discovered that mathematics was derived from the Greek word ‘mathenein’ meaning learning, and ‘techne’ means an art of technique. So, mathematics is a science of discovery, an intellectual game, a tool subject, involves an intuitive method, has its own language, and an abstract science, so, there are many things that define mathematics. But most importantly is that mathematics isn't all about solving, we can also apply mathematics in our everyday life.
Things such as cooking or buying stuff are used with mathematics, it’s for measuring the amount of ingredients in the food or counting your change. Next is, we tackle the history of mathematics. There are six periods of mathematics, the Ancient Period, Greek Period, Hindu-Arabic Period, Period of Transmission, Early Modern Period, and Modern Period. For us to further understand this topic, our teacher showed us a video about ancient time up to the modern time in solving mathematics.
So even before, our ancestors were already using mathematics and they discovered more than one way to solve mathematics. Since they still don’t have technologies before or something called a calculator, then they search for solutions to basic problems such as counting objects, building homes, measuring spaces, keeping track of seasons, or even make a trade.
It is just interesting how mathematics has been solved before and how it changes through time. So we also discover that the early mathematics skills of the child is before starting school, they develop an understanding in addition and subtraction through everyday interaction. Basically, most children learn the most basic of addition and subtraction in their everyday home and through playing.
Throughout the lesson, we also discuss the qualities of a good math teacher. There are more than one qualities of a good mathematics teacher but what I like the most and I also think that every math teacher should have this quality, that a good math teacher should understand that every student learns in a different way and has its own way of understanding mathematics. So, I think for us to become good teachers we must know and understand first that there are different types of learners and they also learn through their own pace.
We also learn the different branches of mathematics such as algebra, trigonometry, calculus, etc. Aside from that, we also tackle the three different teaching styles. Behaviourism, Cognitivism, and Constructivism. In Behaviourism, it is a learning theory that focuses on external events as the cause of changes in observational learning. So as the word itself, this is about how the child behaves or acts. In Cognitivism, it is concerned with the role of the active mind in processing learning opportunities and development of a learner. It is more cognitive like how a child understands and comprehends. In Constructivism, it is a learning based on the belief that knowledge isn't a thing that can be simply given by the teacher at the front of the room to students at their desks. It is a knowledge constructed by learners through an active, mental process of development.
Next is about the whole numbers, place values, and MDAS operations. So, whole numbers are the basic counting numbers such as 0, 1, 2, 3, etc. Place value is the value represented by a digit of a number, like for example, the place value of 5 in 532 is hundreds. Meanwhile, there’s also a place value for decimals, like for example, the place value of 7 in 103.75 is tenths. The MDAS operation is the basic calculations of multiplication, division, addition and subtraction.
We also tried to solve every activity of MDAS with 5 digits or more numbers so although it is basic it’s still not that very easy, especially in multiplication and division. You really need to be extra careful because it’s kind of confusing and just a single mistake can make your whole calculation wrong.
Then we also tackle fractions, it is a number that can represent part of a whole. Like for example, my mother bought an apple, so for me and my brother to eat both, she cut the apple into halves. Each half of the apple is called ½, it means that 1 apple is distributed for 2 people.
Then I also learned about ratios and proportions. Ratios are the comparison between two sets of numbers, like for example, our classroom is composed of 11 girls and 10 boys. So the ratio of girls to boys is 11 to 10, you can write it with a word ‘to’ in between the set of numbers, or using a colon like 11:10, and you can also write it into a fraction like 11/10. Proportions are two ratios of equal value.
Next topic is about the percentage, it is one of the simplest ways of quantifying things. Among everything, percentage is my favorite part of mathematics since it was very easy. Next is multiplying and dividing integers, in this topic signs play an important role. If you’re multiplying two positive numbers, the solution would be positive. If it is both negative, the solution would also be positive. If it is a positive and negative, the solution would always be negative.
Next is the volume and surface area, the volume is the measure of the space inside a solid object, while the surface area is the flat area on the surface of a three-dimensional object such as spheres, cubes, etc. Next is the perimeter and area, perimeter is the distance around the outside edges of any flat shape such as miles, yards, centimetres, etc. While the area is the amount of surface inside a flat shape such as ft. or whatsoever.
Next are the polygons, an object with different shapes or many-sided figures. Polygons such as square, rectangle or diamond were already introduced in early childhood so it was just like exploring many shapes and all. Next is the basics of geometry, I’ve learned that the point lines and planes are the foundations of geometry were also called as undefined terms. Aside from that, I also discovered that quadrilaterals are just like the polygons but focus more on the four-sided objects, as what the word ‘quad’ means ‘four’.
Lastly is the measurements, such as K for Kelvin, it is to measure the hotness or coldness of something using a thermometer. Then S for second(s) that is a measurement through clocks or watches. M for meter, it is the physical distance of an object or something. Kg for kilogram, it is to measure a weight of something using a weighing scale. So these are what I have learned throughout the module of teaching mathematics in elementary grades. It was all just the basics yet some were already a little complicated, but it was actually fun learning math.
