Students begin in Preschool by learning to understand the concept of a number and counting by them. Counting lends itself to addition and subtraction because when you think of it four plus three is the same thing as starting at four and counting up three to seven. The same could be said about subtraction. Preschool students begin to also come across the concepts of foundational measurement and how to manipulate and use data. The last main flagship skill that is explored in Preschool is geometry. At this point we are focused on learning basic geometric shapes and comparing them.
As students approach Kindergarten and move on their first official year of elementary school, we basically work on heightening those Preschool skills. Students spend a good deal of time getting comfortable with numeracy and basic operations. Towards the end of first grade students begin to learn about the base ten system and the concept of place value. As we progress through elementary school, we learn to add and subtract on a much grander scale. Students are introduced to the other two basic operations (division and multiplication). At some point, normally fourth grade, we ask students to begin to become more automatic with their basic operations especially multiplication, which times tables are great for. We take all of these skills and apply them to specific situations in word and story-based problems. I find that students begin to pay much more attention as we start to include the concept of money. When students are completing their elementary math skills, they will normally be introduced to the advanced base ten values and the concept of fractions and operations with them.
Sixth grade marks a new journey for the students as they begin their lives as middle schoolers. From here on, they will learn something new every day. In the field of mathematics, sixth graders will mostly implement the concepts they learned in elementary schools into complex and lengthy problems.
The curriculum of middle schoolers is pretty status quo across the country, although it varies, the common progress in the curriculum usually starts with dividing fractions with fractions. Algebra begins to poke its head up and students work on solving equation with negative numbers. They take it a step further and will learn to solve equations by using ratios, percentages, and rates. Students learn to use integers in real-life situations and display them by using number lines. The underlying goal of middle school math is to help students learn to implement deductive and inductive reasoning and elimination processes to solve real-life scenarios. We spend a significant amount of time solving geometry problems consisting of area, surface area, and volumes. There is also a pretty substantial amount of times working on understanding the basic concepts of statistics, comprising of mean, median, mode, range, and variability. We end of our middle school math careers by learning enhanced concepts of solving problems in different ways rather than just focusing on a single way.
The math experience at the high school level differs all around the country as far as the course ordering or progression series. The foundational subjects are all the same, even though they may not be approached in the same order at the same magnitude. Every great curriculum begins with Algebra which is often broken into two different courses. The first part hyper focuses on exploring equations and expressions in all types of different situations. Students learn how to solve them, manipulate them, and even write their own equations or expressions to model situations. From there most schools choose to present students with geometry which is the study of geometric constructions and advanced forms of measurement. This is where students meet their nemesis geometric proofs which is the height of logical skills at this point. After mastering geometry students jump back into algebra and they explore the concepts of inequalities and functions in this course work. The reason that most schools prefer to place geometry in between the two parts of algebra is because it allows you to present students with trigonometry that goes hand in hand with the Algebra 2 skills they will be working on. Usually he math you take during your Senior year of high school is entirely based upon your next step with your education. If you are college bound, at a minimum you would be taking some form of Pre-college math which normally is in the form of Pre-calculus or Trigonometry. Students that are looking towards a math or technology field will most likely be ready to tackle full on Calculus. While I encourage students to take AP courses to challenge themselves, I would also recommend that use the college credit towards your general course work only. The fundamental core classes in college are that way for a reason, I would not recommend you skip them by using your AP credits.