User:Bmart20/Mathematics education

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Content and age levels
Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries. Sometimes a class may be taught at an earlier age than typical as a special or honors class.

Elementary mathematics in most countries is taught similarly, though there are differences. Most countries tend to cover fewer topics in greater depth than in the United States. During the primary school years, children learn about whole numbers and arithmetic, including addition, subtraction, multiplication, and division. Comparisons and measurement are taught, in both numeric and pictorial form, as well as fractions and proportionality, patterns, and various topics related to geometry.

At the middle grade levels (grades 5th through 8th in the U.S.) students are taught geometry, algebra, and probability and statistics. These three main areas of concentration are centered on what students will focus on at the high school level. Geometry is a class requirement for high school students, at the middle grade level students spend time studying angles, lines, polygons and they will be introduced to trigonometric functions. Algebra in the middle grades is not always an offered corse. However, when students take algebra matters. Some school offer algebra for 8th grade students (only 59%), but others wait until students are in high school (84% for 9th and 10th and 60% for 11th and 12th). As well as some 8th grade schools only give the opportunity to gifted students. Algebra is a required course for graduation so for students who take the class in 8th grade, graduation credit may be given based on the school. The majority of schools who offer algebra at the middle grade level are located on the east coast whereas others who wait till high school are spread around the west coast. Probability and statistics in the middle grades is enough to get students toes wet but nothing further. Students can be seen looking at graphs (bar graph, pie chart, histograms, and others), they will study mean, median, mode and range. Students learn enough here that they can apply it to other areas of mathematics when they reach the high school level.

At high school level, in most of the U.S., algebra, geometry and analysis (pre-calculus and calculus) are taught as separate courses in different years. Mathematics in most other countries (and in a few U.S. states) is integrated, with topics from all branches of mathematics studied every year. Students in many countries choose an option or pre-defined course of study rather than choosing courses à la carte as in the United States. Students in science-oriented curricula typically study differential calculus and trigonometry at age 16–17 and integral calculus, complex numbers, analytic geometry, exponential and logarithmic functions, and infinite series in their final year of secondary school. Probability and statistics may be taught in secondary education classes. In some countries, these topics are available as "advanced" or "additional" mathematics.

Algebraic Reasoning:

Learning about algebra and algebraic reasoning early helps to prepare students for algebra in later grades. In the United States only 24% of students take algebra at the 8th grade level, whether as an honors class or a regular class. As algebra is a graduation requirement for students in the U.S. the timing of when a student takes algebra I matters.