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History[ edit ] Elementary mathematics was part of the education system in most ancient civilisations, including Ancient Greece , the Roman Empire , Vedic society and ancient Egypt. In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste. Illustration at the beginning of a 14th-century translation of Euclid's Elements. In Plato 's division of the liberal arts into the trivium and the quadrivium , the quadrivium included the mathematical fields of arithmetic and geometry. This structure was continued in the structure of classical education that was developed in medieval Europe. Teaching of geometry was almost universally based on Euclid 's Elements. Apprentices to trades such as masons, merchants and money-lenders could expect to learn such practical mathematics as was relevant to their profession. In the Renaissance , the academic status of mathematics declined, because it was strongly associated with trade and commerce, and considered somewhat un-Christian. The first modern arithmetic curriculum starting with addition, then subtraction, multiplication, and division arose at reckoning schools in Italy in the s. They contrasted with Platonic math taught at universities, which was more philosophical and concerned numbers as concepts rather than calculating methods.

Methods of teaching mathematics include the following: Classical education: the teaching of mathematics within the quadrivium , part of the classical education curriculum of the Middle Ages , which was typically based on Euclid's Elements taught as a paradigm of deductive reasoning.

In "Number Bingo," players roll 3 dice, then perform basic mathematical operations on those numbers to get a new number, which they cover on the board trying to cover 4 squares in a row.

Computer-based math an approach based around use of mathematical software as the primary tool of computation. Computer-based mathematics education involving the use of computers to teach mathematics. Mobile applications have also been developed to help students learn mathematics.

Starts with arithmetic and is followed by Euclidean geometry and elementary algebra taught concurrently. Requires the instructor to be well informed about elementary mathematics , since didactic and curriculum decisions are often dictated by the logic of the subject rather than pedagogical considerations.

Other methods emerge by emphasizing some aspects of this approach. Exercises : the reinforcement of mathematical skills by completing large numbers of exercises of a similar type, such as adding vulgar fractions or solving quadratic equations. Historical method: teaching the development of mathematics within an historical, social and cultural context. Provides more human interest than the conventional approach. Adopted in the US as a response to the challenge of early Soviet technical superiority in space, it began to be challenged in the late s.

The New Math method was the topic of one of Tom Lehrer 's most popular parody songs, with his introductory remarks to the song: " The problems can range from simple word problems to problems from international mathematics competitions such as the International Mathematical Olympiad.

Problem solving is used as a means to build new mathematical knowledge, typically by building on students' prior understandings. Recreational mathematics : Mathematical problems that are fun can motivate students to learn mathematics and can increase enjoyment of mathematics.

Relational approach: Uses class topics to solve everyday problems and relates the topic to current events.

Rote learning : the teaching of mathematical results, definitions and concepts by repetition and memorisation typically without meaning or supported by mathematical reasoning.

A derisory term is drill and kill. In traditional education , rote learning is used to teach multiplication tables , definitions, formulas, and other aspects of mathematics. Content and age levels[ edit ] 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 in a similar fashion, though there are differences. Most countries tend to cover fewer topics in greater depth than in the United States. Mathematics in most other countries and in a few U. 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. Science and engineering students in colleges and universities may be required to take multivariable calculus , differential equations , and linear algebra.

Applied mathematics is also used in specific majors; for example, civil engineers may be required to study fluid mechanics , [17] while "math for computer science" might include graph theory , permutation , probability, and proofs. Standards[ edit ] Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on the levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils.

In modern times, there has been a move towards regional or national standards, usually under the umbrella of a wider standard school curriculum. In England , for example, standards for mathematics education are set as part of the National Curriculum for England, [19] while Scotland maintains its own educational system. Ma summarised the research of others who found, based on nationwide data, that students with higher scores on standardised mathematics tests had taken more mathematics courses in high school.

This led some states to require three years of mathematics instead of two.

In , they released Curriculum Focal Points, which recommend the most important mathematical topics for each grade level through grade 8. However, these standards are enforced as American states and Canadian provinces choose.

A US state's adoption of the Common Core State Standards in mathematics is at the discretion of the state, and is not mandated by the federal government. The MCTM also offers membership opportunities to teachers and future teachers so they can stay up to date on the changes in math educational standards. Please help rewrite this section from a descriptive, neutral point of view , and remove advice or instruction. April Learn how and when to remove this template message "Robust, useful theories of classroom teaching do not yet exist".

The following results are examples of some of the current findings in the field of mathematics education: Important results [24] One of the strongest results in recent research is that the most important feature in effective teaching is giving students "opportunity to learn".

Teachers can set expectations, time, kinds of tasks, questions, acceptable answers, and type of discussions that will influence students' opportunity to learn. This must involve both skill efficiency and conceptual understanding. Conceptual understanding [24] Two of the most important features of teaching in the promotion of conceptual understanding are attending explicitly to concepts and allowing students to struggle with important mathematics.

Both of these features have been confirmed through a wide variety of studies. Explicit attention to concepts involves making connections between facts, procedures and ideas. This is often seen as one of the strong points in mathematics teaching in East Asian countries, where teachers typically devote about half of their time to making connections.

At the other extreme is the U. Deliberate, productive struggle with mathematical ideas refers to the fact that when students exert effort with important mathematical ideas, even if this struggle initially involves confusion and errors, the end result is greater learning.

This has been shown to be true whether the struggle is due to challenging, well-implemented teaching, or due to faulty teaching the students must struggle to make sense of.

Formative assessment [26] Formative assessment is both the best and cheapest way to boost student achievement, student engagement and teacher professional satisfaction.

Results surpass those of reducing class size or increasing teachers' content knowledge.

Effective assessment is based on clarifying what students should know, creating appropriate activities to obtain the evidence needed, giving good feedback, encouraging students to take control of their learning and letting students be resources for one another. Geometry and shapes - Free math PDF worksheets on geometry suitable for kids from Pre-k to 7th grades - 10 worksheets.

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Parents, teachers and educators can now present the knowledge using these vividly presented short ppt presentations.

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