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In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.
At different times and in different cultures and countries, mathematics education has attempted to achieve a variety of different objectives. These objectives have included:
* The teaching of basic numeracy skills to all pupils
* The teaching of practical mathematics (arithmetic, elementary algebra, plane and solid geometry, trigonometry) to most pupils, to equip them to follow a trade or craft
* The teaching of ...view middle of the document...
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.
The two most important criteria for helping student’s gain conceptual understanding are making connections and intentionally struggling with important ideas. Research in the 70s and 80s concluded that skill efficiency is best attained by rapid pacing, direct traditional teaching and a smooth transition from teacher modeling to error-free practice. More recent research shows that students who learn skills in conceptually-oriented instruction are better able to adapt their skills to new situations.
Students with difficulties
Students with genuine difficulties (unrelated to motivation or past instruction) struggle with basic facts, answer impulsively, struggle with mental representations, have poor number sense and have poor short-term memory. Techniques that have been found productive for helping such students include peer-assisted learning, explicit teaching with visual aids, instruction informed by formative assessment and encouraging students to think aloud.
Homework which leads students to practice past lessons or prepare future lessons are more effective than those going over today's lesson. Assignments should be a mix of easy and hard problems and ideally based on the student's learning style. Students must receive feedback. Students with learning disabilities or low motivation may profit from rewards. Shorter homework is better than long homework, and group homework is sometimes effective, though these findings depend on grade level. Homework helps simple skills, but not broader measures of achievement.
Most bilingual adults switch languages when calculating. Such code-switching has no impact on math ability and should not be discouraged.
When studying statistics, children need time to explore, study and share reasoning about centers, shape, spread and variability. The ability to calculate averages does not mean students understand the concept of averages, which students conceptualize in a variety of ways—from a simplistic "typical value" to a deeper idea of "representative value." Learning when to use mean, median and mode is difficult.
It is important for elementary school children to spend a long time learning to express algebraic properties without symbols before learning algebraic notation. When learning symbols, many students believe letters always represent unknowns and struggle with the concept of variable....