Students in modern curricula often explore their own methods for multiplying multi-digit numbers, deepening their understanding of multiplication principles before being guided to the standard algorithm.
Parents sometimes misunderstand this approach to mean that the children will not be taught formulas and standard algorithms and therefore there are occasional calls for a return to traditional methods.
Current standards require children to learn basic statistical ideas such as organizing data with bar charts.
More sophisticated concepts such as algebraic expressions with numbers and letters, geometric surface area and statistical means and medians occur in sixth grade in the newest standards.
Critics also sometimes cite the fact that history of mathematics often focuses on European advancements and methods developed by men, thus ignoring equity issues and potentially alienating minorities and women.
Reform math textbooks will often focus on conceptual understanding, usually avoiding immediate instruction of the standard algorithms and frequently promoting student exploration and discovery of the relevant mathematics.
The Common Core does not endorse any particular teaching method, but does suggest students solve word problems using a variety of representations.