Editing Addition (section)

=== Childhood learning ===
Typically, children first master [[counting]]. When given a problem that requires that two items and three items be combined, young children model the situation with physical objects, often fingers or a drawing, and then count the total. As they gain experience, they learn or discover the strategy of "counting-on": asked to find two plus three, children count three past two, saying "three, four, ''five''" (usually ticking off fingers), and arriving at five. This strategy seems almost universal; children can easily pick it up from peers or teachers.{{sfnp|Smith|2002|p=130}} Most discover it independently. With additional experience, children learn to add more quickly by exploiting the commutativity of addition by counting up from the larger number, in this case, starting with three and counting "four, ''five''." Eventually children begin to recall certain addition facts ("[[number bond]]s"), either through experience or rote memorization. Once some facts are committed to memory, children begin to derive unknown facts from known ones. For example, a child asked to add six and seven may know that {{nowrap|1=6 + 6 = 12}} and then reason that {{nowrap|6 + 7}} is one more, or 13.<ref>{{Cite book |last=Carpenter |first=Thomas |author2=Fennema, Elizabeth|author2-link = Elizabeth Fennema |author3=Franke, Megan Loef |author4=Levi, Linda |author5=Empson, Susan|author5-link=Susan Empson |title=Children's mathematics: Cognitively guided instruction |publisher=Heinemann |year=1999 |location=Portsmouth, NH |isbn=978-0-325-00137-1 |url-access=registration |url=https://archive.org/details/childrensmathema0000unse_i5h7 }}</ref> Such derived facts can be found very quickly and most elementary school students eventually rely on a mixture of memorized and derived facts to add fluently.<ref name=Henry>{{Cite journal |last=Henry |first=Valerie J. |author2=Brown, Richard S. |title=First-grade basic facts: An investigation into teaching and learning of an accelerated, high-demand memorization standard |journal=Journal for Research in Mathematics Education |volume=39 |issue=2 |pages=153–183 |year=2008 |doi=10.2307/30034895|jstor=30034895 |doi-access=free }}</ref>

Different nations introduce whole numbers and arithmetic at different ages, with many countries teaching addition in pre-school.<ref>
Beckmann, S. (2014). The twenty-third ICMI study: primary mathematics study on whole numbers. International Journal of STEM Education, 1(1), 1–8.
Chicago
</ref> However, throughout the world, addition is taught by the end of the first year of elementary school.<ref>Schmidt, W., Houang, R., & Cogan, L. (2002). "A coherent curriculum". ''American Educator'', 26(2), 1–18.</ref>