1. The same sum can tell different stories
Take 2 + 3 = 5. It looks like one idea, but it can come from very different situations. The Common Core State Standards, a set of math goals used by many US schools, include a table of the common addition and subtraction situations that young students work with [1]. Three of its families are:
- Add to. Something starts at one amount and grows. "Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?" That is 2 + 3 = ? [1]
- Put together. Two groups exist at the same time and you want the total. "Three red apples and two green apples are on the table. How many apples are on the table?" [1]
- Compare. Two amounts are set side by side and one is described by how much bigger or smaller it is than the other. The table includes both "how many more?" questions and questions where you are told the difference and asked for the bigger or smaller amount [1].
The numbers can be the same in all three. What changes is the story: does something grow, do two groups sit together, or are two amounts being compared? To understand a math problem, look at the situation it describes, not just the symbols.
2. Why "3 more than" can still mean adding
Here is the story type that surprises people. Lucy has 2 apples. Julie has 3 more apples than Lucy. How many apples does Julie have? The Common Core table lists this kind of question under Compare, in the version where the amount you need to find is the bigger one [1].
You know the smaller amount (2) and the difference (3). You want the bigger amount. So you add: 2 + 3 = 5. The word "more" is there, yet the math you need is addition, and nothing is "put together" in the usual sense. Julie's apples are not combined with Lucy's. You are building Julie's number by starting at Lucy's and going up by the difference.
It is tempting to learn a rule like "more means add, fewer means subtract." The compare family shows why that rule can fail. The same table also gives a "fewer" wording of this kind of situation, and there too the question is about the other person's amount [1], so the word alone cannot tell you what to do. A safer habit is to ask: what do I know, and what do I want to find?
So to answer the title: no, addition is not only for putting things together. It also covers adding to something and finding an amount from a difference.
3. Do babies know about adding before school?
If addition is about situations, you might wonder how early people sense them. In 1992, the psychologist Karen Wynn published a short paper in the journal Nature titled "Addition and subtraction by human infants" [2]. It became one of the best-known experiments in the study of how babies think about numbers.
According to a summary of her work, the study reported that five-month-old infants seemed able to work out the outcome of simple addition and subtraction on small sets of objects [3]. Studies of this kind usually work by timing how long a baby looks at something: a result that surprises the baby tends to hold the baby's attention longer. In the classic setup of such studies, a baby sees a toy placed behind a screen, then a second toy added. When the screen is lowered, the baby may look longer at an impossible number of toys than at the right one.
That does not mean a baby can do homework. Researchers have debated what the result shows. One view is that babies are tracking single objects with their eyes and memory. Another is that they have a rough sense of number. I could read only a secondary summary and the bibliographic record of the paper, not the full article, so treat the details above as the general outline rather than precise numbers [3].
Either way, the "add to" story seems to be something people notice very early. School then gives the idea a name and a symbol. Which brings us to the symbol.
4. Where did the plus sign come from, and what did it first mean?
The word plus is Latin for "more," which fits the compare story from earlier. The shape "+" has its own history.
The first printed use meant surplus. Johannes Widmann, a German mathematician, published a business arithmetic book in Leipzig in 1489. The plus and minus signs appeared in print in it, referring to surpluses and deficits in business problems [5]. The MacTutor history of mathematics site, run by the University of St Andrews, describes the same book as the first place the "+" and "−" signs appear [4]. So the first "+" in print was a merchant's mark, roughly "more than the standard amount," and it was not yet an instruction to add. The detail about surplus and deficit comes from Wikipedia, so I treat it as the likely reading and not as a settled quote from the book.
The shape may come from the word "and." A German manuscript from 1456 uses the Latin word et ("and") for addition, written in a way that closely resembles "+". An example in the manuscript is "5 et 7" for 5 + 7. The author of the St Andrews page concludes there is "little doubt" that the sign is simply a ligature, a joined form, of et [6]. Think of how we write "&" quickly: it also began as a fast way to write "and."
Put the two threads together. "And" is the language of putting things together. "More than the standard" is the language of surplus. The sign's history connects both ideas, and that is a good match for what we saw in the story types: the same symbol can serve "put together," "add to," and "compare."
5. Try it: find addition in your day
For one day, notice each time you add. Write the numbers, and then write which story it was: add to, put together, or compare. For example, 4 pencils in a case plus 2 you find in a drawer could be "put together" or "add to," depending on how you tell it. Some problems fit more than one story, and that is a real finding, not a mistake.
If you want to dig further, the Common Core table [1] is a single page, and the St Andrews page [6] is short. Reading those sources will show you more than this page could.