# Average time to solve basic arithmetic problem

I am a game developer currently making a game based on basic arithmetic problems for kids and teens.

Are there any research papers on the average time to solve basic arithmetic problems or on how to evaluate success and improvement rate.

That would help us a lot in creation of this game!

Edit: What I mean by basic arithmetic is simple question like 2+3+0+4, 3*3, 9-4-2, 9/3 etc, you get the idea.

• Can you give some examples of the level of the problems?
– user2139
May 28, 2016 at 4:24
• Welcome to the site and thank you for the question. I broke up the sentences a bit as the long ones were hard to follow for me.
– quid
May 28, 2016 at 12:09
• I remember having learned the 12X12 multiplication table a year ahead of my classmates. There was a test on multiplying, and we had 30 minutes to solve 15 problems. It took me just about 2 minutes, as I was able to write the answers as fast as I could write. 10-15 seconds might be reasonable for the non-rainmen. May 28, 2016 at 18:14
• I imagine companies such as Kumon have a lot of data on this but consider these trade secrets and keep them confidential.
– JRN
May 30, 2016 at 6:52
• @JoeTaxpayer the game is for the general audience for the masses. Jun 2, 2016 at 3:33

This question is almost totally unanswerable unless you clarify what is meant by "basic arithmetic problems for kids and teens".

But let's consider a lower-bound case where you're talking about basic one-digit addition and multiplying facts. In instances like this, the knowledge should be automatic, that is, instantly recalled without effort (at least by the 3rd grade).

A few years ago, when developing a similar gamey practice website (Automatic-Algebra.org), I made a survey of several educators' and practice materials' suggestions for times-tables drills. That's summarized in the chart below:

In short: Simple times-tables facts should be answerable in 2 or 3 seconds on average. Personally, I set up my drill to give twice that much time as a safety buffer (30 seconds for 5 questions, that is, one every 6 seconds).

Best practice would be to test and refine your game with actual users. In the most general sense, questions might take anywhere between zero and infinity seconds, depending on what you're asking.

• What I mean by basic arithmetic is simple question like 2+3+0+4, 3*3, 9-4-2, 9/3 etc, you get the idea. Jun 2, 2016 at 3:36
• What was the audience age group you did your survey upon? Jun 2, 2016 at 3:39
• I'd have to look at the individual materials, but times-table facts are generally considered a 3rd-grade (about age 9) skill. See Common Core math standards for that. Jun 2, 2016 at 4:29
• Is there a way we can contact you? we would like you get your opinion and discuss how we can make the game better. Jun 2, 2016 at 4:41

I'd expect that such data would be quite useless for your game. "Reliable" numbers would originate from large-scale tests which are usually quite far away from the situation of a kid competing in a game.

To appeal to the broadest population, you should keep individual timings for each player and only use them as comparison.

Another point to consider: If you're doing "basic arithmetic" the game is probably colorful and flashy, possibly mousy-pointer-clicky. This captivating gameplay will distract in the beginning and become more and more ignored with more practice. So part of the "improving timings" will be due to the audience learning to deal with the game mechanics and not only with improve numeric skills.

At the risk of posting an answer that doesn't directly answer the question, I'm going to suggest that as a game or computer based software, you consider levels. Start with, say, 10 seconds per problem, and at each level, retire the time a bit, .5 seconds or so, to produce the number of levels you wish.

Better yet, have the reward points count down. At the moment the problem appears, the screen shows they can earn 10 points, and it drops as time passes, to zero when time runs out and the next question pops up.

If you would like to create a game that adapts to its user's skill level, then the best way to go is to research Computerized Adaptive Assessment and Item Response Theory.

As a starting point for this, you would need to create a database of questions that are graded (i.e. in order of difficulty) and that are cross-referenced (so that game can make a decision on the selection of follow-up questions).

Furthermore, a way to give appropriate feedback to the user with respect to their progress would be ideal.