My first recommendation is Xtramath.org, for memorizing basic addition, subtraction, multiplication, and division facts.
Intended users: Teachers, Students, Parents – separate interface for each. Designed for both at home and computer lab use.
This website does one thing, and it does it exceptionally well: fact fluency. Fact fluency is the ability to quickly recall an answer from memory without computation. Specifically, Xtramath works on users ability to recall addition, subtraction, multiplication, and division facts from 0+0=0 to 144/12=12. The reason this website is so great, is that fact fluency is fundamental to learning math, and also excruciating to teach – but Xtramath is a fast, effective, and easy solution.
The ability to quickly recall these answer is critical, not only because it speeds more complicated operations, but because it also instills confidence. One of the greatest things a math teacher ever did to/for me was make me take timed tests converting fractions to decimals. That was fifth grade, and, of course, I hated her for it. I complained about it for years, all the while reaping a huge advantage over less lucky peers who struggled with both fractions and decimals because they failed to see the connection. In contrast, I thought I was naturally gifted with fractions and decimals. At least I was .5 right.
The advantage to fact fluency versus re-computing arithmetic every time is hard to overstate. Fluent students spend 0-2 seconds solving 7*8, while non-fluent middle school students can spend 40-90% of their time for each problem performing basic arithmetic functions – or worse, running to a calculator to punch it in. That lag time slows learning and prolongs misunderstanding. Half the time they’ve forgotten the original problem before they retrieve the fact.
In neuro-geek-speak: the lag time weakens reinforcement of correct intuitions, while errors build an unreasonable aversion to practicing advanced concepts. This can be especially painful during class practice, when teachers cannot spare the time to locate the error behind a verbal wrong answer. Suddenly, despite understanding the concept at hand, a student’s arithmetic error can become a full-blown public failure. This is where Xtramath comes in.
The traditional method of teaching fact fluency is a combination of chanting, flashcards, games, and timed test – all of which can be painful. Don’t get me wrong, they work, but they are boring, or stressful, or both at the same time. Xtramath has three major advantages over the old ways.
- It is shame-less
- It is less boring, because it is tailored to the student, and
- It feels like learning, because you are learning
To elaborate, unlike answering a question out loud in class, chanting with a group, or competing in teams, there is no one standing over your shoulder when you do Xtramath. Unlike a timed test, there is no grade and no one grading. That means no pain in getting it wrong – just a quick prompt of the right answer, type it in, and the mistake is behind you. Stress is bad for memory, so why should learning be stressful?
At first I wasn’t that impressed with Xtramath because it was “just” another flashcard web site, and on some level it is.1 However, Xtramath is distinguished by its laser-like focus, and a smarter algorithm. Flash cards are perfect for fact fluency, because recognizing visual cues and regurgitating the answer is the objective. More significantly, Xtramath repeats problems that are students are slow to answer and those they get wrong. Not only is this a more effective use of students time – it’s less boring, and boring is also bad for learning.2
Which brings me to my third point, Xtramath is brief. Every time students log in, they are prompted to do 2-3 sets of “cards”. This means that students don’t get tired, yet they get the reward of being finished if they stick through 2-3 sets of 25-50 questions.3 I don’t know if they tested and optimized it, or if the teachers who made it just knew from experience – maybe it detects boredom via slow-down and errors. In any case, Xtramath manages to push students into a substantial amount of practice, with out being overwhelming. Learning theorists have long known that splitting up practice is more effective than the same amount of time spent in a single session. This is known as the spacing effect, and it is one of the oldest, most robust, and most substantial principles of behavioral science. If need be, students can quit at any time by closing the window, and they want they can log back in for another session as soon as they want.
1 (a list of flash card websites is on my to-blog list)
2 Craig, S., Graesser, A., Sullins, S., & Gholson, B. (2004). Affect and learning: an exploratory look into the role of affect in learning with autotutor. Journal of Educational Media, 29(3), 241-250. doi: 10.1080/1358165042000283101
3 a rough estimate – I have tried the system my self, and I know it is a sizable number per set, but I don’t have any exact measurements.
**** Pavlik Jr., P. I., & Anderson, J. R. (2008). Using a model to compute the optimal schedule of practice. Journal of Experimental Psychology: Applied, 14(2), 101–117. (Text).
*****Dempster, F. N. (1996). Distributing and managing the conditions of
encoding and practice. In R. A. Bjork & E. L. Bjork (Eds.), Memory (pp.
317–344). New York: Academic Press. (Preview)