The Key Ingredient in Fluency

We just finished analyzing the data we have at Math Facts Pro to see whether or not we were really making a difference in our effort to help students become fluent.  We wrote a research paper about what we found, and how Math Facts Pro meets the qualifications for Response to Intervention, tiers 1,2, and 3.  (I suppose that kind of lets the cat out of the bag.)

The key ingredient that we found was the amount of practice.  The more students practiced, the more they learned.  (I know you're really surprised.)  Our data consists of students who logged-in to practice on Math Facts Pro.  We studied the addition operator, because it actually gets the most use, and we ignored the first 2 weeks of data, to differentiate between facts that students already knew, and facts that became fluent as a result of using Math Facts Pro.  To determine effectiveness, we compared the amount of practice to the amount of new learning; specifically, facts that were learned for the first time after the two week period, and that never fell out of fluency.  You can see our definition of fluency in the report.  What we found was that students who used the site less than 50 facts (5 minutes) per week, averaged 2.2 newly fluent facts per week, while students practicing 250 facts (5 minutes daily) per week, averaged 10.5.  Almost 5 times as many!  Since we did not control any other variables, we can not prove what caused the difference.  I'm sure that some teachers/parents who successfully get their students to practice regularly are also more successful in other aspects of teaching.  But I'm convinced the main difference is just how much they practiced, which is what we measured.  Math Facts in a Flash™ says that, of all their users, they do not have any grade levels where at least 35% of the students practice just three times a week.  With Math Facts Pro, the average student can learn from 10 - 20 new facts each week.  If you assign the practice as homework, you can even log-in in the morning and see who did it, how much they did, and hold them accountable for their learning.  Just 5 - 10 minutes a day.  Here's a look at our results:

So you learn math facts the same way you get to Carnegie Hall: practice, practice, practice.  My advice is to practice smartly, with an effective, efficient program.  You don't have to spend a lot of money, just $1/student/year.

Working Memory and Automaticity

Working memory and automaticity (automatic recall of facts):

· Working memory limits mathematical performance. Gifted children tend to benefit from a superior working memory, while children with mathematical learning disabilities suffer from a deficient working memory. (National Mathematics Advisory Panel (NMAP) Final Report, 2008)

· Students with math facts anxiety typically have difficulty with working memory, and then use the limited working memory for worrying when doing math. (Ashcraft & Kirk, 2001.)

· While working memory increases with age, it can be increased at any age, mainly by developing fast, automatic recall of facts or procedures from long-term memory. (Schneider & Shiffrin, 1977, Shiffrin & Schneider, 1977) This can help any student, but is especially beneficial for those with mathematics learning disabilities or math anxiety.

Math Fact Automatic Recall Benefits

When recall of the math facts is not automatic, it slows down learning in most cases, and stops it completely in some. It also results in extra work and frustration for the teacher. I believe that computers are a perfect match for math fact memorization instruction. They are consistent, entertaining, and methodical. I’m starting a research based list of benefits that come from early math fact automaticity.

· It helps achieve a strong start, which is especially critical for the disadvantaged.

· It allows for more understanding of the current lesson because working memory is not tied up in calculating basic facts.

· “…if basic skills are not well learned and understood, the natural progression to complex topics is impeded.” (National Mathematics Advisary Panel (NMAP) Final Report)

· Fast access to number combinations supports efficient problem solving. (NMAP Final Report)

Why make more math facts software?

Why work to develop the ultimate math facts software? Because:

· “Studies of children in the United States, comparisons of these children with children from other nations with higher mathematics achievement, and even cross-generational changes within the United States indicate that many contemporary U.S. children do not reach the point of fast and efficient solving of single-digit addition, subtraction, multiplication, and division with whole numbers, much less fluent execution of more complex algorithms as early as children in many other countries. Surprisingly, many never gain such proficiency.” (National Mathematics Advisory Panel, (NMAP) Final Report, 2008)

· Many U.S. college students have to use backup strageies because they haven’t memorized all of the addition and subtraction facts, unlike East Asian college students. (Campbell & Xue, 2001; Geary, 1996; Geary & Wiley, 1991; Geary, Frensch, et al., 1993)

· Only 15% of 4^th through 7^th graders solved division problems from memory. 7^th Graders were still using multiplication facts and skip counting to solve most problems. Automaticity of division facts does not seem to increase with age like the other three operators. (Ilg & Ames, 1951; Robinson, Arbuthnott, et al., 2006)

· Chinese students are superior to U.S. students on math facts. Kindergarteners outperform U.S. students by 300% and Chinese 5^th graders are better by 160%. (Stevenson, Lee, Chen, Lummis, et al., 1990)

· “The implication is that many, perhaps most, U.S. children have not achieved fluency with simple multiplication and division.” (NMAP Learning Processes Task Group Report, 2008)

· A study of 130 Australian elementary students only found 3 who had developed automaticity with all 100 addition facts, one each in 4^th, 5^th, and 6^th grades. (Cumming, 1989)