Multiplication - Fluent Math app for iPhone and iPad

An easy and automatic way to learn the times tables. Practice fluency in multiplication without stress until you learn it by heart. Practice in 5-minute sessions with repetition learning.

Learning by heart relieves the working memory aiding more advanced mathematics.

The app allows the student to go from their own strategies based on understanding and number sense to fluency and automaticity in a unique way without time pressure. It combines two of the most efficient study techniques, active recall, and spaced repetition, with feedback and individual adaptation.

Suitable for children, teenagers, and adults who need to review the times tables, identify the multiplications they struggle with, and automate them, e.g., before a new semester.

Practice in a fun, stress-free, and effective way!

HOW IT WORKS
The entire table is reviewed. Multiplications that the student already knows are verified as quickly as possible. Multiplications that the student thinks about for long or answers incorrectly are registered as not automated and then repeated with increased intervals, first after minutes and then after hours and days. The repetition starts over if the student thinks for long or answers incorrectly again. This results in individualization so the pace of learning is automatically adapted to each student (according to the principle of flashcards, spaced repetition, Leitner system, Anki, etc.)
The app is easy to use because it automatically determines what to practice and in what order.

PREMIUM UPGRADE
Fluent In Multiplication is free up to 7×7. Upgrade to premium for multiplications up to 12×12.

*** WHY IT WORKS ***

FROM UNDERSTANDING TO AUTOMATICITY
Younger students should not begin automating too early, but first learn number sense and basic understanding. Later, automation is preferably practiced in parallel with understanding.

When the app is used, students can answer multiplication questions at their own pace and use their own strategies to calculate an answer without stress. Confidence is boosted as this means fewer mistakes (then under time pressure). Until the multiplication is considered automated, it will be repeated frequently. Eventually, the student will either become very fast at the strategy, or learn the multiplication by heart. The knowledge is then consolidated in long-term memory through spaced repetition with active recall.

Simple memorization vs. fluency based on understanding, is a topic of much discussion. Repeated practice using the students own strategies without stress combines the two. Students learn many multiplication facts by heart, reducing cognitive load, while also practicing using strategies effectively in cases where they forget or cannot memorize all multiplication facts.

EFFECTIVE LEARNING
Once a student has proven the automation of the first commutative variant (e.g., 6x3=18), the second variant (e.g., 3x6=18) is introduced in parallel, giving good opportunities for faster automation of it along with the insight that the two are the same thing. This streamlines the learning of half the table.

The app also tries to take advantage of the learning technique interleaving by including open statements (6×_=18) when the student has begun to answer the multiplication quickly. This is to further challenge the student to note and reflect on the relationship between the two commutative variants and the open statements e.g., 6×3=, 3×6=, 6×_=18, _×3=18, etc., and to strengthen the memory association of them as a unit.

LONG-TERM REPETITION
Since unused knowledge weakens, it can be good to review the tables annually. Consistent, long-term, use of the app helps all age ranges automate their memory of times tables.

RESEARCH
The solution has been inspired by research about active recall, spaced repetition, and interleaving.