The development of math fact fluency and automaticity is a core requirement for later success in advanced
mathematics (Nelson, Parker, & Zaslofsky, 2016; Steel & Funnell, 2001). To be considered fluent and automatic,
a student must be able to rapidly recall the correct solutions to basic math operations including addition,
subtraction, multiplication, and division (Geary, 2011). Despite the importance of developing these skills,
several national groups, including the 2008 National Mathematics Advisory Panel, have found that “few
curricula in the United States provide sufficient practice to ensure fast and efficient solving of basic fact
combinations and execution of the standard algorithms.” (NMAP, 2008)
Given this context, Imagine Math Facts is designed to improve math fact fluency and automaticity in
elementary age students by differentiating instruction for each student. The game-based program provides
repeated and focused practice on previously unlearned math facts with constant and immediate feedback
while maintaining engagement through exciting and rewarding gameplay.
During the 2018-2019 school year, a southern Texas school implemented Imagine Math Facts in first through
third grades to help improve addition, subtraction, and multiplication fact fluency and automaticity. Since
students typically need only 6-10 weeks to complete all Imagine Math Facts exercises for each math fact
family (addition, subtraction, etc.), students practiced different math fact families in each semester. During
the first semester, first and second grade students practiced addition while third grade students practiced
subtraction in the program. In the second semester, first and second grade students practiced subtraction
while the third graders worked on multiplication.
To determine the impact of using the Imagine Math Facts program, teachers administered 3-minute, 100-ques-
tion math fact tests at the beginning and end of each semester. Students were instructed to complete as
many problems as possible within the time limit. The number of correct responses was used as the final score.
Imagine Math Facts:
Background
Study Procedures
Imagine Learning Research Department
research@imaginelearning.com | 801.377.5071
T E XA S C A S E ST U DY | I M AG I N E M AT H FAC TS
Significantly Improved Math Fact
Fluency and Automaticity
Results
Students using Imagine Math Facts logged approximately two hours on average in the program during both the
first and second semesters.
mathematics (Nelson, Parker, & Zaslofsky, 2016; Steel & Funnell, 2001). To be considered fluent and automatic,
a student must be able to rapidly recall the correct solutions to basic math operations including addition,
subtraction, multiplication, and division (Geary, 2011). Despite the importance of developing these skills,
several national groups, including the 2008 National Mathematics Advisory Panel, have found that “few
curricula in the United States provide sufficient practice to ensure fast and efficient solving of basic fact
combinations and execution of the standard algorithms.” (NMAP, 2008)
Given this context, Imagine Math Facts is designed to improve math fact fluency and automaticity in
elementary age students by differentiating instruction for each student. The game-based program provides
repeated and focused practice on previously unlearned math facts with constant and immediate feedback
while maintaining engagement through exciting and rewarding gameplay.
During the 2018-2019 school year, a southern Texas school implemented Imagine Math Facts in first through
third grades to help improve addition, subtraction, and multiplication fact fluency and automaticity. Since
students typically need only 6-10 weeks to complete all Imagine Math Facts exercises for each math fact
family (addition, subtraction, etc.), students practiced different math fact families in each semester. During
the first semester, first and second grade students practiced addition while third grade students practiced
subtraction in the program. In the second semester, first and second grade students practiced subtraction
while the third graders worked on multiplication.
To determine the impact of using the Imagine Math Facts program, teachers administered 3-minute, 100-ques-
tion math fact tests at the beginning and end of each semester. Students were instructed to complete as
many problems as possible within the time limit. The number of correct responses was used as the final score.
Imagine Math Facts:
Background
Study Procedures
Imagine Learning Research Department
research@imaginelearning.com | 801.377.5071
T E XA S C A S E ST U DY | I M AG I N E M AT H FAC TS
Significantly Improved Math Fact
Fluency and Automaticity
Results
Students using Imagine Math Facts logged approximately two hours on average in the program during both the
first and second semesters.
T E XA S C A S E ST U DY | I M AG I N E M AT H FAC TS
Imagine Learning Research Department
research@imaginelearning.com | 801.377.5071
Figure 1 presents the average pre- and post-test scores by grade for students who used Imagine Math Facts
during each semester of the 2018-2019 school year. Students in all three grade levels experienced significant
improvements in math fact fluency and automaticity after using the program. Figure 2 demonstrates the positive
correlation between progress within the Imagine Math Facts program and change in performance between the
pre- and post-tests.
10 10
20 20
30 30
40 40
0 0Grade 1:
Addition
Grade 1:
Subtraction
Average Score
Average Score
Grade 2:
Addition
Grade 2:
Subtraction
Grade 3:
Subtraction
Grade 3:
Multiplication
Pre-test Post-test Pre-test Post-test
Figure 1. Average Pre- and Post-Test Performance by Grade.
Semester 1 Semester 2
The results show students using the program in this Texas school during the 2018-2019 school year experienced
signficant improvements in math fact fluency and automaticity as demonstrated by performance on the 100-ques-
tion math facts assessments. Given these findings, we would expect comparable results for other students who
use the Imagine Math Facts program with fidelity.
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology,
47(6), 1539-1552. doi:10.1037/a0025510
National Mathematics Advisory Panel (2008). The Final Report of the National Mathematics Advisory Panel. Washington, DC.
Nelson, P. M., Parker, D. C., & Zaslofsky, A. F. (2016). The Relative Value of Growth in Math Fact Skills Across Late Elementary and Middle
School. Assessment for Effective Intervention, 41(3), 184-192. doi:10.1177/1534508416634613
Steel, S., & Funnell, E. (2001). Learning multiplication facts: a study of children taught by discovery methods in England. J Exp Child Psychol,
79(1), 37-55. doi:10.1006/jecp.2000.2579
References
Figure 2. Correlation between Percent Progress in the Imagine Math
Facts Program and Average Post-Test Performance.
Semester 1 Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2
0 0
20 20
60 60
40 40
-20 -20
0 020 2040 40
Percent Progress in Program Percent Progress in Program
Pearson’s R=0.46 Pearson’s R=0.34
Average Score Growth
Average Score Growth
60 6080 80100 100
Imagine Learning Research Department
research@imaginelearning.com | 801.377.5071
Figure 1 presents the average pre- and post-test scores by grade for students who used Imagine Math Facts
during each semester of the 2018-2019 school year. Students in all three grade levels experienced significant
improvements in math fact fluency and automaticity after using the program. Figure 2 demonstrates the positive
correlation between progress within the Imagine Math Facts program and change in performance between the
pre- and post-tests.
10 10
20 20
30 30
40 40
0 0Grade 1:
Addition
Grade 1:
Subtraction
Average Score
Average Score
Grade 2:
Addition
Grade 2:
Subtraction
Grade 3:
Subtraction
Grade 3:
Multiplication
Pre-test Post-test Pre-test Post-test
Figure 1. Average Pre- and Post-Test Performance by Grade.
Semester 1 Semester 2
The results show students using the program in this Texas school during the 2018-2019 school year experienced
signficant improvements in math fact fluency and automaticity as demonstrated by performance on the 100-ques-
tion math facts assessments. Given these findings, we would expect comparable results for other students who
use the Imagine Math Facts program with fidelity.
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology,
47(6), 1539-1552. doi:10.1037/a0025510
National Mathematics Advisory Panel (2008). The Final Report of the National Mathematics Advisory Panel. Washington, DC.
Nelson, P. M., Parker, D. C., & Zaslofsky, A. F. (2016). The Relative Value of Growth in Math Fact Skills Across Late Elementary and Middle
School. Assessment for Effective Intervention, 41(3), 184-192. doi:10.1177/1534508416634613
Steel, S., & Funnell, E. (2001). Learning multiplication facts: a study of children taught by discovery methods in England. J Exp Child Psychol,
79(1), 37-55. doi:10.1006/jecp.2000.2579
References
Figure 2. Correlation between Percent Progress in the Imagine Math
Facts Program and Average Post-Test Performance.
Semester 1 Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2Pearson's R = 0.46
-20
-10
0
10
20
30
40
50
60
70
Average Score Growth
0 20 40 60 80 100 Percent Progress in Program
Semester 1
Pearson's R = 0.34
-20
-10
0
10
20
30
40
50
60
70
0 20 40 60 80 100 Percent Progress in Program
Semester 2
0 0
20 20
60 60
40 40
-20 -20
0 020 2040 40
Percent Progress in Program Percent Progress in Program
Pearson’s R=0.46 Pearson’s R=0.34
Average Score Growth
Average Score Growth
60 6080 80100 100