Summary of Packard-CSU Ed.D. Pre-Dissertation Fellowship Report
Title: After-school Intervention with Spatial Temporal Mathematics
Ed.D. Candidate: Darielle M. Tom, CSU Long Beach
Research Question(s):
The initial research questions are:
1. What (if any) will be the effect of an after-school spatial temporal mathematics intervention program
on elementary students’ mathematic performance?
2. What (if any) will be the effect of an after-school spatial temporal mathematics intervention program
on students’ performance on the state accountability test in mathematics?
The follow-up research questions will be:
1. What (if any) effects will the after-school intervention have on students’ attitudes or behaviors about
math and their own ability to be successful learners?
Conceptual Framework and/or Guiding Purpose of the Study
The conceptual framework of this study incorporated literature from brain-based research, which led to
the foundation of spatial temporal mathematics, and addresses a number of other areas, including
computerized instruction and after-school interventions. This framework was used as a lens to examine
how spatial temporal mathematics may improve mathematical reasoning via computer-assisted
instruction with high-risk students. High-risk students for this study were defined as those who fall in the
far below basic and below basic categories on the California Standards Test (CST). Through unpacking
past research, issues of how spatial temporal mathematics might enhance future after-school
intervention served as the analytical framework for this study.
Relevant Theoretical and Empirical Literature:
Brain-Based Research
Shaw (1985) was a neurologist who wondered why U.S. students were so far behind in mathematics
(compared globally) and who questioned how the brains of U.S. students processed mathematical
concepts. Shaw researched how neurons were firing in the brain to seek answers. From Shaw’s early
research, one theory emerged: The Mozart Effect (Rauscher & Shaw, 1993).
Mozart Effect
The term “Mozart Effect” originated from an article by Rauscher, Shaw and Ky in 1993. Rauscher et al.
discussed “musical and spatial task performance” of college students. The study found that after listening
to 10 minutes of Mozart’s Sonata for Two Pianos in D Major, college students were better able to solve
spatial temporal reasoning problems than those who had listened to no music or listened to relaxation
music.
Music Mathematics Connection
Levine et al. (1997) stated that listening to music enhanced spatial temporal reasoning. Grandin (1998)
concluded that music instruction enhanced the "hardware" in the brain for spatial temporal reasoning.
Computer-Assisted Instruction
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Summary of Packard-CSU Ed.D. Pre-Dissertation Fellowship Report
Utilizing computers for instruction is a longstanding approach in education. Research in this field can be
found since the 1980s, when computer-based instruction was often called computer-based training. That
term has since been refined and is typically referred to as computer-assisted instruction.
High-Risk Students
Students who need the most growth impact on their mathematics learning are high-risk students; these
students are also referred to as at-risk students. Swanson, Jerman, and Zheng (2008) identified high atrisk and children not at risk for serious math problem solving difficulties by administering a battery of
tests that assessed problem solving, achievement, and cognitive processing. Swanson et al. concluded
that children identified as at risk for serious math problem solving difficulties showed less growth rate and
lower levels of performance on cognitive measures than did children not at risk.
After-School Intervention
Mueller and Maher (2009) showed that students could learn to reason in an informal mathematics afterschool program. Their findings indicated that, within an environment that invites exploration and
collaboration, students could be engaged in defending their mathematical reasoning in both their small
groups and within the larger community.
The literature review summarized brain-based research and the Mozart Effect, which was the foundation
for spatial temporal mathematics. The literature showed how spatial temporal mathematics improved
mathematical reasoning via computer-assisted instruction and also revealed how after-school
interventions enhanced high-risk students’ achievement toward the goal of increasing student
achievement. A particularly efficient and cost effective way to reach that achievement goal is to
incorporate successful intervention strategies into after-school programs.
Methods of Data Collection and Analysis:
The purpose of the study was to examine the effects of an after-school mathematics intervention
program on student achievement in elementary school. The independent variable was the spatial
temporal mathematics intervention. The dependent variable was mathematics achievement as measured
by school district benchmarks tests and the California Statewide Accountability Test in Mathematics.
ANOVAs were conducted using the variables of gender, socioeconomic status, and initial mathematics
proficiency. To assess treatment effects, the Bonferonni method was examined at the .025 level. The
analysis of variance was used to determine if the intervention demonstrated significant differences for the
groups.
The second research question investigated the effect of intervention on students’ performance on the
Statewide Accountability Test in Mathematics. ANOVAs were conducted to examine whether there was a
significant gain for the intervention participants.
Initial Analysis
Thirty-nine second grade students, from four different classes, were invited to participate in the afterschool intervention class. Students with progress below 40% on a spatial temporal mathematics program
were invited to attend a free 45-minute class with a credentialed teacher once a week.
Intervention commenced on April 15, 2011 and ran for seven consecutive weeks. Participation and
progress were tracked on the 39 students to determine their growth compared with a comparison group
and is shown on the table below. Weekly growth was tracked along with total growth. From the original
group of students included in the participants group, three were moved to the non-participants category
for arriving more than 15 minutes late twice and for leaving early on three occasions.
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Summary of Packard-CSU Ed.D. Pre-Dissertation Fellowship Report
Table 1. Comparison of Participant’s and Non-participant’s Progress in the Spatial Temporal
Mathematics Program
Start
Week 1
2
3
4
3
5
6
7
Total Growth
Summary of Packard-CSU Ed.D. Pre-Dissertation Fellowship Report
Initial Analysis and Emerging Recommendations
Average growth with the spatial temporal mathematics computerized program was expected to be about
1-2% for every 45 minutes of participation.
Growth was tracked based on the results of the California State Standards Test in May. Students were
expected to have completed 75% of the spatial temporal mathematics curriculum by May in order to
have covered the material that may be on the test.
The first three weeks of the pilot proceeded as expected with 1-2% growth each week. Since the
students were initially so far behind the 75% goal, a homework module was put in place. This process
allowed students access to the curriculum from home. This home access and utilization was tracked as
well. Starting week four, growth averages ranged from 3% to 12%.
A compelling case exists for the need to conduct further research about the effectiveness of spatial
temporal mathematics as an after-school intervention. The following factors are particularly relevant:

There is currently a strong interest in raising math achievement in the U.S.

The use of computers to assist in math instruction is growing.

The use of spatial temporal mathematics is growing across the nation.

More evidence is needed about spatial temporal mathematics as an after-school intervention.

Other after-school interventions programs have been proven to increase academic achievement,
particularly for high-risk students.
Innovative programs can be administered and examined effectively in after-school environments.
Additional Description:
Students were selected to participate in the study based on their performance on grade-level districtwide benchmark mathematics screening tests administered in the fall of 2010. Items on the benchmark
are aligned with State content standards in mathematics at each grade level and include calculations and
estimations, measurement, geometry, statistics, and probability. Students performing below the 50 th
percentile were offered the intervention. The intervention was offered for 45 minutes once a week for six
weeks. To control for threats to attrition, students were provided with reminder notes the day before
intervention. If a student was chronically absent, he or she was removed from the study.
At the conclusion of the intervention, the benchmark tests were administered a second time. Procedures
for administration and scoring of the test were consistent with district guidelines for assessments.
The following additional assumptions regarding after-school learning were made in the study:

With smaller groups, more individualized instruction can occur.

High-risk students may receive more homework assistance than they may have from working
parents.

With increased achievement, students may also feel more confident to take on advanced
mathematics classes, which could lead to future interest in STEM careers.
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Summary of Packard-CSU Ed.D. Pre-Dissertation Fellowship Report
Selected References:
Grandin, T., Shaw, G. L., et al. (1998). Spatial-Temporal versus Language-Analytic Reasoning: The Role
of Music Training. Arts Education Policy Review 99(6): 11-14.
Levine, L., Wright, E., Dennis, W., Rauscher, F., Shaw, G., & Newcomb, R. (1997). Music training
causes long-term enhancement of preschool children's spatial-temporal reasoning. Neurological
research, 192. Retrieved from RILM Abstracts of Music Literature database.
Mueller, M., & Maher, C. (2009). Learning to Reason in an Informal Math After-School Program.
Mathematics Education Research Journal, 21(3), 7-35. Retrieved from ERIC database.
Rauscher, F. H., & G. L. Shaw (1993). Music and spatial task performance. Nature, 365, 611.
Rauscher, F. H., Shaw, G.L., & Ky, K.N. (1995). Listening to Mozart enhances spatial temporal
reasoning: toward a neurophysiological basis. Neuroscience Letters, 185, 44-47.
Shaw GL, Silverman DJ, & Pearson JC. (1985) Model of cortical organization embodying a basis for a
theory of information processing and memory recall. Proc. Natl. Acad. Science, USA; 82: 23642368.
Swanson, H., Jerman, O., & Zheng, X. (2008). Growth in Working Memory and Mathematical Problem
Solving in Children at Risk and Not at Risk for Serious Math Difficulties. Journal of Educational
Psychology, 100(2), 343-379. Retrieved from ERIC database.
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