Developing Mathematical Creativity in High-Potential Kindergarten English Learners Through Enrichment and Tangram Activities
Abstract
1. Introduction
1.1. Mathematical Creativity in Young English Learners with High Potential
1.1.1. Definition and Characteristics of Mathematical Creativity
1.1.2. Mathematical Creativity in Young Children
1.1.3. Open-Ended Tasks (Tangrams, Block Play, Puzzles)
1.1.4. Mathematics-Specific Knowledge and Skills and Mathematical Creativity
1.2. Instructional Support to Develop Mathematical Creativity
1.2.1. Teacher-Led Interventions
1.2.2. Math Enrichment Programs
1.3. Mathematical Creativity and Gifted English Learners
- (RQ1) To what extent do creativity outcomes differ between intervention and comparison groups?
- (RQ2) Which factors significantly predict creativity outcomes?
2. Materials and Methods
2.1. Participants
2.2. Instruments
2.2.1. Tangram Creativity Assessment (TCA)
Fluency
Flexibility
Originality
2.2.2. Tangram-Specific Problem-Solving Speed (TPSS)
2.2.3. Cognitive Abilities Test
2.2.4. Mathematics Achievement
2.3. Implementation
2.4. Data Analysis
3. Results
3.1. Comparison of Tangram Creativity Assessment Scores
3.2. Path Analysis of Tangram Creativity Assessment Across Fluency, Flexibility, and Originality Scores
4. Discussion
4.1. Predictors of Mathematical Creativity
4.2. Effects of Enrichment Intervention
4.3. Language Proficiency and Creativity Performance
4.4. Limitations and Future Directions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
| ELs | English Learners |
| TCA | Tangram Creativity Assessment |
| CogAT_RAW | Cognitive Abilities Test (CogAT) total raw score |
| CogAT_GPR | Cognitive Abilities Test (CogAT) grade percentile rank |
| TPSS | Tangram Problem Solving Speed |
| NWEA | NWEA MAP Growth Mathematics |
| NWEA PER | NWEA MAP Growth Mathematics Achievement Percentiles |
| INT | Intervention Group |
| COM | Comparison Group |
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| Category | Intervention | Comparison | Total | ||||
|---|---|---|---|---|---|---|---|
| (n = 155, 62%) | (n = 95, 38%) | (n = 250, 100%) | |||||
| n | % | n | % | n | % | ||
| Gender | Female | 83 | 53.5 | 45 | 47.4 | 128 | 51.2 |
| Male | 72 | 46.5 | 50 | 52.6 | 122 | 48.8 | |
| Ethnicity | Hispanic | 94 | 60.6 | 59 | 62.1 | 153 | 61.2 |
| Asian | 23 | 14.8 | 7 | 7.4 | 30 | 12.0 | |
| African American | 5 | 3.2 | 2 | 2.1 | 7 | 2.8 | |
| Not specified | 33 | 21.3 | 27 | 28.4 | 60 | 24.0 | |
| Number of classes | 16 | 61.5 | 10 | 38.5 | 36 | 100 | |
| The White Space Inside the Shape Must Be Completely Covered and Does Not Go Outside the Shape’s Perimeter. | Small Tangram Pieces to Design | Composition of Shapes |
|---|---|---|
![]() | ![]() | ![]() Composition of triangles |
![]() Composition of square | ||
![]() Composition of parallelogram |
| Response | % | f | f Cutoffs | Originality Points | Originality |
|---|---|---|---|---|---|
![]() | 20 | 12 | Occasional (20–40%) | 1 | Moderate |
![]() | 23 | 14 | Occasional (20–40%) | 1 | Moderate |
![]() | 43 | 26 | Common (>40% occurrence) | 0 | Common |
![]() | 13 | 8 | Infrequent (10–19%) | 2 | Elevated |
![]() | 1 | 1 | Rare (<10%) | 3 | Exceptional |
| Child Image Response | Fluency | Flexibility | Originality | TCA Total | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Number of Solutions | Score | Number of Categories | Score | Number of Unusual or Rare Solutions | Score | Adding Fluency, Flexibility, and Originality | ||||||
| A (1, 2) | B (3) | C (4, 5) | 3 (0 pt) | 1, 2 (1 pt) | 4 (2 pt) | 5 (3 pt) | ||||||
![]() | 1 | 1 | 1 | - | - | 1 | - | 1 | - | - | 1 | 3 |
![]() | 1 | 1 | 1 | - | - | 1 | - | 1 | - | - | 1 | 3 |
![]() | 1 | 1 | - | 1 | - | 1 | 1 | - | - | - | 0 | 2 |
![]() | 1 | 1 | - | - | 1 | 1 | - | - | 1 | - | 2 | 4 |
![]() | 1 | 1 | - | - | 1 | 1 | - | - | - | 1 | 3 | 5 |
![]() | 2 | 2 | 1 | - | 1 | 2 | - | 1 | - | 1 | 4 | 8 |
![]() | 3 | 3 | 1 | 1 | 1 | 3 | 1 | 1 | - | 1 | 4 | 10 |
| Item Prompt | Math Focus/Skill | Scoring Criteria | Child Image Response | Score Explanation | |
|---|---|---|---|---|---|
| The triangle covers this part. Please cover this part using the other shapes [point to the white part and the tangram]. | Spatial reasoning and composition of shapes | A. Time Needed to Solve 1st Way ≤30 s (3 pt) ≤1 min (2 pt) ≤3 min (1 pt) ≥3 min (0 pt) Total: 3 pt max | ![]() | ![]() | Solved at 20 s Score: 3 |
![]() | ![]() | Solved at 46 s Score: 2 | |||
![]() | ![]() | Solved at 2 min Score: 1 | |||
![]() | ![]() | Solved at 20 s | |||
![]() | ![]() | + extra at 2:30 Score: 3 | |||
| Assessment | Group | MANOVA | ||||||
|---|---|---|---|---|---|---|---|---|
| Intervention (n = 155, 62%) | Comparison (n = 95, 38%) | |||||||
| Effect | M | (SD) | M | (SD) | Wilks’ Lambda | F (df1, df2) | p | η2p |
| Intercept | 0.630 | 46.374 (3, 246) | <0.001 | 0.370 | ||||
| Group | 0.987 | 1.006 (3, 246) | 0.391 | 0.013 | ||||
| Pre-TCA | 1.55 | (2.02) | 1.37 | (1.80) | ||||
| Pre-Fluency | 0.57 | (0.73) | 0.52 | (0.64) | 0.398 (1, 248) | 0.529 | 0.002 | |
| Pre-Flexibility | 0.55 | (0.66) | 0.45 | (0.60) | 1.341 (1, 248) | 0.248 | 0.006 | |
| Pre-Originality | 0.43 | (0.85) | 0.40 | (0.72) | 0.082 (1, 248) | 0.775 | 0.000 | |
| Post-TCA | 3.05 | (3.07) | 2.22 | (2.67) | ||||
| Post-Fluency | 1.03 | (0.99) | 0.74 | (0.84) | ||||
| Post-Flexibility | 0.94 | (0.86) | 0.70 | (0.77) | ||||
| Post-Originality | 1.09 | (1.45) | 0.77 | (1.18) | ||||
| Measure | Source | F(1, 246) | p | η2p |
|---|---|---|---|---|
| Total TCA | Pre-test | 45.26 | <0.001 | 0.169 |
| Group | 5.72 | 0.018 | 0.025 | |
| Fluency | Pre-test | 49.03 | <0.001 | 0.180 |
| Group | 7.06 | 0.008 | 0.031 | |
| Flexibility | Pre-test | 36.68 | <0.001 | 0.141 |
| Group | 4.62 | 0.033 | 0.020 | |
| Originality | Pre-test | 28.32 | <0.001 | 0.113 |
| Group | 4.38 | 0.038 | 0.019 |
| Mplus Step | χ2(df) | p | CFI | TLI | RMSEA [90% CI] | SRMR | ΔCFI | ΔRMSEA |
|---|---|---|---|---|---|---|---|---|
| Configural (multi-group) | 68.53 (48) | 0.027 | 0.977 | 0.969 | 0.059 [0.021, 0.089] | 0.077 | — | — |
| Metric (loadings equal across groups) | 68.53 (48) | 0.027 | 0.977 | 0.969 | 0.059 [0.021, 0.089] | 0.077 | 0.000 | 0.000 |
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Özbek, G.; Mun, R.U.; Shen, Y.; Lin, W.; Spence, M.; Cho, S. Developing Mathematical Creativity in High-Potential Kindergarten English Learners Through Enrichment and Tangram Activities. Educ. Sci. 2025, 15, 1581. https://doi.org/10.3390/educsci15121581
Özbek G, Mun RU, Shen Y, Lin W, Spence M, Cho S. Developing Mathematical Creativity in High-Potential Kindergarten English Learners Through Enrichment and Tangram Activities. Education Sciences. 2025; 15(12):1581. https://doi.org/10.3390/educsci15121581
Chicago/Turabian StyleÖzbek, Gülnur, Rachel U. Mun, Yuyang Shen, Weini Lin, Melissa Spence, and Seokhee Cho. 2025. "Developing Mathematical Creativity in High-Potential Kindergarten English Learners Through Enrichment and Tangram Activities" Education Sciences 15, no. 12: 1581. https://doi.org/10.3390/educsci15121581
APA StyleÖzbek, G., Mun, R. U., Shen, Y., Lin, W., Spence, M., & Cho, S. (2025). Developing Mathematical Creativity in High-Potential Kindergarten English Learners Through Enrichment and Tangram Activities. Education Sciences, 15(12), 1581. https://doi.org/10.3390/educsci15121581




























