**9. Interpretation of findings**

*Early Childhood Education*

the traditional group, scores on the spatial reasoning scale also increased significantly from pretest to posttest, *t*(242) = 5.5, p < 0.001. Thus, for both groups, scores increased from pretest to posttest. The EIS and traditional groups were also compared separately on the pretest and then on the posttest. These results showed that for the pretest, the groups differed significantly, *t*(449) = 2.8, p < 0.01. For the posttest, the groups were not significantly different, *t*(449) = 0.36, p = 0.72. For the pretest, scores were greater for the traditional than for the EIS group, and on the

Taken together, the results of these analyses show that scores on the spatial reasoning subtest were equal on the posttest across both groups. However, the marginally significant interaction suggests that the change from pretest to posttest was not the same for the two groups. As seen in **Table 2**, the change was greater for the EIS group than for the traditional group. The EIS group began the study with significantly lower scores on the spatial reasoning subtests. The EIS group shows statistically higher gains than the traditional, thus confirming EIS

In summary, the instructional method (EIS vs. traditional) did have a significant effect on first grade students' spatial reasoning. The study demonstrated statistical significance between the treatment groups who implemented the EIS instruction and comparison group who used traditional mathematics instruction. The next

**Group Mean SD Mean SD** EIS 1.24 0.803 1.82 0.871 Traditional 1.46 0.905 1.85 0.912

**Pretest Posttest**

posttest, scores were the same across both groups.

*Estimated marginal means of spatial reasoning.*

**124**

**Table 2.**

has an effect.

**Figure 4.**

**Spatial reasoning**

*Spatial reasoning descriptive statistics.*

The primary focus of the study was to look at the effects on students' conceptual understandings of relational thinking and spatial reasoning when integrating the EIS representations into first grade mathematics lessons. As Cheng and Mix [8] revealed through their research, the need to integrate spatial reasoning tasks is critical for the development of students' conceptual knowledge. Similar claims can be made based on the results of this study.

The EIS group performed statistically higher in relational thinking than the traditional group, doubling mean scores from pretest (0.74) to posttest (1.27). Previous work has shown students who are instructed to solve equations strictly in symbolic form struggle with algebraic thinking [79]. Integrating EIS representation into first grade mathematics lessons with a balanced set of equations has shown to be effective at developing students' relational thinking and spatial reasoning.

As Cheng and Mix [8] revealed through their research, the need to integrate spatial reasoning tasks is critical for the development of students' conceptual knowledge. Similar claims can be made based on the results from this study. We conclude that the integration of spatial reasoning had positive effects on first grade students' spatial reasoning skills, relational thinking, the development of conceptual understanding, and mathematical competency.

The findings support the notion that the integration of EIS representation into mathematics lessons offers students sufficient conceptual knowledge to develop number operations and mathematical competency [48]. Gain scores in facts and context are found to be consistent with earlier works from Carbonneau and colleagues [61], who suggests mathematics instruction should refrain from isolated skill and procedural practice in lieu of the development of conceptual understanding. Curriculum designed to include a progression of enactive, iconic, and symbolic models supports students' conceptual understanding [2, 62, 63]. Students in the EIS group were instructed to enactively build and iconically represent their math facts simultaneously. In doing so, they increased their conceptual understanding of the mathematics. K-12 reform has included an integration of meaningful lessons designed to enhance algebraic thinking across all mathematical domains, and altering the curriculum to include spatial reasoning tasks has shown to improve mathematical performance [54]. Our investigation has demonstrated a positive effect on students' spatial reasoning, relational thinking, and overall mathematical competency when first grade mathematics lessons integrate EIS representations.
