The impact of an intervention program on students’ spatial reasoning: student engagement through mathematics-enhanced learning activities

Malleability of spatial reasoning

As an ability to represent and manipulate symbolic or nonlinguistic information, spatial reasoning is believed to be malleable and transferable across the lifespan (Linn & Petersen, 1985; Terlecki & Newcombe, 2005) and enhanced through training (see Uttal et al., 2013 for a review). Moreover, improvement on spatial tasks is found to be transferable to novel stimuli within the same task or to other spatial tasks (e.g., Wright, Thompson, Ganis, Newcombe, & Kosslyn, 2008). In their meta-analysis Uttal et al. (2013) concluded that there is solid evidence that spatial reasoning skills can be trained, with a mean effect size of .47 for improvement in spatial training across studies.

There is evidence for the development of spatial reasoning skills with age (Newcombe & Huttenlocher, 2003; Piaget & Inhelder, 1956). Previous work by Lowrie, Logan, and Ramful (2017) reported on the effectiveness of a spatial training program for children in grades 5–6 in both their spatial reasoning and mathematics performance. In the present paper we include new data on the implementation of the spatial training with grades 3 and 4 students, in addition to the previously published data for grades 5 and 6, to examine the effectiveness of training across a wider age range. In their meta-analysis, Uttal et al. (2013) found no significant differences in the effectiveness of spatial training across age groups, but they noted that there were very few studies of spatial training in children younger than 13 years. The first aim of this study was to determine whether the intervention program was effective with students of different ages.

The effectiveness of an intervention program for participants of varying spatial skill

Uttal et al. (2013) cite the initial level of spatial performance as a contributing factor in an intervention program’s success. Although only 19 of 206 studies used a screening agent to specifically target low spatial scorers, these studies reported significantly larger effect sizes than the remaining studies. There is evidence of an initial lag in the learning of low spatial participants, who show different improvement trajectories compared to higher performing students (Terlecki, Newcombe, & Little, 2008). After week 6 of Terlecki and colleagues’ mental rotation training program, the low spatial learners got over their initial “hump” and progressed at a comparable rate to that of the high spatial learners. The present intervention extended beyond 6 weeks and did not identify or initially target low performing students since the research design required implementation in whole-class contexts. Nevertheless, the second objective of this study, a novel contribution of the present paper (including new analyses of the grades 5–6 data), was to determine whether the intervention was more effective for students of varying spatial skill.

Components of spatial reasoning skill

Researchers have identified a number of factors constituting spatial reasoning skill; however, to date there is no consensus in its exact structure or consistency in measurement within the literature (Hegarty & Waller, 2004). One of the challenges in assessing the multidimensionality of spatial reasoning is the nature of the assessments themselves. In general, the psychometric measures that are used to define the subconstructs contain markers that explicitly measure the related factor (Kozhevnikov & Hegarty, 2001; Linn & Petersen, 1985). This circular research design does not lend well to robust measures and theoretical development. In addition, many studies employ adult tests of spatial reasoning on child populations without validating their use (Newcombe, 2016).

The spatial training program reported in Lowrie et al. (2017) and subsequently assessed in the present study used a measure of spatial reasoning, the Spatial Reasoning Instrument (SRI), based on the national school curriculum standards in the corresponding population (Ramful, Lowrie, & Logan, 2017). Importantly, the SRI provides broad coverage of three subconstructs of spatial reasoning that have been well established in the research literature (Linn & Petersen, 1985; Lohman, 1979; McGee, 1979), namely mental rotation, spatial orientation, and spatial visualization. This afforded the opportunity to conduct analyses on the effectiveness of the intervention program on students with different levels of spatial reasoning skill with rigor and depth.

Participants

Materials

Spatial Reasoning Instrument

The paper-and-pencil Spatial Reasoning Instrument (SRI; Ramful et al., 2017) was developed specifically for primary school children, based on three constructs (with an equal number of items per construct): mental rotation, spatial orientation, and spatial visualization. The three subscales have strong correlations with measures of these constructs in the cognitive psychology literature (Ramful et al., 2017). Scores on the SRI were the total number of correct items for each participant; unanswered items were assigned a score of 0. Examples of the items are presented in Fig. 1. The 30 items used in the present study were drawn from the pool of items used to construct the SRI. The test items were common across all year levels. Cronbach’s alpha for the 30-item test was .81.

Procedure

In order to recruit teachers, school principals in the authors’ network across the state were contacted. The study ran in the second half of the 2015 school year.²

Effectiveness of the spatial reasoning program

We analyzed group differences on pre-tests using a two-level HLM model (students within classrooms) with conditions dummy coded (1 = intervention and 0 = control). A two-level model was also used to analyze pre-test–post-test gains, with condition groups similarly dummy coded to determine the direct effects of the interaction. An intra-class correlation (ICC) was conducted on these data to determine the variability between and within the group clusters. The ICC measure was .102 with a 95% confidence interval from .031 to .256 [F(17,252) = 2.17, p < .001]. Although the design had a small number of groups for an HLM model, the ICC measure indicated sufficient power and a low degree of dependency on type I error (see Aarts, Verhage, Veenvliet, Dolan, & Van Der Sluis, 2014, for a description of the role of ICC in nesting designs). Additional file 2 provides an example of data analysis using HLM.

Effectiveness of the program in terms of individual differences

Effect sizes (Cohen’s d) between intervention and control group SRI gain scores by spatial rank are presented in Table 4. We can conclude that the spatial reasoning program was beneficial for the intervention group irrespective of their initial spatial reasoning skill.

Student engagement within the pedagogical framework

During the 10-week intervention, student work samples were collected and analyzed to determine levels of fidelity and student engagement within the ELPSA learning cycle. Additional file 1 describes learning activities that were aligned to the five components of the ELPSA model within spatial visualization, contextualized within the Week 9 Reflection and Symmetry activities. The first column represents ideas and activities presented by classroom teachers, including artifacts used to introduce activities within the ELPSA framework, providing evidence that the classroom teachers presented activities and learning ideas within the respective components of the ELPSA framework.

The teachers began the topic from the viewpoint of what students knew about the topic and encouraged active engagement through contextualized whole-class discussions (Experience). They were explicit about the terminology used—increasing the complexity of the language conventions throughout the topic—and encouraged students to reflect upon the relevance of this language at the completion of the lessons (Language). In the Pictorial phase, the teachers modeled symmetry concepts through diagrams and encouraged students to do the same, aiding the transition from concrete and diagrammatical representations to more sophisticated visualization strategies. The teachers then encouraged students to reason analytically, as a transition beyond representing information “in the mind’s eye.” This symbolic reasoning was evident in the development of rules such as the orientation of objects after a diagonal reflection. Finally, the teachers presented open-ended activities that required students to apply concepts to other situations (Application).

The second column of Additional file 1 highlights student work samples within each of the five ELPSA components. The work samples align well with how the teachers modeled conceptual development throughout the unit—highlighting the fidelity of the program. These lessons required the students to encode during each component of the framework as they moved from concrete, to visual, to analytic reasoning. The encoding techniques supported students’ learning as they reflected upon and evaluated their reasoning.

The third column provides examples of student reflections in their own voice as they progressed through the spatial visualization activities of the program. These student reflections highlight the movement toward analytic thinking. The notion that “symmetry is something like butterfly wings” indicates the establishment of context. The language conventions of symmetry are made explicit in comments like “how to flip it on the y or x axis so I was trying to visualize the mirror,” providing evidence for the alignment of everyday ideas to mathematics terminology. At the Pictorial phase, students displayed a decreasing need for concrete manipulatives in solving tasks, for example “picturing it in my mind and trying to think of how the page was folded diagonally.” At the analytic stage the students used gesture to support their problem solving before progressing to more complete understandings of perpendicularity “I was imagining a mirror on the fold of the page, using visual measurements to make it as accurate as possible.” Instances of application were less common; however, detail and accuracy become more commonplace.

The process of concept development was established initially from a shared understanding of contextual knowledge (Experience and Language) and supported through concrete materials and gesture, the encoding of information, and the opportunity to internally visualize (Pictorial). From this point, competent students progressed toward analytic thinking (Symbolic and Application). That is, all students participated (engaged) in spatial visualization learning activities within the first three components of the learning framework. It is not surprising that we found less evidence of engagement in the more analytic components (especially at the Application level).

Growth based on initial spatial reasoning

Spatial reasoning scores for students in the intervention group improved at consistent rates irrespective of initial spatial reasoning score, compared to the control group. Students initially classified with either low, moderate, or high spatial reasoning had moderately high effect size gains—with each cohort achieving greater than d = .4 higher than the comparable control group. The personalized nature of the ELPSA framework, where all students are encouraged to move through the learning cycle in a learner-focused and constructivist manner, might have contributed to these outcomes. In order for students with higher levels of spatial proficiency to also benefit from the training program, it is necessary for these students to engage in symbolic reasoning and more sophisticated levels of pattern abstraction (Jurdak & El Mouhayar, 2014; Landy, Allen, & Zednik, 2014). Within the ELPSA framework, such engagement is promoted in the Symbolic and Application components in particular (Lowrie & Patahuddin, 2015). The Application of spatial thinking developed through the program has the potential reach into STEM practices (DeSutter & Stieff, 2017). Modifications to the program might need to ensure that teachers expose higher performing students to learning activities within the Symbolic and Application components sooner.

Implementation of the pedagogical framework (ELPSA)

The ELPSA framework became a point of reference for how the classroom teachers introduced learning activities and how the students acquired conceptual understanding. Thus, the teaching artifacts provided insights into the fidelity of the instruction, while the student work samples informed our understanding of how students made sense of the activities. In addition, the framework became a point of reference for our capacity to reflect upon the strength of the intervention design. Consequently, we maintain that the classroom-based intervention program should be developed within a pedagogical framework.

Future directions, limitations

Although this investigation has established the success of the intervention program, future work should investigate the extent to which this success is derived from students’ exposure to the learning activities and/or the embedding of the activities into the ELPSA framework. We have evidence that the intervention program is working from both the classroom teachers’ design of lessons and the students’ engagement with these activities—in different schools, with teachers drawn from different contexts, with varying teaching experience. It would be beneficial to capture changes in the classroom teachers’ discipline knowledge as they engage with the professional development (PD) aspects of the design and indeed as they implement the program. These data would allow for insights to be made about targeted PD—with those teachers with poor spatial reasoning skill afforded different levels of exposure to PD. The qualitative data provided promising insights into fidelity of the program; however, more systematic data should be collected on students’ reflections and engagement with the learning activities. Such qualitative depth will afford opportunities for researchers to monitor students’ sense making and skill development.

This investigation does not document learning transfer to other STEM fields, which should be examined in subsequent studies. The study was restricted to determining whether an integrated spatial thinking intervention program could improve student’s spatial thinking beyond a business-as-usual program that included spatial concepts embedded within the geometry and measurements mathematics program. Nevertheless, the study confirms that a classroom-based intervention program can improve student’s spatial reasoning, at scale. Large-scale, classroom-based, intervention programs can now be designed within attainable research budgets to determine transfer among STEM disciplines.