Spatial Reasoning in the Classroom: The Effectiveness of Classroom-based Spatial Intervention Programs STEM Education Research Centre (SERC) Professor Tom Lowrie

Stem Education Increasing emphasis on STEM Education Focusing on trying to integrate STEM content undoes the intent of STEM STEM Practices - not content Focusing on practices ensures understandings are related to real-world contexts and enacted through participation and engagement

What is Spatial Reasoning? Sourced from The Department of Education, Ontario (2014). Paying attention to spatial reasoning. http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf

Spatial Visualisation What is Spatial Reasoning? Theoretical underpinnings Spatial Reasoning Spatial Visualisation Mental Rotation Spatial Orientation

Spatial Reasoning Key predictor of STEM academic success and career choice. (Wai, Lubinski & Benbow, 2009) Skills are malleable and can be trained. (Uttal et al., 2013) A critical vehicle for connecting STEM Practices to how children think in education. (National Research Council, 2012) There is strong evidence that spatial reasoning and mathematics are intrinsically linked and share a lot of common processing skills. (Mix & Cheng, 2012) Spatial Reasoning is one element of Numeracy in the Australian Mathematics Curriculum. Improved spatial thinking provides new affordances for a range of equity groups. (Sorby, 2007)

Spatial Visualisation It involves thinking with the mind’s eye. “At its core, spatial visualization requires making and retaining a mental image and changing or manipulating it in some transformative way”. (Ontario document, 2014, p. 10)

Concepts associated with Spatial Visualisation Systematic manipulation of shapes and images e.g., folding/unfolding paper and paper engineering Symmetry and reflections Cross-sections of 3D objects Spatial structuring; Layering, block counting Composing and decomposing shapes Shifting dimensions from 2D to 3D and vice versa Translations and scaling

Spatial Visualisation

Mental Rotation Mental rotation is a cognitive process in which a person imagines how 2D and 3D objects would appear after they have been turned around a point or an axis by a certain angle. (Shepard & Metzler, 1971)

Concepts associated with Mental Rotation Jigsaw puzzles 2D rotations on the plane: quarter/half turns, clockwise/anticlockwise 2D rotations by degrees: 45o anticlockwise Identifying unique 3D figures with 3, 4 or 5 cube blocks Understanding 3D equivalence 3D rotations around the x, y and z axes Rotations but not reflections

Mental Rotation

Spatial Orientation Egocentric perspective transformations are imagined movements of one’s point of view. An egocentric representation involves locating an object with respect to one’s body as reference. Wayfinding/Navigating One has to mentally or physically position oneself in the place of an object to be manipulated to determine the position of the object or the result of a transformation on the object. The problem solver is required to analyse an object with respect to his/her position. (Zacks, Ollinger, Sheridan, & Tversky, 2002). Perspective taking the ability to imagine how an object or scene looks from perspectives different to the observer’s. It is regarded as the anticipation of location from different vantage points. (Newcombe & Huttenlocher, 1992)

Concepts associated with Spatial Orientation Navigating using cardinal and relative directions Reading, drawing and interpreting maps; including different orientations Visual perspective taking: putting your self in someone else’s shoes Orthogonal views: front, top, side Close links with geography and PE and sport

Spatial Orientation

Mental Rotation vs Spatial Orientation The critical difference between mental rotation and spatial orientation depends on whether the object is manipulated, or the observer’s point of view is manipulated. In mental rotation the object is mentally manipulated, but the observer’s point of view remains fixed. In spatial orientation the object is fixed and the observer’s point of view is manipulated/changed.

Spatial Reasoning and Mathematics “The relation between spatial ability and mathematics is so well established that it no longer makes sense to ask whether they are related.” (Mix & Cheng, 2012, p. 206)

Spatial Reasoning in the Classroom Spatial concepts tend to develop through engagement in our inherently spatial world or through activities that promote particular spatial skills or understandings Two simultaneous classroom-based approaches should be taken to promote spatial reasoning in education Bring spatial thinking into the learning environment through intentional teaching embedded within the curriculum Promoting a spatial habit of mind through new ways of thinking spatially about the world

“Practical” Spatial Reasoning Practice and Practise of Spatial Reasoning

Spatial Reasoning Intervention Framework Practice Practise Pedagogical Framework ELPSA Student focused visualisation Digital Resources 5 learning components: Experience Language Pictures Symbols Application Mandalar Draw Tile Origami paper cutting 3D Shapes

Intervention Programs Embedded into lessons Teachers as Researchers

What have we found so far? In 2015 we implemented a ten week spatial reasoning program (totalling 20 hours) across eight grade 3-6 classrooms. At the conclusion of the program improvements were found in both spatial reasoning and mathematics. A high level of engagement was reported by teachers and students. Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance. British Journal of Education Psychology, 87, 170-186.

What have we found so far in 2018? In early 2018 we conducted cross-sectional testing of primary and high school students across ACT to explore the impact of static and dynamic assessment formats. Students completed maths, spatial and verbal assessments on iPad and pen and paper. Spatial performance positively correlated with performance on both mathematics and verbal assessments. Available content knowledge and spatial ability mediated strategy use on static and dynamic tasks. Improving verbal and spatial ability may improve maths; and digital resources enable students to access a broader range of strategies, making them more likely to succeed.

What is next? Implementation of the spatial reasoning program in grade 8 classrooms – currently happening! 32 grade eight classrooms across ACT and NSW participating in the intervention. The training program consists of 12 hours of lessons delivered over a six week period, replacing geometry and measurement during this time. Intervention covers constructs successfully implemented in Primary Schools. The high school program aligns to curriculum requirements but includes specialised spatial content and new methods of teaching based on ELPSA framework.

High School Intervention Teacher feedback so far has been positive - “There are a few students who have been moved into my classes because of issues with engagement - and they are the students I am finding are most up for the challenge”. “I teach a low level year 8, so they are pretty apathetic towards all maths activities - the class really got into it, and enjoyed it (in spite of themselves!)”. “Most of them have exceeded my expectations for their level of enthusiasm and interest for the topic”.

Thank You SERC Projects supported by Contact Details thomas.lowrie@canberra.edu.au canberra.edu.au/serc @UC_SERC