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Creating powerful learning in mathematics

Lora Bance – Catholic Education Canberra Goulburn Archdiocese and Keith Roberts – Principal, Channel Christian School Tasmania

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T Rex Meets R2D2 – using research and digital technology to create change in mathematics and STEM

Mathematics is an essential building block of STEM literacy. To support student participation and develop positive mathematics identity the three aspects of learning in mathematics outlined below: exploring problems together, visualizing thinking and using spatial reasoning, can be enhanced by harnessing the affordances of technology in the classroom. The enduring outcome of STEM education is the students’ ability to discover, create and use foundational knowledge in STEM in real-life. Quality teaching and learning experiences in STEM education are founded in meaningful real-world challenges, informed by a global perspective, and integrated within community and culture.

Mathematics should be learned through experiences in solving sufficiently challenging problems, use hands-on learning strategies for exploring, and opportunity to share thinking. When designing and delivering lessons in mathematics it is important to give students opportunity to explore problems to demonstrate multiplicity of ideas. Exploring involves discussion, but too often the social aspect of mathematics is lost in a myriad of worksheets and questions to be completed in a limited time. Instead, to develop STEM literacy students should participate in investigations that are discussed together, in order to strengthen ideas. For this to happen students need to experience mathematics in groups, and mathematics through problem-solving. STEM involves rigorous understanding along with collaboration to reach that understanding, being a problem solver is hard fun and involves working with a community of learners (Pound & Lee, 2015).

Students need flexible thinking if they are to be good problem solvers. To increase a student’s capability to explore challenging problems they should be able to provide visual proof of their thinking through ideas of ‘Make, Say, Do, Write’ including drawing, modelling, and explaining (Boaler, 2015). Participating in problem-solving and improving mathematical thinking is more than manipulating abstract symbols systems, it requires sensory-motor action using patterning, abstracting, modelling and play in multimodal settings to support deep understanding (Mishra, 2012). By exploring visual components of mathematics, explaining processes and reasoning, students develop understanding from another point of view, developing empathy for how people see mathematical problems and increase curiosity – a key STEM practice.

Spatial reasoning improves the ability to visualize solutions and is a key contributor to STEM literacy as it is concerned with understanding and working within the physical world (Lowrie, Downes, & Leonard, 2017, p. 27). Using mental transformations, decomposing a pattern into component parts, using scale, estimations, mental imagery, comparison and sequencing are a few examples of elements of spatial reasoning that support student learning. The more opportunities that students have to show their thinking, to work in sense-making activities and discussion, the stronger their mathematical thinking, which supports problem-solving in STEM education.

Digital technologies can play many roles in supporting student participation in STEM education including games for exploring problems and understand thinking, and digital tools for sharing and explaining thinking.

Harnessing the requirement for students to undertake challenging mathematics problems, it is important to select games that are not based on drill and speed, instead select activities that give opportunity to fail fast, for repeated effort, to reconsider problems and collaborative effort.  Mathematics is not a lower order thinking task and memorization is less useful when problems become more difficult. Instead, innovative learning with technology uses higher-order thinking. Digital tools that allow for thinking give student’s opportunity to ponder without asking for help, without an expectation to finish a number of math problems in a short period time, where failure is not about failing to get stuff done, but not yet finding a way to understand the problem being presented, while applying the capability to persist using different possibilities. To develop persistence and reflection use tools that help students visualize their thinking, live drawing, video capable and utilizes feedback.

In our two workshops at the Leading a Digital School Conference, Dinosaurs to Star Wars and Up and Over the Wall, we will expand on how digital technologies have been used in our context to support teachers deliver outcomes in mathematics and contribute to STEM literacy through hands-on activities and discussion.

References

Boaler, J. (2015). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. United States: John Wiley & Sons.

Lowrie, T., Downes, N., & Leonard, S. (2017). STEM education for all young Australians: A Bright Spots Learning Hub Foundation Paper, for SVA, in partnership with Samsung. University of Canberra STEM Education Research Centre.

Mishra, P. (2012). Rethinking Technology & Creativity in the 21st Century: Crayons are the Future. TechTrends, 13-16. doi:10.1007/s11528-012-0594-0

Pound, L., & Lee, T. (2015). Motivating Children – Problem finding and problem-solving. In L. Pound, & T. Lee, Teaching Maths Creatively (pp. 28-44). London: Taylor and Francis.

 


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