Personalizing Instruction
Mathematical Mediation from Zoltan Dienes to Spreadsheets via Data Tables: Technology Immune/Technology Enabled Problems within an Action on Objects AoO Framework
Paper Presentation in a Themed Session Michael Connell
Technology creates new mathematical objects requiring new modes of student interaction - for example, the National Library of Virtual Manipulatives. These online manipulatives draw much of their efficacy from prior embodiment as hands-on materials currently in elementary mathematics classrooms. In preparing teacher candidates to make use of these new manipulative-based online resources Zoltan Dienes writings and views on manipulatives in instruction were explicitly referenced throughout my elementary mathematics methods courses. Dienes is best known for multi-base blocks created for teaching place value – particularly base10 - and seminal algebraic materials and logic blocks. To many mathematics educators, he was seminal in establishing manipulatives in teaching and learning mathematics. The samples of Dienes work used in this paper centered on mathematics in the early grades including manipulatives, games, stories and dance. Following discussion of Dienes and his ideas, students explored a surface area problem where a base10 physical manipulative was used to create a data table of results. This data table then served as a mediational tool for spreadsheet exploration at a level of mathematics much higher than would be otherwise possible. Student comment, work samples, and professor observation showed these teacher candidates demonstrating greater insight into both traditional and technology-enabled online manipulatives than past groups lacking this exposure. The discussion of base10 blocks had powerful and personally meaningful connections with their own experiences as learners. By reminding the students of these experiences, it empowered their use of both traditional and technology enabled manipulatives.
Teaching Grades Eight and Nine Directed Numbers and Algebra: Mathematics Teacher Knowledge
Paper Presentation in a Themed Session Judah P. Makonye
The general low learner performance in mathematics for the lower socio-economic learners has serious ramifications on social equity and human capital development for any country. It is imperative to research for High Leverage Mathematics Teaching Approaches in teaching key mathematics topics such as directed numbers and algebra to ameliorate the under-performance of children from low-income families. High Leverage Mathematics Teaching Approaches are research-informed actions that produce the greatest benefits for one’s efforts. These are closely allied to Pedagogical Content Knowledge (PCK) (Shulman, 1996) and Mathematics Knowledge for Teaching (MKT) (Ball et al., 2008)which informs this research. It is known that transition from arithmetic to algebra is a difficult one for learners. Addressing the knowledge gap in teaching these directed numbers and algebra is imperative to improve learner outcomes as failure to grasp these topics often result in learners dropping mathematics as a school subject altogether. Data will be collected through interviews as well as observations of lessons when teachers teach the topics. This helps to form topic specific knowledge for teaching them.
Using UDL and SAMR for Inclusive Teaching and Learning: Effective Practices in Post-secondary Online Spaces
Paper Presentation in a Themed Session Wendy Kraglund Gauthier
Teaching with technology is not only about the use of particular devices, but also how technology can create engaging and accessible spaces for learning. Effective instructional strategies are integral to the successful delivery of online courses; yet, a lack of familiarity with the pedagogical constructs needed to create effective digital learning environments, and sometimes uncertainty in how to implement them, impacts some educators’ praxis. Universal Design for Learning (UDL) and SAMR help educators meet these outcomes by providing a framework for understanding how to create curricula that reflects a focus on a student-based pedagogy and acknowledging each student differs in interests, learning profile, and level of functioning. Blurring the lines between Theme 7 and 8, this session will be an interactive discussion on the challenges and opportunities that can emerge when educators are mindful of how UDL and SAMR can not only enhance, but also transform post-secondary students’ experiences in online spaces. It will include lessons learned through recent research and activities to bring colleagues accustomed to working in face-to-face classrooms into digital learning spaces that maintain alignment with effective learning pedagogy and UDL principles. It will be an opportunity for participants to reflect on and share their own strategies and effective practices in embedding the four core principles of SAMR into online instruction and student learning. Take-aways will include evidence-based strategies and tips for addressing digital curriculum design and changing mindsets to be more equitable, inclusive, and socially just.
