The Ontario Grade 1 Mathematics Curriculum and the research in “Under Construction: Developing Mathematical Processes” both emphasize that mathematics is a social and cognitive endeavor driven by specific processes rather than just rote calculation.
Integrated Mathematical Processes
Both the Ontario Ministry and the research by Sadownik identify seven core mathematical processes that should be integrated throughout all strands of the curriculum:
- Problem Solving: Moving beyond individual tasks to using logic and multiple perspectives to reach efficient solutions.
- Reasoning and Proving: The ability to justify decisions and engage in mathematical arguments.
- Reflecting: Consciously thinking about one’s own thinking (metacognition) to adjust strategies.
- Connecting: Linking mathematical concepts to other subjects and real-world contexts, such as STEM integration.
- Representing: Using visual tools, drawings, or digital aids to depict information and internalize concepts.
- Communicating: Sharing ideas to clarify understanding and make internal thinking public and permanent.
- Selecting Tools and Computational Strategies: Choosing the most appropriate physical or digital tools to solve a problem.
Research Findings on Digital Implementation
Sadownik’s study highlights how these processes can be enhanced through Computer Supported Collaborative Learning (CSCL) tools like Google Classroom:
- Visible Thinking: Publishing student work online holds them accountable for their logic and honors their “thinking authorship” through time-stamped digital records.
- Asynchronous Discourse: Digital platforms provide a “universal design for learning” by allowing students varying cognitive processing times to reflect before responding.
- Safe Communities: A critical finding is that a safe, respectful environment is required for students to take the risks necessary to share their thinking with others.
- Engagement: Using multimodal tools like podcasts allows students to practice mathematical dialogue, which directly correlates with the development of mathematical cognition.
Summary of the “Sovereign” Shift
The combined goal of these frameworks is a shift from “banking teaching theory” (passive reception) to an active participation model. By using these mathematical processes, students transition from “doing math” to becoming independent mathematical thinkers who can justify their logic outside of traditional textbook constraints.