BIG IDEAS
Big ideas can:
- help you to cluster expectations
- create a more strategic, organized approach
- build stronger connections between strands/expectations/concepts
- deepen learning of fundamental concepts over time
- build fundamental concepts over grades
- simplify your teaching
Engaging students in mathematical processes empowers them in math class. Mathematical processes support the acquisition and use of math knowledge and skills.
What are the seven mathematical processes?
Review the following for a comprehensive understanding of Mathematical Processes:
- Capacity Building document entitled, "Yes I Can:Paying Attention to Well-Being in the Mathematics Classroom" (page 3, especially): http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/math-classroom2018.pdf
- Section on Mathematical Processes (pages 11 to 17) in the front of the Ontario Curriculum, Grades 1-8, Mathematics document: http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
- EduGains provides a resource with sample questions that teachers can ask to develop the math processes. Look at the first two columns: http://www.edugains.ca/resources/LearningMaterials/MathProcesses/MathProcesses_AfL-AaL.pdf
Discussion Post: Which of the mathematical processes is the most important, in your opinion? Why?
How can we give the math process that you identified as the most important a high profile in student learning?
"I would describe a rich task as having a range of characteristics that together offer different opportunities to meet the different needs of learners at different times. What is also apparent to me is that much of what it takes to make a rich task 'rich' is the environment in which it is presented, which includes the support and questioning that is used by the teacher and the roles that learners are encouraged to adopt. That is, an environment in which learners are not passive recipients of knowledge, accepting what is given, but independent assertive constructors of their own understanding who challenge and reflect. On its own a rich task is not rich - it is only what is made of it that allows it to fulfil its potential. With this in mind it might still be useful to list some of the things I might say when describing a rich task. Rich tasks (or good problems):
- are accessible to a wide range of learners,
- might be set in contexts which draw the learner into the mathematics either because the starting point is intriguing or the mathematics that emerges is intriguing,
- are accessible and offer opportunities for initial success, challenging the learners to think for themselves,
- offer different levels of challenge, but at whatever the learner's level there is a real challenge involved and thus there is also the potential to extend those who need and demand more (low threshold - high ceiling tasks),
- allow for learners to pose their own problems,
- allow for different methods and different responses (different starting points, different middles and different ends),
- offer opportunities to identify elegant or efficient solutions,
- have the potential to broaden students' skills and/or deepen and broaden mathematical content knowledge,
- encourage creativity and imaginative application of knowledge.
- have the potential for revealing patterns or lead to generalisations or unexpected results,
- have the potential to reveal underlying principles or make connections between areas of mathematics,
- encourage collaboration and discussion,
- encourage learners to develop confidence and independence as well as to become critical thinkers."
Rich Tasks and Contexts by
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