This year the Math Leadership group will have several titles offered as opportunities for collective learning. One of the titles is Principals to Actions: Ensuring Mathematical Success for All by the National Council of Techers of Mathematics published in 2014. This text begins by highlighting celebrations in math teaching and learning. However, it is noted that we must move from “pockets of excellence” to “systemic excellence.” To achieve this goal, there are some realities that need to be addressed:
- Too much focus is on learning procedures without any connection to meaning, understanding or the applications that require these procedures.
- Too many students are limited by the lower expectations and narrower curricula of remedial tracks from which few ever emerge.
- Too many teachers have limited access to the instructional materials, tools, and technology that they need.
- Too much weight is placed on results from assessments- particularly large-scale, high-stakes assessments –that emphasize skills and fact recall and fail to give sufficient attention to problem solving and reasoning.
- Too many teachers of mathematics remain professionally isolated, without the benefits of collaborative structures and coaching, and with inadequate opportunities for professional development related to mathematics teaching and learning. (p. 3)
This text then proceeds to offer recommended, research –informed actions to address the above bullets. Six essential elements for school mathematics are identified:
- Teaching and learning
- Access and equity
- Tools and technology
The first guiding principle is effective teaching and learning- “ an excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematic ideas and reason mathematically” (p. 7). Teachers need to have understanding not only of the “mathematical knowledge that they are expected to teach” but also a “clear view of how student learning of that mathematics develops and progresses across grades”— and be “skilled at teaching in ways that are effective for learning for all students.” Principles of learning that are basic include experiences that enable the learner to:
- Engage with challenging tasks that involve active meaning making and support meaningful learning
- Connect new learning with prior knowledge and informal reasoning and, in the process, address preconceptions and misconceptions
- Acquire conceptual knowledge as well as procedural knowledge , so that they can meaningfully organize their knowledge, acquire new knowledge, and transfer and apply knowledge to new situations
- Construct knowledge socially, through discourse, activity and interaction related to meaningful problems
- Receive descriptive and timely feedback so that they can reflect on and revise their work, thinking, and understandings,
- Develop metacognitive awareness of themselves as learners, thinkers, and problem solvers, and learn to monitor their learning and performance.
The text further breaks the teaching practices into eight core practices. Productive and unproductive beliefs are identified. Then for each practice, there is a discussion of what the practice is and supporting research, a classroom scenario, and identified specific teacher and student actions ( or what you would observe when the practice is in place). The eight teaching practices are:
- Establish mathematics goals to focus learning
- Implement tasks that promote reasoning and problem solving
- Use and connect mathematical representations
- Facilitate meaningful mathematical discourse
- Pose purposeful questions
- Build procedural fluency from conceptual understanding
- Support productive struggle in learning mathematics
- Elicit and use evidence of student thinking.
Overall the book is easy to read and the conclusions align with research for effective teaching and learning in other content areas – such as standards unpacked and clear, learning targets identified, use questioning and inquiry to promote engagement and higher levels of learning, use formative assessment and feedback to shape learning.
I will have a tool based on the concepts in this book available at the Math Leadership meeting November 14. The tool will assist math leaders to reflect and identify best practices and areas to attend to regarding beliefs and practices. Please register and join us.
If you wish to know more, here is the executive summary of this book.