I've listed my questions below and included two terrific guiding charts from the publication. I recommend that every math teacher read this terrific, timely publication (c. 2014) to spur continued growth and apt math education for every child. You can buy the book version or download the PDF for a very reasonable cost.
My Questions
Note that I wrote questions that I'll use to guide my classroom teaching efforts.
- How do we eliminate racial, ethnic, and income achievement gaps with respect to math education and reach a high level of math learning for all students?
- How do we balance focus on learning procedures with meaningful, relevant application and use of procedures?
- In what ways can we lift, deepen, and broaden the math curriculum?
- How can we teach so that there is less focus on tests?
- In what ways can we eliminate professional isolation, develop greater coaching, promote high quality math professional learning, and develop a collaborative structure for our craft as math educators?
- What do I need to know better in math in order to have a deep understanding of the discipline?
- How can I make sure that students are effective learners and doers of math?
- How can I inspire students' interest and curiosity for math learning and application?
- What "high leverage" practices do I currently use and promote in math class?
- What practices are most effective for learning math?
- When and how do I give students the chance to engage with challenging tasks that support meaningful learning?
- How do I connect new learning with prior knowledge?
- In what ways do I address preconceptions and misconceptions?
- How do I help students meaningfully organize knowledge, acquire new skills, and transfer and apply knowledge to new situations?
- Do I give students the opportunity to socially construct knowledge through discourse, activity, and interaction related to meaningful problems?
- In what ways do I provide meaningful, descriptive feedback so students can reflect on and revise their work, thinking, and understanding.
- How do I help students develop metacognitive awareness of themselves as learners, thinkers, and problem solvers?
- How do I help students learn to monitor their learning and performance?
- How do I move from the old-time, traditional math lesson of "review, demonstration, and practice" to new and more successful patterns that include establishing goals, implementing tasks that promote reasoning and problem solving, using and connecting mathematical representations, facilitating meaningful math discourse, posing purposeful questions, building procedural fluency from conceptual understanding, supporting productive struggle in learning mathematics, and using evidence of student thinking to assess progress and adjust/enrich instruction?
- When introducing a new concept do I set goals, demonstrate rationale, show connections to past learning, and help students to identify the central mathematical ideas and where they are going?
- How do I identify and use tasks that promote high level reasoning and problem solving?
- How do I promote active inquiry and exploration in math class?
- How do students in my class examine, explain, and compare concepts through a variety of representations? How do we make this work explicit to one another?
- In what ways do I promote mathematical discourse?
- Do I pose a variety of meaningful, rich questions in the math class to spur student thought, problem solving, and mathematical reasoning?
- Do I make the connection between procedural fluency and the underlying concept as I coach students toward procedural fluency?
- Do students understand that mathematical fluency means the ability to flexibly choose among methods and strategies to solve problems?
- How do I promote productive struggle and perseverance?
- How do I allow students to reveal, reflect on, critique, assess, and monitor their math thinking?
- How is our commitment to access and equity visible in our math program?
- Do we have a powerful curriculum?
- Do we have appropriate tools and technology?
- Do we employ meaningful and aligned assessment?
- Do we exhibit a culture of professionalism?
- Do I have adequate access to technology, and do I use technology in ways that deepen and further students' mathematical reasoning and problem solving ability?
- Do I use assessments effectively to promote thoughtful, forward moving math education for every child?
- Do I foster, contribute to, and support a culture of professional collaboration and continual improvement?
- Do my colleagues and I work as a professional team to research, analyze, and create best practices with regard to math teaching and learning?
- Do I reflect regularly in ways that develop my practice as a math educator?
- Is the curriculum map a flexible resource which allows for reasonable variation to meet students' needs?
- Have we collectively established criteria and protocols for use of technology in math class?
