They’re really for me but I plan to share them at some upcoming PL sessions. I’ll take any suggestions and comments of how to make them better…
1. Make sense of problems and persevere in solving them – Teachers of mathematically proficient students understand that students will struggle, however that is not an indicator of teacher effectiveness. They understand that students struggle because they’re engaged in problematic tasks and it is their job to ensure that the struggle remains productive, not destructive. Teachers of mathematically proficient students preserver through their own frustration by questioning relentlessly and continuing to improve their own understanding of student pedagogy. They push relational understanding of mathematics by creating a culture and climate that promotes metacognition and embraces student efficacy.
2. Reason abstractly and quantitatively – Teachers of mathematically proficient students expose students to situations where they are able to recognize patterns and relationships as tools to effectively make sense of problems. Teachers of mathematically proficient students ensure that students are provided multiple opportunities to explore mathematics by flexibly relating numbers and quantities in and out of contextualized situations.
3. Construct viable arguments and critique the reasoning of others –Teachers of mathematically proficient students understand the importance of communication, both verbal and non-verbal. They continually seek for ways to engage students in dialogue and encourage ideas that are wondered, noticed, and questioned. Teachers of mathematically proficient students expect their students to make conjectures through the use of models and diagrams. When conjectures are made, a teacher of mathematically proficient students expect that students are able to explain why it works.
4. Model with mathematics – Teachers of mathematically proficient students understand the importance of teaching in context and the role it plays in the development of relational understanding. They expect that students use mathematics to make sense of the world around them. Contextualized situations create opportunities for students to derive, test, and validate assumptions.
5. Use appropriate tools strategically – Teachers of mathematically proficient students expose and encourage the use of multiple tools to make sense of mathematics. Most importantly, the teacher understands that it is the student who chooses the tool. Teachers of mathematically proficient students recognize that tool selection stems from the student’s understanding of its limitations and restraints.
6. Attend to precision – Teachers of mathematically proficient students model verbal and written precision continuously. They calculate accurately and efficiently through the correct use of numbers, symbols, and mathematical conventions. All of this is accomplished as they simultaneously relate their understanding in context. And because teachers of mathematically proficient students consistently model precision…they expect the same from their students.
7. Look for and make use of structure – Teachers of mathematically proficient students provide meaningful tasks that encourage a relational understanding of patterns, rather than instrumental. The use and sense making of mathematical structure is encouraged to promote efficiency. Teachers of mathematically proficient students understand the importance of a student being able to compose and decompose objects because of their mathematical understanding.
8. Look for and express regularity in repeated reasoning – Teachers of mathematically proficient students encourage generalizations. They are continually asking students “does that work all the time” or “is there a more efficient solution path”. They encourage students to analyze their work, identify shortcuts, and/or derive a rule based on their intermediate results.