The NCTM process standards, Adding it Up mathematical proficiency strands, and Common Core State Standards for mathematical practices are all saying the same thing but why do I get the feeling that the Mathematical Practices Standards is out to get the math teachers.
The NCTM’s process standards of problem solving, reasoning and proof, communication, representation, and connections describe for me the nature of mathematics. They are not easy to understand especially when you think that school mathematics is about stuffing students with knowledge of content of mathematics. But, over time you find yourselves slowly shifting towards structuring your teaching in a way that students will understand and appreciate the nature of mathematics.
The five strands of proficiency were also a great help to me as a teacher/ teacher-trainer because it gave me the vocabulary to describe what is important to focus on in teaching mathematics.
With the Mathematical Practices Standards I had this picture of myself in the classroom with a checklist of the standards in one hand and a lens on the other looking for evidence of proficiency. The NCTM and Adding it Up standards actually said more about math. The ones in Common Core are saying more about what students should attain. I wonder which will encourage ‘teaching to the test’. The day teachers start to ‘teach to the test’ is the beginning of the end of any education reform.
NCTM Process Standards |
Five Strands of Mathematical Proficiency |
CCSS Mathematical Practices |
Problem Solving
Reasoning and Proof
Communication:
Connections
Representation
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Conceptual Understanding refers to the “integrated and functional grasp of mathematical ideas”, which “enables them [students] Procedural fluency is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and Strategic competence is the ability to formulate, represent, and solve mathematical problems. Adaptive reasoning is the capacity for logical thought, reflection, explanation, and justification. Productive disposition is the |
Mathematically proficient students …
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