Math Proficiency

  • April 1st, 2011
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All young Americans must learn to think mathematically, and they must think mathematically to learn. (Adding It Up, p. 1)

Mathematics empowers individuals to describe, analyze, and understand the world around them. Today’s world functions on a high level of mathematical applications. Students and adults who lack a real understanding of mathematics find many closed doors of opportunity. Learning mathematics is a way to ensure that options exist for individuals in the world around them.

The term mathematical proficiency captures what it means for anyone to learn mathematics successfully. Developing mathematical proficiency rests on a foundation of concepts and skills. All students must have the opportunity to learn and meet the same high standards if they are to access the knowledge and skills necessary in their post-school lives.

Based on the book Adding It Up: Helping Children Learn Mathematics, a mathematically proficient student has developed the following:

  • conceptual understanding — comprehension of mathematical concepts, operations, and relations
  • procedural fluency — skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
  • strategic competence — ability to formulate, represent, and solve mathematical problems
  • adaptive reasoning — capacity for logical thought, reflection, explanation, and justification
  • productive disposition — habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

In order for students to become proficient in mathematics, instruction must include content standards and process standards, as well as the areas of mathematical proficiency.

Mathematics education is a balance of both content and process. The content standards represent what is to be learned. The process standards represent ways of doing mathematics in the way of acquiring and using content knowledge.

An integrated and balanced development of all five strands of mathematical proficiency and the content/process standards should guide the teaching and learning of school mathematics. The coordination of curriculum, instructional materials, assessment, instruction, professional development, and school organization around the development of mathematical proficiency should drive school improvement efforts.

PaTTAN provides an array of resources, training and technical assistance with regard to improving educational practices in order to meet the needs of diverse learners, including learners with disabilities.

The foci of PaTTAN’s math efforts include, in part, the following:

  • Lesson Study: A multi-day training event that is to be sustained and expanded by participants when they return to their schools. Lesson study includes the collaborative development of a math lesson that includes research on the content, high-level tasks, common misconceptions, prerequisite skills and embedded formative assessment.
  • Building Conceptual Understanding: This training event provides participants with information related to ensuring that students gain conceptual understanding of the mathematical content they are learning in addition to relevant procedural skills.
  • Progress Monitoring in Algebra: A recording and relevant materials are available to learn about the content, administration and scoring of the AAIMS progress monitoring probes.
  • Blog/Podcasts: Current information and ongoing discussion to occur
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  • Dennis Cullen
    Mathematics, Paraprofessionals, Multi-Tiered Systems of Support (MTSS/RtII)
  • Tara Russo
    Mathematics, Paraprofessionals, Multi-Tiered Systems of Support (MTSS/RtII)
  • Jonathan Regino
    Mathematics, Multi-Tiered Systems of Support (MTSS/RtII)
  • Jared Campbell
    Autism, Mathematics, Multi-Tiered Systems of Support (MTSS/RtII)
  • Elaine Neugebauer
    Mathematics, Family Engagement, Multi-Tiered Systems of Support (MTSS/RtII)
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