What is math Proficiency?

Similar to reading and writing, we can think of math proficiency as a blending of:1

  • Concepts (Understanding concepts, operations, and relations)
  • Procedures (Using procedures flexibly, accurately, and efficiently)
  • Strategies (Formulating, representing, and solving problems)
  • Reasoning (Reflecting, explaining, and justifying)
  • Disposition (Seeing math as sensible, useful, and worthwhile)

To help students achieve math proficiency, teachers should:2

Use a focused, coherent progression of math learning with emphas is on proficiency in key topics

 

Use multiple approaches to meet the needs of students; explicit instruction should be used during routine core instruction and supplemental instruction

Develop conceptual understanding, procedural fluency, and problem-solving skills at the same time

 

Use formative assessment on a regular basis to assess student learning

 

Focus on proficiency with whole numbers, fractions, geometry, and measurement; these are critical for algebra

 

To help students experiencing math difficulty with math proficiency, teachers should:3

  1. Use explicit instruction
  2. Teach clear and concise math language
  3. Use concrete, pictorial, and virtual representations
  4. Use number lines for learning concepts and procedures
  5. Provide deliberate instruction for solving word problems
  6. Use timed activities to build math fluency

(1) National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Retrieved from: https://nap.nationalacademies.org/catalog/9822/adding-it-up-helping-children-learn-mathematics.
(2) National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education. Retrieved from https://files.eric.ed.gov/fulltext/ED500486.pdf.
(3) Fuchs, L.S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K.S., Woodward, J., Clarke, B., Jordan, N. C., Gersten, R., Jayanthi, M., Keating, B., and Morgan, S. (2021). Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from http://whatworks.ed.gov/.