Teaching and Learning: Selecting the Right Math Strategy

By Cathy Buyrn, M.Ed.


“Strategy” has become an education buzzword.  Educators often use terms like research-based strategy, evidence-based strategy, strategic reader, strategic thinker, instructional strategy, learning strategy, metacognitive strategy, etc.  The language regarding teaching and learning seems to be “strategy”-rich, and, yet, the field continues to struggle to solve overwhelming achievement gaps.  How is this possible when we have so many strategy-focused resources at our fingertips?  Why do some students seem to respond to strategies, while others continue to struggle?  As the stakes get higher each year, how can educators navigate the sea of strategy-focused resources and appropriately match them to student needs?

In the September/October 2011 Link Lines article “Designing Interventions:  The Chicken or the Egg” (Davis-Perry), a teacher and student worked together to match reading strategies to student need.  This narrative provided an eye-opening view of the complex process involved in balancing teaching and learning strategies in order to close specific skill gaps.  The teacher used her knowledge of effective instructional match principles outlined in the September/October 2010 Link Lines article, “Celebrating Quality Instruction and Highly Effective Teachers” (Buyrn), to target concerns and select interventions.  This type of instructional reflection is critical if educators are to improve student outcomes.   

Teachers cannot select the right strategies until they’ve asked the right questions.  Many assessment tools lead teachers to focus on student deficits with the result that they end up chasing the list of skills that a student does not have instead of focusing on the skills the student does have.  The best entry point for goal setting and strategy selection is the knowledge and skills the student demonstrates (Gravois, Gickling, & Rosenfield, 2011, p. 50). 

In order to gain the right information, teachers must ask five critical assessment questions:

1. What does the student know? (Gravois et al., 2011, p. 46)

2.  What can the student do? (Gravois et al., 2011, p. 46)

These first two questions will help teachers work through the difference between what a student knows and what he or she can do.  While the two questions might seem like they are tapping into the same thing; in reality, students can often explain how to do something even though they are unable to transfer that knowledge to concrete tasks.  Jumping to solutions before reflecting on these questions can lead to frustration for both the teacher and the student. 

Once teachers have fully probed what a student knows and can do, they can start to explore the next critical question:

3.  How does the student think? (Gravois et al., 2011, p. 46)

Scripted assessment tools ask students to simply respond to a set of predetermined questions or task demands. Teachers should not forget to ask students to think aloud as they attack academic tasks.  A simple “What were you thinking when you did that?” can save a tremendous amount of time and energy in establishing strategies that the student may already be using or confusing.

What the student did …

What the teacher thought …

What the student said …


“The student doesn’t know how to regroup, so she flips the numbers in order to be able to subtract.”

“When I add, I always start with the largest number and count on to get the answer.  I thought you were always supposed to start with the largest number.”


In the example above, the teacher discovered that the student was applying to subtraction the “count-on” strategy she had learned for adding numbers.  After exploring a little further, the teacher discovered that the student actually knew how to regroup. 

This exercise demonstrates how critical it is to fully explore a student’s thinking before designing a strategy.  If the teacher had not uncovered this simple misapplication of an addition strategy to subtraction, both the teacher and the student might have wasted precious time  working on an unnecessary regrouping strategy.  Once the teacher realized that the student knew how to regroup and could regroup accurately, she could focus on the fact that the student needed to know when to use operation-specific strategies.  This example also provides the answer to the next critical question:

4.  What does the student do when unsure? (Gravois et al., 2011, p. 46)

This student applied a known addition strategy when unsure of what to do when subtracting.  The good news is that the student can independently apply strategies.  Therefore, the need to be addressed is knowing when to use specific strategies.  All too often, teachers race ahead and apply good solutions to the wrong problems.  Now that the problem is clearly defined, the teacher can move on to the last critical question:

5.  Now, as the teacher, what do I do? (Gravois et al., 2011, p. 46)

The teacher and the student designed the cue card below to help the student organize her strategies so that she could learn when to use them.  As the student progresses in math, she can add strategies to her cue card and remind herself of specific points when using an operation.  (Math strategy resources may be found in the Math Strategies Links section at the end of this article but should never be used to apply strategies without fully exploring the critical assessment questions.)


  • Count on from the largest number
  • Order/commutative property of addition
  • Make a ten


  • Don’t change the order of the numbers!
  • Start on top no matter what!
  • Count back when it is close
  • Use addition to check


  • Order/commutative property of multiplication
  • The 9s trick only works for the 9s!



  • Don’t change the order of the numbers!
  • If I know my X facts, I know my ÷ facts!

Involving students in designing strategies is critical to building their metacognitive skills.  Once teachers realize how much more efficient it is to engage students in conversations about their thinking and learning, they will be able to apply strategies more effectively.  If they consult directly with students by exploring the critical questions presented in this article, teachers will be more likely to meet student needs before having to consult with a specialist (Gravois & Gickling, 2008; Gravois et al., 2011, p. 21).


Gravois, T., Gickling, E., & Rosenfield, S. (2011). Training in instructional consultation, assessment, and teaming: Book 1 ICAT introductory session. Baltimore, MD: ICAT® Publishing, LLC. 

Gravois, T., & Gickling, E. (2008). Best practices in instructional assessment. In A. Thomas & J. Grimes (Eds.), Best practices in school psychology-V, Volume 2. Washington, DC: National Association of School Psychologists.

Additional Resources

Buyrn, C. (2010, September/October).  Celebrating quality instruction and highly effective teachers.  Link Lines Newsletter.  Williamsburg, VA:  The College of William and Mary Training and Technical Assistance Center.  Retrieved from http://education.wm.edu/centers/ttac/resources/articles/teachtechnique/celebratingquailityinstruction/index.php

Davis-Perry, D. (2011, September/October). Designing interventions:  The chicken or the egg?  Link Lines Newsletter.  Williamsburg, VA:  The College of William and Mary Training and Technical Assistance Center.  Retrieved from http://education.wm.edu/centers/ttac/resources/articles/teachtechnique/designinginterventions/

Doerries, D. (2002). Instructional assessment:  An essential tool for designing effective instruction. [Considerations Packet]. Williamsburg, VA: The College of William and Mary Training and Technical Assistance Center.  Available by request at:  http://education.wm.edu/centers/ttac/resources/considerations/index.php

Math Strategy Links

MathVIDS is an interactive website for teachers who are teaching mathematics to struggling learners. The website is supported by the Virginia Department of Education.




Packing Mathematical Strategy Suitcases for the Next Grade Level is a Link Lines article that provides connections to math strategies that empower students.



The Making Math Meaningful Wikispace was created as a resource for teachers seeking math resources focused on Bloom’s taxonomy depth-of-knowledge categories.



The Math Problem Solving Wikispace contains resources focused on building math problem-solving skills.