Math Interventions and Strategies

Go to: Instructional Methods, Strategies and Technologies to Meet the Needs of All Learners

Ch. 20 Math Interventions and Strategies- The purpose of this chapter is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics.

Table of Contents

  • Concrete, representational and abstracts models of math.
  • Questioning used in mathematics.
  • Feedback
  • Teaching Math Vocabulary
  • Building Math Fluency
  • Error Analysis


Early Childhood Education and Mathematics Instruction

Early Numeracy
“‘Numeracy’ is a term that refers to all the mathematics that young students learn including number, operations, and geometry and measurement concepts” (Learning Pathways in Numeracy, 2014). Research has shown that the mastery of early mathematics concepts (number sense and counting) upon school entry is the strongest predictor of future academic success (Duncan 2007). Young children can have mathematical ideas that are complex and sophisticated for their developmental levels. Learning to make sense of mathematics early helps build future math proficiency and confidence.

Pre-kindergarten children can explore mathematics ideas, including number concepts and quantities, number relationships and operations, geometry and spatial sense, patterns, and measurement and comparison. The important idea to convey is that early numeracy is about developing and making sense of mathematics rather than repetitive pencil and paper activities. For example, asking a child to count the number of cups to distribute at snack time, to notice some of the windows on the playhouse are circles and some are squares, or to discuss how a big step is as tall as two regular steps demonstrates the relevance of mathematics. Making sense of mathematics happens through play, number sense games, and other daily routines.

A critical success factor, and an important tie-in to early literacy, is to get children to communicate their ideas and explain their thinking about mathematics in their natural language. Providing opportunities for children to share their thinking helps educators understand what concepts the child understands and surfaces any gaps in their mathematical understanding. Teachers can then direct students in additional learning, refining their thinking or extending their thinking in mathematical ways.

Representation includes concrete manipulation of objects, pictures, and numerical symbols. Working with physical objects and visuals informs and strengthens abstract thinking. Manipulatives and visual representations of mathematics should be routinely utilized in early learning, along with activities and tasks that are relevant to the child’s developmental age and grounded in the Mathematics K–12 Learning Standards.

Early learners develop mathematical skills and encounter math concepts through natural and routine activities and play. Educators and caregivers can support this process by creating time and space for exploration and manipulation. As adults observe and listen to children at play, they can notice math ideas students are utilizing in their play. For example, children playing outdoors might use positional language to describe how they are climbing “up high” or running “under” the slide. Gently nudging a child through use of questions and the introduction of new language can help them build mathematical understanding, though adults should be cautious not to take over or direct a child’s play. Observing and talking with students at play can help teachers determine natural interest areas that can become the basis for selecting books and topics for classroom projects to further develop mathematical understandings and skills.


Reykdal, C. (2020). Strengthening Student Educational Outcomes Mathematics Menu of Best Practices and Strategies, State Superintendent, Office of  Superintendent of Public Instruction, Olympia Washington,  Except where otherwise noted, this work by the Office of Superintendent of Public Instruction is licensed under a Creative Commons Attribution License

Graphic from Pixabay, public domain