Kristi Kafka

Nationally Certified School Psychologist


Math Interventions



Students with lesser developed cognitive abilities often benefit from manipulatives.  Manipulatives are concrete objects such as:


geometric shapes (for use with classification or patterning tasks)

counting cubes or beads

base-ten blocks (for representing and performing operations on multidigit numbers)

fraction pieces


Pitfalls to manipulatives

Potentially confusing, especially if presentation is disorganized or lacks appropriate guidance  (guide use and allow opportunity for practice)

May be source of distraction (if so, consider using  visual or pictorial representations)


Teaching operations involving whole numbers

Use objects that are uniform

Use objects that accurately represent base-ten relationships (ie:  a "ten" should be ten times as big as a "one")

Use a mat for organizing manipulatives and for children to work on - organized from right to left to reflect the way numerals are written





Components of Effective Mathematics Instruction, by Louise Spear-Swerling (2005)

National Council of Teachers of Mathematics Position Statements -

K-12 Mathematics Benchmarks -

Flashcard creator -

Math activities/games -

Big Ideas in Early Mathematics Assessment -

Research-based Instruction (page 6/Table 2 offers recommendations) -