Introduction 5of knowledge, students must build strong foundations in critical
math concepts. All of the concepts in this book are interrelated
components of number, operations, and base ten. The focus on
specifi c concepts does not imply that we need to teach math
concepts in isolation. Productive math instruction is inclusive,
interrelated, rigorous, and rich. The reason we need to focus on
specifi c concepts in intervention is because we need to identify
gaps in knowledge and misconceptions that students have in
their understanding of mathematics. Intervention does not
replace math instruction. Intervention is in addition to high
quality math instruction.
What Makes Math Intervention Successful?
Students who struggle in mathematics often need explicit
instruction. Explicit instruction is provided when teachers give
students ongoing feedback, clear models, a variety of examples,
time for practice, and opportunities to talk through the
hows and whys of the math situation (National Mathematics
Advisory Panel 2008). Successful math intervention is precise
and focused on students’ immediate learning needs.
Diagnosing and addressing students’ needs are part of
Response- to-Intervention (RTI). Although the use of RTI is
common practice in language arts, RTI is completely applicable
to mathematics, as well. RTI promotes the identifi cation
and diagnosis of potential learning problems by analyzing
students’ responses to instruction and providing corrective
feedback. With RTI students are offered specifi c interventions
and progress is frequently monitored. Tier 2 (small group) and
Tier 3 (individual) are excellent group structures for providing
the specifi c interventions presented in this book. Successful
mathematics intervention applies the structure of RTI—identify,