Draft:Numeracy Consultants Math Intervention Programs

Numeracy Consultants Math Intervention Programs Numeracy Consultants is an educational company specializing in research-informed math intervention programs designed to support struggling learners and close achievement gaps in foundational mathematics. These programs are structured to address common misconceptions, build conceptual understanding, and promote student reasoning in line with best practices in mathematics education.

Overview Numeracy Consultants’ intervention programs are grounded in contemporary research on how students learn mathematics, including cognitive learning theory, schema development, and evidence-based instructional design. The company emphasizes the Concrete–Representational–Abstract (CRA) instructional model, progress monitoring, and diagnostic teaching as central components of effective intervention. Its programs are aligned with national standards such as the Common Core State Standards (CCSS) and are widely used in RTI (Response to Intervention) frameworks.

Program Descriptions

Primary Numeracy Program The Primary Numeracy Program targets early elementary students (Grades K–3) who need additional support in developing number sense, counting, and place value concepts. The program follows the CRA progression—starting with hands-on manipulatives (concrete), moving to visual models (representational), and ending with symbolic work (abstract). Lessons are designed to promote flexible thinking with numbers and provide frequent formative assessments to guide instruction.1

Multiplicative Thinking Program The Multiplicative Thinking Program supports students in Grades 3–5 who are transitioning from additive to multiplicative reasoning. It focuses on helping students build an understanding of multiplication and division through arrays, equal groups, and ratio models. The program is research-informed and includes progress monitoring tools to track students’ conceptual development and fluency over time.2

Fractional Reasoning Program The Fractional Reasoning Program is designed for upper elementary and middle school students struggling with fractions. The program addresses common student misconceptions, such as interpreting fractions as two whole numbers rather than as a single quantity. Instruction is structured using the CRA model, supported by visual fraction models (e.g., number lines, area models), and includes regular progress monitoring to assess growth and adjust instruction accordingly.3

Word Problem Intervention Program The Word Problem Intervention Program emphasizes schema-based instruction to help students make sense of various word problem types. By categorizing problems (e.g., additive, multiplicative, comparison), students learn to identify key structures and represent problems using bar models and equations. The program supports language development in math and integrates progress monitoring strategies to evaluate comprehension and problem-solving skills.4

Instructional Approach All Numeracy Consultants programs are guided by the following principles:

Research-Informed Design: Built on current findings from mathematics education research, cognitive psychology, and intervention science.

CRA Instructional Model: Every lesson follows the Concrete–Representational–Abstract approach to support conceptual understanding.

Progress Monitoring: Students are regularly assessed through informal and formal tools, allowing educators to adjust instruction based on learning needs.

Visual and Verbal Reasoning: Emphasizing mathematical discourse, representation, and justification.

Educator Support: Programs are accompanied by professional development, on-demand video training, and implementation guides.

Reception and Use

Numeracy Consultants’ intervention programs are used in public, charter, and private schools across North America and internationally. Educators report that students participating in these programs show improved mathematical reasoning, confidence, and performance on benchmark assessments. Although more peer-reviewed research is needed, school-based data and independent case studies suggest positive outcomes when the programs are implemented with fidelity.5