Intervention

Expeditions to Numeracy with Digi-Block Mathematics

A Place Value Based Intervention

Expeditions to Numeracy is a powerful intervention program that targets with thoroughness, depth, and singularity of purpose the most significant topic in elementary mathematics --- number sense and operations --- and it does so by using place value as the fundamental connection among all base-10 concepts and skills.

A quick look: Expeditions info 451 KB

Introduction

Designed for small group instruction, Expeditions makes it possible for teachers to interact closely with struggling students in order to individualize assessment and instruction. It operates under the assumption that numeracy, the ability to understand and work with numbers, underlies success in mathematics and can be accomplished by fixing attention on place value, the organizing principle of the number systems. Its diagnosis-and-treatment approach to intervention allows teachers to uncover gaps in understanding and map an instructional sequence that fills those gaps and develops a strong base for continued mathematical growth. Using the explicitly stated learning objectives as guides, teachers can pinpoint where instruction is needed.

Curriculum

The program includes 5 units which facilitate learning through exploration of CountOn County (see map at left).

In Place Value City, explorers use the ten-frame and Digi-Block to unlock the mysteries of place value. They continually return to the City’s sequenced number-set sections to build the conceptual understanding of place value that gives them entry to the corresponding number-set sections in the Town and the Village.

In Add’n’Subtract Town and Multiply’n’Divide Village, explorers use their place value understanding and the full set of whole number blocks to explore the concepts and procedures related to the four basic number operations.

Understanding of place value is used again in Money Island where explorers learn the system of bills and coins as an application of the base-10 number system. Money Island is a stand-alone unit.

Proficiency Park is a popular area in CountOn County. Explorers visit the Park regularly to engage in games and activities that extend, strengthen, and apply the skills they are developing in the other regions.

To learn more about each unit, download a complete scope and sequence here.

Instruction and Assessment

Expeditions to Numeracy takes a diagnosis-and-treatment approach to intervention. In order to be effective, such an approach requires thorough, detailed, and comprehensive assessment, a critical component of Expeditions.

Three purposes for assessment are addressed through its three types of assessments. Teachers record all assessment results and comments on individual Student Record Sheets.

Diagnostic Assessments

- Placement Pre-tests guide teachers in determining the most appropriate place to introduce students into the program. The pre-tests are organized by region (Place Value City, Add’n’Subtract Town, Multiply’n’Divide Village, and Money Island) and then by number-set section within each region (0-10, 0-99, 0-999, etc.).

- Readiness Pre-tests: Once students are placed in the program and begin the explorations, a readiness pre-test, provided on the first page of each exploration, serves to assess students’ readiness to address the learning defined by the exploration’s objective. Teachers use the results to tailor instruction by deciding how many and which activities the students needs. (If students demonstrate mastery on the exploration pre-test, teachers give the pre-test for the next exploration.)

Formative Assessments

Teachers use the evidence-of-learning statement at the end of each activity to gauge their students’ learning, informing them of the student’s need for additional instruction or readiness to proceed to the next activity. Each evidence of learning is tied directly to the activity’s learning objective.

Summative Assessments

When students have completed the set of activities in an exploration, the assessment task that was used as an exploration pre-test is now used as an exploration post-test to ensure that students have mastered the content defined by the exploration’s learning objective.

Download sample assessment sheets here:

Placement Pre-Test
Readiness Pre-Test (also used as a post-test)
Student's Progress Record

Download a sample exploration here:

Place Value City Exploration 1, Activity 4

Additional Information

Download a paper detailing the curriculum-based research and literature study that have been done for Expeditions here.

About the Authors

Peggy Akin, a retired mathematics and English teacher, has taught for twenty-seven years in grades 8-12 and now spends her time writing curriculum. Her programs include The Mighty Sentence: Mastering the Art of Sentence Writing, Building Math Power: A Unique Approach to Secondary Mathematics, Module 0: The Power of 10, and, with Kimberly Rimbey, Expeditions to Numeracy: A Place-Value-Based Intervention for K-4.

Kimberly Rimbey, a veteran classroom teacher with twenty years of classroom experience, holds two Master's Degrees and is National Board Certified in Early Adolescent Mathematics. A recipient of the Presidential Award for Excellence in Mathematics and Science Teaching, she has authored many publications, including the Math Academy series. Kim's experiences as a kindergarten and first-grade teacher, an elementary literacy specialist, a K-6 mathematics specialist/coach, a mathematics coordinator, and a sought-after professional developer make her the versatile educator she is today. Currently, Kim works for the Rodel Charitable Foundation of Arizona, whose main goal is to raise student achievement at schools in high-poverty communities, and is pursuing a Ph.D. in Curriculum and Instruction with an emphasis in mathematics education at Arizona State University.