About Cross-Number
Development
Celia had an idea to develop a series to help children learn numeracy concepts. From her years as a math educator, she imagined a product that would:
- Help students learn and help teachers teach
- Be interactive and provide immediate teaching feedback for students
- Contain a large database of questions so students could have ample opportunities to master concepts
- Be practical, fun, and easy to use
Celia researched the available methods and discovered the Math Recovery Instructional Framework in Early Numbers. She tested it on her early prototypes and it worked so well that she used the framework to develop her entire Cross-Number series. She also met with James Martland, one of the creators of the Instructional Framework in Early Numbers, for further advice and clarification.
She then spent the next 10 years developing, testing, piloting, and refining the Cross-Number series in collaboration with teachers, parents, math consultants, and James Martland. Tests in schools showed that students working below grade level were able to advance their learning after using her puzzles.
How It Works
At Their Own Pace, But At the Same Time
The series is based on grade-level curriculum, but its use is not restricted to grade level. Each child should work on a puzzle based on where they are in their learning. A Grade 4 student not performing at grade level will benefit from the puzzles in Cross-Number Discovery Puzzles & Games Level 3, while an advanced Grade 2 student will embrace the challenges in Cross-Number Discovery Puzzles & Games Level 3. An entire classroom can be working on Cross-Number Discovery Puzzles & Games at the same time, with each student at their level. Further, the puzzles from Level 2 - 4 all look the same, allowing learning to be differentiated but not obviously.
Not Quite Your Typical Math Sheet
In Cross-Number, each question is linked to a specific outcome from the Instructional Framework of Numbers. This enables educators to quickly determine which outcomes the child knows and which are still being developed. In addition, new concepts, strategies, and skills are often introduced by pairing them with a previous known outcome. This enables children to more easily grasp new material.
Each book is organized in groups of five puzzles with accompanying games. Each group of five puzzles and games has similar learning outcomes, and each subsequent group of puzzles moves to more advanced concepts while reinforcing previous concepts.
Building Understanding Incrementally
This is based on the outcomes in the Instructional Framework in Early Numbers. This model outlines five developmental stages all children move through as they learn about early number concepts and the learning outcomes. In each stage, there is a progressive set of outcomes; in total, the framework includes over 200 outcomes. This detail allows educators to identify where a child is in his learning, to identify any gaps in the learning, and to show how best to move him or her forward at the appropriate pace. Cross-Number is based on these outcomes.
Instructional Framework in Early Numbers
|
Phase 1 Emergent Child |
Phase 2 Perceptual Child |
Phase 3 Figurative Child |
Phase 4 Counting-on Child |
Phase 5 Facile child |
|
|
Number ID |
1-10 |
1-20 |
1-100 |
1-1000 |
1 - 1000 |
|
Number word sequences |
1-20 |
1-30 |
1-100 |
2, 5, 10, 3 & 4 to 100 |
10 & 100 on and off the decade |
|
Counting |
Visible items |
Screened items |
Count on and count back to solve addition and subtraction questions |
Incrementing by 1s and 10s to 100 |
Advanced addition and subtraction* Incrementing by 1s and 10s to 1000 |
|
Grouping |
Spatial and finger patterns |
Equal groups and sharing |
Anchoring by 5 and 10 Combining and partitioning from |
Basic addition and subtraction* Developing multiplication and division |
Advanced addition and subtraction*
Basic multiplication and division |
|
*Basic addition and subtraction includes basic facts and adding and subtracting to decade numbers, and advanced addition and subtraction includes 2-digit addition and subtraction and higher decade addition and subtraction. |
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Tutorial on Cross-Number
Recommended reading:
Teaching Number: Advancing Children’s Skills and Strategies (2nd Edition), Robert J. Wright, Garry Stanger, Ann K. Stafford, James Martland, Sage Publishing, 2010.
Developing Number Knowledge: Assessment, Teaching & Intervention with 7-11-Year-Olds, Robert J. Wright, David Ellemor-Collins, Pamela D.Tabor, Sage Publishing, 2012.
Early Numeracy Assessment for Teaching Intervention (2nd Edition), Robert J. Wright, James Martland, Ann K. Stafford, Sage Publishing, 2006.
Teaching Number in the Classroom with 4-8-year-olds (CD Rom), Robert J. Wright, Garry Stanger, Ann K. Stafford, James Martland, Sage Publishing, 2006.
Math Recovery Overview: An elementary school implementation of an early intervention program to identify and service “at risk” mathematics students (white paper), Jenny Cobb, Ann Stafford, Pamela Tabor, U.S. Math Recovery Council, 2004.