The Number Knowledge Test: Overview

The Number Knowledge test was designed to measure the intuitive knowledge of number that the average child has available at the age-levels of 4, 6, 8 and 10 years. This knowledge has been referred to elsewhere as a set of "central conceptual structures for number” and “powerful organizing schemas” that help children make sense of quantitative problems. Research has shown that the knowledge assessed at each age level of this test is essential for successful learning of arithmetic in school and is foundational for higher mathematics learning. A major goal of the Number Worlds Program is to ensure that all children acquire this knowledge in a well-consolidated fashion at the appropriate age and grade levels and have ample opportunity to use it to solve a wide range of quantitative problems.

Understanding the test -
The Number Knowledge test is a developmental test. This means that knowledge assessed at Level 0 is generally acquired before knowledge assessed at Level 1, and this knowledge is generally acquired before knowledge assessed at Level 2, etc. It also means that knowledge at each level of the test is a prerequisite, providing the conceptual building block for knowledge at the next level of the test. This information is important for instructional planning. If you know the developmental level at which each child in your classroom is presently functioning, you can make informed and appropriate instructional decisions: ones that will enable each child to strengthen his or her present knowledge and to move, in easy and manageable steps, from one level to the next. The Number Knowledge test was designed for this purpose.


The Preliminary item -
This item is generally mastered around the age of 3 years. It is included in this test as a warm-up item, to orient children to the nature of the test and to give them a successful experience at the start. It will also alert you to children who have not yet mastered this skill and who will need opportunities to do so. These opportunities are identified in the Learning Objectives that accompany each activity in the Number Worlds program.


Level 0 items -
These items assess children's ability to count and to quantify small sets, when concrete objects are available and can be touched and manipulated. This knowledge provides an important building block for success at the next level which requires children to deal with quantities, and changes in quantity, that can not be touched or seen, and that have to be imagined.


Level 1 items -
There are two classes of items at this level. Items 2, 3, 4, 5, 6 and 9 assess children's knowledge of the number sequence. Items 1, 7, and 8 assess children's ability to handle simple arithmetic problems. Concrete objects are not available for any of these items (although a few are accompanied by a visual display so children can make sense of the problem). To solve items at this level, children need to rely on something like a "mental counting line" inside their heads. Their success at this level will give you some idea of whether or not they have constructed this knowledge structure. Knowledge at this level provides an important building block for handling problems at the next level.


Level 2 items -
There are two classes of items at this level as well: those that assess knowledge of the number sequence and those that assess knowledge of arithmetic. The primary distinction between items at level 1 and level 2 is that items at this level require children to deal with double-digit numbers (i.e., tens and ones) and/or depend on the use of two mental number lines for successful solution.


Level 3 items -
Like the earlier levels, there are two classes of items at this level: those that assess knowledge of the number sequence and those that assess knowledge of arithmetic. The primary distinction between items at level 2 and level 3 is that items at this level require children to deal with triple-digit numbers and/or to solve more complex problems involving double-digit numbers (e.g. addition and subtraction problems that require re-grouping).


For selected items on this test (such as items 1, 3, and 7 at Level 1; items 1, 2, and 8 at Level 2; items 1, 5, and 6 at Level 3), it is also helpful to ask, “How do you know?” or “How did you figure that out?” if this information is not apparent in the child's behavior. This will give you valuable information on the strategies children have available to solve number problems. For example, they might rely on the earliest strategy to be acquired, developmentally, which is starting from 1 and counting up. Or they might use a more sophisticated strategy and count on from the largest addend. Or they may retrieve the answer from memory and say, “I already knew the answer. It was in my head.” Like children's answers to the problems themselves, the strategies children use to solve these problems can help you determine their level of understanding.