Number Knowledge Test

Method 

The Number Knowledge Test is an oral test administered individually to students. Children also provide an oral response. Students are not permitted to use paper and pencils to determine answers. To measure intuitive knowledge, it is important children problem solve in their mind. Administering the test orally allows an educator to determine the level of complexity in the way a student strategizes, and problem solves. The results of this test can be used to create instructional strategies to support student learning. At the kindergarten level, the test takes approximately five to 10 minutes to complete.  

Before administering the test, a test kit will need to be prepared. This includes visual props required for items, including a scoring sheet for each student and preparing all necessary materials so they can be easily and comfortably manipulated. It is strongly recommended you practice administering the test to a friend or colleague before using it with a student. This preparation will allow you to focus your attention on the student's responses, problem-solving strategies, and other behaviors (e.g., expressions of frustration), all of which provide an indication to their level of understanding. 

This assessment is also cumulative, i.e., knowledge required to complete tasks in Level 1 typically build off knowledge previously acquired knowledge needed to complete Level 0. Results from this information are useful because it allows educators to plan instructional strategies to support students so that they can answer the questions asked at the next level.  

Goals 

1. To establish whether a student is functioning below, at, or above their respective age/grade range in number sense. 
2. To establish the number sense topics a student understands, has yet to learn and those that need improvement. 
3. To measure a student’s development over time. 
4. To establish which level a student should begin the test at, to determine which instructional strategies should be implemented. 

Age Levels 

Each level of this Number Knowledge Test (i.e., Level 0, Level 1, etc.) is associated with the age levels mentioned above (i.e., Level 0 would typically be suitable for children of 4 years). It is important to note, however, the ages associated with each test level represent the midpoint of the age range where children would usually demonstrate this knowledge. Children do not acquire conceptual skills all at one given age (McGraw-Hill Education) . Rather, a student’s comprehension of numbers develops in complexity approximately every two years throughout middle childhood. For instance, at the four-year-old level, children typically acquire this knowledge as early as three years, or as late as five years (McGraw-Hill Education).  

There are many factors that influence the acquisition of numeracy skills. Research has posited that most students acquire these foundational skills at the start of the age range for each level. However, students who experience adverse conditions that affect their learning, tend to demonstrate these skills on the back end of the age range. Moreover, research also demonstrates students from lower socioeconomic backgrounds do not meet expectations for the age range or grade level and succeed at levels one or two below which they should. As a result, this translates to a developmental deficit in number sense of at least two years (McGraw-Hill Education).  

Levels of the Test 

Preliminary: In this stage, children three-years-old and younger are typically able to count with ease. This test is used as an introductory exercise to have students access prior knowledge that is required for a successful test. Moreover, this exercise will indicate whether a student is unprepared for more complex skills and will require more practice refining this skill. 

Level 0 (4-year-old): The tasks in this level determine a student’s capacity to count and to compare small groups of physical objects (counters). These objects can be used as a tactile aid for students.  

Level 1 (6-year-old): At this level, the tasks seek to establish a student’s understanding of simple arithmetic problems and order of numbers. In this assessment, there are no concrete objects available to students. They must rely on methods such as mental math. 

Level 2 (8-year-old): Again, at this level, there are two areas being assessed: understanding of arithmetic problems and order of numbers. In this more advanced level, students encounter more complex problems such as those involving double-digit numbers. 

Level 3 (10-year-old): Once more, this level will assess understanding of arithmetic problems and order of numbers. Again, this level is more complex and will require students to solve harder problems that involve triple-digit numbers possibly requiring mental regrouping.  

Administering the Test 

• Plan a time when students in your class are occupied, limiting the possibility of being interrupted. 

• Choose your location carefully so that materials in the surroundings, such as a number line, will not provide visual aids. 
• Prepare the student for the test by explaining that the questions will be easy at first and increase in difficulty. Let them know that you don't expect them to know all the answers.  
• For children who are six-years-old and younger, start at the preliminary level and continue testing until the child has incorrectly answered sufficient items at any level to progress to the next level, as specified on the test form. Whenever possible, enter the child's answer on the scoring form and mark each item as a pass or fail in a way that failures are not apparent to the child. 
• For children who are eight-years-old and older, omit the preliminary item and Level 0 and begin testing at Level 1. As a general rule, start testing at a level that is at least two years below the age of the child you. This will ensure children experience success on the initial tests and provide an index of their baseline knowledge.  
• Administer all items at each level that the student progresses to (unless the child is terribly frustrated) in order to determine the child’s maximum potential. 

• Provide frequent reinforcement throughout. For example, saying "Good" after each response will not indicate whether the answer is right or wrong. 
• If a child’s strategy is not apparent, you may wish to ask, "How did you figure that out?" Record the strategy used or reported on the scoring sheet. Directions for coding strategy use on the scoring sheet are provided below. 

Coding Strategy Use  

For selected items on the 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), additional information about a child’s number knowledge can be gained by coding strategy use. If the strategy used is not apparent in a child’s responses, ask how they figured out the answer (i.e., “How did you figure that out?”). Based on the child’s explanation, mark one of the following on the test record form: 

CU = Count up from “one.” Circle CU if the child uses a counting up from “one” strategy for solving addition problems. 

CO = Count on. Circle CO if the child enters the counting sequence at the point of one of the addends and then counts on, one number at a time. 

R = Retrieval. Circle R if the child says that she figured out the answer in her head (e.g., “I just knew it”, “My brain told me”, “I learned that”). 

Several other strategies are possible to solve these problems. Some students may use “friendly numbers” or “counting down.” If additional strategies are used, teachers should record the strategy with an acronym of their choosing or under “other strategies.” 

Scoring the Test 

One point is assigned for each item passed at Levels 0, 1, 2 and 3. For all two-part items, both (a) and (b) must be passed to earn one point. If testing commences at Level 1 (for children who are at least eight-years-old), points are automatically assigned for Level 0 items. 

A total raw score for each child on this test can be computed by summing the number of points the child received across all levels of the test. A chart to convert raw scores to developmental levels scores is provided below and can be used if you find this information useful. It is important to note in this context that a developmental level describes the knowledge or the performance of an abstract entity: the "average" child in our culture. In practical terms, this means that about 60 per cent of the U.S. children who have taken this test perform at the level indicated. About 20 per cent perform somewhat better, some as high as the next whole level up. About 20 per cent perform somewhat worse, some as low as the next whole level down. For this reason, developmental level scores provide only a rough index of a child's knowledge or growth. 

Developmental Level Conversion Chart 

Interpreting the Test  

Although test results can be used to compare the performance of a particular child to the rest of the class or to compare your class to national averages, a far more important use of the test is for instructional planning. When used at the beginning of the year, the test can give you valuable information on the kind of number knowledge each child brings to the learning situation, along with the strategies each child has available to make sense of number problems. During instruction, you may wish to group children so that all children in the group are at a similar level in their number understanding or you may wish to group children in such a fashion that more knowledgeable children can function as group leaders or "mini-teachers." 

When used at the end of the year, the test can give you a measure of each child's learning progress, knowledge growth, and readiness for mathematics learning at the next grade level. The test can also be used in the middle of the year if an interim measure of children's knowledge is desired.

Test results can also be used to help determine the strengths and weaknesses of your class as a whole; for example, you can determine the number of children who pass or fail particular sections of the test. This information can be invaluable for instructional planning. If you discover that most children in your class have an easier time telling you which numbers are bigger than one but struggle with finding the number that is closest to one, you may wish to practice this skill with your students by using activities such as “Closest To…” in the Robertson Program Math Lessons. 

Finally, as with individual children, the information you gather at the beginning of the year for your class can be used at the end of the year to give you a picture of the progress your class has made as a group. When you compare beginning- to end-of-year results, you may obtain a well-deserved sense of accomplishment as you identify areas of growth. If growth is not as great as you expected or hoped for, you can use these results to modify or adapt your instructional planning for the next school year.