Relative Weakness in Quantitative Reasoning (Q–)

Research-based Principle

Guidelines for Adapting Instruction

Learner Characteristics

When compared with students who have an even (A) profile across all three batteries, students who display a relative weakness in quantitative reasoning tend to score somewhat lower across all portions of standardized achievement tests, especially at the primary level. The difference is largest on the mathematics, computation, and language tests. 

A relative weakness in quantitative reasoning abilities generally has a broader impact on the achievement of students than does a relative strength in quantitative reasoning. The connection between lower achievement on the computation and language tests could reflect a common difficulty in learning rule-based systems, or it could reflect a lack of instruction in both areas. Only someone familiar with the students and the educational curricula they have experienced can make this judgment.

There are many causes of a relative weakness in quantitative reasoning. Some students have difficulty creating, retaining, and manipulating symbolic representations of all sorts. For some students, this problem seems confined to numerals; for others, however, it stems from a more fundamental difficulty in thinking with abstract, as opposed to concrete, concepts. For example, even the most elementary concepts in mathematics are abstractions. When counting objects, students must recognize that the number 3 in “3 oranges” means the same thing as the number 3 in “3 automobiles.”

Relative Weakness

Indicators of a relative weakness in quantitative reasoning include the following:

Some students prefer more concrete modes of thinking and often disguise their failure to think abstractly when using verbal concepts. For example, a student may use the word dog appropriately but may think only about her or his dog when using the word. 

For other students, the difficulty lies in the failure to develop an internal mental model that functions as a number line. For these students, solving even basic computations such as adding 2 to a given number is a challenge. When performing computations, such students often make substantial errors that they do not detect unless prompted—and even then they may not notice the errors. 

And for other students, the weakness represents nothing more than a lack of experience in thinking and talking about quantitative concepts. This is fairly common in the primary grades. It surfaces again at the secondary level among those who avoid mathematics. At the middle school and high school levels, math anxiety can also be a significant issue.

Shoring Up the Weakness

Remediating a weakness in quantitative reasoning requires an understanding of the source of the deficit. Select strategies from the following list that seem most appropriate for the student and the learning situation:

If students have difficulty reasoning abstractly, help them focus on the quantitative aspects of a stimulus while ignoring more compelling perceptual features (as in the previous example of 3 oranges/3 automobiles).

If students have not established or cannot readily use a mental model for representing numeric quantities, give them practice in drawing a number line and then trying to envision and use a mental number line to solve basic addition and subtraction problems. It will take a substantial amount of practice before they can automatically conceive and use a mental number line to solve problems.

If the difficulty is a lack of experience or the presence of anxiety, provide greater structure, reduce or eliminate competition, reduce time pressures, and allow students greater choice in the problems they solve. Experiencing success will gradually reduce anxiety; experiencing failure will cause it to spike to new highs.

Help these students discover how to use their better-developed verbal and spatial reasoning abilities for solving mathematical problems. At all grades, but especially in middle school and high school, encourage these students to develop the habit of restating mathematical expressions in words. Encourage them to talk about mathematical concepts rather than silently solving problems on work sheets or computer screens. When learning computation skills, they can recite mathematical facts orally and in groups.

Provide opportunities for these students to exploit their stronger spatial reasoning abilities by encouraging them to create drawings that represent essential aspects of a problem. Show them how drawings can range from concrete depictions of the objects described in the problem to increasingly abstract representations that capture only the essential aspects of the problem. 

Encourage students to use computers and other tools to offload lower-level computation processes and to focus instead on higher-level concepts. This is often best done using graphic representations of geometric and algebraic concepts.