Because mathematics instruction is gradual and multilayered, students who struggle with its basic concepts will find advanced subjects impossible to comprehend. That is why it is so important for teachers and parents to identify deficits early and pinpoint areas requiring further instruction. One set of tools educators can use to identify needs and assess current skills is the math reasoning subtest questions in the Woodcock-Johnson Tests of Achievement, 3rd Edition.

Test 6: Math Fluency

The math fluency subtest assesses a student's ability to quickly and accurately solve basic addition, subtraction and multiplication problems. Assessors provide students with a test booklet containing several pages of single- and double-digit mathematics problems and then set a timer for three minutes. The student writes the answers to as many problems as possible within the three-minute time frame. This subtest is scored based on the total of correct answers that the student gives.

Test 10: Applied Problems

The applied problems subtest is a series of word problems designed to assess several mathematical skills including mathematical ability, the ability to filter extraneous information and the ability to select the appropriate numbers in order to perform a calculation. In the early parts of this test, the student looks at a diagram while the assessor reads the question. As the student answers correctly, the test progressively becomes more difficult. Later, text replaces the diagrams so the student reads along with the assessor.

Test 18: Quantitative Concepts

There are two subtests that assess quantitative skills in the Extended Battery -- tests numbered 13 to 22. The first assesses the student's grasp of mathematical concepts like counting, signs, vocabulary, symbols and shapes. Students provide all answers orally. For example, students might see a problem such as 4>3 and be asked whether it is true or false. A correct answer indicates that the student can interpret the symbols and that he or she has the number skills to know that four is greater than three.

Test 18: Quantitative Concepts -- Number Sense

The second subtest in the Quantitative test assesses a student's number sense. The Number Series subtest provides the students with series of numbers and the student identifies missing numbers. The early part of the test begins with basic number series, like counting by one or two. The subtest gets progressively harder and includes number series that require more difficult addition, subtraction, multiplication and division in order to find the correct missing number. Missing numbers may be at the beginning, middle or end of the series.

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