What can students expect on the Fourth-grade Proficiency Test in Mathematics?

The Fourth-grade Proficiency Test in Mathematics is defined by twenty-five learning outcomes. These learning outcomes, based on Ohio’s Model Competency-Based Mathematics Program, were developed by committees made up of Ohio citizens (educators and business members) through a consensus-building process. These learning outcomes have been identified from the eight strands in the State Board adopted model curriculum.

Each form of the proficiency tests includes some embedded field test items. There are 5 field test items embedded in the mathematics test, making a total of 45 items, only 40 of which are counted to obtain the students’ mathematics scores. These field test items give ODE the potential to continue adding to the item bank for future test forms.

Each form will contain 30 multiple-choice items, 8 short-answer items, and 2 extended-response items. Altogether, the 30 multiple-choice items are worth 30 points, the 8 short-answer items are worth 16 points, and the 2 extended-response items are worth 8 points, making a total of 54 points. In all, the multiple-choice items account for about 55% of the total score; short-answer items, 30%; and extended-response items, 15%.

Short-answer items might ask students to carry out a calculation and write an answer; to examine a situation and describe why one alternative or another was correct; to measure or draw a figure; to complete a table; or to provide a numerical, verbal, or visual representation of their solution.

Extended-response items require students to construct their own responses and to demonstrate problem solving, mathematical reasoning, and application of concepts and skills. Extended-response items require students to communicate their understanding of the problem situation, verify and interpret results with respect to the problem, and justify their answers and solution processes. Each strand has at least one short-answer or one extended-response item. Since credit for answers is usually based on demonstrated understanding of concepts, students should be encouraged always to explain their answers, when asked to do so. The more understanding that a student demonstrates, the more credit may be assigned.

A fourth-grade level of literacy and competency requires understanding of concepts, recall of basic mathematical facts, performance of mathematical procedures, and application of concepts and skills to problem-solving situations. Thst items assess the learning outcomes at one of three levels of understanding. These levels are described below.

Conceptual Understanding (approxImately 50% of the items on the test)

Items in this category test the student’s ability to recognize examples and counter examples, use various representations of concepts, apply facts and definitions, compare and contrast related concepts and principles, judge the characteristics of solutions, and interpret charts and tables.

Knowledge and Skills (approximately 25% of the items on the test)

Items in this category test the student’s knowledge of important basic terms, facts, methods, procedures, and skills. This includes the ability to recall important definitions and relationships; read graphs and tables; and perform rounding, ordering, and estimating operations.

Application and Problem Solving (approximately 25% of the items on the test)

Items in this category test the student’s ability to use reasoning in new situations. This includes the ability to translate between pictorial and mathematical representations of a problem; determine the sufficiency and consistency of data; use strategies and data to solve problems; and use spatial, inductive, and deductive reasoning.

What are the fourth-grade learning outcomes in mathematics and what do they mean to students and teachers?

The learning outcomes define the proficiencies fourth-grade students are expected to possess and apply as a result of their learning experiences in kindergarten through February of the fourth-grade year. The twenty-five outcomes are grouped into eight strands:

• patterns, relations, and functions
• problem-solving strategies
• numbers and number relations
• geometry
• algebra
• measurement
• estimation and mental computation
• data analysis and probability

The learning outcomes and related information about test content are provided on the following pages. The information included in this guide applies to most test items: however, the descriptions may not cover all items that could be used on the tests.

What is some additional information concerning the learning outcomes?

Because the learning outcomes were taken from the State Board adopted curriculum which is used in Ohio classrooms, the use of manipulatives has been emphasized throughout the test. While manipulatives are not given to the students during the test administration, pictorial representations appear when appropriate.

How are the tests scored?

Each multiple-choice item on the test is worth one point; each short-answer item is worth two points; and each extended-response item is worth four points. Altogether, the thirty multiple-choice items are worth 30 points; the eight short-answer items are worth 16 points; and the two extended-response items are worth 8 points. The total test score is 54 points.

Conventions of writing (sentence structure, word choice, usage, grammar, spelling, and mechanics) will not affect the scoring of short-answer or extended-response items, unless there is interference with the clear communication of ideas.

Short-answer items will be scored on a 2-point scale based on these general guidelines:

A 2-point response shows complete understanding of the concept or task, logical reasoning and conclusions, and correct set up and/or computations.

A 1-point response contains minor flaws in reasoning, neglects to address some aspect of the task, or contains a computational error.

A 0 is assigned if the response indicates no mathematical understanding of the concept or item.

Extended-response items will be scored on a 4-point scale based on these general guidelines:

A 4-point response contains an effective solution. It shows complete understanding of the concept or task and thoroughly addresses the points relevant to the solution. It contains logical reasoning and valid conclusions, communicates effectively and clearly through writing and/or diagrams, and includes adequate and correct computations and/or set up when required. It may go beyond the requirements of the item.

A 3-point response contains minor flaws. Although it indicates an understanding of the concept or item, communicates adequately through writing and/or diagrams, and generally reaches reasonable conclusions, it contains minor flaws in reasoning and/or computation, or neglects to address some aspect of the item.

A 2-point response indicates gaps in understanding and/or execution. It contains some combination of the following flaws: an incomplete understanding of the concept or item, failure to address some points relevant to the solution, faulty reasoning, weak conclusions, unclear communication in writing and/or diagrams, or a poor understanding of relevant mathematical procedures or concepts.

A 1-point response indicates some effort beyond restating the item or copying given data. It contains some combination of the following flaws: little understanding of the concept or item, failure to address most aspects of the item or solution, major flaws in reasoning that led to invalid conclusions, a definite lack of understanding of relevant mathematical procedures or concepts, or it omits significant parts of the item and solution or response.

A 0 is assigned if the response indicates no mathematical understanding of the concept or item.

Facts from the Fourth-grade Proficiency Field lest

Test items based on the mathematics learning outcomes were field tested in April 1994. While the number of students responding to each test item was limited, some general observations regarding student achievement can be made. The summary below is based upon review of student performance on multiple-choice items only. Scored examples of short-answer and extended-response items found on the practice test are included in the Resource Manual for Teachers of Fourth Grade.

• Student performance was highest on multiple-choice items measuring outcomes 1,6,7,10,17, and 24
• Student performance was lowest on multiple-choice items measuring outcomes 3, 4, 5, 8,13,22, and 25.

For more information on the mathematics learning outcomes, see the Ohio Model Competency-Based Mathematics Program.

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