Samples of Evaluating Student Performance

Sample 3..........Grade 4

Curriculum Organizer: Number (Number Operations)

Learning Outcomes

It is expected that students will:

demonstrate and describe the process of addition and subtraction of numbers up to 10 000 using manipulatives, diagrams, and symbols

In addition to these outcomes the teacher will assess students':

attitudes towards mathematics
reasoning and problem-solving skills
communication skills

Planning for Assessment

The teacher provided opportunities for students to solve problems involving addition, subtraction, multiplication, and division during the first term of the school year. Students used a variety of materials (e.g., counters, base-ten blocks) and calculation approaches (e.g., mental math, paper and pencil, and calculators). The class kept a list of "invented algorithms" ‚ alternative ways that individual students solved the problems. Students were required to choose from the four operations to solve a given problem and to select the most appropriate way to do the calculations depending on the degree of accuracy required.

Defining Criteria

Students were given specific examples of how the teacher might know if they were working towards meeting the criteria while working on the task.

Attitudes

To what extent does the student:

creatively respond to problem situations in new ways and quickly become engaged in the task

Mathematical Thinking

To what extent does the student:

demonstrate understanding of how to subtract large numbers up to 10 000
know when to choose the operation of subtraction to solve a problem

Communication

To what extent does the student:

explain how to subtract large numbers using an algorithm
use mathematical words, pictures, and symbols to communicate her/his ideas

Assessing and Evaluating Student Performance

The teacher gave students the following instructions "You want to teach your younger cousin how to subtract using four-digit numbers. Write out what you will say. Use concrete materials, pictures, and symbols to make your explanation clear. Give examples of a few word problems that you could solve using subtraction. Solve one of them in a different way than the one you described to your cousin." The teacher examined students' written products and used a scoring rubric to evaluate each student's response based on the degree to which the student met the criteria. The teacher followed up with conversations and interviews with students who had experienced difficulty explaining their thinking in written form. The teacher also used the Evaluating Mathematical Development Across Curriculum reference set to determine the level of performance demonstrated by students.

Holistic Scale
Outstanding (5)	The explanation response is correct, complete, and clear for the intended audience (the younger cousin). It includes words, pictures, and symbols to help explain the ideas. Several examples are included that illustrate some of the complexities of specific cases (e.g., requiring regrouping). More than two different approaches are described.
Very good (4)	The response is correct and the explanation is clear. It includes words, pictures, and symbols. Sample problems are included with some complexity involved. Two methods for solving subtraction problems are illustrated.
Good (3)	The response is correct. The explanation is reasonable. Sample problems are included that show beginning levels of complexity. One method for solving subtraction is illustrated.
Satisfactory (2)	The response is correct and indicates that the student understands the solution, but the explanation lacks clarity. The student is able to describe his/her thinking orally.
IP (1)	The response indicates a partial solution. The student's understanding of the solution is not complete. The explanation is present but indicates some confusion. Further individual instruction and intervention is required.

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Revised: October 20, 1997

BC Ministry of Education