Samples of Evaluating Student Performance

Sample 2..........Grades 2 to 3

Curriculum Organizer: Patterns and Relations (Patterns)

Learning Outcomes

It is expected that students will:

identify, create, and describe number and non-number patterns
translate patterns from one mode to another, using manipulatives, diagrams, charts, calculators, spoken and written terms, and symbols
explain the rule for a pattern and make predictions on patterns using models and objects

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

attitudes towards mathematics
reasoning and problem-solving skills
group skills
communication skills

Planning for Assessment

The teacher provided students with a variety of learning experiences using manipulatives such as pattern blocks, coloured counters, and classroom objects to create patterns and extend them in a variety of ways. Students translated patterns from one mode to another using a variety of materials and described their patterns verbally. They predicted how the patterns would continue based on repetition of shape, spatial organization, or numerical patterns.

Defining Criteria

The criteria were developed and explained to students. During the class discussion, students were given specific examples of how they might demonstrate attitudes, mathematical thinking, and communication skills while working on various patterning tasks.

Attitudes

To what extent does the student:

persevere at mathematical tasks

Mathematical Thinking

To what extent does the student:

recognize, extend, and describe mathematical patterns orally and numerically
explain the rule for a pattern
predict patterns based on a rule

Communication

To what extent does the student:

show a willingness to participate with others
seek and share ideas

Assessing and Evaluating Student Performance

Students were shown a "growing pattern" using concrete objects such as Unifix cubes and were encouraged to describe the rules of the pattern.

The teacher asked questions to prompt and challenge students' thinking. (e.g., What changes happen from one step to the next? What stays the same? How might you extend this pattern?) The teacher observed the ways each student described the pattern using spatial (e.g., The square is getting bigger), numerical (e.g., First there is 1, then 4, then 9 . . .), or less formal mathematical language (e.g., . . . a little house, an apartment building, a skyscraper . . .). The teacher extended the task by asking students to extend two more patterns.

Students, in groups of two or three, used manipulatives to copy and extend the patterns for three or four more steps. They recorded the number of objects in each step. Students explained the rule for each pattern and made predictions based on the numerical pattern they identified.

In order to assess attitudes, mathematical thinking, and communication skills, the teacher created a performance rubric based on the criteria to describe expected student performance. The Evaluating Mathematical Development Across Curriculum reference set was also used as an assessment tool. The teacher told students what she would be looking for in her observations. The students were encouraged to comment on things they noticed that provided evidence that they or other students were working towards meeting their goals. Student performance and progress over the course of the term was indicated on individual rubric sheets by highlighting the appropriate descriptors and shading them in. This information was shared with the children and used to set learning goals.

A Performance Rubric: Patterns and Relations (Patterns)
	Beginning	Understanding and Applying	Extending
Attitudes self-motivated to pursue and continue with the challenge	completes two "growing patterns" with concrete objects; with support, is able to describe concrete patterns verbally and numerically	completes two or more "growing patterns" with minimal support	independently completes two or more "growing patterns"; sets personal challenges that may include: extending the same pattern in a different way creating new "growing patters"
Mathematical Thinking recognize, extend, and describe mathematical patterns orally and numerically explain the rule for a pattern predict patterns based on a rule	recognizes, creates, and extends basic patterns with concrete objects describes patterns numerically and verbally with teacher support unable to explain the rule, or explanation is not clear makes general predictions such as "It gets bigger."	recognizes, creates and extends two or more patterns; describes patterns requires prompting to explain the rule makes predictions based on numerical data or concrete representations	student representation reveals a complexity in choice of materials, additional dimensions (2D->3D), and/or symbolic representation explains the rule in a logical manner without assistance makes accurate predictions based on numerical data
Communication willing to participate with others in seeking and sharing ideas	may work alone beginning to accept partner or group suggestions	accepts most of the partner or group members suggestions and ideas beginning to share ideas with the small group and the class	accepts and encourages group interactions frequently contributes ideas in a variety of settings listens attentively to others

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Revised: October 20, 1997

BC Ministry of Education