BC Education - Mathematics 10 to 12 Appendices

The samples in this appendix illustrate procedures teachers might use in assessing student understanding of content and processes in grade 10 to 12 mathematics courses. The focus of the samples is ongoing assessment and evaluation as a way of supporting learning in the classroom. Ongoing assessment includes observation, questioning, oral and written communication and peer and self-assessment. The assessment activities in each sample focuses on an understanding of mathematical processes, communication of ideas, emerging understanding of concepts, abilities to apply concepts and attitudes toward learning as well as on the end product.

Teacher-constructed tests and quizzes are recognized as a valid means of assessing certain aspects of student learning. The samples presented here represent alternatives that teachers might use to support and supplement traditional tests on a particular unit of work. Some samples include assessment ideas teachers might want to use to look at their students' communication skills or their abilities to work effectively and productively in groups. Following the samples is information about various assessment and evaluation practices, including test construction that teachers will find useful as a resource when developing classroom tests.

Using a variety of assessment techniques provides students with opportunities to demonstrate what they have learned more readily and gives teachers a broader base of information on students' mathematical development.

The assessment practices described in the samples are supported by current theories of assessment, including the Evaluation Standards outlined by the National Council of Teachers of Mathematics:

The assessment practices described in the following samples include those that focus on assessment and evaluation of:

Samples of student performance should reflect learning outcomes and identified criteria. The samples clarify and make explicit the link between evaluation and learning outcomes, criteria, and assessment.

Where a student's performance is not a product, and therefore not reproducible, a description of the performance sample should be provided.

Criterion-referenced evaluation may be based on these steps:
Step 1		Identify the expected learning outcomes (as stated in this Integrated Resource Package).
Step 2		Identify the key learning objectives for instruction and learning.
Step 3		Establish and set criteria. Involve students, when appropriate, in establishing criteria.
Step 4		Plan learning activities that will help students gain the knowledge or skills outlined in the criteria.
Step 5		Prior to the learning activity, inform students of the criteria against which their work will be evaluated.
Step 6		Provide examples of the desired levels of performance.
Step 7		Implement the learning activities.
Step 8		Use various assessment methods based on the particular assignment and student.
Step 9		Review the assessment data and evaluate each student's level of performance or quality of work in relation to criteria.
Step 10		Where appropriate or necessary, assign a letter grade that indicates how well the criteria are met.
Step 11		Report the results of the evaluations to students and parents.

Prescribed learning outcomes, expressed in measurable terms, provide the basis for the development of learning activities, and assessment and evaluation strategies. After a general discussion of assessment and evaluation, this appendix uses sample evaluation plans to show how activities, assessment, and evaluation might come together in a particular mathematics program. The final section, Assessment Practices, provides some general guidance for classroom assessment and evaluation.

Assessment is the systematic gathering of information about what students know, are able to do, and are working toward. Assessment methods and tools include: observation, student self-assessments, daily practice assignments, quizzes, samples of student work, pencil-and paper tests, holistic rating scales, projects, oral and written reports, performance reviews, and portfolio assessments.

Students performance is evaluated from the information collected through assessment activities. Teachers use their insight, knowledge about learning, and experience with students, along with the specific criteria they establish, to make judgments about student performance in relation to prescribed learning outcomes.

Students benefit most when evaluation is provided on a regular, ongoing basis. When evaluation is seen as an opportunity to promote learning rather than as a final judgment, it shows learners their strengths and suggests how they can develop further. Students can use this information to redirect efforts, make plans, and establish future learning goals.

In criterion-referenced evaluation, a student's performance is compared to established criteria rather that to the performance of other students. Evaluation referenced to prescribed curriculum requires that criteria are established based on the learning outcomes listed under the curriculum organizers for grade 11 and 12 mathematics courses.

Criteria are the basis of evaluating student progress. They identify the critical aspects of a performance of product that describe, in specific terms, what is involved in meeting the learning outcomes. Criteria can be used to evaluated student performance in relation to learning outcomes. For example, weighting criteria, using rating scales, or performance rubrics (reference sets) are three ways that student performance can be evaluated using criteria.