Assessing Mathematics Understanding what they understand

Assessment Assessment is the systematic process of gathering information on student learning. – Atlantic Canada Curriculum Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. – NCTM, 2000

Types of Assessment Formative On-going Information is used to improve student performance and classroom practice Can be formal or informal Summative Typically formal assessment Used to measure achievement

Thinking About Assessment How do we know students have learned? What do we value as mathematics learning? Procedural knowledge, recall of facts, application, problem solving? What assessment approaches allow students to truly demonstrate their learning?

Alignment Our assessment techniques should be aligned with our teaching techniques. If we teach with a goal of relational understanding we must assess for relational understanding. Instructional strategies and assessment strategies should be consistent.

Assessment Strategies Documenting classroom behaviours Observations of group work, problem solving, communication, etc. Portfolios and journals Responding to open-ended questions, monitoring their own learning, reflecting on their learning, sharing and discussing with the teacher Projects and investigations Tests, quizzes and exams

Levels of Questions Level 1: Knowledge and Procedures Remembrance could be simple recall (Examples: Defining a term, recognizing an example, stating a fact, stating a property). Questions are within one representation (Examples: performing an algorithm, completing a picture) Reading information from a graph

Levels of Questions Level 2: Comprehension of Concepts and Procedures Makes connections between mathematical representations of single concepts (Examples: Switching representations – drawing a graph from an equation, creating a word problem to fit a graph or equation, etc.)

Levels of Questions Level 2: Comprehension of Concepts and Procedures Making inferences and generalizations, or summarizing (Examples: Extrapolate or interpolate from a graph, find and continue a pattern) Estimates and predicts Explanations

Levels of Questions Level 3: Problems Solving Multi-step, multi-concept, multi-task Non-routine problems Requires application of problem solving strategies New and novel applications

Break down of questions Level 1 – 25% Level 2 – 50% Level 3 – 25% This should be an average breakdown for your overall unit assessment plan but does not necessarily apply to each assessment tool.