Assessing Mathematics

1
Assessing Mathematics

• Understanding what they understand

2
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

3
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

4
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?

5
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.

6
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

7
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

8
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.)

9
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

10
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

11
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.