Assessment In Mathematics

1. Assessment In Mathematics Math 468.50 September 26, 2008

2. Understanding Assessment • Assessment of learning (Summative) • Assessment for learning (Formative) • The assessment cycle Planning Assessment Setting clear goals Using Results Making decisions Gathering Evidence Employing multiple methods Interpreting Evidence Making inferences Van de Walle (2005) p.66

3. Four purposes of Assessment Promote Growth Purposes of Assessment Monitoring student progress Making instructional decisions Modify Program Evaluating programs Improve Instruction Evaluating student achievement Recognize Accomplishment Van de Walle (2005) p.68

4. The Assessment Standards • Mathematics • Focus on Content and Process Standards in conjunction with curriculum outcomes • Learning • Assessment should inform instruction and promote student learning • Equity • High standards and high expectations with focus on finding out what students do know not what they don’t know • Openness • Establish clear expectations and criteria and ensure all stakeholders are aware of assessment processes • Inferences • What does the data tell me and how will I use it for future plans • Coherence • Assessment is aligned with instruction, there is a balance of assessment methods that emphasize conceptual and procedural understanding NCTM (1995) Assessment Standards for School Mathematics

5. Task Selection • Good problems • Begin where they are • Focus on important mathematics • Requires justification and explanation • Promotes doing mathematics and encourages understanding • May be open-ended • Open Process: many ways to arrive at the answer • Open End Product: many possible solutions • Open Question: can explore new problems related to the old problem • Promotes the Big Five!

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

7. Levels of questions Level 2: Comprehension of Concepts and Procedures • Makes connections between mathematical representations of single concepts (creating a story problem for an addition sentence, drawing a number line picture to show the solution to a story problem, stating a number sentence for a given display of base ten blocks) • Makes inferences, generalizations, or summarizes ( makes inferences from a graphical display, finds and continues a pattern) • Estimates and predicts • Explanations

8. Verbal: Explain it in Words Concrete: Use Concrete Materials to Build It Contextual: Write a Story Problem Pictorial: Draw a Picture Model Symbolic: Write it in Mathematical Symbols Multiple Representations

9. Levels of questions Level 3: Problem Solving and Application • Multi-step, multi-concept, multi-task • Non-routine problems • Requires application of problem solving strategies • New and novel applications Break Down • Level 1 – 25% • Level 2 – 50% • Level 3 – 25%

10. Assessment Strategies • Observations • Observations of group work, problem solving, communication, etc. • Conversations and Interviews • 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 • Presentations • Tests, quizzes and exams