Assessment In Mathematics February 15, 2007

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

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

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

Assessment and Instruction Assessment and instruction need to be properly aligned Good learning tasks are good assessment tasks Assessment should be integrated Evidence is used to inform future instructional tasks

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!

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.

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

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

Some types of Assessment Rubrics Observation Journals and writing Tests Portfolios Interviews