Assessment In Mathematics

1. Assessment In Mathematics Math 412 January 22, 2007

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. 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

4. 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

5. 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

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. 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

9. Multiplication Example • Level 1: Multiply 13 x 5. • Level 2:What multiplication fact is shown by the picture below? • Draw a picture to show a way to find the solution to 13 x 5. • Kevin wants to make treat bags for his birthday party. He needs 8 bags and he wants to put 14 pieces of candy in each bag. How many pieces of candy will he need to make the treat bags?

10. Multiplication Example • Level 3:The grade three class is making Valentine’s treats for the whole school. They make heart-shaped sugar cookies and round chocolate chip cookies with red frosting. They want to make sure they have one of each treat for each of the 114 students and 6 teachers in the school. They have cookie sheets that will hold 5 rows of 4 heart-shaped sugar cookies or 6 rows of 5 chocolate chip cookies. How many pans of each cookie do they need to make?

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