Authentic assessment: a school's interpretation

Focus on Learning Problems in Mathematics, Wntr, 2002 by Roland G. Pourdavood, Lynn M. Cowen, Lawrence V. Svec

The student's solution in May shows growth. Invented money is absent. Also, a detailed rendering of a dollar bill is absent. This lack of detail might be interpreted as a more sophisticated way of communicating. Included now are two illustrated functions-three dollars per fish and two dollars per day. Also included is a written response to the question. "Does he have enough money to buy three fish that cost $3 each?" The student response of "yes" indicates her/his-self-evaluation. The "self portrait" in the corner may be the student's self-evaluation indicating pride (smile) and mathematical power (muscles flexed).

Targeting the Performance Tasks: Teacher-Designed Instruction

The use of students' prior knowledge and experiences as the foundation for problem solving demonstrated the importance of relevant context. All mathematical calculations were done within a context to which children could easily relate. Rarely did students solve abstract algorithms without the context of money, volume, area, length, weight, chance, etc. Lessons were child-oriented-teachers designed lessons that reflected student experiences and how children used mathematics in their lives. Therefore, mathematics problems were centered on the home, school, and local shopping center. Problem-solving was often personalized. Frequently, teachers would use students as main characters in problem-solving situations. This attention to the mathematical activities children do and observe daily and the use of real student names engaged children. These methods were enthusiastically endorsed by parents. The examples that follow are teacher-created lessons designed to connect to the performance tasks (see Appendix 2).

Figure 5 in Appendix 2 is a fourth grade measurement lesson developed by a fourth grade teacher. Figure 6 in Appendix 2 represents a student's solution. The lesson is an example of how teachers coordinate instruction with performance tasks.

The format of Figure 6, Appendix 2 is different. All illustrations were originally included on one small poster. This mathematical artwork was displayed in the hallway. These classroom posters conveyed that mathematics learning could be relevant, contextual, and meaningful for young children. Measuring their room, their head size, height, arm span, food size, etc. allowed them the opportunity to graph relevant, personal data and reflect on the relationships among the data.

Teachers who understood and supported the instructional reform were challenged to create lessons that provided memorable problem-solving experiences aimed at the concepts and processes required for success on the performance tasks. Instruction needed to connect with assessment. Teachers wanted to prepare students to do the final performance (assessment) task in May.

For example, a kindergarten teacher who prepared a student to do the "chance" task about arranging three different colored buttons on a shirt had to create plenty of similar experiences for the children during the school year. The teacher might create the following types of problem for the whole class to solve together.