1. Tests for 6-graders in Chile Raimundo Olfos Raimundo.olfos@ucv.cl Pontificia Universidad Católica de Valparaíso Chile

2. SIMCE (MS of QEE) Chilean measurement system of quality and equity in education Chilean Educational System provides yearly tests in language, mathematics, science, English and physical education. Tests in mathematics are provided in 2 nd, 4 th, 6 th, 8 th and 10 th grades in every schools. Results are informed by class and school, but not by students (teachers ae controlled, school are ranked).

3. Mathematics tests structure Tests include around 30 questions. 10% are open response question, 90% are 3 or 4 alternative closed question. 6-grade test include questions referred to numbers and operations, patterns and algebra, geometry, measurement, and data and probabilities In general, mathematics tests considers three cognitive domains: knowledge, application, and reasoning.

4. Example of question The graph below shows the results of a survey about people’s favorite ice-cream flavors. Favorite ice-cream flavors. What percentage of people surveyed prefer strawberry ice-cream? A. 12% B. 19% C. 27% D. 42%

5. Cognitive domains knowledge, application, and reasoning Knowledge includes basic cognitive processes such as remembering and recognizing concepts, properties and mathematical procedures. It also includes the ability to recognize symbolic representations and factual, conceptual and procedural knowledge which is the basic mathematical language and knowledge essential to develop mathematical thinking. Also considers the direct use of procedures that can be performed mechanically and that involves remembering a set of actions and how to implement them. Finally, it includes the ability to extract information from tables and graphs; and classification of individual elements according to their properties

6. Example of Knowledge domain question What is the value of “y” in the equation: 2y + 6 = 24? A. 6 B. 9 C. 15 D. 16

7. Example of Knowledge domain question What is the answer to 2,5 - 2 0,01 + 0,1? A. 2,38 B. 2,58 C. 0,123 D. 0,105

8. Application domain The application considers cognitive processes such as the ability to solve routine problems, ie those problems in which a strategy or previously known method for solving must be selected. It also includes the generation of equivalent representations for reporting quantities, operations and given relations and represent and interpret information and data in charts, tables or graphs. Finally, it provides the ability to use and apply models and construct simple mathematical models, identifying characteristic patterns of situations, objects or phenomena.

9. Example of application Knowledge domain question Eduardo has bought 2 1/2 kilos of apples, 1 1/2 kilos of bananas and 3 1/2 kilos of oranges. He puts them all into a bag. How many kilos does the bag weigh? A. 3 1/2 B. 5 1/2 C. 6 1/2 D. 7 1/2

10. Reasoning domain The reasoning includes cognitive processes such as inductive reasoning necessary to discover patterns and regularities, to make generalizations and finding strategies, representations and models to solve non-routine problems. Consider the logical and systematic thought it possible to make deductions based on specific rules and assumptions, misstatements of differentiating true, argue the validity of a result, communicating ideas and conclude correctly using mathematical knowledge.

11. Application domain question The entrance of the tend is built with a triangular net. The hight of the tend is 1,84 m and the base is 2,1 m. If the netting breaks, what is the exact measurement that is needed to replace it? A. 6,3 m 2 B. 1,97 m 2 C. 1,932 m 2 D. 3,864 m 2

12. Reasoning level Fernanda writes her grades for this semester for her Language class in her journal. What is the average of the grades Fernanda has got for her language class this semester? A. 5, 3 B. 5, 9 C. 6, 0 D. 6, 2

13. Some reflections Items construction and categorization are complex. An item should means knowledge for some student and application or reasoning to others. The level of complexity should be related to each national curriculum