ASSESSING MATHEMATICAL COGNITIVE COMPETENCIES
Fair assessment at school must be guided by a clear definition of what do you want to measure. Assessment of competencies in mathematics is related to define the cognitive structures, such as schemes, that underlie the ability to recognize meaningful patterns of information. It is important to create evaluation procedures to assess mathematical competencies such as the meaningful use of mathematical language, modeling and problem solving skills. Items must be organized in terms of knowledge of principles rather than concrete examples, in terms of rules rather than their applications. Science and mathematics teachers in Mexico have a fragile formation in test construction and scale development. The purpose of our study was to improve the skills and knowledge in developing assessment procedures of mathematics cognitive competencies. Two groups of high school teachers participated in a program on Assessment of competencies, skills and knowledge in reading, mathematics and science. The focus of that program was to define, with those teachers, central schemes, patterns, procedures and knowledge that high school students must develop and construct. Teachers develop and item pool that was administered to students and afterward psychometric properties of those items were discussed and analyzed. Based on the assessment procedures produced teachers redefined the objectives of their teaching, in a way that assessment guide lessons. We emphasized on developing a congruent relationship between the school curriculum objectives, teaching and assessment.
In relation to mathematical content our first focus was on relational thinking. Beginning with fractions, ratios, proportions, linear functions, and trigonometric functions teachers analyze and define central schemes that underlie different kind of problems and developed teaching procedures to facilitate their construction by students. Knowledge organization can be viewed as a social construction process.
Although the results obtained with the items and test procedures developed by teachers are positive, one of the most interesting evaluations of our program is the next PISA 2012 assessment. We will analyze the results obtained by students attending schools were teachers whom participate in our program work.