High Expectations and World-Class Tests
To provide math experiences at home and school based on high expectations for our very-smart U.S. children; and to improve our international rankings in mathematics, public education in the U. S. needs two things:
- A set of learning goals (standards) commensurate with those in high-achieving countries.
- Methods of assessing student proficiency levels (basic, intermediate, proficient, or advanced) relative to the adopted learning goals.
For a set of learning goals or standards to define what we mean by world-class math proficiency, let’s begin with the Top-Ten List above.
Many test questions on my blog come from third grade standardized tests currently being administered in many states: the SmarterBalanced and the PARCC (Partnership for Assessment of Readiness for College and Careers). In the educational assessment world, these two test are called “criterion-referenced tests” because they use a student’s raw score to classify the student into 4 or 5 levels of knowledge and capability. (A typical four-level scale might be basic; apprentice; proficient; advanced.) It’s possible on a criterion-referenced test for all test takers to be classified into one or two categories, such as 50% proficient and 50% advanced which is what we want for our U.S. students. Contrarily, norm-referenced scoring of a test assigns percentile scores to test takers relative to a normal distribution. The majority of scores (about 68%) will be within one standard deviation of the mean score. Norm-referencing classifies only a few test-takers ( 5-10%) as either high scorers or low scorers.
A little warning about the blog … I don’t just tell you what time it is;
but tell you how to make the watch!
Blog readers should expect a long and complete answer to a short question. Not only do I discuss the problem in detail but also provide ideas for early steps along learning trajectories which lead to mastery of these types of problems by third grade.