Students' Mathematical Beliefs Implicitly Learned Through Assessment
Students come to beliefs about what mathematics is through a host of factors. One of these is through the way that they are assessed. Through summative, standardized achievement tests, students are evaluated on what it is they know in mathematics. The resulting evaluation tells students how well they learned the material. The grades they get let them know how “good” they are at math. And yet, this is not necessarily true. Assessments do not fully evaluate students’ mathematical knowledge. Assessments fall short of this, especially in the vision of mathematics that reform movements are calling for. And as students continue to take tests throughout their years in public schools – as they take tests to go to be placed in advanced or remedial classes, tests to enter into college, or to simply just pass their current class – they come to implicitly learn what “counts” as knowing mathematics. Students have come to believe that math is about following rules, answering quickly, and getting the right answer. Interestingly, reform mathematics calls for a shift away from all of these things. However, these reform movements are struggling to take hold in a society that has attached even more high stakes to tests – tests that still reward rule following, answering quickly, and getting the right answer. This paper looks at what reform mathematics calls for and juxtaposes this with what students come to believe about mathematics through assessment. It ends with a discussion of what an alternative, reform mathematics assessment might value and what all of this means for my practice as a teacher.