Summative assessments need to be aligned with the desired outcomes of instruction. If “off the shelf” tests focus on skills and procedures, they will fail to demonstrate students’ problem solving skills and other impacts of robust instruction. This is at best is demoralizing; worse, since testing often drives instruction, using such tests may have a significant negative impact on instruction.
Recognizing this, the Mathematics Assessment Project designed a series of “novice,” apprentice,” and “expert” tasks dealing with grade 6-10 mathematics. Novice tasks explicitly test particular items of content knowledge. Expert tasks are far less structured, requiring strategic problem solving skills in addition to content knowledge: in these tasks students face significant sense making demands and have great latitude with regard to the choice of methods. Apprentice tasks lie in-between the two. Their problem statements provide enough scaffolding so that students, while still required to do problem solving, are oriented in the direction of productive approaches. A “balanced diet” of Novice, Apprentice and Expert tasks is needed to properly assess the Mathematical Practices.
A collection of 94 summative tasks can be found at http://map.mathshell.org/tasks.php. Each task includes a scoring rubric, a set of pre-scored sample student work, and the same set of work without the scores. (Scoring practice for this type of task can be an effective professional development activity.) These tasks can be used whenever it seems appropriate, during the year. The MAP team has also compiled a number of end-of-year tests, with accompanying scoring rubrics. Those are available at http://map.mathshell.org/tests.php.