Assessing for Learning

Assessing for Learning

Sue Pawula

Summary

This is a report on research-based strategies using levels of math cognition to create and improve assessment design and practice in the classroom.  The strategies were applied to warm-up formative assessments, informal questioning, classroom discussions, practice problem sets, evaluation and feedback, and some summative assessments, such as unit tests, projects, and quizzes.  The design of these assessments was based on Cangelosi’s seven cognitive learning levels: construct a concept, discover a relationship, simple knowledge, comprehension and communication, algorithmic skill, application, and creative thinking.   These are designed with consideration for typical mathematical thinking and are ordered according to levels of perceived learning progression.  Students usually construct a concept and discover relationships before proceeding to simple knowledge and algorithmic skills.  As students progress in understanding they must also be able to express this knowledge through formal notation and vocabulary as their comprehension deepens.  Instructional integration of comprehension and communication learning will prepare students for the deductive thinking required for application and allow them to acquire the knowledge to become creative mathematical problem solvers.  Creating a rubric will make teacher evaluation of student progress easier and provide the student with meaningful and useful feedback.  When measuring the “construct a concept” learning level on the assessment, teacher could require students to sort or categorize since that can help display concepts and connections they have acquired. Another way to show this could be asking students to describe concept attribute as well as creating example of them or non-examples to show acquisition.  To evaluate their “discover a relationship” learning level, it is best to prompt them to recall something similar and write about it, since that will indicate that the thoughtfully doing a discovery activity is valued as much as knowing the answer.  “Simple knowledge” should be measured through a simple recall question and can be modified as they progress to become a “comprehension and communication” level item by asking them to explain the method.  “Algorithmic skill” can be evaluated through requirements to recall the steps and follow the mathematical procedures. “Application” can be evaluated through students’ demonstration in their ability in deciding how to solve problems. Evaluating “creative thinking” will require some synectic work where the teacher, through little spontaneous and playful exchanges with the students, sparks their curiosity and creativity.  It can also be assessed through open-ended application prompts.  When teachers design tests with rubrics that explicitly tell the students the expectations, they will actually learn from their errors.

Reflection

Designing meaningful assessment for students is equally as important as the daily instruction.  When they are evaluated in a format that gives them meaningful feedback, they are more inclined and able to learn from their mistakes since they will know what is expected and how to improve their level of learning.  However, we always need to individualize not only our instruction but also our evaluation process.  We cannot evaluate every student the same even when using the same rubric.  We always have to keep in mind: “What did the student know at the start?  Have they made progress?  How much progress is enough?  What level should be their next goal?”  When we keep these questions in mind then we truly will make the rubrics meaningful to each and every student. Cangelosi’s seven cognitive learning levels are great building blocks to use as we make rubrics for our students because they can work as the base from which to build these meaningful rubrics.

Kohler, B., & Alibegovic, E. (2015).  Assessing for learning. Mathematics Teaching in the Middle School, 20(7), 424-433.