Assessing for Learning

This article is all about research-based strategies that uses the different levels of mathematical cognition to design assessment items. To develop meaningful assessments, it is helpful to organize expectations of students into cognitive types, or different learning levels. These learning levels include: constructing a concept, discovering a relationship, simple knowledge, comprehension and communication, algorithmic skill, application, and creative thinking. These learning levels describe the different kinds of thinking that are typically required in learning mathematics. they are placed in order according to a learning progression that is meant to help teachers plan instruction.  There are different assessment strategies and designs for each learning level. When students are constructing a concept, give students prompts that require sorting or categorizing. By sorting examples into categories, students display how they have built a concept in their minds. Other approaches for testing the construct a concept learning level include asking students to describe concept attributes and create examples or nonexamples of their own. When students are at the discovery learning level, teachers can require students to report narratives of the experience of discovery. Many times at this level students have used inductive reasoning to make mathematical discoveries and they may have had a personal and unique experience. Students are more likely to understand what they have done after writing it all out. For simple knowledge level’s assessment, think stimulus and response and ask students to respond based on what they remember. Assessment at the comprehension and communication level requires a prompt that induces students to formulate explanations involving literal and/or interpretive understanding of a technical mathematical expression or message. This helps to assess students’ understanding of mathematics and fluency with their use of the relevant mathematical language. To demonstrate algorithmic skill learning, students should be able to recall a sequence of steps and execute the specified mathematical procedure. Teachers need to be sure to emphasize the PROCESS and not the outcome. Students show achievement of application level learning if they demonstrate proficiency deciding how to solve problems. They show that they can decide if a particular situation is an example of a broader mathematical principle or not, exhibiting deductive reasoning. Assessment items at this level should be created to avoid clue words that tell students what they need to do. Assessment design at the application level can also be done using shorter-format problems. To design items that test your students at the creative thinking level, we recommend using synectics, the juxtaposition of seemingly unrelated ideas. Open-ended application prompts is an example for an assessment that can be used to assess creativity. I believe that by adapting and using these strategies in your assessment and test design, students will actually learn from taking the test.  

Kohler, B., & Alibegovi'c, E. (2015). Assessing for Learning. Mathematics Teaching in the Middle School, 20(7), 424-433. Retrieved June 28, 2015, from http://www.nctm.org/Publications/mathematics-teaching-in-middle school/2015/Vol20/Issue7/Assessing-for-Learning/