Looking at How Students Reason.

The article focuses on the assessment in teaching used by mathematics teachers to determine whether the lesson was accessible to all students, what the students learned and how one can improve the lesson to make it more effective. The article author was a was a devotee of discovery learning, sometimes called inquiry learning. This instructional approach involves designing learning activities that help students discover concepts and make sense of facts and principles for themselves, rather than relying on textbooks or teacher explanations. Students need to be able to look at mathematical situations from different perspectives. Incorporating student's reasoning into both written assignments and classroom discussions was a crucial step toward making assessment an integral and ongoing aspect of article author's classroom instruction and now it has become a staple of her mathematics teaching. One of the main strategies she uses to assess students' learning is incorporating writing in mathematics assignments. There are many ways to present writing assignments that yield as much information as possible about what students are thinking. Solving mathematics problems often requires making false starts and searching for new approaches. A good technique for assessing students' understanding as well as differentiating instruction is to make an assignment adjustable in some way. Solving mathematics problems often require making false starts and searching for new approaches.