Role of Student Work in Promoting Understanding and Reasoning

CMP3 features student work implicitly throughout the curriculum. It is intended that students will analyze the work of their peers in every lesson during the Explore and Summarize phases of the lesson. However, if the Standards for Mathematical Practice are to be tested on national assessments, students need opportunities that develop the practices as well as make those practices explicit. To this end, CMP3 uses examples of student work throughout the student editions and teacher support to address the standard: Construct viable arguments and critique the reasoning of others. These examples enhance students’ conceptual understanding, refine their competence with mathematical procedures, and broaden their capacity make sense of situations.

Student work occurs in three places with slightly different purposes. In each case, the examples occur after students have had time to work on the ideas themselves. Student work in CMP3 exemplifies the goals detailed below.

• Connect mathematical ideas within a learning progression Usually located between two Problems, the purpose is to review or summarize strategies just developed and transition into the next Problem.
• Refine student understanding Located within a Problem, some student work serves to refine student thinking, surface alternate strategies, and push students toward some resolution of the mathematical situation. Student work can provide a quicker way to engage students in examining aspects of mathematics that are not easily discovered or noticed. Such examples tend to occur in units that focus on developing algorithms, for example, solving equations.
• Strengthen student understanding of and proficiency with a procedure or concept Student work appears in the ACE exercises in various forms. The purpose is to strengthen students’ mathematical reasoning and skill by situating content in new contexts. Student work in the ACE often involves presenting solutions that include common errors in which students are asked to examine the solution and correct any errors they may find.

Many instances of student work address all three goals. These most often occur within a Problem so that nuances may be explored during the discussions in the Summarize.

For more information about current research on student work carried out by the CMP staff, visit the Student Work in Curriculum Materials Research Project.