CMP provides a variety of tools for student assessment. These assessments fall into the three broad categories of Checkpoints, Surveys of Knowledge, and Observations.
Some of the assessment tools give teachers and students an opportunity to check student understanding at key points in the Unit. Checkpoints help students solidify their understanding, determine the areas that need further attention, and help teachers make decisions about whether students are ready to move on.
By assigning ACE exercises as homework, teachers can access each students’ developing knowledge of concepts and skills. Mathematical Reflections questions can help teachers assess students’ developing conceptual knowledge and skills in the investigation. The Looking Back can be used as a review, helping students to stand back and look at the “big” ideas and connections in the Unit.
Many teachers also require their students to keep organized notebooks, which include homework, notes from class, vocabulary, and assessments. Each Unit includes a checklist to help students organize these notebooks before they turn them in for teacher feedback. For classes using Student Place, homework, class notes, and vocabulary are all part of the ACTIVe-book. Teachers can also assess student understanding during their study of the Unit by examining their work or summaries for particular Problems.
Surveys of Knowledge
Check-ups, quizzes, tests, self-assessments, and projects provide teachers with a broad view of student knowledge both during a Unit and at the end of a Unit.
Check-ups are short, individual assessment instruments. Check-up questions tend to be less complex and more skill-oriented than questions on quizzes and Unit tests. These questions provide insight into student understanding of the baseline mathematical concepts and skills of the Unit. Student responses to Check-ups can help teachers plan further instruction for the Unit.
Each unit has at least one partner quiz. Quiz questions are richer and more challenging than checkup questions. Many quiz questions are extensions of ideas students explored in class. These questions provide insight into how students apply the ideas from the Unit to new situations. The quizzes were created with the following assumptions:
- Students work in pairs.
- Students are permitted to use their notebooks and any other appropriate materials, such as calculators.
- Pairs have an opportunity to submit a draft of the quiz for teacher input. They may then revise their work and turn in the finished product.
Each Unit includes a test that is intended to be an individual assessment. The test informs teachers about a student’s ability to apply, refine, modify, and possibly extend the mathematical knowledge and skills acquired in the Unit. Some of the questions draw on ideas from the entire Unit, while others are smaller, focusing on a particular idea or concept. Some of the questions are skill oriented, while others require students to demonstrate problem-solving abilities and more in-depth knowledge of the Unit concepts. Teachers can use holistic scoring techniques and rubrics that take into account the many dimensions addressed by the test.
After every Unit, students complete a self-assessment, summarizing the mathematics they learned in the Unit and the ideas with which they are still struggling. The self-assessment also asks students to provide examples of what they did in class to add to the learning of the mathematics. The goal of this activity is to have students reflect on their learning. For many students, self-assessment is a new experience, and they may struggle with this at first. However, by receiving feedback from teachers and using other students’ work as models, students can learn to reflect on their own progress in making sense of mathematics.
At least three Units in each grade include projects that can be used to replace or supplement the Unit test. Projects give teachers an opportunity to assign tasks that are more product/performance-based than those on traditional tests. Project tasks are typically open-ended and allow students to engage in independent work and to demonstrate broad understanding of ideas in the Unit. Through students’ work on the projects, teachers can gather information about their disposition toward mathematics. Project guidelines, student examples, and scoring rubrics appear in the Unit Project section of the Teacher Support. The table on the next page gives locations and descriptions of projects by grade level.
The curriculum provides teachers with numerous opportunities to assess student understanding by observing students during group work and class discussions. Many Problems provide the opportunity to observe students as they “do mathematics,” applying their knowledge, exhibiting their mathematical disposition, and displaying their work habits as they contribute to group tasks. The summary portion of each Problem and the Mathematical Reflections at the end of each Investigation provide ongoing opportunities to assess students’ understanding through class discussions. This type of observation as a form of assessment is important, since some students are better able to show understanding in verbal situations than in formal, written assignments. Teachers may also receive feedback from parents—who may comment on their child’s enthusiasm or involvement with a particular Problem—and from students who may observe that another student’s method is more efficient or useful, or who may offer an important observation, conjecture, or extension.