The Math Trailblazers Assessment Program serves the following purposes:
- It provides information to teachers about what students know and can do. This information is used to guide instruction. An activity may help teachers answer questions about whole-class instruction: What do I do next? In the next minute? Next lesson? Next class? Next unit? Other assessments may help teachers decide how to support individual students, including those who struggle with a concept and those who are ready to be challenged.
- It communicates the goals of instruction to parents and students. What teachers choose to assess communicates to the class what they value. For example, if teachers want students to work hard at communicating problem-solving strategies, then it is important to assess mathematical communication.
- It provides feedback to students and parents about student progress. This includes teacher evaluation of student progress as well as students’ assessment of their own progress.
The following components of the assessment program provide teachers with the tools to plan instruction and communicate student progress on the mathematical content.
Key Mathematical Ideas and Expectations
The mathematical content in Math Trailblazers is organized around a set of Key Ideas. These Key Ideas are based on the National Council of Teachers of Mathematics (NCTM) Standards for the grade band as well as current thinking in the mathematics education community, e.g., Charles (2005), NCTM (2000), and Van de Walle (2006). There is a set of Key Ideas for each content strand: Number, Algebra, Geometry, Measurement, and Data. They are based on “big ideas” in mathematics and describe what students should be able to do within each strand. The Key Ideas are shown in the table in Figure 1.
To monitor students’ growth across and within grades, there is a set of Expectations that describe what students are “expected” to do within each content strand. Expectations show the growth of the mathematical content within the Key Ideas for each strand.
Content Expectations. Because all the Algebra Key Ideas arise from and are closely connected to ideas in the other content strands, Expectations related to algebra will also be listed under a second content strand. The Content section of the Key Assessment Opportunities Chart identifies some of the activities in the unit that are appropriate for assessing students’ abilities with the expectations. See Figure 2. The Math Facts section of the same chart identifies activities in the unit that are appropriate for assessing students’ math facts strategies.
Figure 2: Key Assessment Opportunities Chart with Benchmark Expectations Circled
Benchmark Expectations. Some of the Expectations might be prioritized as Benchmark Expectations because they are particularly important concepts and skills to be learned in the unit. Benchmark Expectations identify the concepts and skills that are central to the unit, are prerequisites for learning content in an upcoming unit, are the last significant opportunity for assessment in the curriculum or grade, or are concepts commonly associated with difficulties or misconceptions. Benchmark Expectations are clearly indicated on Expectation lists in each unit.
Math Practices Expectations. Students use the Math Practices Expectations on the Math Practices page in the Student Guide Reference section to help them focus on practices related to both problem solving and communication. See Figure 3. Students become more comfortable with these Expectations by reviewing them before, during, and after solving a problem and by deciding how well they are met in their work and the work of others. The Math Practices section of the Key Assessment Opportunities Chart identifies activities in the unit that are appropriate for assessing students’ use and development of the math practices.
Figure 3: Math Practices
Tools for Feedback and Monitoring
Feedback Boxes. Feedback Boxes are provided with several activities to report progress toward the Expectations. Small black squares on the Unit 11 Key Assessment Opportunities Chart indicate assessments with Feedback Boxes. See Figure 2. Figure 4 shows a Feedback Box. In this unit, students will also get better acquainted with the Math Practices Expectations by discussing them in the context of a specific problem, receiving feedback, and revising their work.
Figure 4: Sample Grade 3 Content and Math Practices Feedback Box
Monitoring Progress. Progress can be monitored and reported over time using assessment tools (Unit Assessment Records, Unit Individual Assessment Records, Math Facts Class Record), and by collecting reviewed student work samples in a portfolio.
- Unit Assessment Record. See Figure 5. Use this vehicle to record student progress on each of a unit’s Content Expectations. The Key Assessment Opportunities Chart as shown in Figure 2 identifies activities within each lesson that are appropriate for assessing each Expectation in the unit.
Figure 5: Unit Assessment Record for Grade 3 Unit 11
- Unit Individual Assessment Record. See Figure 6. Upon completion of each unit, transfer information from the Unit Assessment Record to Individual Assessment Records. This latter tool becomes a compilation of the progress for each student across the units.
Figure 6: Individual Assessment Record for Grade 3 Unit 11
- Math Facts Class Record. See Figure 7. Use this tool to track the progress of students’ fluency with the fact groups that are practiced and assessed in the Daily Practice and Problems.
Figure 7: Grade 3 Math Facts Class Record
Using Assessment to Meet Individual Needs
The explicit Expectations and assessment tasks in each unit describe what it means to “get it.” Providing feedback on these Expectations helps identify students who need to access the content another way, need further practice opportunities, or are ready to extend or deepen their understanding of a concept. Instructional opportunities that help support the varied needs of students also need to be identified. These opportunities provide models that can be replicated or used multiple times and can be used in a variety of settings (e.g., home, transitions, support classroom, as a center).
Targeted Practice. Every unit provides opportunities for additional targeted practice for some of the Expectations. These opportunities connect directly to assessment tasks so the practice can be tailored to the current level of student progress.
- For students who are struggling with the Expectation, practice is targeted toward the foundational concepts and skills involved and often provides a different way to access the content.
- For students who are making significant progress toward the Expectation, practice is designed to help move toward proficiency and autonomy.
- For students who are already meeting the Expectation, opportunities are provided to deepen or extend understanding.
See a sample of opportunities for targeted practices from Grade 4 Unit 3 in the table in Figure 8.
Figure 8: Expectations for Grade 4 Unit 3 with opportunities for targeted practice
Workshops. Much of the targeted practice is in Workshops, which provide a menu of activities that revisit key concepts and skills developed earlier in the unit. Based on students’ self-assessment of their confidence with Expectations, students select activities from a Workshop Menu. See Figure 9 for a sample Self-Check Question and Workshop Menu. Teacher guidance can help students find the appropriate level of practice based on evidence from earlier assessment tasks. The menu describes practice tailored to the needs of individual students for specific Expectations.
Figure 9: Self-Check Question and Workshop Menu for Grade 5 Unit 4 Lesson