simpler content and more complex content elaborate on the target content. For example, figure 1.10 shows a proficiency scale for a grade 8 mathematics standard.
Figure 1.10: Proficiency scale for graphing functions at grade 8.
The elements at the 3.0 level describe what the student does essentially as the learning standard states. The 2.0 level articulates simpler content for each of these elements, and the 4.0 level articulates beyond what the teacher taught.
Figure 1.11 shows an individual student’s progress on one topic for which there is a proficiency scale. The student began with a score of 1.5 but increased his or her score to 3.5 over five assessments. The strategy of using formative scores throughout a unit of instruction helps teachers and students monitor progress and adjust if necessary. This is different from summative scores, which represent a student’s status at the end of a particular point in time. To collect formative scores over time that pertain to a specific proficiency scale, the mathematics teacher uses the strategy of utilizing different types of assessments, including obtrusive assessments (which interrupt the flow of classroom activity), unobtrusive assessments (which do not interrupt classroom activities), or student-generated assessments.
Figure 1.11: Student growth across five assessments on the same topic.
For further guidance regarding the construction and use of proficiency scales, see Formative Assessment and Standards-Based Grading (Marzano, 2010a) and Making Classroom Assessment Reliable and Valid (Marzano, 2018). By clearly articulating different levels of performance relative to the target content, both teachers and the students themselves can describe and track students’ progress. They can use a line graph or bar graph of the data to show students’ growth over time.
Figure 1.12 (page 20) shows a student proficiency scale with a self-reflection component for planning. This can help with the strategy of charting student progress as a student sets a goal relative to a specific scale at the beginning of a unit or grading period and then tracks his or her scores on that scale. At the end of the unit or grading period, the teacher assigns a final, or summative, score to the student for the scale.
Figure 1.12: Student proficiency scale for self-rating and planning.
Visit go.SolutionTree.com/instruction for a free reproducible version of this figure.
We recommend that teachers use the scale in figure 1.13 to rate their current level of effectiveness with element 2, tracking student progress.
Figure 1.13: Self-rating scale for element 2—Tracking student progress.
Element 3: Celebrating Success
Celebrating success in the mathematics classroom should focus on students’ progress on proficiency scales. That is, teachers should celebrate students for their growth. This may differ from what teachers traditionally celebrate in the classroom. For instance, a teacher might be used to celebrating how many mathematics problems students can answer correctly in three minutes, the winner of math drills, or how well students perform on a standardized test. While there may be benefits to these types of celebrations, they are not as conducive to reliable measurement as progress on a proficiency scale, which allows the teacher to celebrate knowledge gain—the difference between a student’s initial and final scores for a learning goal. To celebrate knowledge gain, the teacher recognizes the growth each student has made over the course of a unit. Mathematics teachers can also use the strategies of status celebration (celebrating students’ status at any point in time) and verbal feedback (emphasizing achievement and growth by verbally explaining what a student has done well) throughout the unit.
Figure 1.14 presents the self-rating scale for element 3, celebrating success.
Figure 1.14: Self-rating scale for element 3—Celebrating success.
GUIDING QUESTIONS FOR CURRICULUM DESIGN
When teachers engage in curriculum design, they consider this overarching question for communicating clear goals and objectives: How will I communicate clear learning goals that help students understand the progression of knowledge they are expected to master and where they are along that progression? Consider the following questions aligned to the elements in this chapter to guide your planning.
• Element 1: How will I design scales and rubrics?
• Element 2: How will I track student progress?
• Element 3: How will I celebrate success?
Summary
Providing and communicating clear learning goals involves three elements: (1) providing scales and rubrics, (2) tracking student progress, and (3) celebrating success. In the mathematics classroom, how teachers state these learning goals can make the difference between students reaching proficiency or not. They can support students in thinking in complex ways about mathematics, but only if they are communicated in a way that students understand and that inspires them to solve problems. Tracking student progress and celebrating success is not only important in the classroom but crucial in mathematics, as students are continually pursuing perseverance in problem solving and need support and affirmation to help them along the way.
CHAPTER 2
Using Assessments
The second design area from The New Art and Science of Teaching framework involves the use of effective assessments. Some mathematics teachers use assessments only as evaluation tools to quantify students’ current status relative to specific knowledge and skills. While this is certainly a legitimate use of assessments, the primary purpose should be to provide students with feedback they can use to improve. When mathematics teachers use assessments to their full capacity,
