and procedural knowledge. We believe this distinction is critical simply because assessments should reflect the type of knowledge on which they focus. We describe how to do this in chapter 3 (page 43).
For now, suffice it to say that different subject areas have differing proportions of declarative and procedural knowledge. To illustrate, we consider a McREL (2014b) study in which researchers analyze the standards in fourteen different subject areas and determine the distributions of declarative and procedural knowledge in those subject areas. They updated their analysis in 2008, producing the results we depict in table 1.1.
Table 1.1: Standards Relating to Percentages of Declarative Versus Procedural Knowledge
| Subject | Declarative | Procedural |
| Mathematics | 139 | 84 |
| ELA | 86 | 254 |
| Science | 253 | 8 |
| History | 1,240 | 41 |
| Geography | 230 | 8 |
| Arts | 147 | 122 |
| Civics | 426 | 1 |
| Economics | 159 | 0 |
| Foreign Language | 52 | 56 |
| Health | 121 | 15 |
| Physical Education | 47 | 58 |
| Behavioral Studies | 100 | 0 |
| Technology | 106 | 38 |
| Life Skills | 67 | 241 |
| Total | 3,173 (77.41 percent) | 926 (22.59 percent) |
Note: Procedural and contextual have been combined.Source: McREL, 2014b.
Notice that, in general, there are far more declarative standards than procedural standards. More specifically, 77 percent of the standards in this study involve declarative content, and 23 percent involve procedural content. That noted, there is some significant variation from subject area to subject area. For example, physical education, life skills, arts, and foreign language are about equal in terms of their distribution of declarative and procedural content, whereas behavioral studies and economics have no procedural content.
A Small List of Measurement Topics
Ultimately, the purpose of analyzing and restating standards is to identify a relatively small set of measurement topics as the subject of classroom assessment and instruction. This list constitutes the assessment-friendly curriculum that is essential for a new paradigm of classroom assessment.
Developing the assessment-friendly curriculum is somewhat of a value-driven decision, but research guidance does exist. Specifically, Simms (2016) finds that if one removes the redundancy in standards and considers only those that national assessments typically contain, then the list of essential measurement topics is quite small. Table 1.2 reports the number of essential topics in mathematics, science, and ELA.
Table 1.2: Essential Topics in Mathematics, Science, and ELA
Source: Simms, 2016.
The list of essential measurement topics is available in The Critical Concepts (Simms, 2016). Educators can use this list as a starting place as they translate their local or state standards into measurement topics. As we indicate in table 1.2, there are a relatively small number of measurement topics at each grade level or grade-level span. For example, consider fifth grade. There are fourteen essential measurement topics in mathematics, ten in science, and fifteen in ELA. Contrast this with the seventy-three topics from the Common Core State Standards for ELA at the eighth-grade level, which we discussed previously.
Narrowing down all the content in state and national standards into a small set means that the measurement topics will not include all content. What, then, do we do with all this leftover content? There are two basic approaches to answering this question: (1) relying on incidental learning and (2) creating a supplemental measurement topic.
Relying on Incidental Learning
Incidental learning is a largely untapped resource that teachers can leverage to enhance content coverage in a classroom that focuses on standards. To understand how this works, assume that a teacher was working with the following ten measurement topics in fourth-grade science.
1. Energy
2. Motion
3. Light and vision
4. Waves
5. Geographic features
6. Earth changes
7. Natural hazards
8. Natural resources
9. Plant needs
10. Animal needs
As we have discussed, national, provincial, state, and local standards documents would surely contain many other topics like Earth’s history, human impacts on resource use, and scientific contributions throughout history. Even though the measurement topics do not specifically include these topics, the teacher might integrate the content into instruction formally or informally. Formally means that the teacher actually plans for direct instruction in the supplemental content. Informally means that the teacher does not plan for direct instruction in the content but addresses it if it comes up naturally during class. For example, while discussing the topic of different methods of energy production, which is part of the measurement topic energy, the teacher might remember that the supplemental topic of human impact on resource use also applies to the example he or she is providing. This approach inserts additional content into the instructional process but doesn’t necessarily assess that content.
Relying on incidental learning mitigates the common misconception that if a teacher doesn’t test on it, then students don’t learn it. While it is true that students stand a better chance of remembering content they’ve taken tests on, it is also true that brief exposure to content gives
