The New Art and Science of Classroom Assessment. Robert J. Marzano
Understands how specific plant behaviors affect successful reproduction
• Uses empirical evidence and scientific reasoning to explain how and why specific plant behaviors affect successful reproduction
In effect, standards documents typically embed so much content in a single statement that it would be impossible to assess (or teach) all those topics in the amount of time available to teachers. To illustrate, Robert J. Marzano, David C. Yanoski, Jan K. Hoegh, and Julia A. Simms (2013) identify seventy-three standards statements (which they refer to as elements) for eighth-grade English language arts (ELA) within the Common Core State Standards (CCSS; NGA & CCSSO, n.d.a, n.d.b, 2010a, 2010b, 2010c). If we assume an average of five topics embedded in each element, which seems reasonable given the previous example, then we can conclude that eighth-grade ELA teachers must assess and teach 365 topics in a single school year.
This problem is prevalent in every subject area. Figure 1.1 provides a few more examples of standards with embedded topics.
Source for standards: McREL, 2014a.
Figure 1.1: Multiple topics in content standards.
Redundancy
The second problem with standards is that they include a great amount of redundant content. This was one of the findings of Julia A. Simms (2016) in her analysis of the CCSS. To illustrate, consider the topic of “examining claims and evidence.” When examining the eighth-grade CCSS for ELA standards and benchmarks, Simms (2016) finds overlapping aspects of this in seven different standards or benchmark statements. See figure 1.2, which depicts six unpacked ELA standards at the eighth-grade level: RI.8.8, W.8.1b, W.8.1a, W.8.1, SL.8.3, and SL.8.1d.
Source for standards: NGA & CCSSO, 2010a.
Figure 1.2: Overlapping components in ELA standards at the eighth-grade level.
When unpacked, the Common Core standard RI.8.8 has five statements, standard W.8.1b has two statements, and so on. In all, there are twenty-two statements embedded in six standards. Even though these statements employ different phrasing, they pretty much all deal with claims, evidence, and reasoning. While the problem of redundancy might seem to mitigate the problem of too much content, it still adds to the teacher’s workload by requiring him or her to analyze standards in the manner that Simms (2016) exemplifies.
Equivocal Descriptions of Content
The final problem with current standards statements is that many of them are highly equivocal—they are open to a number of possible interpretations. To illustrate, consider the following standard from grade 4 mathematics:
Solve multistep word problems with whole numbers and have whole number answers using the four operations (addition, subtraction, multiplication and division) including division word problems in which remainders must be interpreted. (4.0A.A.3, NGA & CCSSO, 2010b)
While it is clear that the standard’s overall focus is multistep problems with whole numbers and whole-number answers, such problems are very different across the operations for addition, subtraction, multiplication, and division. Consider the following four problems that would appear to fulfill this standard.
1. Addition problem: James wants to paint racing stripes around his room. His room is 11 feet long and 10 feet wide. If James paints a stripe to go around the top and bottom of his room, how many linear feet of racing stripes will he need?
We might represent the reasoning involved in this problem in the following way.
♦ 10 + 10 + 11 + 11 = 42 feet
♦ Top of room = 42 feet
♦ Bottom of room = 42 feet
♦ 42 + 42 = 84 feet
James will need to paint 84 feet of racing stripes.
2. Subtraction problem: Kelly works at her family’s pet store. She put 272 bags of dog food on the shelf. Last week, customers bought 117 bags. How many bags were left? Her parents also need to place an order to buy more dog food when they reach 50 bags. How many more bags can they sell before they need to place a new order?
We might represent the reasoning involved in this problem in the following way.
♦ 272 – 117 = 155 bags remaining
♦ 155 – 50 = ?
♦ 155 – 50 = 105
The family can sell 105 bags before they need to reorder.
3. Multiplication problem: Aidan collects baseball cards. His collection currently includes 48 players. His brother has 4 times as many cards, and his friend has 3 times as many. How many cards do Aidan’s brother and friend have in all?
We might represent the reasoning involved in this problem in the following way.
♦ 48 × 4 = brother
♦ 48 × 3 = friend
♦ Brother = 192 cards
♦ Friend = 144 cards
♦ 192 + 144 = 336 cards
Aidan’s brother and friend have 336 cards in all.
4. Division problem: Libby collects concert shirts. Each shirt costs $12. If Libby has $120, how many concert shirts can she buy? If Libby saved $9 per month, how long would it take her to save enough money to buy that many shirts?
We might represent the reasoning involved in this problem in the following way.
♦ $120 ÷ 12 = 10 shirts
♦ Libby can buy 10 shirts with $120.
♦ $120 ÷ $9 = 13.33
It would take Libby thirteen months and about ten days to save enough money to buy ten shirts.
Clearly the steps in reasoning necessary to solve these problems have some significant differences from type to type. The steps to solving the addition problem are straightforward. Students find the perimeter by adding the length of the sides and then doubling that quantity to account for the two stripes.
The steps to the subtraction problem are more involved. Students first determine the remaining number of bags after 117 are sold. This is quite simple. Students then compute the difference between the remaining number of bags and the threshold number of 50. Although this step involves subtraction, as did the first step, it has a totally new perspective.
The multiplication problem begins with students multiplying two numbers—one for the brother and one for the friend. The next step involves addition.
The division problem involves the most complex set of steps. It begins with a straightforward division task—the total amount of money available divided by the cost of each shirt. The problem then shifts contexts. Students must take the total amount of money available and divide it by an amount of money that Libby can save each month. However, this step also involves dealing with a remainder, which adds complexity.
Looking at the problem types, the subtraction problem is the only one of the four that requires students to perform an operation on a quantity that the directions to the problem do not explicitly state. The division problem is the only one that involves a remainder. One can also make the case that each of the four problems makes some unique cognitive demands simply to understand it.
The reason this standard is equivocal, then, is that it does not make