Give a series of examples and non examples about {{Topic}} along with teacher wording for each. Follow these principles, but do not refer to them explicitly. Simply write the script for the teacher (explanations and questions) along with the examples the teacher should use. Write your response in {{Language}}.

###Principles:
A key idea is that students need to see only relevant contrasts not arbitrary differences. In other words, when teaching a concept, the differences shown to a student should highlight the specific quality that defines that concept. A non-example should be almost identical to the example, differing only in the defining feature otherwise, students might focus on the wrong thing. Engelmann and Carnine developed five principles to do this:

1. The Wording Principle: To keep instruction clear, teachers should use consistent or nearly identical wording across examples. This minimises distractions and helps students focus on key details. Here, one pair maintains consistent wording, while the other introduces unnecessary variation, causing confusion.
Following the wording principle:
3/2
The larger number is on top
2/3 
The smaller number is on top

Not Following the wording principle:
3/2
The larger number is on top
2/3 
The larger number is on bottom


2. The Setup principle: When introducing a new concept, examples and non-examples should be as similar as possible, differing only in the critical feature. If unnecessary differences exist, students may misinterpret the rule. Figure 2.2 demonstrates this: in the incorrect example, multiple differences create ambiguity—students might mistakenly associate the concept with shape, color, or position. Without careful control of contrasts, learning becomes guesswork rather than clarity. Direct Instruction prioritises precision to eliminate confusion.

Following the setup principle:
+++|+++
This did not get wider
+++|++++
This got wider

Not Following the setup principle:
+++|+++
This did not get wider
+++|^^^^
This got wider


3. The Difference Principle. Positive and negative examples are most effective when they differ only slightly, but for this distinction to be clear, they must be presented consecutively. Without direct comparison, the key difference is less obvious, and the learner may fail to recognize the defining feature. Juxtaposition ensures that critical distinctions are immediately noticeable, reinforcing accurate concept formation.

Following the Difference principle:
+++ | ++++
This got wider
+++ | +++
This did not get wider

Not Following the Difference principle:
+++ | ++++
This got wider
aaa | aaa
This did not get wider


4. The Sameness principle. To emphasize sameness, examples should be highly different yet share the same label. Here, various instances of "wider" are shown—some are +s some are ^s, some go from three to four, some go from four to five. Despite these differences, the label remains the same, reinforcing that changes do not alter the meaning of "wider." The examples follow the wording principle (consistent phrasing), setup principle (same objects), and sameness principle (varying examples with the same label). By juxtaposing diverse cases, learners see that observed differences are irrelevant to the concept being taught.

Example
Teacher Wording
+++ | ++++
This got wider
++++ | +++++
This got wider
^^^ | ^^^^
This got wider
^^^^ | ^^^^^
This got wider


5. The Testing principle. To test learning, examples should be juxtaposed without a predictable pattern. After students see sameness and difference, they are tested on their ability to apply these generalizations. The immediate test follows the same setup as the demonstration, ensuring they grasp the key distinctions. If successful, expansion tests introduce new wording and contexts. The key question is: Can the learner apply the concept to new examples within the original setup? To avoid cueing responses, test examples should vary unpredictably—some familiar, some new, with no alternating patterns. In the example below, the answers that follow the testing principle are no, no, yes, yes, no, no, yes, whereas in the column that does not follow the testing principles, the answers vary predictably, between yes and no.

Following the testing principle
Not following the testing principle
2/4 Is this an improper fraction?
4/3 Is this an improper fraction?
3/5 Is this an improper fraction?
3/5 Is this an improper fraction?
8/5 Is this an improper fraction?
8/5 Is this an improper fraction?
48/32 Is this an improper fraction?
15/32 Is this an improper fraction?
18/12 Is this an improper fraction?
18/12 Is this an improper fraction?
6/7 Is this an improper fraction?
6/7 Is this an improper fraction?
9/3 Is this an improper fraction?
9/3 Is this an improper fraction?





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