<![CDATA[The purpose of this study is to explain the doctrine expectations of learning mathematics. Data was collected through testing, interviews, and documentation. Researchers have designed a virtual learning trajectory (HLT) based on examining the obstacles students face when learning mathematics. Next, a didactic design was developed from HLT. The method of doctrine was implemented, and the results showed that the situation of the three principles expected by researchers was the doctrine of scaffolding strategy. When determining values that correspond to a pattern of numbers, researchers want to learn lessons and provide instructions in the form of education to solve problems. The researcher's expectation of giving other examples of arithmetic progressions when choosing a definition and the arithmetic progression examples help students better understand collaborative learning. The value of the nth term and the sum of the first n math terms are sent to each shirt to confirm the work and interact directly.]]>
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