<![CDATA[The material of sequences and series has many benefits in daily life, so mastery of sequences and series is essential, especially for job selection. This study is based on Didactical Design Research (DDR), which focuses on five twelfth-grade vocational high school students as research subjects. This study uses a methodological framework, which includes three analysis stages: prospective, metapedagogical, and retrospective. The results of this study reveal that: (1) learning obstacles experienced by students are divided into three types, namely ontogenical obstacles, epistemological obstacles, and didactical obstacles; (2) the didactic design developed by the researcher includes hypothetical didactic design 1 (which includes material, examples, and practice questions regarding number arithmetic operations and number patterns), hypothetical didactic design 2 (which includes material, examples, and practice questions regarding arithmetic series and geometric series), and hypothetical didactic design 3 (which contains material, examples, and practice questions regarding types of number series in psychological test questions); (3) Learning obstacles can be overcome by utilizing didactic design; and (4) The empirical didactic design is a synthesis of the material and analysis obtained from hypothetical didactic designs 1, 2, and 3 which have been implemented effectively.]]>
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