These strategies involve Meta-cognitive (Self- Evaluation), Motivational (Goal Setting and Planning, Rehearsing and Memorizing, Organizing and Transforming), and Behavioral (Environmental and Structuring) processes of self-regulated learning. Thus, high self-regulated learners have used powerful self-regulated strategies in regulating their learning to attain high academic mathematics performance. The learners’ high level of self- regulation has also significant relationship with logical/ mathematical intelligence, and high academic performance in mathematics. It was found out that students with high self-regulation utilized higher frequencies of self-regulation strategies compared to their low self-regulated peers. A Pearson Correlation using SPSS 23.0 also unravel the significant correlation between high level of academic self-regulation and logical/ mathematical intelligence, as well as the academic mathematics performance. A qualitative method was used to delve into the different self-regulated strategies of high and low self-regulated learners. The respondents of the study were grade 10 students comprised of fifteen (15) high self-regulated and fifteen (15) low self-regulated learners of Bulak National High School, in the Cebu Province Division for school year 2016- 2017. Hence, this study looked into the self-regulated learning strategies, multiple intelligences, and academic mathematics performance of high and low self-regulated learners. These processes embodied the students’ self-regulated learning. To define a sequence by recursion, one needs a rule, called recurrence relation to construct each element in terms of the ones before it.ABSTRACT Mathematics education experts elaborate that motivational, meta-cognitive, and behavioral processes are as important as cognitive processes of students’ mathematics learning. This is in contrast to the definition of sequences of elements as functions of their positions. Sequences whose elements are related to the previous elements in a straightforward way are often defined using recursion. In mathematical analysis, a sequence is often denoted by letters in the form of a n, but it is not the same as the sequence denoted by the expression.ĭefining a sequence by recursion The first element has index 0 or 1, depending on the context or a specific convention. The position of an element in a sequence is its rank or index it is the natural number for which the element is the image. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6. Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.įor example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. The number of elements (possibly infinite) is called the length of the sequence. Like a set, it contains members (also called elements, or terms). In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. For other uses, see Sequence (disambiguation). For the manual transmission, see Sequential manual transmission.
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