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There is a growing body of research support for Merrill's First Principles of Instruction. In one study, researchers surveyed 140 students at 89 different higher education institutions and discovered that students were 9 times more likely to report that they had mastered learning the course objectives when First Principles of Instruction were used and when they spent ample time and effort ...
Merrill developed a performance/content matrix which can be used to ascertain the levels of performance that is required for an area of content. [5] The dimension of content consist of four areas: facts, procedures, concepts and principles; while the performance dimension consists of remembering, using and finding. [ 4 ]
The word "algebra" is derived from the Arabic word الجبر al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Al-Khwārizmī, whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing.
Algebra is the branch of mathematics that studies algebraic structures and the operations they use. [1] An algebraic structure is a non-empty set of mathematical objects, such as the integers, together with algebraic operations defined on that set, like addition and multiplication.
Multiple choice questions lend themselves to the development of objective assessment items, but without author training, questions can be subjective in nature. Because this style of test does not require a teacher to interpret answers, test-takers are graded purely on their selections, creating a lower likelihood of teacher bias in the results. [8]
For instance, if one had x×x, the only algebra tile that would complete the rectangle would be x 2, which is the answer. Multiplication of binomials is similar to multiplication of monomials when using the algebra tiles . Multiplication of binomials can also be thought of as creating a rectangle where the factors are the length and width. [2]
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods ...
Since the center of a simple k-algebra is a field, any simple k-algebra is a central simple algebra over its center. In this section, a central simple algebra is assumed to have finite dimension. Also, we mostly fix the base field; thus, an algebra refers to a k-algebra. The matrix ring of size n over a ring R will be denoted by R n.
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