Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

Números racionais e estrutura algébrica corpo: problematizando o currículo da formação inicial de professores de matemática <br> Rational numbers and algebraic structure of field: problematizing the curriculum of mathematics teacher education

“…A Tarefa 2 tem como objetivo apresentar a construção lógico-formal dos números racionais enquanto classes de equivalência de pares ordenados de números inteiros, além de explorar a coletividade dos axiomas (WASSERMAN, 2014), fazendo emergir a estrutura algébrica corpo.…”

The Profile of Structure Sense in Abstract Algebra Instruction in an Indonesian Mathematics Education

“…Whereas, Basturk (2010) asserts that evidence and proof are considered to be the most important mathematical activities by mathematicians and mathematical educators, so it is reasonable that in abstract algebra, a proof is the most important part of learning. Algebra and algebraic structures are important aspects of algebraic thinking for students of secondary schools and universities (Wasserman, 2014). Understanding of abstract algebra can influence the teaching of structure in early algebra (Wasserman, 2017) so that the proof structure is the part that must be possessed by a Mathematics pre-service teacher like the students of Mathematics Education Study Program as a teacher candidate in secondary school.…”

“…This question is answered in Novotna & Hoch's (2008) study which revealed that students' difficulties in algebraic structures (abstract algebra) are partly due to a lack of understanding of structural ideas in arithmetic. According to Wasserman (2014), the idea of the basics of algebraic structure in arithmetic properties is important, because it is used to assume certain properties about addition and multiplication. The arithmetic properties are known that they can form the axiomatic foundation of the algebraic structure needed, even in the early stages of algebraic reasoning by manipulating and solving equations (Wasserman, 2014).…”

“…According to Wasserman (2014), the idea of the basics of algebraic structure in arithmetic properties is important, because it is used to assume certain properties about addition and multiplication. The arithmetic properties are known that they can form the axiomatic foundation of the algebraic structure needed, even in the early stages of algebraic reasoning by manipulating and solving equations (Wasserman, 2014). The notion of algebraic structures in human thought is a cognitive process involved in the conceptualization of abstract algebraic structures (Hausberger, 2015).…”

“…Understanding of the structure affects the performance of evidence (Stylianou, Chae, & Blanton, 2006), as in the study of Wasserman (2014) which introduces an approach to introducing group structures and fields through the arithmetic properties needed to solve simple equations for the combined interests of these axioms as an algebraic rationale which is discussed through an example of an abstract group. Exploring the potential aspects of abstract algebra for algebraic teaching in schools (Wasserman, 2016) is a part of the steps taken to help introduce the structure of evidence.…”