Primary Mathematics Standards for Pre-Service Teachers in Chile

Teaching Mathematics through Concept Motivation and Action Learning

“…In order to develop such proficiency, "teachers should know ways to use mathematical drawings, diagrams, manipulative materials, and other tools to illuminate, discuss, and explain mathematical ideas and procedures" ( [63], p. 33). In Chile, mathematics teachers are expected to "use representations, call on prior knowledge, put forward good questions, and stimulate an inquisitive attitude and reasoning among students" ( [64], p. 37). In Australia, mathematics teachers know how to motivate "curiosity, challenge students' thinking, negotiate mathematical meaning and model mathematical thinking and reasoning" ( [65], p. 4).…”

Using Wolfram Alpha with Elementary Teacher Candidates: From More Than One Correct Answer to More Than One Correct Solution

“…A search for an alternative method in solving a problem may result in the development of a new concept and, in the words of Singaporean educators, "to promote greater diversity and creativity in learning" [26] (p. 17). One of the goals of mathematics education programs in Chile is to make sure "that teachers are able to use a wide variety of tools that allow them to address problems from different points of view" [27] (p. 104). In the age of technology, problem solving can be significantly enhanced by the use of computational experiments as "a clear and attractive alternative to traditional paper-and-pencil skills wherever arithmetic computation is required" [28] (p. 241).…”

“…The candidates need to be informed of what young children are capable of when asking mathematical questions and must have experience and knowledge on how "to deal with difficult questions posed by students" [27] (p. 101). Since questions are the major means that drive the learning of mathematics around the world [23][24][25][26][27][29][30][31][32], such discussions are an important part of the courses taught by the author.…”

“…The candidates need to be informed of what young children are capable of when asking mathematical questions and must have experience and knowledge on how "to deal with difficult questions posed by students" [27] (p. 101). Since questions are the major means that drive the learning of mathematics around the world [23][24][25][26][27][29][30][31][32], such discussions are an important part of the courses taught by the author. An interesting comment, indicative of the traditional view of a mathematics classroom rooted in the false dichotomy between the teacher's and the student's roles in the learning process, was provided by a candidate: "Before this class, I never really thought you could have conversations or open-ended questions when it came to math.…”

“…The importance of providing teachers with more time for taking care of the intellectual advancement of their students was recognized at the outset of the teaching machine movement by Pressey [41] (p. 376), who argued that "mechanical aids are possible which would leave the teacher more free for her most important work, for developing in her pupils fine enthusiasms, clear thinking and high ideas". Such work occurs in the classroom and a teacher wants to be confident that problems students are asked to solve are pedagogically appropriate and satisfy the modern-day worldwide standards [9,[25][26][27][30][31][32]35,42,43].…”