The Common Core State Standards for Mathematics provide teachers with guidance on how to promote mathematical practices that emphasize reasoning and justification through problem solving and that encourage an exploration of viable strategies, through mathematical modeling and facilitating communication in the classroom, to critique

mathematical arguments (National Governors Association, 2010).

We are sympathetic to an ethical preference for not treating discrimination as a good, but we are somewhat puzzled by the author's

mathematical argument.

About 280 B.C., he noted the size of the shadow cast by Earth on the Moon and, following a correct line of

mathematical argument, estimated that the Moon was a body with a diameter one-third that of the Earth.

The reason is that in examining a

mathematical argument, the symbols are divorced from any meaning, and we examine only the formal correctness of the mathematics.

But Why Does It Work?:

Mathematical Argument in the Elementary Classroom

Evolution by the numbers; the origins of

mathematical argument in biology.

Furthermore, the materials helped his group to see the problem clearly and they developed their

mathematical argument in a strategic and organised manner.

WM: 5.75--Students follow a formal

mathematical argument of several steps presented by the teacher, such as Pythagoras' theorem.

We must commit to conjecture and prove or disprove said conjecture; we must do in order to learn; through real inquiry learning is achieved, and hence this paper proposes an archetype of mathematical pedagogy such that the experience of doing a

mathematical argument is the reason enough for an exercise and inquiry-based learning (IBL) enacted via a modified Moore method (MMM) is an authentic way to actualise a learning environment where the content studied is the centre of the experience.

Wakeley (Harvard U.) approaches coalescent theory primarily from the biological end, and assumes most readers are biologists, but gives full due to the

mathematical argument without losing non-experts.

In a book-length

mathematical argument that has been percolating through the set theory community for the last few years, Woodin has proved--apart from one missing piece that must still be filled in--that elegant axioms do exist and, crucially, that every elegant axiom would make the continuum hypothesis false.