series and sequences math and science initiative

#Series and sequences math and science initiative series

National Aeronautics and Space Administration (on its website, cached 11/1/15), ‘Ninety-seven percent of climate scientists agree that climate-warming trends over the past century are very likely due to human activities.’ The ‘human activities’ the scientists refer to are carbon production – the burning of coal to create energy, and the use of oil and gasoline to fuel cars, for example. Global climate change is being caused by man-made carbon emissions. Here’s an example of an inductive argument. ‘Reasoning’ (what Toulmin calls the ‘warrant’) is the analytic, rational explanation that shows how the evidence ‘proves’ (or strongly supports) the argumentative claim.

In this model of inductive argument, ‘evidence’ is made up of a data set, facts, examples analogies, textual references, research, appeals to authority – objective, individual ‘reasons’ that the argumentative claim is likely to be true.

His The Uses of Argument (Cambridge University Press, 1958) laid out the highly influential inductive argument model of Claim – Data – Warrant (Argument-Centered Education typically uses the terms ‘evidence’ instead of ‘data’ and ‘reasoning’ instead of ‘warrant’ – though Toulmin’s original terms are still common, the C-E-R nomenclature sounds to most students less arcane, while naming the very same thing as C-D-W). The most famous name in inductive argumentation over the past 50 years is probably Stephen Toulmin. According to philosopher Anthony Weston, in his A Rulebook for Arguments (Hackett Publ., 2009), ‘In arguments, the conclusion unavoidably goes beyond the premises – that’s the very point of arguing by example, authority, and so on – whereas the conclusion of a valid deductive argument only makes explicit what is already contained in the premises.’ They move from the bottom up, from the particular to the more general. Inductive arguments have reasons that lead to probable but not certain conclusions. The other major category, contrasting with deductive, is the inductive argument. Logicians (i.e., those who study and write about logic) have proliferated the categories of syllogisms to a total of 24 valid types, applying variant terms like ‘not’ and ‘some’ (e.g., ‘Reptiles are not warm-blooded, snakes are reptiles, therefore snakes are not warm-blooded’ and ‘No candy has protein, some of the food on the table is candy, therefore some of the food on the table has no protein.’). The most famous of all syllogisms is the one from the ancient Greek philosophers who originated the form: They lay out a major premise, then a minor premise, followed at the end by a necessary conclusion. Syllogisms are a prominent three-termed, three-step form of deductive argumentation. One fundamental dichotomy in the field separates deductive arguments and inductive arguments.Īccording to Argumentation : Understanding and Shaping Arguments (Strata Publ., 2007), by Hope College professor of communication James Herrrick, ‘ Deductive argumentsare arguments that lead to necessary conclusions when their reasons are true.’ Their ‘reasons’ are often called ‘premises,’ and they typically move top down, from the abstract to the particular: from a general or major premise coupled with a more specific observation (sometimes called a ‘minor premise’), to a conclusion which, if the premises are true, also must be true.

#Series and sequences math and science initiative series

The algebraic number sequences and series unit gives us an opportunity to investigate differences in the basic ‘types of reasoning’ recognized by authorities in argument education. The Common Core Standards took mathematical argument – ‘a line of reasoning that intends to show or explain why a mathematical result is true,’ according to the Encyclopedia of Mathematics Education (Springer Media, 2014) – a step further when in their Standards of Math Practice 3 they require that students demonstrate a proficient ability to ‘construct viable arguments and critique the reasoning of others.’ ‘Explanations should include mathematical arguments and rationales, not just procedural descriptions or summaries’.‘Analyze and evaluate the mathematical thinking and strategies of others’.‘Select and use various types of reasoning and proofs’Īs part of mathematical ‘communications,’ students must be able to:.‘Develop and evaluate mathematical arguments and proofs’.The National Council of the Teachers of Mathematics established five ‘process standards’ for mathematical proficiency, and two of them (40%) are closely connected to argument: ‘reasoning and proof’ and ‘communications.’ As part of mathematical ‘reasoning and proof,’ students must be able to: Mathematics education has over the past 15 years increasingly elevated argumentation.