We are developing a course on Logic for high school students, and are seeking to work with teachers who are willing to offer it as a semester long course. We are interested in creating an offering of this course using the Wolfram platform. In this note, we give our rationale for the need for such a course and outline our approach. Interested teachers can get in touch with us via email as specified at the end of this article.
Some elements of logic already appear in secondary school courses, for example, elementary proofs in Geometry, discussion of fallacies in writing courses, etc. Logic, however, is not taught as a standalone topic in most secondary schools today.
It is our belief that logic is important enough to deserve treatment as a standalone topic. First of all, it is essential for many STEM disciplines, and especially for computer science. Logic is important to Computer Science in the same way as Calculus is important to Physics. In modern times, as Computer Science is as important as Physics, it only behooves us to teach Logic at the high school level. More broadly, logic is useful to everyone. For example, in government and politics, logic plays a central role in understanding and analyzing political arguments. Logic is a more relate-able mathematical subject for students who see relationships between people and things but who are uncomfortable reducing everything to numbers.
Logic is closely related to two of the standards for mathematical practice required by Common Core. (1) Reason abstractly and quantitatively: The students are able to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents. (2) Construct viable arguments and critique the reasoning of others: Students can build a logical progression of statements to explore the truth of their conjectures. They justify their conclusions, communicate them to others, and respond to the arguments of others. They can distinguish correct logic or reasoning from that which is flawed, andif there is a flaw in an argumentexplain what it is.
Logic directly supports two of the practices for science and engineering identified by the Next Generation Science Standards. (1) Constructing explanations and designing solutions: The goal for students is to construct logically coherent explanations of phenomena that incorporate their current understanding of science, or a model that represents it, and are consistent with the available evidence. (2) Engaging in argument from evidence: In science, reasoning and argument are essential for identifying the strengths and weaknesses of a line of reasoning and for finding the best explanation for a natural phenomenon. In engineering, reasoning and argument are essential for finding the best possible solution to a problem. Engineers use systematic methods to compare alternatives, formulate evidence based on test data, make arguments from evidence to defend their conclusions, evaluate critically the ideas of others, and revise their designs in order to achieve the best solution to the problem at hand.
We propose that Logic should be a one semester course to be offered to advanced high school students (in grades 11 or 12). The course material will cover two broad topics: propositional logic and relational logic. In the module on propositional logic, we will introduce the students to logical connectives (and, or, not), contrapositives, converses, inverses, counterfactuals, deMorgans laws, truth tables, and simple propositional proofs. The module on relational logic will cover variables and quantifiers, quantifier order, model checking, and simple relational proofs. We will also introduce the distinction between knowing not versus not knowing (i.e., negation as failure), and computer applications such as spreadsheets and general game playing.
We already have available a textbook on logic for high school students that features interactive exercises, a hyperlinked glossary, and online tools such as truth tables, proof editors, and logic-enabled immersive games (see http://logic.stanford.edu/intrologic ). We also provide an annotated slide deck that can be adapted by high school teachers for courses aimed at students or teacher training. Our material is based on experience in teaching Stanford undergraduate students over a period of 20 years, and also in using the same material in a Massively Open Online Course with an enrollment of over 500,000 students.
While our course can be taught in a standalone manner in the current form, we are interested in working with a teacher who can develop a version of this course by leveraging Wolfram's platform. We are open to discussion on how this might be done.
There are three innovative aspects of our teaching of logic as compared to other prevalent approaches: (a) our research has developed new semantics for logic making it much easier to teach; (b) we have new interactive textbook technology that can help the students in learning; (c) we have developed computational metaphor in which the students can immediately apply the logic concepts to solve practical problems.
We are driven by the vision that Logic is an essential skill for succeeding in the 21st century. The time is right to introduce this subject as a stand-alone course in the high school curriculum. In addition to providing necessary mathematical foundation for students who will major in computer science, it will impart students with critical thinking skills that cut across all disciplines.
Interested teachers can get in touch with us at email@example.com and firstname.lastname@example.org.