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Stu­dents ex­am­ine the ra­tio­nale and ped­a­gogy for the ef­fec­tive use of tech­nol­ogy in the mid­dle and high school math­e­mat­ics class­rooms. The tech­nolo­gies con­sid­ered may in­clude graph­ing cal­cu­la­tors, com­puter al­ge­bra sys­tems, spread­sheets, and dy­namic geom­e­try soft­ware.

Students examine the rationale and pedagogy for the effective use of technology in the middle and high school mathematics classrooms. The technologies considered may include graphing calculators, computer algebra systems, spreadsheets, and dynamic geometry software.

This course ex­am­ines the his­tor­i­cal, philo­soph­i­cal, and so­ci­o­log­i­cal foun­da­tions un­der­ly­ing the de­vel­op­ment of Amer­i­can ed­u­ca­tional in­sti­tu­tions. The role of the schools, the aims of ed­u­ca­tion, di­verse learn­ers, the math­e­mat­ics cur­ricu­lum in New York State, legal prin­ci­ples that af­fect ed­u­ca­tion, and the role of state, local, and fed­eral agen­cies will be em­pha­sized.

This course examines the historical, philosophical, and sociological foundations underlying the development of American educational institutions. The role of the schools, the aims of education, diverse learners, the mathematics curriculum in New York State, legal principles that affect education, and the role of state, local, and federal agencies will be emphasized.

This course is an in­tro­duc­tion to num­ber the­ory. Top­ics in­clude di­vis­i­bil­ity (di­vi­sion al­go­rithm, GCD, etc), primes, con­gru­ence, the fun­da­men­tal the­o­rem of arith­metic, qua­dratic rec­i­proc­ity, num­ber the­o­retic func­tions and Fer­mat’s lit­tle the­o­rem. Some ap­pli­ca­tions will be done, which can be com­puter based, to en­cour­age stu­dents to pro­pose and test con­jec­tures. Avatar taken from https://​www.​atm.​org.​uk/​Association-​of-​Teachers-​of-​Mathematics Header taken from https://​www.​win.​tue.​nl/~bdeweger/getalthe­o­rie.html

This course is an introduction to number theory. Topics include divisibility (division algorithm, GCD, etc), primes, congruence, the fundamental theorem of arithmetic, quadratic reciprocity, number theoretic functions and Fermat’s little theorem. Some applications will be done, which can be computer based, to encourage students to propose and test conjectures. Avatar taken from https://www.atm.org.uk/Association-of-Teachers-of-Mathematics Header taken from https://www.win.tue.nl/~bdeweger/getaltheorie.html

This course is de­signed to pre­pare stu­dents for an ad­vanced math­e­mat­ics cur­ricu­lum by pro­vid­ing a tran­si­tion from Cal­cu­lus to ab­stract math­e­mat­ics. The course fo­cuses on the processes of math­e­mat­i­cal rea­son­ing, ar­gu­ment, and dis­cov­ery. Top­ics in­clude propo­si­tional and first order logic, learn­ing proofs through puz­zles and games, ax­iomatic ap­proach to group the­ory, num­ber the­ory, and set the­ory, ab­stract prop­er­ties of re­la­tions and func­tions, el­e­men­tary graph the­ory, sets of dif­fer­ent car­di­nal­i­ties, and the con­struc­tion and prop­er­ties of real num­bers. Avatar and Header im­ages cre­ated using ze­frank’s Scrib­bler toy: http://​www.​zefrank.​com/​scribbler

This course is designed to prepare students for an advanced mathematics curriculum by providing a transition from Calculus to abstract mathematics. The course focuses on the processes of mathematical reasoning, argument, and discovery. Topics include propositional and first order logic, learning proofs through puzzles and games, axiomatic approach to group theory, number theory, and set theory, abstract properties of relations and functions, elementary graph theory, sets of different cardinalities, and the construction and properties of real numbers. Avatar and Header images created using zefrank’s Scribbler toy: http://www.zefrank.com/scribbler

Eng­lish Com­po­si­tion I is a course in ef­fec­tive essay writ­ing and basic re­search tech­niques, in­clud­ing use of the li­brary. Col­lege-level read­ings are as­signed for class­room dis­cus­sion and as a basis for essay writ­ing. CUNY cer­ti­fi­ca­tion in read­ing and writ­ing is the pre­req­ui­site for this course.

English Composition I is a course in effective essay writing and basic research techniques, including use of the library. College-level readings are assigned for classroom discussion and as a basis for essay writing. CUNY certification in reading and writing is the prerequisite for this course.