Program Cover Document --- MAT 117 Discrete Math for Middle School Teachers

Transcription

1 Prgram Cver Dcument --- MAT 117 Discrete Math fr Middle Schl Teachers I. Learning Gals Currently, this curse is nt a part f any prgram ffered by the Department f Mathematics & Statistics. It is ne f a series f curses ffered t meet the needs f Elementary Educatin majrs wh wish t btain the New Jersey middle schl subject matter endrsement in mathematics. This requires 15 credits in mathematics and passing the Middle Schl Mathematics Praxis exam. Many students wh have taken MAT 105 and/r 106, curses required fr elementary educatin majrs, wish t cntinue their study f mathematics in rder t btain the endrsement and teach mathematics in grades 6-8. Teaching mathematics effectively at the middle grades requires that teachers have a deep and prfund understanding f the K-12 mathematics curriculum. The main gal f these curses is t enable middle grades teachers t develp an advanced viewpint f the mathematics that they will teach. Each curse in the series f curses that are ffered t middle schl mathematics teachers is fcused n a particular cntent strand frm the New Jersey Cre Curriculum Cntent Standards (NJCCCS). The ther curses are MAT 111, Number Thery and Systems fr Middle Schl Teachers, MAT 112, Data Analysis & Prbability fr Middle Schl Teachers, MAT 114, Patterns, Functins & Algebra fr Middle Schl Teachers, MAT 115, Gemetry fr Middle Schl Teachers, and MAT 118, Calculus cncepts fr Middle Schl Teachers. Althugh Discrete mathematics is part f the Data Analysis, Prbability, and Discrete Mathematics strand in the NJCCCS, there are nt many middle schl teachers wh have experience with Discrete Mathematics r even knw what it is. It is a tpic that has nt traditinally been taught in K-12 until the creatin f the NJCCCS in Discrete mathematics encmpasses many mathematical tpics and has many applicatins t real life prblems. This curse will allw future middle schl mathematics teachers t explre this exciting tpic in mre depth and learn hw t address the Discrete Mathematics Standards in their classrms. II. Student Assessment Assessment in this curse is similar t the assessment dne in the prerequisites, MAT 105 and 106. Preservice teachers can demnstrate their cntent knwledge thrugh a variety f assessment methds that require them t slve prblems, explain their reasning, and use mathematical representatins. III. Learning Activities Middle schl mathematics curricula are used as a basis fr in-depth study f the mathematics cntent in all f the curses. Many class sessins are devted t discussins f the mathematics cntent and the develpment f the mathematical cncepts and skills necessary in the mathematical educatin f middle-schl grades. Other class sessins cnsist f hands-n experiences in rder fr the teachers t learn hw t use cncrete manipulative materials, pictrial mdels, and technlgy in the develpment f the mathematical cncepts fr middle-schl grades. Students are expected t cmplete readings, and prepare prjects and/r assignments that are apprpriate fr the curse. Using middle schl mathematics curricula as mtivatin fr in-depth study f the mathematical cncepts cnnects the curse cntent t the middle schl classrm. Teachers appreciate that what they are learning is relevant t their teaching. Teachers must experience standards-based teaching and learning in rder t understand hw t implement it. A variety f strategies and methds f instructin shuld be used t mdel effective teaching f mathematics.

2 Departmental Curse Syllabus MAT 117 Discrete Math fr Middle Schl Teachers I. Basic Infrmatin A. Purpse statement: Teaching discrete mathematics effectively at the middle grades requires that teachers have a deep and prfund understanding f the discrete math that is part f the K-12 curriculum. The main gal f this curse is t enable middle grades preservice teachers t develp an advanced viewpint f the discrete mathematics that they will teach. The curse is geared tward elementary educatin majrs wh wish t get the New Jersey subject matter endrsement in mathematics t teach in grades 6-8. B. Curse descriptin: This curse gives the middle schl mathematics teacher a deeper understanding f discrete mathematics. Physical materials, mdels, technlgy, and middle schl curricula will be used t explre these tpics. Explratin f ways t engage middle schl students meaningfully in experiences that lay a strng fundatin fr mre frmal wrk in discrete math will be integrated with the mathematics cntent. C. Curse prerequisites: MAT 105 r 106 r by permissin f Math Educatin crdinatr II. Learning Gals A. Cntent gals: Teachers will engage in a thrugh develpment f the cncepts and methds f slving prblems in discrete mathematics. Thrugh this prcess, they will develp understanding f the prcesses and algrithms fund in middle schl mathematics and discver purpses beneath the symbls and techniques. Many students will enter the curse with the miscnceptin that mathematics is all abut cmputatin and fllwing prcedures. Thrugh careful cnsideratin f many types f prblems fund in NSF-refrm curricula, such as Cnnected Math, and alternative algrithms, students will cme t understand that mathematics is much mre than cmputatin, and that there is ften mre than ne apprach t slving any prblem. Many students will als enter the curse withut any knwledge f what discrete mathematics is, and they will gain an understanding f the subject and all the tpics it encmpasses. B. Perfrmance gals: By the cmpletin f the curse, the successful student will be able t demnstrate all f the fllwing: Deeper understanding f the cncepts, prcesses and algrithms, and the purpses beneath them, fund in the middle schl mathematics curriculum, with a fcus n discrete mathematics. Imprved ability t cmmunicate mathematical ideas apprpriately using the language f mathematics. Imprved ability t reasn mathematically and begin develping mathematical prfs. Willingness and ability t slve varius types f mathematical prblems invlving discrete mathematics using apprpriate strategies. T strengthen knwledge f the many relatinships f discrete mathematics t ther subjects, their applicatins in sciety, and relatinships within mathematics itself. Increased understanding f natinal and state standards relating t discrete mathematics

3 T strengthen knwledge f the use f cncrete manipulative materials and pictrial representatins necessary in the understanding f discrete mathematics cncepts and skills. T use technlgy as an aid in understanding discrete mathematics cncepts. III. Student Assessment A. Assessment plan: Students will be assessed and receive regular feedback n their wrk thrugh the assignment f hmewrk, written and ral cmmunicatin, grup and/r individual prjects, in-class examinatins, and a final exam. B. Ratinale: Hmewrk assignments will prvide students with pprtunities t attempt lengthier, mre challenging prblems than is pssible n an examinatin as well as ffering students practice at examstyle prblems. Written and ral cmmunicatin will be used t directly assess sme f the perfrmance gals listed abve. Grup and individual prjects prvide students with the pprtunity t explre a cncept mre deeply, and at the same time, assess many f the perfrmance gals listed abve. Examinatins, which nrmally preclude bth the use f bks and the practice f grup discussin, enable the prfessr t assess the knwledge an individual student has readily available C. Methds and criteria: The final grade will be based n the fllwing: 30% 3 quests (shrt tests) 20% prject 20% hmewrk/class participatin 30% final exam Quests will cver crrect use f mathematical terminlgy and mathematical cncepts studied. The prject will allw students t explre a cncept mre deeply in a real-wrld cntext. This will be due at the middle f the semester. Hmewrk will be assigned regularly t reinfrce the advanced mathematical cncepts learned in class. A great deal f time in class will be spent n prblemslving activities frm NSF-refrm curricula, such as Cnnected Math, and class discussin f advanced cncepts and their relatinship t these prblems. Prblem-slving rubric scale (used t describe perfrmance n hmewrk prblems and quest prblems): 4 Student demnstrates cmplete understanding f task r prblem. Apprpriate slutin strategies were clearly written and crrectly implemented t slve the prblem. All wrk is mathematically crrect and neat. A clear explanatin and/r justificatin is prvided if necessary. 3 Student demnstrates understanding f task r prblem. Apprpriate slutin strategies were selected, but minr prcedural errrs were made while implementing the strategy, r the wrk was nt cmplete. An explanatin and/r justificatin is prvided if necessary. Or althugh wrk is mathematically crrect, it is difficult t determine if the student understands the prblem r task because there is unclear, little, r n explanatin prvided. 2 Student demnstrates at least partial understanding f task r prblem, but there are significant errrs in thinking. Wrk is at least partially crrect.

4 1 Very little, if any, understanding f the task r prblem is evident. Wrk is attempted, but is incrrect. Written Wrk Rubric scale (used t describe perfrmance n explanatins r ther written hmewrk r quest questins) 4 Apprpriate mathematical vcabulary was used. The explanatin was specific and cncisely identified the pint(s) raised fr discussin. The explanatin was entirely crrect. 3 There is a minr errr in the use f vcabulary r in articulating the pint raised fr discussin. Otherwise the explanatin is entirely crrect and specifically and cncisely identified the pint(s) raised fr discussin. 2 The pint(s) raised fr discussin was identified, hwever the writing was evasive and/r vague. Terminlgy was avided r inapprpriately used. 1 Inapprpriate writing r n attempt. IV. Learning activities A. Summary f learning activities: Middle schl mathematics curricula will be used as a basis fr in-depth study f the mathematics cntent. Many class sessins will be devted t discussins f the mathematics cntent and the develpment f the mathematical cncepts and skills necessary in the mathematical educatin f middle-schl grades. Other class sessins will cnsist f hands-n experiences in rder fr the students t learn hw t use cncrete manipulative materials, pictrial mdels, and technlgy in the develpment f the mathematical cncepts fr middle-schl grades. Students will be expected t cmplete readings, and prepare prjects and/r assignments that are apprpriate fr the curse. B. Calendar r utline: The fllwing is a suggested guide t the rganizatin f curse tpics. Graph thery Intrductin t Vertex-Edge graphs Euler and Hamiltn Paths and Circuits Cmplete graphs Bipartite graphs Planar graphs Clring graphs and applicatins f clring Trees and tree diagrams Directed graphs Number patterns and recursive sequences Cmbinatrics Cmbinatins and permutatins Pascal s triangle Pigenhle and Inclusin-Exclusin Principle C. Ratinale: Using middle schl mathematics curricula as mtivatin fr in-depth study f the mathematical cncepts will cnnect the curse cntent t the middle schl classrm. Teachers will appreciate that what they are learning is relevant t their teaching. Teachers must experience standards-based teaching and learning in rder t understand hw t implement it. A

5 variety f strategies and methds f instructin shuld be used t mdel effective teaching f mathematics.