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MATH METHODS TEST 1 EXAM QUESTIONS AND ANSWERS LATEST TOP SCORE., Exercises of Advanced Education

MATH METHODS TEST 1 EXAM QUESTIONS AND ANSWERS LATEST TOP SCORE.MATH METHODS TEST 1 EXAM QUESTIONS AND ANSWERS LATEST TOP SCORE.MATH METHODS TEST 1 EXAM QUESTIONS AND ANSWERS LATEST TOP SCORE.MATH METHODS TEST 1 EXAM QUESTIONS AND ANSWERS LATEST TOP SCORE.MATH METHODS TEST 1 EXAM QUESTIONS AND ANSWERS LATEST TOP SCORE.

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MATH METHODS TEST 1 EXAM QUESTIONS AND
1. According to our book what are factors that influence the teaching of
Mathematics effective?: According to our book, the two most important factors to
consider in becoming an effective teacher of mathematics are conceptual under-
standing and procedural fluency. If we think about it, do we just want our students to
know formulas and facts? Or, do we want our students to know why that formula and
mathematical equation is important in life and where they will use it in the future?
As future educators, we want our students to know why mathematics is important
and how it is used in our every day lives. It is more than just some formulas, facts,
and equations. We also want our students to know how to apply different procedures
to different problems so they use them accurately and appropriately. Therefore, this
is why it is important that teachers emphasize procedural fluency. Mathematics is
about analyzing and reflecting on different procedures and processes to ensure the
right method or procedure is being used to enhance results. Another way to look at
these factors is analyzing a doctor or nurse. Our textbook reminds us how medicine
and techniques have evolved over the years. Therefore, would you just want a doctor
or nurse performing a technique on you that worked 10 years ago? Or, would you
want that doctor or nurse to reflect and analyze which technique might work better
since medicine and techniques have come such a long way since 10 years ago? The
same goes for mathematics. Mathematics has evolved and changed so much in the
past 10 years so it is our responsibility as future educators to emphasize conceptual
understanding and procedural fluency. This will ensure our students become critical
thinkers and are reflecting on mathematics in a more in-depth context. or Knowledge
of standards and practices.
2. The mathematical needs in society have changed and are influencing what
should be taught in pre-K-8 mathematics classrooms. What are some key
factors promoting the change?: Data on the performance of U.S. students in
national and international studies.
3. What did the National Assessment of Educational Progress reveal about
grades 4 and 8 achievement in 2015? How did the U.S. students performed
at the International?: In the most recent NAEP mathematics assessment in 2015,
less than half of all U.S. students in grades 4 and 8 performed at the desirable
levels of proficient and advanced (40 percent in fourth grade and 33 percent in
eighth grade) -- students' performance in 2015 still reveals disappointing levels of
competency. For the first time in 25 years the number of students performing at
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MATH METHODS TEST 1 EXAM QUESTIONS AND

  1. According to our book what are factors that influence the teaching of

Mathematics effective?: According to our book, the two most important factors to consider in becoming an effective teacher of mathematics are conceptual under- standing and procedural fluency. If we think about it, do we just want our students to know formulas and facts? Or, do we want our students to know why that formula and mathematical equation is important in life and where they will use it in the future? As future educators, we want our students to know why mathematics is important and how it is used in our every day lives. It is more than just some formulas, facts, and equations. We also want our students to know how to apply different procedures to different problems so they use them accurately and appropriately. Therefore, this is why it is important that teachers emphasize procedural fluency. Mathematics is about analyzing and reflecting on different procedures and processes to ensure the right method or procedure is being used to enhance results. Another way to look at these factors is analyzing a doctor or nurse. Our textbook reminds us how medicine and techniques have evolved over the years. Therefore, would you just want a doctor or nurse performing a technique on you that worked 10 years ago? Or, would you want that doctor or nurse to reflect and analyze which technique might work better since medicine and techniques have come such a long way since 10 years ago? The same goes for mathematics. Mathematics has evolved and changed so much in the past 10 years so it is our responsibility as future educators to emphasize conceptual understanding and procedural fluency. This will ensure our students become critical thinkers and are reflecting on mathematics in a more in-depth context. or Knowledge of standards and practices.

  1. The mathematical needs in society have changed and are influencing what

should be taught in pre-K- 8 mathematics classrooms. What are some key factors promoting the change?: Data on the performance of U.S. students in national and international studies.

  1. What did the National Assessment of Educational Progress reveal about

grades 4 and 8 achievement in 2015? How did the U.S. students performed at the International?: In the most recent NAEP mathematics assessment in 2015, less than half of all U.S. students in grades 4 and 8 performed at the desirable levels of proficient and advanced (40 percent in fourth grade and 33 percent in eighth grade) -- students' performance in 2015 still reveals disappointing levels of competency. For the first time in 25 years the number of students performing at

2 / 13 proficient and advanced dropped two points at fourth grade and three points at eighth grade

  1. What is NCTM?: NCTM is known as the National Council of Teachers of Mathe- matics. They are the largest mathematics education organization with over 60, members. The purpose of this organization is to support teachers in doing what

4 / 13 communicate their thinking. Using these five process standards allows teachers to help students build a strong mathematical foundation, which is crucial for a student to be successful.

  1. Teaching and learning, Access and equity, curriculum, tools and technology, assessment, professionalism are all guiding principles from the principles to actions, what is the message of each?:
  2. What are the characteristics, habit of thought, skills, and dispositions that must be continuously cultivated to reach success as an effective teacher of mathematics?:
  3. Which of the following is an example of a statement spoken in the language of doing mathematics? "Memorize these steps," "Compute this answer," "Ex- plain how you solved the problem," or "Copy down these steps into your notebooks" explain your choice.: "explain how you solved the problem"
  4. Doing mathematics begins with posing worthwhile tasks. What are some verbs that align with activities that lead to higher-level thinking? Lower-level thinking?: When planning your math lessons you want to be sure to not have the students doing lower-level thinking tasks such as asking them to listen, copy, mes- merizing, or doing drills. Instead you want to use verbs in your lessons that engage students in higher-level thinking such as analyze, critique, formulate, investigate, or justify, just to name a few. You will also find these word on the higher level of Bloom's Taxonomy. It's important to teach students that math is a process. it is generating strategies to solve a problem, applying strategies, and checking to see if it makes sense.
  5. What is productive struggle?: Productive struggle is critical to developing conceptual understanding (Hiebert & Grouws, 2007). Notice the importance of both words in "productive struggle." Students must have the tools and prior knowledge to solve a problem, and not be given a problem that is out of reach, or they will struggle without being productive, yet students should not be given tasks that are straightforward and easy or they will not be struggling with mathematical ideas.
  6. Understanding exists along a continuum from an understanding to a understanding. Explain the continuum and give an example.: instrumental understanding (knowing something by rote or without meaning) to a relational understanding (knowing what to do and why) things that have been memorized have likely been forgotten.
  7. What is the zone of proximal development?: is a concept that was created by the psychologist, Lev Vygotsky. it is the invisible area that shows the range of abilities that a student can do with or without assistance. This concept is where the idea of scaffolding from the teacher comes into play for helping students get close to mastering skills independently. Scaffolding can be viewed as instructions

5 b/ b 13 for activities and examples. As time goes by, scaffolding can be eliminated and the students could do the skills independently.

  1. What is constructivism?: According to the book, it is a part of Jean Piaget's work. This simply states that learners are the composer, also known as "constructor" of their own learning. Math is all about students learning how to work out a problem on their own and making them do the work. Students use their own knowledge and tools to make connections on their own work. Everyone remembers things by different strategies, so using it is a great way for any student to work on building those connections.
  2. What is sociocultural theory?: Sociocultural Theory was developed between the 1920s and 1930s by psychologist Lev Vygotsky. Vygotsky compared it to con- structivism, but it is the way that information is internalized or learned depending on the learner's zone of proximal development. To see how a leaner social interaction with others helps the development of the individual. For example, each student in the classroom plays a role in the development of their classmates. If there is a student that is making noise, then that affects the learning abilities of the students that are trying to focus on the teacher but can't due to the interruption. This is relating back to how the culture of the teacher not only affects the student, but the culture of the classmates can affect the other students too.
  3. Intertwined strands of proficiency includes conceptual understanding and procedural fluency, what are they and why are they important?:
  4. Pick a particular mathematics topic and develop a web that might demon- strate a student's conceptual understanding of the topic.:
  5. What are three approaches to problem solving that are used in class- rooms? What are advantages or disadvantages to each?: Visualize- advantages are that this would work very well for our visual learners but the disadvantage would be for our non-visual learners. Simplify or change the problem It is easier for students to break down a mathematical problem. It makes it easier to understand and analyze. It takes students to practice and time in order to fully simplify a problem. Simplifying equations is not easy the first time. This disadvantage means teachers would need to practice and test over simplifying problems in order to get their students on track. Write an equation Writing an equation gives helpful insights into the structure of the problem. Students can use numbers, symbols, and equations for modeling a situation. Students also need to understand where to actually put the symbols and numbers in the corrects places in an equation. Teachers could practice and test their students over writing an equation.

7 b/ b 13 §111.5.bGrade b 3 b(b) bKnowledge band bskills b(1) bMathematical bprocess bstandards.bThe bstudent buses bmathematical bprocesses bto bacquire band bdemonstrate bmathematical bunderstanding.bThe bstudent bis bexpected bto: b(A) bapply bmathematics bto bproblems barising bin beveryday blife, bsociety, band bthe bworkplace; What bis bin bred bis bthe bstrand, bgreen bis bthe bknowledge band bskill bstatement, band bpink bis bthe bstudent bexpectation

  1. PracticebIdentifyingbthebstrand,bcontent,brigorbandbspecificitybofbabparticular bTEK.: b Identify bthe bstrand, bcontent, brigor band bspecificity bof ba bparticular bTEK. §111.6. b(6) bGeometry band bmeasurement. bThe bstudent bapplies bmathematical bprocess bstandards bto banalyze bgeometric battributes bin border bto bdevelop bgeneralizations babout btheir bproperties. bThe bstudent bis bexpected bto: b(A) bidentify bpoints, blines, bline bsegments, brays,angles, band bperpendicular band bparallel blines; Strand:bGeometry band bMeasurement bContent: bGeometric bAttributes Rigor: bAnalyze band bIdentify Specificity:bidentifybpoints, blines, bline bsegments,brays,bangles, bandbperpendicular band bparallel blines.
  2. Given ba bTEKs bwrite ban binstructional bobjective.: b An binstructional bobjective bis ba bstatement bthat bwill bdescribe bwhat bthe blearner bwill bbe bable bto bdo bafter bcompleting bthe binstruction
  3. What bare bthe blesson btypes byou bshould buse bin bthis bcourse?: b the blesson btypes bshould bbe bbased bon bthe bTEKS
  4. What bteaching bmethods byou bshould buse bin bthis bcourse?:
  5. What bis bdifferentiating binstruction band bwhat bare bthe bthree bcritical belements bthat byou bcan bdifferentiate bacross?: b Differentiating binstruction bmeans bthat bthe blesson bplan bincludes bstrategies bto bsupport bthe brange bof bdifferentiate bacademic bbackgrounds bin bthe bclassrooms bthat bare bacademically, bculturally, band blinguistically bdiverse. bFirst bconsider bthe blearning bprofile bof beach bstudent, bthen bconsider bwhat bcan bbe bdifferentiated. The bthree bcritical belements bare bcontent, bprocess, band bproduct.bContent bis bwhat byou bwant beach bof byour bstudents bto bknow.bIt bcan bbe bdifferentiated bby bincluding bresources bor bmanipulative's bor bmathematical bvocabulary bdeveloped bto bname ba bfew. bProcess bis bhow byou bwill bengage bthem bin bthinking babout bthe bcontent.bTeacher's bshould bthink babout bselecting bstrategies bthat bbuild bon bstudents breadiness, binterests, band blearning bpreferences.bProduct bis bwhat bthey bwill bshow, bwrite, bor btell bto bdemonstrate bwhat bthey bhave blearned.
  6. What bis ba btiered blesson?: b A btiered blesson bplan bis ba bgrouping bof bsimilar bmath bproblemsbthat ball blead bto bthebsamebgoal.bThese barebmeant bto bbebgeared bto babvarietybof blearners bwhich bcan bbe bput bin bdifferent bgroups band bgiven bdifferent btasks bto bcomplete.

8 b/ b 13 This bcan bbe bdetermined bby bthe, b"degree bof bthe bassistance", b"how bstructured bthe btask bis", b"the bcomplexity bof bthe btask bgiven", band b"the bcomplexity bof bthe bprocess."

  1. What bis ba bparallel btask?: b A bparallel btask bis bwhen bstudents bare bworking bon bdifferent btasks/assignments bat bdifferent bdevelopmental blevels bbut bare ball bfocused bon bthe bsame blearning bgoal.bThey bresemble bthose bof btiered blessons. bIt bis bso bimportant to binclude bparallel btasks bin bthe bclassroom bbecause bstudents bare bnot ball bon bthe bsame bdevelopmental blevel. bThis ballows bstudents bto ball bwork btowards bthe bsame blearning bgoal bbut bin bdifferent bways band bdevelopmental blevels. bParallel btasks balso bpromote bstudent bchoice, band bit bis bcrucial bto bgive bstudents bchoice band bcontrol bof btheir bown blearning. Students bare bable bto bchoose btasks bthat bare bdifficult benough bto bchallenge bthem bbut balso, bnot bto bdifficult bto bcomplete band bnavigate bthrough. bI bbelieve bparallel btasks bcan benhance bstudent blearning bthrough bchoice band ballowing bstudents bto blearn/succeed bon btheir bdifferent bdevelopmental blevels.
  2. Why bis bflexible bgrouping bimportant?: b Flexible bgrouping bis ba bpractice bthat bshould bbe bincorporated bin bevery bclass bespecially bmathematics.bThe bgroups bcan brange bfrom bsmall bgroups, blarge bgroups, band bpairs bdepending bon bthe bneed bfor bthe blesson bor bcontent.bThese bgroups ballow bstudents bto bhear band bsee bdifferent bperspectives bwhen bit bcomes bto bsolving bproblems bor bgetting bhelp bto bsolve bproblems. bNot bonly bdo bflexible bgrouping bhelp bbuild bunderstanding, bbut bit bis ban bimportant blife bskill bthat bcan bbe btransferred bwhen bstudents bget bolder.bThese bgroups bshould bbe bintentional band bnever bability bbased. bGroups bcan bbe bchosen bbased bon bthe bstudents' bacademic babilities, blanguage bneeds, bsocial bdynamics, band bbehavior. bBefore bgrouping btakes bplace, bthe bexpectations bas bwell bas bindividual baccountability band bshared bresponsibility bmust bbe bdiscussed bfor beffective bcooperative blearning.
  3. The bNCTM bPrinciples band bStandards bstress btwo bmain bideas bof bintegrating assessment binto binstruction, bwhat bare bthey?: b Valuable btool bfor bmaking binstruc- btional bdecisions. bis bone bof bthe bkey bideas
  4. What bis bthe bdifference bbetween bformative band bsummative bassessment?: b- b Formative bassessment bis bassessment bfor blearning. bIt bis bthe bprocess bof bgathering bevi- bdence bof bstudent blearning, bproviding bfeedback bto bstudents band badjusting binstructional band blearning bstrategies bthat benhance bachievement. bBy bproviding btargeted bfeedback bto bthe bstudent band busing bthe bresults band bevidence bcollected bto binform bdecision bmaking babout bthe bnext bsteps bin bthe blearning bprocess. bTo bbe bformative bit bmust binclude ba bplan bof baction. Summative bassessment bis bassessing bof blearning. bIt btakes bplace bafter binstruction b is bcomplete.It bis busually ba bsingle bscore bthat bmeasures boverall bprogress btowards bcontent band bpractice/process bstandards, bsuch bas ban bend bof bthe bunit btest bor ba bstate bstandardized btest.

10 b/ b 13

  1. adding bon: b the bteacher bask bfor bfurther bparticipation bregarding bthe bidea bor brea- bsoning bbeing bshared bduring bthe bconversation. CWould bsomeone blike bto baddbon bto bthis? bEX
  2. revise: b - bit ballows bstudents bto brevise btheir bthinking bas bthey bhear/ blearn bnew binsights.
  • how bhas banyones bthinking bchanged? bEX
  • would byou blike bto brevise byour bthinking? bEX
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  • can byou bgive buse bmore bdetails bon bwhat byour bthinking.bEX
  • how bdid byou bcome bto bthe bconclusion? bGive bus bmore.bEX
  1. revocing:b teacher brevoicing bwhat bthe bstudent bjust bsaid bas ba bquestion. Say bmore- bmore binformation Who bcan brepeat?- bputting bit binto byour bown bwords
  2. there bmust bmebWHAT bthroughout ba blesson:b questions
  3. waitbtime:b teacher bmove bQuiet btime Partner btalk- bshoulder bpartner
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  5. Simplify bor bchange bthe bproblem .
  6. Write ban bequation
  7. visualize: b Students bneed bto bSEE bthe bconcept bthat bis bbeing bshown bin bable bto bunderstand. bStudents bcould bdraw ba bpicture, bact bit bout, bor buse btechnology bto bhep bunderstandbmathematical bviews.bOne bdisadvantage bfor bvisualizing bwould bbe bthat bnot beveryone bare bvisualizers.bTeachers bwould bneed bto baccommodate bfor beveryone bif bthey bwould blike bto bincorporate bvisualizing bin bthe bactivity.
  8. simplify bor bchangebthe bproblem: b It bis beasierbforbstudents bto bbreak bdown ba bmath- bematical bproblem. bIt bmakes bit beasier bto bunderstand band banalyze. bIt btakes bstudents bpractice band btime bin border bto bfully bsimplify ba bproblem. bSimplifying bequations bis bnot beasy bthe bfirst btime.bThis bdisadvantage bmeans bteachers bwould bneed bto bpractice band btest bover bsimplifying bproblems bin border bto bget btheir bstudents bon btrack.
  9. write ban bequation: b Writing ban bequation bcan bgive bhelpful binsights binto bthe bstruc- bturebofbthebproblem.bStudentsbcanbusebnumbers,bsymbols,bandbequationsbforbmodeling

11 b/ b 13 a bsituation. bStudents balso bneed bto bunderstand bwhere bto bactually bput bthe bsymbols band bnumbers bin bthe bcorrects bplaces bin ban bequation. bTeachers bcould bpractice band btest btheir bstudents bover bwriting ban bequation.

  1. Polyas bsolving bproblem:b Step b1:bUnderstand bthe bproblem. bStep b2: bDevise ba bplan b(translate). Step b3: bCarry bout bthe bplan b(solve). Step b4: bLook bback b(check band binterpret).
  2. Explainbeachbofbthe bfollowingbassessmentbmethods:bObservations,banecdo- btal bnotes, bcheck blist,bquestions, binterviews band btasks.: b There bare bmany bdifferent btypesbof bassessment, band ball bof bthem bcan bbe beffective bif bused bproperly.bObservations barebabgreatbwaybforbabteacherbtobfindboutbvaluablebinformationbaboutbabstudent,bandbitbis ba bvery bsimple bprocess.bThe bteacher bneeds bto bpay bclose battention bto ball bher bstudents bduring ball baspects bof bthe bclassroom, band bshe bcan buse bthese bobservations bto bhelp bthe bstudent bsucceed. bAnecdotal bnotes bfall bunder bobservation, band bthey bcan balso bbe bknown bas bprofessional bwatching.bThe bthree bphases bof banecdotal bnotes bare battending, binterpreting, band bdeciding. bChecklists bare bused btrack bstudent bunderstanding.bThey bcan bbe bdone btwo bdifferent bways: beach bstudent bhas btheir bown bchecklist band bthere bare bdifferent btask band bdifferent blevels bof bproficiency bor ball bstudents bare bon bone bchecklist band bthere bis bone bconcept bwith bdifferent blevels bof bproficiency. bAnother btype bof bassessment bis busing bquestions.bThere bare bfour bdifferent btypes bof bquestions, band bstudents bshould bbe basked ba bvariety bof bthese bquestions bbecause bthese bquestions ballow bteachers bto bfind bout bwhere bstudents bare. bInterviews bare ba bgreat bway bto bget in-depth binformation babout ba bstudents bknowledge bon bconcepts.bThe bpurpose bof bthis interviewbisbtobseebhowbabstudents bisbsolvingbabproblemsbisbseebhowbtheybarebthinking. bThe bpurpose bof btasks bis bfor ball bstudents bto bdemonstrate btheir bknowledge, bskill, bor bunderstanding.bThere bare bthree bdifferent btypes bof btasks band bthey bare bproblem-based btasks, btranslation btasks, band bwriting.bThe bmain bgoal bof bassessment bis bto bdrive binstruction, bso ba bteacher bcan buse ball bof bthese bmethods bto bbetter bher binstruction bfor bhis bor bher bstudents.
  3. What bis bNCTM bposition bon baccess band bequity?: b All bstudents bshould bbe bheld bto bhigh blevels bof bperformance bregardless bof brace, bethnicity, bgender band bsocioeconomic bstatus band blinguistic bbackground.
  4. Mathematics bfor beach band bevery bstudents brequires bthe buse bof baccom- bmodations band bmodifications bdefine beach band bdescribe bhow bthey bmight bbe bused.: b Accommodations band bmodifications bare bused bevery bday bin bevery bsubject bto bhelp bthe bstudents bwho bmight bneed bextra bhelp.bThe bbook bdefines baccommodations bas ba bresponse bto bthe bneed bof bthe benvironment bor bthe blearner.bFor bexample, binstead bof bsaying bthe binstructions bout bloud, byou bmay bhave bto bwrite bthem bdown bon bpaper for ba bstudent bso bthat bthey bcan bunderstand bthem.bWhere, bon bthe bother bhand, ba

13 b/ b 13

  1. what bdoes bit bmean bto bdo bmathematics?: b Doing bmathematics bmeans bgener- bating bstrategies bfor bsolving ba bproblem, bapplying bthat bstrategy, band bchecking bto bsee bwhether ban banswer bmakes bsense.
  2. procedural bknowledge: b refers bto bhow bto bcomplete ban balgorithm bor bprocedure.
  3. conceptual bknowledge: b refers bto bconnected bknowledge: b"mental bconnections bamong bmathematical bfacts, bprocedures, band bideas"
  4. RTI: b A bmulti btiered bstudent bsupport bmodel bthat bfocuses bon bprevention, bproviding bstudents bwith bsupport bbefore bthey bbegin bto bfail.
  5. Doing bmathematics bbegins bwith bposing bworthwhile btasks.bWhich bverbs balign bwith bactivities bthat blead bto bhigher-level bthinking?:b B) bInvestigate, bconstruct band bformulate.