Students can learnmathematicsthrough exploringand solvingcontextual andmathematicalproblems.An effective teachermakes themathematics easy forstudents by guidingthem step by stepthrough problemsolving to ensure thatthey are not frustratedor confused.The role of thestudent is tomemorize informationthat is presented andthen use it to solveroutine problems onhomework, quizzes,and tests.All students need to have arange ofstrategies and approachesfrom which to choose insolving problems,including, but not limited to,general methods, standardalgorithms, andprocedures. The role of the teacheris to engage studentsin tasks that promotereason ing andproblem solving andfacilitate discourse thatmoves students towardshared understandingof mathematics.The role of the student is tobe actively involved inmaking sense ofmathematics tasks byusing varied strategies andrepresentations, justifyingsolutions, makingconnections to priorknowledge or familiarcontexts and experiences,and consideMathematics learningshould focus ondevelopingunderstanding ofconcepts andprocedures throughproblem solving,reasoning, anddiscourse.Students canlearn to applymathematicsonly after theyhave masteredthe basic skills. Students need onlyto learn and use thesame standardcomputationalalgorithms and thesame prescribedmethods to solvealgebraic problems. The role of the teacheris to tell studentsexactly whatdefinitions, formulas,and rules they shouldknow and demonstratehow to use thisinformation to solvemathematics problems. An effective teacherprovides students withappropriate challenge,encouragesperseverance insolving problems, andsupports productivestruggle in learning. Mathematicslearning shouldfocus on practicingprocedures andmemorizing basicnumbercombinations. Students can learnmathematicsthrough exploringand solvingcontextual andmathematicalproblems.An effective teachermakes themathematics easy forstudents by guidingthem step by stepthrough problemsolving to ensure thatthey are not frustratedor confused.The role of thestudent is tomemorize informationthat is presented andthen use it to solveroutine problems onhomework, quizzes,and tests.All students need to have arange ofstrategies and approachesfrom which to choose insolving problems,including, but not limited to,general methods, standardalgorithms, andprocedures. The role of the teacheris to engage studentsin tasks that promotereason ing andproblem solving andfacilitate discourse thatmoves students towardshared understandingof mathematics.The role of the student is tobe actively involved inmaking sense ofmathematics tasks byusing varied strategies andrepresentations, justifyingsolutions, makingconnections to priorknowledge or familiarcontexts and experiences,and consideMathematics learningshould focus ondevelopingunderstanding ofconcepts andprocedures throughproblem solving,reasoning, anddiscourse.Students canlearn to applymathematicsonly after theyhave masteredthe basic skills. Students need onlyto learn and use thesame standardcomputationalalgorithms and thesame prescribedmethods to solvealgebraic problems. The role of the teacheris to tell studentsexactly whatdefinitions, formulas,and rules they shouldknow and demonstratehow to use thisinformation to solvemathematics problems. An effective teacherprovides students withappropriate challenge,encouragesperseverance insolving problems, andsupports productivestruggle in learning. Mathematicslearning shouldfocus on practicingprocedures andmemorizing basicnumbercombinations. 

Productive and Unproductive Beliefs about Teaching and Learning Mathematics, NTCM - Call List

(Print) Use this randomly generated list as your call list when playing the game. Place some kind of mark (like an X, a checkmark, a dot, tally mark, etc) on each cell as you announce it, to keep track. You can also cut out each item, place them in a bag and pull words from the bag.


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  1. Students can learn mathematics through exploring and solving contextual and mathematical problems.
  2. An effective teacher makes the mathematics easy for students by guiding them step by step through problem solving to ensure that they are not frustrated or confused.
  3. The role of the student is to memorize information that is presented and then use it to solve routine problems on homework, quizzes, and tests.
  4. All students need to have a range of strategies and approaches from which to choose in solving problems, including, but not limited to, general methods, standard algorithms, and procedures.
  5. The role of the teacher is to engage students in tasks that promote reason ing and problem solving and facilitate discourse that moves students toward shared understanding of mathematics.
  6. The role of the student is to be actively involved in making sense of mathematics tasks by using varied strategies and representations, justifying solutions, making connections to prior knowledge or familiar contexts and experiences, and conside
  7. Mathematics learning should focus on developing understanding of concepts and procedures through problem solving, reasoning, and discourse.
  8. Students can learn to apply mathematics only after they have mastered the basic skills.
  9. Students need only to learn and use the same standard computational algorithms and the same prescribed methods to solve algebraic problems.
  10. The role of the teacher is to tell students exactly what definitions, formulas, and rules they should know and demonstrate how to use this information to solve mathematics problems.
  11. An effective teacher provides students with appropriate challenge, encourages perseverance in solving problems, and supports productive struggle in learning.
  12. Mathematics learning should focus on practicing procedures and memorizing basic number combinations.