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# Elementary Math

### Mathematics Methods for Elementary

Question | Answer |
---|---|

What is tracking? | When students are placed in a lower-level track or in a “slow” group, expectations decline accordingly |

What is an accommodation? | is a response to the needs of the environment or the learner; it does not change the task. |

What is a modification? | changes the task, making it more accessible to the student |

What would be a successful environment for doing mathematics? | posing worthwhile tasks and then creating an environment where students take risks and share and defend mathematical ideas |

What is constructivism? | learners are not blank slates but rather creators (constructors) of their own learning |

What is sociocultural theory? | mental processes exist between and among people in social learning settings, and that from these social settings the learner moves ideas into his or her own psychological realm |

Explain the Zone of Proximal Development | the way in which information is internalized (or learned) depends on whether it was within a learner’s zone of proximal development |

What is Semiotic Mediation? | the “mechanism by which individual beliefs, attitudes, and goals are simultaneously affected and affect sociocultural practices and institutions” |

What is relational understanding? | knowing what to do and why |

What is instrumental understanding? | doing something without understanding |

What is conceptual understanding? | knowledge about the relationships or foundational ideas of a topic |

What is procedural fluency? | knowledge and use of rules and procedures used in carrying out mathematical processes and also the symbolism used to represent mathematics |

What is strategic competence? | You have a problem; you need to figure out how you will solve it. If at first you don’t succeed, try, try again |

What is adaptive reasoning? | capacity to reflect on your work, evaluate it, and then adapt, as needed |

What is productive disposition? | a “can do” attitude |

What is classroom discourse? | the interactions that occur throughout a lesson |

What is revoicing? | restating the statement as a question in order to clarify, apply appropriate language, and to involve more students. |

What is rephrasing? | Asking students to restate someone else’s ideas in their own words |

What is reasoning? | asks the student what they think of the idea proposed by another student. |

What is elaborating? | a request for students to challenge, add on, elaborate, or give an example |

what is waiting? | Quiet time should not feel uncomfortable, but should feel like thinking time |

What should be considered during questioning? | The level of the question, the type of knowledge, the pattern of questioning, who is answering, and the response to the answer |

What is metacognition? | refers to conscious monitoring (being aware of how and why you are doing something) and regulation (choosing to do something or deciding to make changes) of your own thought process |

What is teaching FOR problem solving? | This approach can be summarized as teaching a skill so that a student can later problem solve |

What is teaching ABOUT problem solving? | involves teaching students how to problem solve, which can include teaching the process (understand, design a strategy, implement, look back) or strategies for solving a problem. |

What is teaching THROUGH problem solving? | students learn mathematics through real contexts, problems, situations, and models. |

What is practice? | different problem-based tasks or experiences, spread over numerous class periods, each addressing the same basic ideas. |

What is a drill? | repetitive, non-problem-based exercises designed to improve skills or procedures already acquired. |

What is iteration? | measuring the same desktop with a single index card by repeatedly moving it from position to position and keeping track of which areas the card has covered |

What are cuisenaire rods? | math learning aids for students that provide a hands-on elementary school way to explore math and learn math concepts, such as the four basic arithmetical operations, working with fractions and finding divisors. |

What is an isometric drawing tool? | 3D drawings. They show three sides, all in dimensional proportion, but none are shown as a true shape with 90 degree corners. |

What is a tangram? | a Chinese geometric puzzle consisting of a square cut into seven pieces that can be arranged to make various other shapes |

What is mathematical discourse? | whole-class discussions in which students talk about mathematics in such a way that they reveal their understanding of concepts |

What is dynamic geometry software? | : computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. |

What is graphical representation software? | a category of application program used to create sequences of words and pictures that tell a story or help support a speech or public presentation of information (Power Point) |

Created by:
cgibbs906