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# TExES Competency 013

### Mathematics Instruction

Term | Definition |
---|---|

The 6 principles that should guide mathematics instruction: | Equity, Curriculum, Teaching, Learning, Assessment, Technology |

High expectations and strong support for all students | Equity |

Focused on mathematics and well- articulated concepts across the grades. | Curriculum |

Requires understanding of what students know and need to learn and then challenging and supporting students to learn it well. | Teaching |

Students must learn mathematics with understanding actively building new knowledge from experience and previous knowledge. | Learning |

_____ should support the learning of important mathematics concepts, and furnish useful information to both teachers and students. | Assessment |

_____ is essential in teaching and learning mathematics; it influences the teaching of mathematics and enhances student's learning. | Technology |

What are the content standards for math: | Numbers and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability |

This standard deals with understanding numbers, developing meanings of operations, and computing fluently. | Number and Operations |

___ is best learned as a set of concepts and techniques tied to the representation of quantitative relations and as a style of mathematical thinking for formalizing patterns, functions, and generalizations. | Algebra |

Calls students to analyze characteristics of geometric shapes and make mathematical arguments about the geometric relationship, as well as to use visualization, spatial reasoning, and geometric modeling to solve problems. | Geometry |

This standard is crucial in the school mathematics curriculum because of its practicality and pervasiveness in so many aspects of life. Includes understanding the attributes, units, systems, and processes of measurement as well as applying the techniques. | Measurement |

This standard emphasizes learning appropriate statistical methods to analyze data, making inferences and predictions based on data, and understanding and using the basic concepts of probability. | Data Analysis and Probability |

The process standards for Math are: | Problem solving, Reasoning and Proof, Communication, Connections, Representations |

The Texas Mathematics Standards: | Number Concepts, Pattern and Algebra, Geometry and Measurement, Probability and Statistics, Mathematical Processes, Mathematical Perspectives, Mathematical Learning and Instruction, Mathematical Assessment, Professional Development |

___ learning through examples. | Inductive Teaching |

____ learning step by step. | Deductive Approach |

The sensorimotor stage is from : | Birth-2 years |

Preoperational Stage is from: Symbolic functioning, concentration, intuitive thought, ego-centrism, and inability to conserve | 2 years-7 years |

Concrete Operational stage is from: Exhibit the developmental processes of: decentering, reversibility, conservation, serialization, classification, and elimination of ego centrism. | 7 years-11 years |

Formal Operational Stage is from: The characteristics of this stage focus on the ability to use symbols and think abstractly. | 11 years-adult |

Characterized by a child focusing only on one aspect of a situation or problem. | Centration |

Understanding that quantity, length, or number of items is unrelated to the arrangement or appearance of the object or items. | Conservation |

____where the child can take into account multiple aspects of a problem to solve it. Can form conclusion based on reason rather than perception | Decentering |

___ where the child understands that the objects can be changed, then returned to their original state. Can determine that 4+4=8 & 8-4=4 | Reversibilty |

___ where the child understands that quantity, length, or number of items is unrelated to the arrangement or appearance of the object. Can discern that if water is transferred to a pitcher it will conserve the quantity and be equal to the other filled cup | Conservation |

___ where the child is able to arrange objects in an order according to size, shape, or any other attribute. Can arrange geometric forms by shape, size, color, and thickness of the form. | Seriation |

___ where the child can name and identify sets of objects according to appearance, size, or other characteristic. Can arrange objects based on characteristics. | C;assification |

__ where the child is able to view things from another's perspective. Can retell a story from another child's perspective. | Elimination of Edocentrism |

Children can benefit from group instruction and the use of concrete objects and__? Can be used to provide a "hands-on-learning" for kindergarten to high school students. | Manipulatives |

___ are the projects, questions, problems, constructions, applications, and exercises in which students engage. | Tasks |

__ refers to the way of presenting thinking, talking, and agreeing and disagreeing that teachers and students use to engage in these tasks. | Discourse |

__represents the setting for learning. | Environment |

___is the systematic reflection in which teachers engage. | Analysis |

Professional Standards for Teaching Mathematics are: | Classrooms as mathematical communities, logic an mathematical evidence as verification, mathematical reasoning, problem solving, connecting mathematics, its ideas, and its applications |

____ is the organization off curriculum content based on themes or topics. | Thematic instruction |