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135 Cards in this Set

  • Front
  • Back
Students must experience mathematics that what?
makes sense
Students must come to believe what?
That they are capable of making sense of mathematics
What should teachers stop doing?
teaching by telling
Name some of the verbs of "DOING" mathematics. (not to be confused with the daily objective verbs)
In a productive classroom culture, what is the currency of the classroom?
In a productive classroom culture, students have autonomy with what?
respect to the methods used to solve problems
In a productive classroom culture, how are mistakes viewed?
as an opportunity to learn
In a productive classroom culture, reasonability lies in what?
The logic and structure of the subject, not the person or social status of the participants.
Which principle includes high expectations and is shown through words, actions, and parental involvement?
Equity principle
Which principle states that one should know the content and know how students learn?
Teaching princple
The ___________ principle is coherent, focused, and well articulated across grade levels.
curriculum principle
In the ________ principle, new knowledge is built through connections with prior knowledge and experiences.
learning principle
The _________ principle enhances students learning, allows for more/deeper mathematics to be taught.
What are the 5 content strands
number and operations
data and analysis
What are the 5 process standards?
problem solving
reasoning and proof
The ____________ process standard is how students learn mathematics.
problem solving
The ________ process standard states that logical thinking should determine if and why answers are correct; providing a rationale should be part of every answer.
Reasoning and proof
The __________ process standard includes talking about, writing about, explaining, and describing mathematical ideas.
In the connections process standard, there are two ways to make connections. What are they?
within and among mathematics ideas
to the real world and other disciplines
Using symbols, charts, diagrams, graphs, and manipulatives is part of what process standard?
When "doing" mathematics, you do what?
devise a plan
apply the plan to see if it leads to a solution
check to see if solution makes sense
What should the act of doing mathematics in the classroom closely model?
the act of doing mathematics in the real world
What does Piaget believe about children?
that they create their own learning
Piaget believes that people construct their own knowledge according to what?
their previous knowledge, which gives them meaning to things they think about
What is understanding?
a measure of the quantity and quality of the connections that an idea has with existing ideas
What does understanding exist on?
a continuum
________________ understanding is when ideas are highly connected and the person knows what to do and why.
relational understanding
_______ understanding takes a lot of work and effort.
relational understanding
___________ understanding is when concepts and connections develop over time, and not in a day.
relational understanding
_____________ understanding is when ideas are isolated completely. It involves doing with understanding.
instrumental understanding
Effective learning of new concepts and procedures is a benefit of what?
relational understanding
With ______________ understanding, there is less to remember, increased retention and recall, enhanced problem solving abilities, and improved attitudes and beliefs.
relational understanding
__________ understanding is knowledge about the relationships or foundational ideas of a topic.
conceptual understanding
___________ understanding is knowledge of the rules and procedures used in carrying out mathematical processes and of the symbolism that is used to represent mathematics.
procedural understanding
Is conceptual or procedural understanding taught first?
Pictures, written symbols, manipulative models, real world situations, and oral language are what?
Ways of representing mathematical ideas
When should written symbols be used during a lesson?
at the end
How many ways of representing mathematical ideas should be used?
at least 3
Which three ways of representing mathematical ideas should be used at all times?
manipulative models
real world situations
Which way of representing a mathematical idea should be used in groups?
oral language
A ____________ is a task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific correct solution or method.
When solving a problem, student should do what?
work through it on their own.
There are 3 features of a problem for learning math. The first feature states that it should begin where?
Where the students are
Students should have the appropriate ideas to engage and solve the problem, yet still find it what?
challenging and interesting
The problematic or engaging aspect of the problem must be due to what?
the mathematics that the students are about to learn
Students should be primarily concerned with making sense of mathematical ideas and then doing what?
developing an understanding of those ideas
In a problem for learning math, it must require what?
explanations and justifications for answers
What is the value of teaching through problem solving?
A teacher changes her philosophy of how she thinks children learn. and how she can best help them learn.
Models can be thought of as what?
thinker toys
___________ are used to help students develop new concepts or relationships.
___________ are used to help students make connections between concepts and symbols.
__________ are use to assess students' understanding.
Good problems will integrate what?
multiple topics
Teaching with problems focuses students' attention on what?
ideas and sense making
Teaching with problems allows _____________ for a wide range of students.
an entry point for a wide range of students
Teaching with problems provides what?
ongoing assessment data
Teaching with problems allows for what?
extensions and elaborations
What are the 3 types of information teachers should provide for students?
mathematical conventions
alternative methods
clarification of student methods
Symbols, terminology, definitions, and labels are what?
mathematical conventions
Student writing is important because it is a ________ process.
In the three-part lesson format, the before phase has the teacher doing what three things?
activating prior knowledge
making sure the task is understood
establishing clear expectations
In the three-part lesson format, the during phase says that teachers should do what?
let the students do it on their own
In the during phase of the three-part lesson plan, the teacher should provide appropriate what?
For students who finish quickly, the teacher should provide what?
worthwhile extension ideas
In the three-part lesson format, the after phase says to promote what?
a mathematical community of learners
Teacher should encourage student-student what?
What should be requested to accompany all answers?
Teachers should listen actively without what?
Teachers should summarize main ideas and identify what?
future problems
Problems that can be approached in several different ways depending on the ability and learning style of the student is what?
a multiple point entry problem
_______________ is a provision of a different environment or circumstance made with particular students in mind.
___________ refers to a change in the problem or task itself.
____________ refers to different problem based tasks or experiences, spread over numerous class periods, each addressing the same basic ideas.
__________ refers to repetitive, non-problem-based exercises designed to improve skills or already acquired skills.
___________ can provide an increased facility with a strategy but only with a strategy already learned.
With ___________, there is a review of facts or procedures so they are not forgotten.
With __________, there is a focus on a singular method and an exclusion of flexible alternatives.
With ___________, there can be a false appearance of understanding.
_______ only focuses on what is known.
____________ provides an increased opportunity to develop conceptual ideas and more elaborate and useful connections.
___________ provides an opportunity to develop alternative and flexible strategies.
___________ provides a greater chance for all students to understand, particularly students with special needs.
_____________ provides a clear message that mathematics is about figuring things out and making sense.
When doing practice, you should practice the use of what?
flexible conceptual approaches, not isolated meaningless procedures learned by rote
How long should practice be?
15 minutes, 3 to 4 times per week
What are the reasons you have students practice?
To help them become quick, yet flexible
What does homework communicate to parents and students?
the importance of conceptual understanding
When home work is drill, it should be what?
kept short
have an answer key
not be graded on correctness
not gone over in class
When teaching with a textbook, the goal is to teach what?
the big ideas, not the pages
When using a textbook, the pace of the lessons should be determined by what?
student performance and understanding
__________ is the process of gathering evidence about a students' knowledge of, ability to use, and disposition toward mathematics and of making inferences from that evidence for a variety of purposes.
The purpose of _________ is to monitor student progress.
The purpose of ___________ is to make instructional decisions.
The purpose of ________ is to evaluate student achievement.
The purpose of __________ is to evaluate programs.
What three things should be assessed in mathematics?
concepts and procedures
mathematical processes
productive dispositions
True/false questions should be limited to what?
How many matching should there be on a test?
between 5-15
What kinds of lists should be used with matching?
Where should the main idea be stated in a multiple choice question?
in the stem
_________ is comparing students' work to correct answers or specific criteria that describes what we expect the work to be
________ is the result of accumulating scores and other information about a student's work for the purpose of summarizing and communicating to others.
________ are frameworks that can be designed or adjusted by the teacher for a particular group of students or a particular mathematics task; used to"score the task".
_____________ are task specific statements that describe what performance looks like at each level of the rubric and in doing so establish criteria for acceptable performance.
performance indicators
____________ are brief write-ups about certain students, kept on individual note cards or on large peel-off labels.
anecdotal records
___________ are useful for planning purposes.
observational rubrics
__________ is one checklist per student, but each contains the same set of specific processes to be observed.
individual checklists
______________ are one page charts with places for checks when certain "behaviors" have been observed or not.
checklists for full classes
What are the advantages of writing in the math classroom?
it's private
it can be revised or edited
it can be re-read at a later time
includes pictures, graphs, and symbols
What are the 4 types of writing in the math classroom?
journal writing
problem solving
explaining the idea
reflective writing
Give an example of a math writing prompt.
If math were a color, what would it be?
I need help with _________ because..............
A ______ is a statistic that is used to communicate to others the achievement level that a student has attained in a particular area of study.
When looking at the grade at the end of a period, it should reflect what?
all areas of grading, not just tests
Grades assigned should reflect all of what?
What are the 6 assessment standards?
ol mice
Using the frameworks to determine what the students should know and do and basing assessments on those essential concepts and processes is which standard?
mathematical standard
Incorporating assessment as an important part of instruction and not an interruption or at the end of the unit is part of what standard?
learning standard
In the _______ standard, the teacher should determine students' misunderstanding of the material and go deeper.
learning standard
In the __________ standard, the teacher should respect the unique qualities, experiences, and expertise of all students.
In the __________ standard, the teacher should maintain high expectations for students, while recognizing their individual needs.
In the _________ standard, the teacher should look at how the students can demonstrate what they know.
In the ___________ standard, the teacher should avoid looking at the answers and give attention to the examination of the thinking processes students used.
In the ____________ standard, the teacher should provide students with examples of responses that meet expectations and those that don't meet expectations.
In the _________ standard, the teacher should reflect seriously and honestly on what students are revealing about what they know.
In the _______ standard, the teacher should use multiple assessments and avoid bias by establishing a rubric that describes the evidence needed and the value of each component used for scoring.
In the _______ standard, the teacher should match his/her assessment techniques with both objectives of the instruction and the methods of the instruction,
coherence standard
In the ___________ standard, the teacher should ensure that assessments are a reflection of the content the teacher wants the student to learn, and develop a system of assessment that allows the teacher to use the results to inform the teachers instruction in a feedback loop.
coherence standard
In _________, students must be actively participants in the development of their own understanding.
In ___________, students make connections between old ideas and the new ones.
Students are not _______, they do not absorb new ideas.
blank slates
In the teaching principle, the teacher should use what?
appropriate instructional tasks
In the teaching principle, the teacher should use a journal for what?
to reflect on lessons
In the teaching principle, the teacher should share ideas and what?
plan ahead
____________ principle is used to guide instructional decision.
Assessments should be done ____ students.