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135 Cards in this Set
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 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)

use
explain predict investigate formulate justify verify explore represent 

In a productive classroom culture, what is the currency of the classroom?

ideas


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.

technology


What are the 5 content strands

number and operations
algebra geometry measurement data and analysis 

What are the 5 process standards?

problem solving
reasoning and proof representations communication connections 

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.

communication


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?

representation


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?

conceptual


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
pictures 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.

problem


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.

models


___________ are used to help students make connections between concepts and symbols.

models


__________ are use to assess students' understanding.

models


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.

reflective


In the threepart 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 threepart 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 threepart lesson plan, the teacher should provide appropriate what?

hints


For students who finish quickly, the teacher should provide what?

worthwhile extension ideas


In the threepart lesson format, the after phase says to promote what?

a mathematical community of learners


Teacher should encourage studentstudent what?

dialogue


What should be requested to accompany all answers?

explanations


Teachers should listen actively without what?

evaluation


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.

accommodation


___________ refers to a change in the problem or task itself.

modification


____________ refers to different problem based tasks or experiences, spread over numerous class periods, each addressing the same basic ideas.

practice


__________ refers to repetitive, nonproblembased exercises designed to improve skills or already acquired skills.

drill


___________ can provide an increased facility with a strategy but only with a strategy already learned.

drill


With ___________, there is a review of facts or procedures so they are not forgotten.

drill


With __________, there is a focus on a singular method and an exclusion of flexible alternatives.

drill


With ___________, there can be a false appearance of understanding.

drill


_______ only focuses on what is known.

drill


____________ provides an increased opportunity to develop conceptual ideas and more elaborate and useful connections.

practice


___________ provides an opportunity to develop alternative and flexible strategies.

practice


___________ provides a greater chance for all students to understand, particularly students with special needs.

practice


_____________ provides a clear message that mathematics is about figuring things out and making sense.

practice


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.

assessment


The purpose of _________ is to monitor student progress.

assessment


The purpose of ___________ is to make instructional decisions.

assessment


The purpose of ________ is to evaluate student achievement.

assessment


The purpose of __________ is to evaluate programs.

assessment


What three things should be assessed in mathematics?

concepts and procedures
mathematical processes productive dispositions 

True/false questions should be limited to what?

10


How many matching should there be on a test?

between 515


What kinds of lists should be used with matching?

homogeneous


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

scoring


________ is the result of accumulating scores and other information about a student's work for the purpose of summarizing and communicating to others.

grading


________ 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".

rubric


_____________ 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 writeups about certain students, kept on individual note cards or on large peeloff 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 reread 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.

grade


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?

objectives


What are the 6 assessment standards?
ol mice 
Openness
Learning Mathematics inferences coherent equity 

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.

equity


In the __________ standard, the teacher should maintain high expectations for students, while recognizing their individual needs.

equity


In the _________ standard, the teacher should look at how the students can demonstrate what they know.

openness


In the ___________ standard, the teacher should avoid looking at the answers and give attention to the examination of the thinking processes students used.

openness


In the ____________ standard, the teacher should provide students with examples of responses that meet expectations and those that don't meet expectations.

openness


In the _________ standard, the teacher should reflect seriously and honestly on what students are revealing about what they know.

inferences


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.

inferences


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.

constructivism


In ___________, students make connections between old ideas and the new ones.

constructivism


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.

assessment


Assessments should be done ____ students.

for
