Math Methods Test 1

Front 1

Students must experience mathematics that what?

Back 1

makes sense

Front 2

Students must come to believe what?

Back 2

That they are capable of making sense of mathematics

Front 3

What should teachers stop doing?

Back 3

teaching by telling

Front 4

Name some of the verbs of "DOING" mathematics. (not to be confused with the daily objective verbs)

Back 4

use
explain
predict
investigate
formulate
justify
verify
explore
represent

Front 5

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

Back 5

ideas

Front 6

In a productive classroom culture, students have autonomy with what?

Back 6

respect to the methods used to solve problems

Front 7

In a productive classroom culture, how are mistakes viewed?

Back 7

as an opportunity to learn

Front 8

In a productive classroom culture, reasonability lies in what?

Back 8

The logic and structure of the subject, not the person or social status of the participants.

Front 9

Which principle includes high expectations and is shown through words, actions, and parental involvement?

Back 9

Equity principle

Front 10

Which principle states that one should know the content and know how students learn?

Back 10

Teaching princple

Front 11

The ___________ principle is coherent, focused, and well articulated across grade levels.

Back 11

curriculum principle

Front 12

In the ________ principle, new knowledge is built through connections with prior knowledge and experiences.

Back 12

learning principle

Front 13

The _________ principle enhances students learning, allows for more/deeper mathematics to be taught.

Back 13

technology

Front 14

What are the 5 content strands

Back 14

number and operations
algebra
geometry
measurement
data and analysis

Front 15

What are the 5 process standards?

Back 15

problem solving
reasoning and proof
representations
communication
connections

Front 16

The ____________ process standard is how students learn mathematics.

Back 16

problem solving

Front 17

The ________ process standard states that logical thinking should determine if and why answers are correct; providing a rationale should be part of every answer.

Back 17

Reasoning and proof

Front 18

The __________ process standard includes talking about, writing about, explaining, and describing mathematical ideas.

Back 18

communication

Front 19

In the connections process standard, there are two ways to make connections. What are they?

Back 19

within and among mathematics ideas
to the real world and other disciplines

Front 20

Using symbols, charts, diagrams, graphs, and manipulatives is part of what process standard?

Back 20

representation

Front 21

When "doing" mathematics, you do what?

Back 21

devise a plan
apply the plan to see if it leads to a solution
check to see if solution makes sense

Front 22

What should the act of doing mathematics in the classroom closely model?

Back 22

the act of doing mathematics in the real world

Front 23

What does Piaget believe about children?

Back 23

that they create their own learning

Front 24

Piaget believes that people construct their own knowledge according to what?

Back 24

their previous knowledge, which gives them meaning to things they think about

Front 25

What is understanding?

Back 25

a measure of the quantity and quality of the connections that an idea has with existing ideas

Front 26

What does understanding exist on?

Back 26

a continuum

Front 27

________________ understanding is when ideas are highly connected and the person knows what to do and why.

Back 27

relational understanding

Front 28

_______ understanding takes a lot of work and effort.

Back 28

relational understanding

Front 29

___________ understanding is when concepts and connections develop over time, and not in a day.

Back 29

relational understanding

Front 30

_____________ understanding is when ideas are isolated completely. It involves doing with understanding.

Back 30

instrumental understanding

Front 31

Effective learning of new concepts and procedures is a benefit of what?

Back 31

relational understanding

Front 32

With ______________ understanding, there is less to remember, increased retention and recall, enhanced problem solving abilities, and improved attitudes and beliefs.

Back 32

relational understanding

Front 33

__________ understanding is knowledge about the relationships or foundational ideas of a topic.

Back 33

conceptual understanding

Front 34

___________ understanding is knowledge of the rules and procedures used in carrying out mathematical processes and of the symbolism that is used to represent mathematics.

Back 34

procedural understanding

Front 35

Is conceptual or procedural understanding taught first?

Back 35

conceptual

Front 36

Pictures, written symbols, manipulative models, real world situations, and oral language are what?

Back 36

Ways of representing mathematical ideas

Front 37

When should written symbols be used during a lesson?

Back 37

at the end

Front 38

How many ways of representing mathematical ideas should be used?

Back 38

at least 3

Front 39

Which three ways of representing mathematical ideas should be used at all times?

Back 39

manipulative models
pictures
real world situations

Front 40

Which way of representing a mathematical idea should be used in groups?

Back 40

oral language

Front 41

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.

Back 41

problem

Front 42

When solving a problem, student should do what?

Back 42

work through it on their own.

Front 43

There are 3 features of a problem for learning math. The first feature states that it should begin where?

Back 43

Where the students are

Front 44

Students should have the appropriate ideas to engage and solve the problem, yet still find it what?

Back 44

challenging and interesting

Front 45

The problematic or engaging aspect of the problem must be due to what?

Back 45

the mathematics that the students are about to learn

Front 46

Students should be primarily concerned with making sense of mathematical ideas and then doing what?

Back 46

developing an understanding of those ideas

Front 47

In a problem for learning math, it must require what?

Back 47

explanations and justifications for answers

Front 48

What is the value of teaching through problem solving?

Back 48

A teacher changes her philosophy of how she thinks children learn. and how she can best help them learn.

Front 49

Models can be thought of as what?

Back 49

thinker toys

Front 50

___________ are used to help students develop new concepts or relationships.

Back 50

models

Front 51

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

Back 51

models

Front 52

__________ are use to assess students' understanding.

Back 52

models

Front 53

Good problems will integrate what?

Back 53

multiple topics

Front 54

Teaching with problems focuses students' attention on what?

Back 54

ideas and sense making

Front 55

Teaching with problems allows _____________ for a wide range of students.

Back 55

an entry point for a wide range of students

Front 56

Teaching with problems provides what?

Back 56

ongoing assessment data

Front 57

Teaching with problems allows for what?

Back 57

extensions and elaborations

Front 58

What are the 3 types of information teachers should provide for students?

Back 58

mathematical conventions
alternative methods
clarification of student methods

Front 59

Symbols, terminology, definitions, and labels are what?

Back 59

mathematical conventions

Front 60

Student writing is important because it is a ________ process.

Back 60

reflective

Front 61

In the three-part lesson format, the before phase has the teacher doing what three things?

Back 61

activating prior knowledge
making sure the task is understood
establishing clear expectations

Front 62

In the three-part lesson format, the during phase says that teachers should do what?

Back 62

let the students do it on their own

Front 63

In the during phase of the three-part lesson plan, the teacher should provide appropriate what?

Back 63

hints

Front 64

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

Back 64

worthwhile extension ideas

Front 65

In the three-part lesson format, the after phase says to promote what?

Back 65

a mathematical community of learners

Front 66

Teacher should encourage student-student what?

Back 66

dialogue

Front 67

What should be requested to accompany all answers?

Back 67

explanations

Front 68

Teachers should listen actively without what?

Back 68

evaluation

Front 69

Teachers should summarize main ideas and identify what?

Back 69

future problems

Front 70

Problems that can be approached in several different ways depending on the ability and learning style of the student is what?

Back 70

a multiple point entry problem

Front 71

_______________ is a provision of a different environment or circumstance made with particular students in mind.

Back 71

accommodation

Front 72

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

Back 72

modification

Front 73

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

Back 73

practice

Front 74

__________ refers to repetitive, non-problem-based exercises designed to improve skills or already acquired skills.

Back 74

drill

Front 75

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

Back 75

drill

Front 76

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

Back 76

drill

Front 77

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

Back 77

drill

Front 78

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

Back 78

drill

Front 79

_______ only focuses on what is known.

Back 79

drill

Front 80

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

Back 80

practice

Front 81

___________ provides an opportunity to develop alternative and flexible strategies.

Back 81

practice

Front 82

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

Back 82

practice

Front 83

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

Back 83

practice

Front 84

When doing practice, you should practice the use of what?

Back 84

flexible conceptual approaches, not isolated meaningless procedures learned by rote

Front 85

How long should practice be?

Back 85

15 minutes, 3 to 4 times per week

Front 86

What are the reasons you have students practice?

Back 86

To help them become quick, yet flexible

Front 87

What does homework communicate to parents and students?

Back 87

the importance of conceptual understanding

Front 88

When home work is drill, it should be what?

Back 88

kept short
have an answer key
not be graded on correctness
not gone over in class

Front 89

When teaching with a textbook, the goal is to teach what?

Back 89

the big ideas, not the pages

Front 90

When using a textbook, the pace of the lessons should be determined by what?

Back 90

student performance and understanding

Front 91

__________ 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.

Back 91

assessment

Front 92

The purpose of _________ is to monitor student progress.

Back 92

assessment

Front 93

The purpose of ___________ is to make instructional decisions.

Back 93

assessment

Front 94

The purpose of ________ is to evaluate student achievement.

Back 94

assessment

Front 95

The purpose of __________ is to evaluate programs.

Back 95

assessment

Front 96

What three things should be assessed in mathematics?

Back 96

concepts and procedures
mathematical processes
productive dispositions

Front 97

True/false questions should be limited to what?

Back 97

10

Front 98

How many matching should there be on a test?

Back 98

between 5-15

Front 99

What kinds of lists should be used with matching?

Back 99

homogeneous

Front 100

Where should the main idea be stated in a multiple choice question?

Back 100

in the stem

Front 101

_________ is comparing students' work to correct answers or specific criteria that describes what we expect the work to be

Back 101

scoring

Front 102

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

Back 102

grading

Front 103

________ 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".

Back 103

rubric

Front 104

_____________ 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.

Back 104

performance indicators

Front 105

____________ are brief write-ups about certain students, kept on individual note cards or on large peel-off labels.

Back 105

anecdotal records

Front 106

___________ are useful for planning purposes.

Back 106

observational rubrics

Front 107

__________ is one checklist per student, but each contains the same set of specific processes to be observed.

Back 107

individual checklists

Front 108

______________ are one page charts with places for checks when certain "behaviors" have been observed or not.

Back 108

checklists for full classes

Front 109

What are the advantages of writing in the math classroom?

Back 109

it's private
it can be revised or edited
it can be re-read at a later time
includes pictures, graphs, and symbols

Front 110

What are the 4 types of writing in the math classroom?

Back 110

journal writing
problem solving
explaining the idea
reflective writing

Front 111

Give an example of a math writing prompt.

Back 111

If math were a color, what would it be?
I need help with _________ because..............

Front 112

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.

Back 112

grade

Front 113

When looking at the grade at the end of a period, it should reflect what?

Back 113

all areas of grading, not just tests

Front 114

Grades assigned should reflect all of what?

Back 114

objectives

Front 115

What are the 6 assessment standards?
ol mice

Back 115

Openness
Learning
Mathematics
inferences
coherent
equity

Front 116

Using the frameworks to determine what the students should know and do and basing assessments on those essential concepts and processes is which standard?

Back 116

mathematical standard

Front 117

Incorporating assessment as an important part of instruction and not an interruption or at the end of the unit is part of what standard?

Back 117

learning standard

Front 118

In the _______ standard, the teacher should determine students' misunderstanding of the material and go deeper.

Back 118

learning standard

Front 119

In the __________ standard, the teacher should respect the unique qualities, experiences, and expertise of all students.

Back 119

equity

Front 120

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

Back 120

equity

Front 121

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

Back 121

openness

Front 122

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

Back 122

openness

Front 123

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

Back 123

openness

Front 124

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

Back 124

inferences

Front 125

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.

Back 125

inferences

Front 126

In the _______ standard, the teacher should match his/her assessment techniques with both objectives of the instruction and the methods of the instruction,

Back 126

coherence standard

Front 127

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.

Back 127

coherence standard

Front 128

In _________, students must be actively participants in the development of their own understanding.

Back 128

constructivism

Front 129

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

Back 129

constructivism

Front 130

Students are not _______, they do not absorb new ideas.

Back 130

blank slates

Front 131

In the teaching principle, the teacher should use what?

Back 131

appropriate instructional tasks

Front 132

In the teaching principle, the teacher should use a journal for what?

Back 132

to reflect on lessons

Front 133

In the teaching principle, the teacher should share ideas and what?

Back 133

plan ahead

Front 134

____________ principle is used to guide instructional decision.

Back 134

assessment

Front 135

Assessments should be done ____ students.

Back 135

for