Math Methods Test 1

Front 1

Definition of Mathematics

Back 1

* a study of patterns and relationships
*a way of thinking
*an art
*a language
*a tool

Front 2

Factors Influencing Math Being Taught

Back 2

*Needs of the Subject
*Needs of the Child
*Needs of Society

Front 3

5 process standards

Back 3

*Problem Sovling
*Reasoning and Proving
*Communicating
*Connecting
*Representing

Front 4

5 Content Standards

Back 4

*Number & Operations
*Algebra
*Geometry
*Measurement
*Data Analysis & Probability

Front 5

Behaviorism

Back 5

*Behavior can be shaped through reinforcement
*Practice promotes desired behavior

Front 6

Constructivism

Back 6

*Learners actively create or invent (construct) their own knowledge
*Students create new mathematical knowledge by reflecting on their physical and mental actions.

Front 7

Procedural Knowledge

Back 7

based on a series of actions, rules, and algorithms (behaviorism)

Front 8

Conceptual Knowledge

Back 8

Based on meaningful connections among existing and new concepts (constructivism)

Front 9

Conceptual or Procedural?
1) to divide 23 candies among 4 friends, Steve knows each must receive an equal amount and there may be some left
2) To take 23 divided by 4, Steve knows to take 5 x 4 and subtract the reult form 23

Back 9

1) conceptual (understands concept)
2) procedural (using rules)

Front 10

Conceptual or Procedural?
1) Sara knows when counting, 7 follows 6
2) Sara knows 7 represents 7 objects

Back 10

1) procedural (following rules)
2) conceptual (making a connection between objects)

Front 11

Conceptual or Procedural?
1) Joe knows that to find 25% of a price he can cut the price in half, then half againt o find one-fourth.
2) Joe knows that to find 25% of a price he can multiply the price by .25

Back 11

1) conceptual (using own method)
2) procedural (using rule)

Front 12

Conceptual or Procedural?
1) Nancy knows that to find the area of a rectangle, she must find out how much space it covers.
2) Nancy knows that to find the area of a rectangle she must multiply the length times the width.

Back 12

1) conceptual (understand what the concept of area is)
2) procedural (understands the rule of finding area)

Front 13

6 types of computer software

Back 13

*Drill-and-practice software
*tutorial software
*Simulation software
*Educational game software
*Problem-solving software
*Tool Software

Front 14

What Are Investigative Lessons?

Back 14

*Develop problem solving skills, learning new concepts or applying and deepending understanding of previously learned ideas
*involved students in pursing a problem or exporation on their own, the lesson revolves aroudn ideas taht the students generate through their own invesigations

Front 15

What are the parts of an investigative lesson?

Back 15

*Launch: motivation i sprovided for the lesson and the probelm at hand is expalined
*Investigate: migh involved learning stations, individual work, paried problem solving, or cooperative groups. Teacher OBSERVES and interjects questions/comments
*Summarize: class comes back together to talk about their findigs. THis is the apprpriate time for identifying generalities or starting rules that have been formulated.

Front 16

Direct Instruction Lessons

Back 16

Appropriate when teh teacher wants to communicate specific knowledge to instroduce a new vocabulary or to teach certain procedures.
*Teacher exercises more control and the lesson has a tighter focus.
*LAUNCH, INSTRUCT (whole-class teacher instruction, class/individual activities), SUMMARY

Front 17

Prenumber concepts

Back 17

*classification
*patterns
*Comparisons
*conservation
*group recognition
THESE CONCEPTS DO NOT RELY ON NUMBER BUT PROVIDE A FOUNDATION FOR LATER NUMBER CONCEPTS/SKILLS

Front 18

Classification

Back 18

*helps identify what is to be counted
*fosters thinking skills
*forces defense of answers
*no counting words in beginning (use words like more, few, many, most, and none)

Front 19

Patterns

Back 19

*early exploration w/ patterns helps develop ordering, sequencing, and counting
*later patterns help students develop thinking strategies for basic facts
*even later these skills contribute to growth in graphing, number theory, and geometry

Front 20

Comparisons

Back 20

*comparing leads to one-to-one correspondence
*early learners need connectors as a visual reminder of one-to-one correspondence
*use of square paper or index cards brovides a graphical framework

Front 21

Subitizing definition

Back 21

the skill to instantly see how many

Front 22

Group Recognition

Back 22

*subitizing

Front 23

Conservation

Back 23

*A given number doesn't vary
*a young child may think taht a number varies depending on arrangement or configuarion
*children rarely conserve number before 5 or 6 years old.
*a child can be very good at counting, and remaind naive about conservation

Front 24

Referent, Chunking, and Utilizing

Back 24

*REFERENT: "I am about 6 feet tall so the door must be about 7 feet tall"
*CHUNKING: (break the object into subparts and estimate each part) " I know it's a yard to the know, another yard to here, so a little more than 2 yards
*UTILIZING: Each cement block is about 8 inches. Therea re 10 blocks so about 80 inches

Front 25

Proportional palce value manipulatives

Back 25

*Proportional models are recommended for grades 1-3
EX: Base-ten blocks and bundling (popsicle sticks)

Front 26

Nonproportional place value manipulatives

Back 26

*reccommended ofr those students who are in grades 4 and up
EX: money, abacus, colored counters

Front 27

Appropriate sequence of place value models

Back 27

Place value must be taught in the following sequence: concrete physical models, semi-concrete organizational models, symbolic representation models.