MATH

BY MEAGHAN, ROWEN, ELSIE

CONTENT LIST

▪ INTRODUCTION: Past vs Present

▪ SELECTING APPROPRIATE MATH: Math Standards

▪ RESEARCH ON MATH INSTRUCTION: W.H.W., Effective Math

▪ CONCRETE, SEMI-CONCRETE, AND ABSTRACT SEQUENCE

▪ ASSESSMENT AND ERROR ANALYSIS

▪ PROBLEM SOLVING

INTRODUCTION PAST pg 117

▪ LACKING HIGHER LEVEL COGNITIVE &

UNDERSTANDING

▪ ROUTE LEARNING

▪ ALGORITHIMS

▪ PAPER PENCIL PROCESS

▪ LIMITED SCOPE

INTRODUCTION CURRENT ISSUE pg 117

▪ SOCIETY’S RAPID ADVANCE

▪ NEED EXPERIENCE DISCOVERY &

CONNECTION

“We are what we experience”

▪ TEACH UNDERSTANDING &ENGAGE

STUDENTS

SELECT APPROPIRATE MATH: NATIONAL standards K-12 pg 118

▪ NUMBER AND OPERATIONS

▪ ALGEBRA

▪ GEOMETRY

▪ MEAUREMENT

▪ DATA ANALYSIS, PROBLEM SOLVING, REASONING AND PROOF, COMMUNICATION, CONNECTIONS, REPRESENTATION

http://nctm.org/standards

SELECT APPROPIRATE MATH: NATIONAL standards K-12 pg 118

NUMBER & OPERATIONS

▪ Understand: #’s– Ways of representing #’s– Relationship between #’s– Number Systems

▪ Meaning of operations & its relationship

▪ Compute & Estimate

ALGEBRA

▪ Understand:– Patterns, relations, functions

▪ Represent & Analyze– Situations, structures,

symbols

▪ Use math models– Quantitative relationships

▪ Analyze

SELECT APPROPIRATE MATH: NATIONAL standards K-12 pg 118

GEOMETRY

▪ Analyze 2 &3 dimmesional shapes

▪ Specify & describe

▪ Apply transformations

▪ Use visualization, spatial reasoning, geometric modeling

MEASUREMENT

▪ Understand measurable attributes:– Objects, units, systems,

processes

▪ Apply appropriate:– Techniques– Tools– Formulas

SELECT APPROPIRATE MATH:

OTHER NATIONAL standards K-12 pg 119

▪ DATA ANALYSIS & PROBABILITY

▪ PROBLEM SOLVING

▪ REASONING & PROOF

▪ COMMUNICATION

▪ CONNECTIONS

▪ REPRESENTATION

SELECT APPRORIATE MATH-HCPS III: STATE pg 120

▪ NUMBER AND OPERATIONS

▪ MEASUREMENT

▪ GEOMETRY AND SPATIAL SENSE

▪ PATTERNS, FUNCTIONS, AND ALGEBRA

▪ DATA ANALYSIS, STATISTICS, AND PROBABILITY

RESEARCH ON MATH INSTRUCTION pg 121

▪ WHAT TO DO vs HOW TO DO

– Understanding can be applied to new tasks

– Learning meanings make procedures easier to

remember

– Reasoning is an effective goal

RESEARCH ON MATH INSTRUCTION pg 121

▪ EFFECTIVE MATH PROGRAM

1. Solve Problems- meaningful situations

2. Use Manipulative

3. Work Cooperatively- others, small groups

4. Develop Own Procedures- discuss, explain, modify

5. Use Thinking Strategies

6. Incorporate Math

CONCRETE, SEMI-CONCRETE, AND ABSTRACT SEQUENCE pg 122

1. The CSA sequence is used for teaching a basic understanding of math throughout the span of concepts, skills, and word problems.

▪ The different levels of math understanding

CONCRETE LEVEL pg 122

Involves the manipulation of objects

Helps students make a connection to manipulative solid objects and the computational processes that are involved in math problems

Students should have multiple opportunities to manipulate concrete objects in order to learn important math conceptso Example: Using blocks to represent all the possible sums

of 8 (students group blocks into all possible combinations of 8; 1+7, 2+6, 5+3, 4+4)

-GUIDELINES FOR USING MANIPULATIVE OBJECTS (Dunlap and Brennan 1979)

1.Elevating Progression: Before abstract experiences, instruction must proceed

from concrete (Manipulative) experiences to semi concrete experiences.

2.Visualization: The main objective is to help students understand and

develop mental images of mathematical processes.

3.Consistency: The activity must accurately represent the actual

process. For example, a direct correlation must exist between the manipulative activities and the paper pencil activities

4. Multiple angles: More than one manipulative should be used in a teaching

concept.

5. Full participation: The manipulative should be used individually by each

student

6. Active Learning The manipulative experience must involve the moving of

objects. Learning occurs from the student’s physical actions on the objects, not from the objects themselves.

-GUIDELINES FOR USING MANIPULATIVE OBJECTS (Dunlap and Brennan 1979) continued

SEMI-CONCRETE LEVEL pg 122

Representational level

Use of two-dimensional drawings (i.e. pictures or lines or tallies)

o Example: A paper and pencil task that requires the learner to match the sets of the same number of items.

ABSTRACT LEVEL pg 122

Solve problems without using objects or drawings to solve computation problems

Student reads the problem, remembers the answer or thinks of a way to compute the answer, and writes the answer.

Mastery at this level is essential

ASSESSMENT AND ERROR ANALYSIS pg 133

• Computation errors: The student translates the problem into the correct equation, but makes an error in figuring out the answer.

• Basic fact errors: The student translates the problem correctly, but makes an error in one of the basic facts.

• Decoding errors: The student reads one of the critical words incorrectly.

• Vocabulary errors: The student does not know the meaning of words.

• Translation errors: The student uses the wrong operation or does not translate the problem into the correct equation.

ASSESSMENT AND ERROR ANALYSIS continued pg 133

APPROACH TO PROBLEM SOLVING pg 125

▪ Understand the problem

▪ Plan how you can solve it

▪ Carry out the plan

▪ Look back over the problem

PROBLEM SOLVING STRATEGIES pg 127

▪ Use a pattern

▪ Make a table

▪ Make a list

▪ Guess and check

▪ Act it out

▪ Draw a picture

▪ Work backward

▪ Make a model

▪ Use objects

PROBLEM SOLVING STRATEGIES continued pg 127