MATH

1. MATH BY MEAGHAN, ROWEN, ELSIE

2. 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

3. INTRODUCTION PAST pg 117 • LACKING HIGHER LEVEL COGNITIVE & UNDERSTANDING • ROUTE LEARNING • ALGORITHIMS • PAPER PENCIL PROCESS • LIMITED SCOPE

4. INTRODUCTION CURRENT ISSUE pg 117 • SOCIETY’S RAPID ADVANCE • NEED EXPERIENCE DISCOVERY & CONNECTION “We are what we experience” • TEACH UNDERSTANDING &ENGAGE STUDENTS

5. 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

6. SELECT APPROPIRATE MATH: NATIONAL standards K-12 pg 118 NUMBER & OPERATIONS ALGEBRA Understand: Patterns, relations, functions Represent & Analyze Situations, structures, symbols Use math models Quantitative relationships Analyze • Understand: #’s • Ways of representing #’s • Relationship between #’s • Number Systems • Meaning of operations & its relationship • Compute & Estimate

7. SELECT APPROPIRATE MATH: NATIONAL standards K-12 pg 118 GEOMETRY MEASUREMENT Understand measurable attributes: Objects, units, systems, processes Apply appropriate: Techniques Tools Formulas • Analyze 2 &3 dimmesional shapes • Specify & describe • Apply transformations • Use visualization, spatial reasoning, geometric modeling

8. SELECT APPROPIRATE MATH: OTHER NATIONAL standards K-12 pg 119 • DATA ANALYSIS & PROBABILITY • PROBLEM SOLVING • REASONING & PROOF • COMMUNICATION • CONNECTIONS • REPRESENTATION

9. 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

10. 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

11. RESEARCH ON MATH INSTRUCTION pg 121 • EFFECTIVE MATH PROGRAM • Solve Problems- meaningful situations • Use Manipulative • Work Cooperatively- others, small groups • Develop Own Procedures- discuss, explain, modify • Use Thinking Strategies • Incorporate Math

12. CONCRETE, SEMI-CONCRETE, AND ABSTRACT SEQUENCE pg 122 • 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

13. 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 concepts • 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)

14. -GUIDELINES FOR USING MANIPULATIVE OBJECTS (Dunlap and Brennan 1979) • Elevating Progression: • Before abstract experiences, instruction must proceed from concrete (Manipulative) experiences to semi concrete experiences. • Visualization: • The main objective is to help students understand and develop mental images of mathematical processes. • 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

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

16. SEMI-CONCRETE LEVEL pg 122 • Representational level • Use of two-dimensional drawings (i.e. pictures or lines or tallies) • Example: A paper and pencil task that requires the learner to match the sets of the same number of items.

17. 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

18. 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.

19. ASSESSMENT AND ERROR ANALYSIS continued pg 133 • 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.

20. APPROACH TO PROBLEM SOLVING pg 125 • Understand the problem • Plan how you can solve it • Carry out the plan • Look back over the problem

21. PROBLEM SOLVING STRATEGIES pg 127 • Use a pattern • Make a table • Make a list • Guess and check • Act it out

22. PROBLEM SOLVING STRATEGIES continued pg 127 • Draw a picture • Work backward • Make a model • Use objects