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 ▪ 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

7. 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

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 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

12. 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

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 o 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) 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

15. 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

16. 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.

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. 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

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