1. SPED 114<br />TTH 0200 – 0430 pm<br />Curriculum and Instruction for Exceptional Children<br />
2. MATHEMATICS<br />Group 3<br />Arellano, Joy Dominique <br />Buot, Rachelle Marie<br />Gelasque, Jonalyn<br />Gomez, Hanna Rose<br />Kabingue, Jessadel Christine<br />Kangleon, YasmeenSydney<br />Villamor, Ray Paulo<br />
3. Elementary mathematics was part of the education system in most ancient civilisations, including Ancient Greece, the Roman empire, Vedic society and ancient Egypt. <br />In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste.<br />HISTORY<br />
4.
5. <ul><li> The key to teaching math so students internalize and transfer their knowledge is to make learning math personal.
6. No matter how many worksheets students complete, they will never make the connection between math concepts until it is concrete and relates to their personal environment.
7. Math needs to be real and not just a set of numbers or endless problems to calculate.
8. Personal math allows students to link concepts as whole and not a lot of independent ideas (or baseballs) with no connection.</li></li></ul><li>The following techniques aid students transferring math concept knowledge to other math concepts for linking concepts<br />
9. The following techniques aid students transferring math concept knowledge to other math concepts for linking concepts<br /><ul><li>Problem-Based Learning (PBL)
10. Interactive Math Tools
11. Using Manipulatives to Model Math Problems
12. Explain How to Solve Math Problems in Writing
13. Making Connections</li></li></ul><li>Techniques that aid students to transfer math concept knowledge to other math concepts for linking concepts.<br />Problem-Based Learning (PBL)<br />The best strategy in PBL is the use of case studies which present students with real life problems that require applications of math to solve or find a solution. Students:<br />determine what they know by identifying what is known, what needs to be find out, what they want to learn (KWL) based on a given case study scenario.<br />develop a problem statement which contains steps for solving the problem and factors for determining successful completion.<br />
14. Techniques that aid students to transfer math concept knowledge to other math concepts for linking concepts.<br />Problem-Based Learning (PBL)<br />The best strategy in PBL is the use of case studies which present students with real life problems that require applications of math to solve or find a solution. Students:<br />gather information through online resources, surveys, interviews, observations, measurements, etc.<br />develop possible solutions using concept maps, Venn diagrams, graphic organizers, etc.<br />present a solution to the case study based on what was learned.<br />
15. Techniques that aid students to transfer math concept knowledge to other math concepts for linking concepts.<br />Interactive Math Tools<br />Choose an interactive tool that requires students to use problem solving strategies that use formal operational skills and proportional reasoning. <br />The best interactive math tools require students to solve problems by applying more than one math concept.<br />Interactive math addresses the problem of engaging students through the use of virtual manipulatives to help them visualize math relationships. Virtual math learning environments allow students to apply logic and reasoning for problem solving.<br />
16. Techniques that aid students to transfer math concept knowledge to other math concepts for linking concepts.<br />Using Manipulatives to Model Math Problems<br />Learning and understanding mathematics, at every level, requires student engagement. <br />Students must be engaged in the learning process through practical applications of math. <br />Whether the manipulatives are purchased in kits or created from available materials, this hands-on learning approach engages students’ minds as they use manipulatives to create models and representations to solve math problems.<br />
17. Techniques that aid students to transfer math concept knowledge to other math concepts for linking concepts.<br />Explain How to Solve Math Problems in Writing<br />This technique involves students solving a problem and then writing a story describing how the problem was solved. <br />Writing provides students with a creative method to think and internalize how they linked math concepts in real life problem solving situations. <br />These student writings also provide teachers with an insight into a student’s true understanding of math that a dozen work sheets could never provide.<br />
18. Techniques that aid students to transfer math concept knowledge to other math concepts for linking concepts.<br />Making Connections<br />When students are engaged in learning math that is personal to them, they are engaged in the learning process.<br /> Problem solving situations, case studies, and traditional math problems focused on students provide increased opportunities to internalize and make connections. <br />Students like to participate and not watch demonstrations of how to solve problems; true understanding comes from hands-on, minds-on math.<br />
25. <ul><li>QUESTIONING</li></ul>Effective teachers ask more process questions (calling for explanations) and more product questions (calling for short answers.<br /><ul><li>ENCOURAGEMENT</li></ul>Effective teachers are more encouraging (e.g., providing reinforcement for questions and requests for help) and receptive to student input<br />EFFECTIVE MATHEMATICS TEACHING<br />
26. <ul><li>MODELLING</li></ul>Effective teachers exhibit more problem solving behavior and communicate the importance of problem solving.<br /><ul><li>CLARITY</li></ul>Effective teachers exercise more clarity (i.e., careful use of vocabulary and systematic explanations)<br />EFFECTIVE MATHEMATICS TEACHING<br />
27. <ul><li>EXPECTATIONS</li></ul>Set firm and appropriate expectations. High academic expectations are a major factor that differentiates effective schools from ineffective ones.<br />EFFECTIVE MATHEMATICS TEACHING<br />
28. TELLING TIME<br />
29.
30. Telling Time<br />You can tell what time it is in several ways:<br />the position of the sun in the sky, <br />the length of shadows, <br />the activities people are doing, <br />and clocks and watches.<br />
31. Telling Time<br />Direct student's attention to the clock. <br />How many big numbers are on the clock? <br />Have students point to the hour hand. <br />Tell them that when the hour hand moves from one number to the next, one hour has passed. <br />Have students point to the minute hand. <br />Tell them that when the minute hand moves from one tick mark to the next, one minute has passed. <br />
32. Write the minutes to tell time.<br />3:15<br />9:05<br />15 minutes past 3<br />5 minutes after 9<br />
33. Write the minutes to tell time.<br />10:40<br />04:30<br />20 minutes before 11<br />5 minutes after 4<br />
34. Write the minutes to tell time.<br />Combine visuals<br />Equivalent answers<br />With word problems and/or statements<br />6:21<br />21 minutes past 6<br />
37. Basic Operations<br />ADDITION<br />Adding two (or more) numbers means to find their sum (or total). <br />The symbol used for addition is '+'.<br /> 8 - addend<br />+ 4 - addend<br />12 - Sum <br />
38. Basic Operations<br />ADDITION<br />For example, 5 + 10 = 15<br />This is read as five plus ten is equal to fifteen or simply, five plus ten is fifteen.<br />Find the sum of 9 and 8.<br />Solution:<br /> 9 + 8 = 17<br />
39. Basic Operations<br />SUBTRACTION<br />Subtracting one number from another number is to find the difference between them. <br />The symbol used for subtraction is '–'. <br />This is known as the minus sign.<br />We call the ‘total’ or result of subtraction as difference.<br />
41. Basic Operations<br />SUBTRACTION<br />For example, 17 – 8 = 9<br />This is read as seventeen take away eight is equal to nine or<br />seventeen take away eight is nine. <br />Also, we can say that 17 minus 8 is 9.<br />
42. Basic Operations<br />MULTIPLICATION<br />Multiplication means times (or repeated addition). <br />The symbol used for multiplication is '×'.<br />A product is the result of the multiplication of two (or more) numbers.<br />
43. Basic Operations<br />MULTIPLICATION<br />For example, 7 × 2 = 14This is read as seven times two is equal to fourteen or simply, seven times two is fourteen.<br />To multiply a large number with another number, we write the numbers vertically and generally multiply the larger number with the smaller number<br />
45. Basic Operations<br />DIVISION<br />Division 'undoes' multiplication and involves a number called the dividend being 'divided' by another number called the divisor.<br />The symbol used for division is '÷‘.<br />Clearly, 9 x 8 = 72<br />Therefore, 72 ÷ 9 = 8<br />And 72 ÷ 8 = 9<br />
47. Basic Operations<br />SUMMARY<br />Adding two (or more) numbers means to find their sum (or total).<br />Subtracting one number from another number is to find the difference between them.<br />Multiplication means times (or repeated addition). A product is the result of the multiplication of two (or more) numbers.<br />Division 'undoes' multiplication.<br />
48. 4 BASIC OPERATIONS:<br />ADDITION<br />Game: The Boat is Sinking<br />Flow of the game:Everyone must participate in this game.<br />Group yourselves according to what the reporter says.<br /><ul><li>The boat is sinking, 5+2=? group yourselves!!
49. The boat is sinking, 8+2=? group yourselves!!
50. The boat is sinking, 2+2=? group yourselves!!
51. The boat is sinking, 4+5=? group yourselves!!
52. The boat is sinking, 1+4=? group yourselves!!</li></li></ul><li>4 BASIC OPERATIONS:<br />2. Subtraction <br />Flashcard Game<br />Material: Flashcards<br />Flow of the game: Each group must have 1 representative.<br />The starting point of the game will start at the back of the room.<br />Each correct answer entitles the player a step forward.<br />The first representative that can answer fast will be the winner.<br />
53. 4 BASIC OPERATIONS:<br />3. Multiplication<br />Show me your answer!<br />Materials: Paper, pentelpen<br />Flow of the game: The reporters will dictate questions that needs to be solved in each group (e.g. 2 x 2=?).<br />Each group will choose 1 representative to give their answers.<br />The first group that can give their correct answer/s will gain points.<br />
54. 4 BASIC OPERATIONS:<br />4. Division –<br />Follow instructions.<br />Speed and accuracy wins you the game.<br />Get it right. Get it fast.<br />
57. CONTENT – meaning of FRACTIONS<br />TEACHING Strategy – Discussion with examples<br />ASSESSMENT – Paper-Pen Test<br />(specifically Identification Test)<br />
58. FRACTIONS<br />Fractions are parts of a whole<br />The shaded portion in the circle below is part of a whole. It is one half of the whole circle.<br />In fraction, it is written as ½ and is read as one half<br /> 1 – numerator<br /> 2 – denominator <br />
59. FRACTIONS<br />
60. PROBLEM SOLVING<br />
61. Teach word problems by the following guidelines recommended by Blankenship and Lovitt (1976)<br />
62. Guidelines in teaching Word Problems<br />Teachers should identify and teach story problems by type, according to various characteristics (Examples: Extraneous information, verb tense, number and types of nouns).<br />Make up several problems of each type in order to provide practice.<br />A group of instruction technology should be outlined and used. It may be necessary to vary the technology according to the needs of each student; however, a systematic plan is essential<br />
63. Clue Words in Word Problems<br />
64. Solve this!<br />Arrange 9 toothpicks to form 5 triangles. The triangles do not all have to be the same size<br />
65. Answer<br />
66. SOLVING WORD PROBLEMS<br />1. Read the problem carefully.<br />2. Cross out unnecessary information.<br />3. Show your work. Don't do it in your head.<br />4. Don't erase your mistakes. Cross out errors<br />instead.<br />5. Re-read your problem and check your<br />answers.<br />6. Draw a picture that illustrates the problem.<br />7. Write in your own words how you got your<br />answer.<br />
67. Word Problems<br />1. Shelby went to an Easter party at her friend’s house. She found 38 chocolate eggs during the egg hunt. She gave half of the eggs to her sister. How many eggs did she give to her sister?<br />
68. Word Problems<br />2. Bart won the jellybean estimation contest at his class Easter party. He won 28 Easter stickers. He gave a quarter of the stickers to his friend, Rob. How many stickers did Bart give Rob?<br />
69. Word Problems<br />3. Josh colored 3 dozen Easter Eggs for his school egg hunt. What was the total number of eggs colored?<br />