Report Card Comments
Some sample generic report card comments are given below. Remember, it is more helpful and informative for parents if you can provide specific rather than general comments whenever possible.
Here are words that are useful... able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious
Speaking
· speaks in good sentences
· speaks clearly
· has difficulty using (pronouns, verbs) correctly - enjoys dramatization
· enjoys participation in conversation and discussion - expresses ideas clearly
· has a good oral vocabulary
· takes turns talking
· speaks with confidence to the group
Writing
· uses punctuation correctly
· is able to place periods and question marks correctly - uses colorful words
· uses (complex, simple) sentences
· is now able to write a complete sentence independently - participates in group story telling (composition) - can write an original story of (one or two sentences, of a few sentences)
· puts words in the appropriate order
· is able to read his sentences back
· shows self confidence in writing
· can compose several related sentences
Spelling
· is building a good spelling vocabulary - uses his individual dictionary to find unfamiliar words - enjoys learning to spell new words
· is able to learn to spell words easily - sometimes reverses letters in a word
· has difficulty remembering the spelling of non-phonetic words - is helped by using hand or body motions to remember spelling
Printing
· often reverses letters, such as __, __, etc. - has good (poor) fine-motor skills
· is able to print on the lines
· spaces letters and words correctly
· some printing is excellent but is often untidy in daily assignments - enjoys doing neat careful work
Math
· can work with numbers to 10 (?) with understanding - understands the signs +, -, = and uses them to make number statements - understands and uses basic facts of addition and subtraction to ____ - reverses some numbers still
· understands place value to _____
· can use manipulatives to add and subtract - can use manipulatives to show place value to _____ - understands money (pennies, dimes, nickels) - relies heavily on concrete objects
· knows the basic shapes
· can count to ______
· is able to create graphs using simple data - understands several methods of graphing - is beginning to memorize the number facts ----------------
For listening
· can follow directions
· enjoys listening to poetry
· enjoys listening to stories
· listens carefully
· evaluates what he hears
Phonics
· (is able to distinguish, has difficulty distinguishing) sounds in words
· now knows and is able to use _____ consonant and vowel sounds - confuses the sounds ___ and ___
· is able to blend short words using the vowel(s) _____ with (without) assistance
· is learning to attack words independently - uses the phonics skills to attack new words
Reading
· reading is (smooth, jerky, hesitant, rapid, irregular, fluent) - comprehends what he reads
· is interested in books and reading
· can read to follow directions
· can now recognize ____ sight words
· reads for pleasure
· needs lots of repetition and practice in order to retain reading vocabulary
· is still confusing words which look alike - is beginning to read words in groups (phrases) - reading is becoming (not yet becoming) automatic - enjoys discussing the stories
· has had difficulty with learning (phonics, sight vocabulary) so in the coming term we will focus on (sight vocabulary, phonics)
General Remarks
· is friendly and cooperative
· cooperates well
· helps others
· has a sense of humor
· has a good attitude towards school
· is working well in all subjects
· lacks independence, is gaining independence - is too easily distracted
· is becoming more self-reliant
· is an attentive student
· all work is neatly and accurately done - is a polite conscientious pupil
· works too slowly
· does not complete assignments in the allotted time. - seems unable to finish required work
· does colorful and interesting art work - is especially good at ______
· requires too much supervision. Please encourage him to do things on his own.
· should be encouraged to _____
· needs frequent encouragement
· is maturing
· is learning to concentrate
· is learning to listen carefully
· is gaining self-confidence
· is very thoughtful
· takes pride in work well done
· is eager to learn
· makes little effort when not under direct supervision - often seems tired at school
· is not very appreciative of the value of ( time, courtesy, sharing, neatness, accuracy)
· shows initiative; thinks things through for himself ! Here's a sample.
Here are words and phrases that are useful...
able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious Is a good citizen Is learning to share and listen. Is becoming more dependable during work periods. Is developing a better attitude toward ___ grade. Is showing interest and enthusiasm for the things we do. Is learning to occupy his time constructively. Wants responsibilities and follows through. Can be very helpful and dependable in the classroom. Always uses her time wisely. Has strengthened her skills in ___. Has great potential and works toward achieving it. Working to full capability. Is strong in _____. Is learning to be a better listener. Is learning to be careful, cooperative, and fair. Is continuing to grow in independence. Enthusiastic about participating. Gaining more self-confidence. Has a pleasant personality. Has earned a very fine report card. Has improved steadily. Is learning to listen to directions more carefully. Now accepts responsibility well. _____'s work habits are improving. Has been consistently progressing. Has shown a good attitude about trying to improve in ___. The following suggestions might improve his ____. I am hoping this recent interest and improvement will continue. Seems eager to improve. Has shown strong growth in ____. Is cooperative and happy. Volunteers often. Is willing to take part in all classroom activities. Works well with her neighbors. _____'s attitude toward school is excellent. Has the ability to follow directions. Handwork is beautifully done. Learns new vocabulary quickly. Has a sense of humor and enjoys the stories we read. Is a steadfast, conscientious worker. Is very helpful about clean-up work around the room. Anxious to please. Brings fine contributions. Has a pleasant disposition. Works well. Is hard working. Is pleasant and friendly. Needs to increase speed and comprehension in reading. Needs to apply skills to all written work. Gets along well with other children. Your constant cooperation and help are appreciated. Has shown an encouraging desire to better herself in ___. Making steady progress academically. Quality of work is improving. Responds well. Is maintaining grade-level achievements. Works well in groups, planning and carrying out activities. Seems to be more aware of activities in the classroom. Takes an active part in discussions pertinent to ___. Accepts responsibility. Extremely conscientious. Bubbles over with enthusiasm. Has a sense of humor we all enjoy. Has an excellent attitude. Work in the areas of ____ has been extremely good. Is an enthusiastic worker during the ____ period. Needs to work democratically with others in groups. Possible for ___ to exceed grade expectations. Grasps new ideas readily. Needs to develop a better sense of responsibility. Enthusiastic about work in general. Performs well in everything he undertakes. Unusually mature. Seeks information. Mature vocabulary. Doing strong work in all areas. Is a clear thinker. Excels in writing original stories and poems. Is a good student who appears to be a deep thinker. Reads extensively. Has good organization of thoughts. Has a vast background knowledge of ___. Is a very fine and serious student and excels in ___. Rate of achievement makes it difficult for ___ to keep up with the class. Must improve work habits if ___ is to gain the fundamentals needed for ___ grade work. _____'s academic success leaves much to be desired. Handwriting needs to be improved. Cooperative, well mannered. Is a very happy, well-adjusted child, but ___. Makes friends quickly and is well liked by classmates. Cries easily. Good worker and attentive listener. Good adjustment. Good attitude. Capable of achieving a higher average in areas of ____. Has difficulty retaining process of addition, etc. Is inconsistent in his efforts, especially in ___. Sacrificing accuracy for unnecessary speed in his written work. Needs to listen to directions. Never completes assignments in the allotted time. Fails to finish independent assignments. Would improve if he developed a greater interest in ___. Comprehends well, but needs to work more quickly. Needs to be urged. Report Card Comments
Some sample generic report card comments are given below. Remember, it is more helpful and informative for parents if you can provide specific rather than general comments whenever possible.
Here are words that are useful... able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious
Speaking
· speaks in good sentences
· speaks clearly
· has difficulty using (pronouns, verbs) correctly - enjoys dramatization
· enjoys participation in conversation and discussion - expresses ideas clearly
· has a good oral vocabulary
· takes turns talking
· speaks with confidence to the group
Writing
· uses punctuation correctly
· is able to place periods and question marks correctly - uses colorful words
· uses (complex, simple) sentences
· is now able to write a complete sentence independently - participates in group story telling (composition) - can write an original story of (one or two sentences, of a few sentences)
· puts words in the appropriate order
· is able to read his sentences back
· shows self confidence in writing
· can compose several related sentences
Spelling
· is building a good spelling vocabulary - uses his individual dictionary to find unfamiliar words - enjoys learning to spell new words
· is able to learn to spell words easily - sometimes reverses letters in a word
· has difficulty remembering the spelling of non-phonetic words - is helped by using hand or body motions to remember spelling
Printing
· often reverses letters, such as __, __, etc. - has good (poor) fine-motor skills
· is able to print on the lines
· spaces letters and words correctly
· some printing is excellent but is often untidy in daily assignments - enjoys doing neat careful work
Math
· can work with numbers to 10 (?) with understanding - understands the signs +, -, = and uses them to make number statements - understands and uses basic facts of addition and subtraction to ____ - reverses some numbers still
· understands place value to _____
· can use manipulatives to add and subtract - can use manipulatives to show place value to _____ - understands money (pennies, dimes, nickels) - relies heavily on concrete objects
· knows the basic shapes
· can count to ______
· is able to create graphs using simple data - understands several methods of graphing - is beginning to memorize the number facts ----------------
For listening
· can follow directions
· enjoys listening to poetry
· enjoys listening to stories
· listens carefully
· evaluates what he hears
Phonics
· (is able to distinguish, has difficulty distinguishing) sounds in words
· now knows and is able to use _____ consonant and vowel sounds - confuses the sounds ___ and ___
· is able to blend short words using the vowel(s) _____ with (without) assistance
· is learning to attack words independently - uses the phonics skills to attack new words
Reading
· reading is (smooth, jerky, hesitant, rapid, irregular, fluent) - comprehends what he reads
· is interested in books and reading
· can read to follow directions
· can now recognize ____ sight words
· reads for pleasure
· needs lots of repetition and practice in order to retain reading vocabulary
· is still confusing words which look alike - is beginning to read words in groups (phrases) - reading is becoming (not yet becoming) automatic - enjoys discussing the stories
· has had difficulty with learning (phonics, sight vocabulary) so in the coming term we will focus on (sight vocabulary, phonics)
General Remarks
· is friendly and cooperative
· cooperates well
· helps others
· has a sense of humor
· has a good attitude towards school
· is working well in all subjects
· lacks independence, is gaining independence - is too easily distracted
· is becoming more self-reliant
· is an attentive student
· all work is neatly and accurately done - is a polite conscientious pupil
· works too slowly
· does not complete assignments in the allotted time. - seems unable to finish required work
· does colorful and interesting art work - is especially good at ______
· requires too much supervision. Please encourage him to do things on his own.
· should be encouraged to _____
· needs frequent encouragement
· is maturing
· is learning to concentrate
· is learning to listen carefully
· is gaining self-confidence
· is very thoughtful
· takes pride in work well done
· is eager to learn
· makes little effort when not under direct supervision - often seems tired at school
· is not very appreciative of the value of ( time, courtesy, sharing, neatness, accuracy)
· shows initiative; thinks things through for himself ! Here's a sample.
Here are words and phrases that are useful...
able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious Is a good citizen Is learning to share and listen. Is becoming more dependable during work periods. Is developing a better attitude toward ___ grade. Is showing interest and enthusiasm for the things we do. Is learning to occupy his time constructively. Wants responsibilities and follows through. Can be very helpful and dependable in the classroom. Always uses her time wisely. Has strengthened her skills in ___. Has great potential and works toward achieving it. Working to full capability. Is strong in _____. Is learning to be a better listener. Is learning to be careful, cooperative, and fair. Is continuing to grow in independence. Enthusiastic about participating. Gaining more self-confidence. Has a pleasant personality. Has earned a very fine report card. Has improved steadily. Is learning to listen to directions more carefully. Now accepts responsibility well. _____'s work habits are improving. Has been consistently progressing. Has shown a good attitude about trying to improve in ___. The following suggestions might improve his ____. I am hoping this recent interest and improvement will continue. Seems eager to improve. Has shown strong growth in ____. Is cooperative and happy. Volunteers often. Is willing to take part in all classroom activities. Works well with her neighbors. _____'s attitude toward school is excellent. Has the ability to follow directions. Handwork is beautifully done. Learns new vocabulary quickly. Has a sense of humor and enjoys the stories we read. Is a steadfast, conscientious worker. Is very helpful about clean-up work around the room. Anxious to please. Brings fine contributions. Has a pleasant disposition. Works well. Is hard working. Is pleasant and friendly. Needs to increase speed and comprehension in reading. Needs to apply skills to all written work. Gets along well with other children. Your constant cooperation and help are appreciated. Has shown an encouraging desire to better herself in ___. Making steady progress academically. Quality of work is improving. Responds well. Is maintaining grade-level achievements. Works well in groups, planning and carrying out activities. Seems to be more aware of activities in the classroom. Takes an active part in discussions pertinent to ___. Accepts responsibility. Extremely conscientious. Bubbles over with enthusiasm. Has a sense of humor we all enjoy. Has an excellent attitude. Work in the areas of ____ has been extremely good. Is an enthusiastic worker during the ____ period. Needs to work democratically with others in groups. Possible for ___ to exceed grade expectations. Grasps new ideas readily. Needs to develop a better sense of responsibility. Enthusiastic about work in general. Performs well in everything he undertakes. Unusually mature. Seeks information. Mature vocabulary. Doing strong work in all areas. Is a clear thinker. Excels in writing original stories and poems. Is a good student who appears to be a deep thinker. Reads extensively. Has good organization of thoughts. Has a vast background knowledge of ___. Is a very fine and serious student and excels in ___. Rate of achievement makes it difficult for ___ to keep up with the class. Must improve work habits if ___ is to gain the fundamentals needed for ___ grade work. _____'s academic success leaves much to be desired. Handwriting needs to be improved. Cooperative, well mannered. Is a very happy, well-adjusted child, but ___. Makes friends quickly and is well liked by classmates. Cries easily. Good worker and attentive listener. Good adjustment. Good attitude. Capable of achieving a higher average in areas of ____. Has difficulty retaining process of addition, etc. Is inconsistent in his efforts, especially in ___. Sacrificing accuracy for unnecessary speed in his written work. Needs to listen to directions. Never completes assignments in the allotted time. Fails to finish independent assignments. Would improve if he developed a greater interest in ___. Comprehends well, but needs to work more quickly. Needs to be urged.
Report Card Comments
Some sample generic report card comments are given below. Remember, it is more helpful and informative for parents if you can provide specific rather than general comments whenever possible.
Here are words that are useful... able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious
Speaking
· speaks in good sentences
· speaks clearly
· has difficulty using (pronouns, verbs) correctly - enjoys dramatization
· enjoys participation in conversation and discussion - expresses ideas clearly
· has a good oral vocabulary
· takes turns talking
· speaks with confidence to the group
Writing
· uses punctuation correctly
· is able to place periods and question marks correctly - uses colorful words
· uses (complex, simple) sentences
· is now able to write a complete sentence independently - participates in group story telling (composition) - can write an original story of (one or two sentences, of a few sentences)
· puts words in the appropriate order
· is able to read his sentences back
· shows self confidence in writing
· can compose several related sentences
Spelling
· is building a good spelling vocabulary - uses his individual dictionary to find unfamiliar words - enjoys learning to spell new words
· is able to learn to spell words easily - sometimes reverses letters in a word
· has difficulty remembering the spelling of non-phonetic words - is helped by using hand or body motions to remember spelling
Printing
· often reverses letters, such as __, __, etc. - has good (poor) fine-motor skills
· is able to print on the lines
· spaces letters and words correctly
· some printing is excellent but is often untidy in daily assignments - enjoys doing neat careful work
Math
· can work with numbers to 10 (?) with understanding - understands the signs +, -, = and uses them to make number statements - understands and uses basic facts of addition and subtraction to ____ - reverses some numbers still
· understands place value to _____
· can use manipulatives to add and subtract - can use manipulatives to show place value to _____ - understands money (pennies, dimes, nickels) - relies heavily on concrete objects
· knows the basic shapes
· can count to ______
· is able to create graphs using simple data - understands several methods of graphing - is beginning to memorize the number facts ----------------
For listening
· can follow directions
· enjoys listening to poetry
· enjoys listening to stories
· listens carefully
· evaluates what he hears
Phonics
· (is able to distinguish, has difficulty distinguishing) sounds in words
· now knows and is able to use _____ consonant and vowel sounds - confuses the sounds ___ and ___
· is able to blend short words using the vowel(s) _____ with (without) assistance
· is learning to attack words independently - uses the phonics skills to attack new words
Reading
· reading is (smooth, jerky, hesitant, rapid, irregular, fluent) - comprehends what he reads
· is interested in books and reading
· can read to follow directions
· can now recognize ____ sight words
· reads for pleasure
· needs lots of repetition and practice in order to retain reading vocabulary
· is still confusing words which look alike - is beginning to read words in groups (phrases) - reading is becoming (not yet becoming) automatic - enjoys discussing the stories
· has had difficulty with learning (phonics, sight vocabulary) so in the coming term we will focus on (sight vocabulary, phonics)
General Remarks
· is friendly and cooperative
· cooperates well
· helps others
· has a sense of humor
· has a good attitude towards school
· is working well in all subjects
· lacks independence, is gaining independence - is too easily distracted
· is becoming more self-reliant
· is an attentive student
· all work is neatly and accurately done - is a polite conscientious pupil
· works too slowly
· does not complete assignments in the allotted time. - seems unable to finish required work
· does colorful and interesting art work - is especially good at ______
· requires too much supervision. Please encourage him to do things on his own.
· should be encouraged to _____
· needs frequent encouragement
· is maturing
· is learning to concentrate
· is learning to listen carefully
· is gaining self-confidence
· is very thoughtful
· takes pride in work well done
· is eager to learn
· makes little effort when not under direct supervision - often seems tired at school
· is not very appreciative of the value of ( time, courtesy, sharing, neatness, accuracy)
· shows initiative; thinks things through for himself ! Here's a sample.
Here are words and phrases that are useful...
able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious Is a good citizen Is learning to share and listen. Is becoming more dependable during work periods. Is developing a better attitude toward ___ grade. Is showing interest and enthusiasm for the things we do. Is learning to occupy his time constructively. Wants responsibilities and follows through. Can be very helpful and dependable in the classroom. Always uses her time wisely. Has strengthened her skills in ___. Has great potential and works toward achieving it. Working to full capability. Is strong in _____. Is learning to be a better listener. Is learning to be careful, cooperative, and fair. Is continuing to grow in independence. Enthusiastic about participating. Gaining more self-confidence. Has a pleasant personality. Has earned a very fine report card. Has improved steadily. Is learning to listen to directions more carefully. Now accepts responsibility well. _____'s work habits are improving. Has been consistently progressing. Has shown a good attitude about trying to improve in ___. The following suggestions might improve his ____. I am hoping this recent interest and improvement will continue. Seems eager to improve. Has shown strong growth in ____. Is cooperative and happy. Volunteers often. Is willing to take part in all classroom activities. Works well with her neighbors. _____'s attitude toward school is excellent. Has the ability to follow directions. Handwork is beautifully done. Learns new vocabulary quickly. Has a sense of humor and enjoys the stories we read. Is a steadfast, conscientious worker. Is very helpful about clean-up work around the room. Anxious to please. Brings fine contributions. Has a pleasant disposition. Works well. Is hard working. Is pleasant and friendly. Needs to increase speed and comprehension in reading. Needs to apply skills to all written work. Gets along well with other children. Your constant cooperation and help are appreciated. Has shown an encouraging desire to better herself in ___. Making steady progress academically. Quality of work is improving. Responds well. Is maintaining grade-level achievements. Works well in groups, planning and carrying out activities. Seems to be more aware of activities in the classroom. Takes an active part in discussions pertinent to ___. Accepts responsibility. Extremely conscientious. Bubbles over with enthusiasm. Has a sense of humor we all enjoy. Has an excellent attitude. Work in the areas of ____ has been extremely good. Is an enthusiastic worker during the ____ period. Needs to work democratically with others in groups. Possible for ___ to exceed grade expectations. Grasps new ideas readily. Needs to develop a better sense of responsibility. Enthusiastic about work in general. Performs well in everything he undertakes. Unusually mature. Seeks information. Mature vocabulary. Doing strong work in all areas. Is a clear thinker. Excels in writing original stories and poems. Is a good student who appears to be a deep thinker. Reads extensively. Has good organization of thoughts. Has a vast background knowledge of ___. Is a very fine and serious student and excels in ___. Rate of achievement makes it difficult for ___ to keep up with the class. Must improve work habits if ___ is to gain the fundamentals needed for ___ grade work. _____'s academic success leaves much to be desired. Handwriting needs to be improved. Cooperative, well mannered. Is a very happy, well-adjusted child, but ___. Makes friends quickly and is well liked by classmates. Cries easily. Good worker and attentive listener. Good adjustment. Good attitude. Capable of achieving a higher average in areas of ____. Has difficulty retaining process of addition, etc. Is inconsistent in his efforts, especially in ___. Sacrificing accuracy for unnecessary speed in his written work. Needs to listen to directions. Never completes assignments in the allotted time. Fails to finish independent assignments. Would improve if he developed a greater interest in ___. Comprehends well, but needs to work more quickly. Needs to be urged.
Report Card Comments
Some sample generic report card comments are given below. Remember, it is more helpful and informative for parents if you can provide specific rather than general comments whenever possible.
Here are words that are useful... able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious
Speaking
· speaks in good sentences
· speaks clearly
· has difficulty using (pronouns, verbs) correctly - enjoys dramatization
· enjoys participation in conversation and discussion - expresses ideas clearly
· has a good oral vocabulary
· takes turns talking
· speaks with confidence to the group
Writing
· uses punctuation correctly
· is able to place periods and question marks correctly - uses colorful words
· uses (complex, simple) sentences
· is now able to write a complete sentence independently - participates in group story telling (composition) - can write an original story of (one or two sentences, of a few sentences)
· puts words in the appropriate order
· is able to read his sentences back
· shows self confidence in writing
· can compose several related sentences
Spelling
· is building a good spelling vocabulary - uses his individual dictionary to find unfamiliar words - enjoys learning to spell new words
· is able to learn to spell words easily - sometimes reverses letters in a word
· has difficulty remembering the spelling of non-phonetic words - is helped by using hand or body motions to remember spelling
Printing
· often reverses letters, such as __, __, etc. - has good (poor) fine-motor skills
· is able to print on the lines
· spaces letters and words correctly
· some printing is excellent but is often untidy in daily assignments - enjoys doing neat careful work
Math
· can work with numbers to 10 (?) with understanding - understands the signs +, -, = and uses them to make number statements - understands and uses basic facts of addition and subtraction to ____ - reverses some numbers still
· understands place value to _____
· can use manipulatives to add and subtract - can use manipulatives to show place value to _____ - understands money (pennies, dimes, nickels) - relies heavily on concrete objects
· knows the basic shapes
· can count to ______
· is able to create graphs using simple data - understands several methods of graphing - is beginning to memorize the number facts ----------------
For listening
· can follow directions
· enjoys listening to poetry
· enjoys listening to stories
· listens carefully
· evaluates what he hears
Phonics
· (is able to distinguish, has difficulty distinguishing) sounds in words
· now knows and is able to use _____ consonant and vowel sounds - confuses the sounds ___ and ___
· is able to blend short words using the vowel(s) _____ with (without) assistance
· is learning to attack words independently - uses the phonics skills to attack new words
Reading
· reading is (smooth, jerky, hesitant, rapid, irregular, fluent) - comprehends what he reads
· is interested in books and reading
· can read to follow directions
· can now recognize ____ sight words
· reads for pleasure
· needs lots of repetition and practice in order to retain reading vocabulary
· is still confusing words which look alike - is beginning to read words in groups (phrases) - reading is becoming (not yet becoming) automatic - enjoys discussing the stories
· has had difficulty with learning (phonics, sight vocabulary) so in the coming term we will focus on (sight vocabulary, phonics)
General Remarks
· is friendly and cooperative
· cooperates well
· helps others
· has a sense of humor
· has a good attitude towards school
· is working well in all subjects
· lacks independence, is gaining independence - is too easily distracted
· is becoming more self-reliant
· is an attentive student
· all work is neatly and accurately done - is a polite conscientious pupil
· works too slowly
· does not complete assignments in the allotted time. - seems unable to finish required work
· does colorful and interesting art work - is especially good at ______
· requires too much supervision. Please encourage him to do things on his own.
· should be encouraged to _____
· needs frequent encouragement
· is maturing
· is learning to concentrate
· is learning to listen carefully
· is gaining self-confidence
· is very thoughtful
· takes pride in work well done
· is eager to learn
· makes little effort when not under direct supervision - often seems tired at school
· is not very appreciative of the value of ( time, courtesy, sharing, neatness, accuracy)
· shows initiative; thinks things through for himself ! Here's a sample.
Here are words and phrases that are useful...
able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious Is a good citizen Is learning to share and listen. Is becoming more dependable during work periods. Is developing a better attitude toward ___ grade. Is showing interest and enthusiasm for the things we do. Is learning to occupy his time constructively. Wants responsibilities and follows through. Can be very helpful and dependable in the classroom. Always uses her time wisely. Has strengthened her skills in ___. Has great potential and works toward achieving it. Working to full capability. Is strong in _____. Is learning to be a better listener. Is learning to be careful, cooperative, and fair. Is continuing to grow in independence. Enthusiastic about participating. Gaining more self-confidence. Has a pleasant personality. Has earned a very fine report card. Has improved steadily. Is learning to listen to directions more carefully. Now accepts responsibility well. _____'s work habits are improving. Has been consistently progressing. Has shown a good attitude about trying to improve in ___. The following suggestions might improve his ____. I am hoping this recent interest and improvement will continue. Seems eager to improve. Has shown strong growth in ____. Is cooperative and happy. Volunteers often. Is willing to take part in all classroom activities. Works well with her neighbors. _____'s attitude toward school is excellent. Has the ability to follow directions. Handwork is beautifully done. Learns new vocabulary quickly. Has a sense of humor and enjoys the stories we read. Is a steadfast, conscientious worker. Is very helpful about clean-up work around the room. Anxious to please. Brings fine contributions. Has a pleasant disposition. Works well. Is hard working. Is pleasant and friendly. Needs to increase speed and comprehension in reading. Needs to apply skills to all written work. Gets along well with other children. Your constant cooperation and help are appreciated. Has shown an encouraging desire to better herself in ___. Making steady progress academically. Quality of work is improving. Responds well. Is maintaining grade-level achievements. Works well in groups, planning and carrying out activities. Seems to be more aware of activities in the classroom. Takes an active part in discussions pertinent to ___. Accepts responsibility. Extremely conscientious. Bubbles over with enthusiasm. Has a sense of humor we all enjoy. Has an excellent attitude. Work in the areas of ____ has been extremely good. Is an enthusiastic worker during the ____ period. Needs to work democratically with others in groups. Possible for ___ to exceed grade expectations. Grasps new ideas readily. Needs to develop a better sense of responsibility. Enthusiastic about work in general. Performs well in everything he undertakes. Unusually mature. Seeks information. Mature vocabulary. Doing strong work in all areas. Is a clear thinker. Excels in writing original stories and poems. Is a good student who appears to be a deep thinker. Reads extensively. Has good organization of thoughts. Has a vast background knowledge of ___. Is a very fine and serious student and excels in ___. Rate of achievement makes it difficult for ___ to keep up with the class. Must improve work habits if ___ is to gain the fundamentals needed for ___ grade work. _____'s academic success leaves much to be desired. Handwriting needs to be improved. Cooperative, well mannered. Is a very happy, well-adjusted child, but ___. Makes friends quickly and is well liked by classmates. Cries easily. Good worker and attentive listener. Good adjustment. Good attitude. Capable of achieving a higher average in areas of ____. Has difficulty retaining process of addition, etc. Is inconsistent in his efforts, especially in ___. Sacrificing accuracy for unnecessary speed in his written work. Needs to listen to directions. Never completes assignments in the allotted time. Fails to finish independent assignments. Would improve if he developed a greater interest in ___. Comprehends well, but needs to work more quickly. Needs to be urged.
Report Card Comments
Some sample generic report card comments are given below. Remember, it is more helpful and informative for parents if you can provide specific rather than general comments whenever possible.
Here are words that are useful... able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious
Speaking
· speaks in good sentences
· speaks clearly
· has difficulty using (pronouns, verbs) correctly - enjoys dramatization
· enjoys participation in conversation and discussion - expresses ideas clearly
· has a good oral vocabulary
· takes turns talking
· speaks with confidence to the group
Writing
· uses punctuation correctly
· is able to place periods and question marks correctly - uses colorful words
· uses (complex, simple) sentences
· is now able to write a complete sentence independently - participates in group story telling (composition) - can write an original story of (one or two sentences, of a few sentences)
· puts words in the appropriate order
· is able to read his sentences back
· shows self confidence in writing
· can compose several related sentences
Spelling
· is building a good spelling vocabulary - uses his individual dictionary to find unfamiliar words - enjoys learning to spell new words
· is able to learn to spell words easily - sometimes reverses letters in a word
· has difficulty remembering the spelling of non-phonetic words - is helped by using hand or body motions to remember spelling
Printing
· often reverses letters, such as __, __, etc. - has good (poor) fine-motor skills
· is able to print on the lines
· spaces letters and words correctly
· some printing is excellent but is often untidy in daily assignments - enjoys doing neat careful work
Math
· can work with numbers to 10 (?) with understanding - understands the signs +, -, = and uses them to make number statements - understands and uses basic facts of addition and subtraction to ____ - reverses some numbers still
· understands place value to _____
· can use manipulatives to add and subtract - can use manipulatives to show place value to _____ - understands money (pennies, dimes, nickels) - relies heavily on concrete objects
· knows the basic shapes
· can count to ______
· is able to create graphs using simple data - understands several methods of graphing - is beginning to memorize the number facts ----------------
For listening
· can follow directions
· enjoys listening to poetry
· enjoys listening to stories
· listens carefully
· evaluates what he hears
Phonics
· (is able to distinguish, has difficulty distinguishing) sounds in words
· now knows and is able to use _____ consonant and vowel sounds - confuses the sounds ___ and ___
· is able to blend short words using the vowel(s) _____ with (without) assistance
· is learning to attack words independently - uses the phonics skills to attack new words
Reading
· reading is (smooth, jerky, hesitant, rapid, irregular, fluent) - comprehends what he reads
· is interested in books and reading
· can read to follow directions
· can now recognize ____ sight words
· reads for pleasure
· needs lots of repetition and practice in order to retain reading vocabulary
· is still confusing words which look alike - is beginning to read words in groups (phrases) - reading is becoming (not yet becoming) automatic - enjoys discussing the stories
· has had difficulty with learning (phonics, sight vocabulary) so in the coming term we will focus on (sight vocabulary, phonics)
General Remarks
· is friendly and cooperative
· cooperates well
· helps others
· has a sense of humor
· has a good attitude towards school
· is working well in all subjects
· lacks independence, is gaining independence - is too easily distracted
· is becoming more self-reliant
· is an attentive student
· all work is neatly and accurately done - is a polite conscientious pupil
· works too slowly
· does not complete assignments in the allotted time. - seems unable to finish required work
· does colorful and interesting art work - is especially good at ______
· requires too much supervision. Please encourage him to do things on his own.
· should be encouraged to _____
· needs frequent encouragement
· is maturing
· is learning to concentrate
· is learning to listen carefully
· is gaining self-confidence
· is very thoughtful
· takes pride in work well done
· is eager to learn
· makes little effort when not under direct supervision - often seems tired at school
· is not very appreciative of the value of ( time, courtesy, sharing, neatness, accuracy)
· shows initiative; thinks things through for himself ! Here's a sample.
Here are words and phrases that are useful...
able, accurate, active, aggressive, ambitious, anxious, attentive, capable, cheerful, confident, cooperative, conscientious, courteous, dependable, determined, eager, energy, energetic, friendly, generous, happy, helpful, imaginative, industrious, initiative, interested, keen, neat, nervous, observant, orderly, pleasant, polite, prompt, quiet, receptive, reliant, resourceful, studious Is a good citizen Is learning to share and listen. Is becoming more dependable during work periods. Is developing a better attitude toward ___ grade. Is showing interest and enthusiasm for the things we do. Is learning to occupy his time constructively. Wants responsibilities and follows through. Can be very helpful and dependable in the classroom. Always uses her time wisely. Has strengthened her skills in ___. Has great potential and works toward achieving it. Working to full capability. Is strong in _____. Is learning to be a better listener. Is learning to be careful, cooperative, and fair. Is continuing to grow in independence. Enthusiastic about participating. Gaining more self-confidence. Has a pleasant personality. Has earned a very fine report card. Has improved steadily. Is learning to listen to directions more carefully. Now accepts responsibility well. _____'s work habits are improving. Has been consistently progressing. Has shown a good attitude about trying to improve in ___. The following suggestions might improve his ____. I am hoping this recent interest and improvement will continue. Seems eager to improve. Has shown strong growth in ____. Is cooperative and happy. Volunteers often. Is willing to take part in all classroom activities. Works well with her neighbors. _____'s attitude toward school is excellent. Has the ability to follow directions. Handwork is beautifully done. Learns new vocabulary quickly. Has a sense of humor and enjoys the stories we read. Is a steadfast, conscientious worker. Is very helpful about clean-up work around the room. Anxious to please. Brings fine contributions. Has a pleasant disposition. Works well. Is hard working. Is pleasant and friendly. Needs to increase speed and comprehension in reading. Needs to apply skills to all written work. Gets along well with other children. Your constant cooperation and help are appreciated. Has shown an encouraging desire to better herself in ___. Making steady progress academically. Quality of work is improving. Responds well. Is maintaining grade-level achievements. Works well in groups, planning and carrying out activities. Seems to be more aware of activities in the classroom. Takes an active part in discussions pertinent to ___. Accepts responsibility. Extremely conscientious. Bubbles over with enthusiasm. Has a sense of humor we all enjoy. Has an excellent attitude. Work in the areas of ____ has been extremely good. Is an enthusiastic worker during the ____ period. Needs to work democratically with others in groups. Possible for ___ to exceed grade expectations. Grasps new ideas readily. Needs to develop a better sense of responsibility. Enthusiastic about work in general. Performs well in everything he undertakes. Unusually mature. Seeks information. Mature vocabulary. Doing strong work in all areas. Is a clear thinker. Excels in writing original stories and poems. Is a good student who appears to be a deep thinker. Reads extensively. Has good organization of thoughts. Has a vast background knowledge of ___. Is a very fine and serious student and excels in ___. Rate of achievement makes it difficult for ___ to keep up with the class. Must improve work habits if ___ is to gain the fundamentals needed for ___ grade work. _____'s academic success leaves much to be desired. Handwriting needs to be improved. Cooperative, well mannered. Is a very happy, well-adjusted child, but ___. Makes friends quickly and is well liked by classmates. Cries easily. Good worker and attentive listener. Good adjustment. Good attitude. Capable of achieving a higher average in areas of ____. Has difficulty retaining process of addition, etc. Is inconsistent in his efforts, especially in ___. Sacrificing accuracy for unnecessary speed in his written work. Needs to listen to directions. Never completes assignments in the allotted time. Fails to finish independent assignments. Would improve if he developed a greater interest in ___. Comprehends well, but needs to work more quickly. Needs to be urged.

Remarks for students

How to write remarks for students
She is skillful and has potential to do better.
She needs to be more communicative.
She is friendly and communicative, yet she needs to keep herself neat and tidy.
Her progress is satisfactory, she has made little headway.
She is obedient and trustworthy. She is proficient in her study.
She is positive and optimistic, yet she should put all her effort on her study.
She is doing well. She is more attention-seeking.
She is punctual, talented and diligent.
She is clever. Still she should prepare herself to run the race.
She needs to be industrious.
He is in a progressive way. He is positive and promising.
He is improving. He needs to be hard-working.
He is amiable and cheerful.
He is more childish and attention-seeking and needs to be more laborious.
He is a bit introvert. Thus needs to be more interactive.
He is a bit introvert. Thus needs to be more interactive.
He is a smart boy. He is brainy, helpful, promising and optimistic.
He is a good boy. He is positive and courteous.
He needs to be more hard-working.
He is lovely, polite and hard-working.
He is creative, has artistic quality and obedient.
He is very childish and introvert. Thus he needs to be more communicative.
He is lovely, agreeable and delightful.
He is thoughtful, brainy and has potential to bring about outstanding performance.
She is a bit shy. She needs to pay her full attention to her study.
He is a little touchy. He has to go a long way. So he needs to be more studious.
She is very childish, cheerful and decent.
He needs to be more diligent and should improve his handwriting.
He needs to be more diligent and pay more attention to his study.
He is a fine fellow. He is helpful, polite and virtuous.
He is improving. He has potential to do better.
He is playful, clever and cheerful.
He is doing well. He has the potential to do much better.
He is a fine fellow. He is optimistic, and capable of doing even better.
If there were all students like him, how nice would be the class!
He can do very well only if he pays his full attention to his study.
She needs to be more careful about her study and all.
She needs guidance most of the time. If she applies her cleverness in her study, she could come up with flying colours.
She is a bit introvert. Thus she needs to be more communicative plus studious.

R. Skemp's Psychological Learning & its Implications in Teaching Mathematics

Background
i.Introduction to the study
Evaluation on Foundation of Mathematics in master's level consists of two parts in its curriculums. First is theoretical formal examination which is taken by Tribhuwan University and the second is practical part. On that sequence according to the instruction of syllabus we should be given to prepare a report on one of the learning theories learnt of be in Math. Ed. 501 for master's degree. So we were given to prepare a brief report on "R Skemp's Psychological Learning and its implication on Teaching Mathematics" as the partial fulfillment of the practical work, which made us search about that and present as a report and we have tried to show it well.
iiObjectives of the study
The objectives of the preparing this report are as follows:
· To present the different phases and types of R Skemp's Psychological Learning
· To present the implications of R Skemp's Psychological Learning and its implication on Teaching Mathematics
iii. Limitations of the study
As it is well known fact for the related level, there are certain limitations on any type of research. Similarly there were also some limitations on our study and for preparation of this report. We were given the time period of one month. In that period we consulted with different books and T.U. Photocopy papers and some websites. The instruction of teacher was also very useful for to prepare this report.















Methodology
i. Sources of Materials
To prepare this report main source is the part of notes given by our instructor. Furthermore we have taken the help of different photocopy papers from TU and books written by different psychologists such as Hillgard, Deway and others. We have also taken the information from other books which are mentioned in the part of bibliography.

ii. Work Division
After getting the instruction of way of preparing report we four members of our group divided the work in to two parts and started to collect the information from different sources of materials.

iii. Discussion
After collecting material we and information we chose one place for further discussion and discussing with each other we drew conclusions. There were some problems too but we consulted with subject experts for the correct solutions of the problems appeared.

iv. Draft Preparation
Completing the group discussion and drawing conclusions prepared the draft of the report and tried to present in the proper and simplest way.




















About Learning
Background of Learning
We will agree with the fact that we have schools in order to prepare children for different roles in the society. The main objectives of school as an institution is to bring certain desirable changes in the behavior of children through the process of learning. The process of learning begins from the birth of the child and continues till his death. All living creatures learn. When the child is born, his mind is just like clean slate. As soon as he comes in the contact with his environment, he starts reacting and in its process of interaction of the individual and his environment, the foundation of learning are laid down.
History of Learning
Learning is a continuous process which has started from ancient time. At that time elders used to give instruction to the smaller and instruct them, who had knowledge about something they have used to explain for them, similarly in a family father, mother used to teach their son and daughter and instruct the things what is wrong and what is right. Gradually learning has got the system of religious way and with their behavior. In western side, Christianity in eastern Hinduism and in Buddhism was speared who would spray knowledge according to their religion. They use to give education in the cottage.
In the middle age, it was slightly changed in the education system prevailed in the past. In this age learning process was started in the formal system. It was accepted to solve the problems of the society. In this age learning was taken the adjustment in the changing society and able to adjust. In short, this stage learning was used to avoid religious miss concepts and making healthy society.
In the modern age, educational psychology was developed and with the help of this psychological education was started. In fact, learning was achieved from different ways such as formal, informal, non-formal way. In this age of 21st century we should not take learning as a process of teaching, reading, writing and understanding only. Learning can be done anywhere house, society, school, film hall, or on the way in any way formal, inform or nonformula. Learning is not the system of rote learning. it is the process of self realization and experience learning. It is also not the process of getting only certificate, owner of degree. It is wrong thinking to be proud with getting certificate, but it is the system of changing behavior in activities or in practical life.
Meaning and Definition of Learning
Learning means to bring changes in the behavior of an organism. It is very difficult to give a universally acceptable definition of learning because various theories developed by psychologists attempt to define the term from different angles. Learning in psychology has the status of construction. Construct mean an idea of image that cannot be directly observed like elections or genes but which interfere the behavior of the organism. Learning is a relatively enduring change in behavior which is the function of prior behavior( usually called practice.).
Ø What is theory:
ü Theory is a systematic interpretation of knowledge, ideas and facts.
ü Theory is a set of properties on which a system of ideas are intended to explain the facts or events.
ü Theory is the principle on which subject of study is based.

Ø What is learning:
ü Learning is a process of change on human behavior through experiences and training.
ü Learning is acquisition of knowledge, skill and attitude.

· Learning process is different according to different fields of psychology. For example
Behaviourism
Stimulus response experiences learning behaviour change
Cognitivism
Problem perception central meditation new relationship insight learning behaviour change
Learning is a behavior. learning is a process of behavior ways of human action.
Human behavior
ü way of thinking
ü way of feeling
ü way of acting / doing

v Why learning:
Learning is necessary for:
· learning for development (Qualitative + Quantitative)
· learning for growth (Physical, mental, social , emotional)
· learning for experience (Concrete or abstract)
· learning for adjustment (Internal or External)
· learning for behavior change (way of thinking, way of feeling, and way of doing)
· learning for knowledge (Facts, principles, events, trends, definition, theory, etc.), skills (Manipulation, handling, constructing, dancing, writing, reading, singing, etc.) and attitude (values, belief, feeling, etc.)


Learning theories
Formalized learning theory in late thirties hen proponents of various approaches attempted to build their own theory to explain the problems of learning. we can quote the definition of a theory as "a provisional explanatory proposition or set of propositions, concerning some natural phenomena and consisting of symbolic representations of 1) the observed relationships among independent and dependent variables, 2) the mechanisms or structures presumed to underlie such relationships, or 3) inferred relationships and underlying mechanisms intended to account for observed data in the absence of any direct empirical manifestations of the relationships." (Learning Theories edited by Melvin H Marx)
Implications of learning theories
The implications of learning theories are as follows:
a. learning theories helps to identify their physical, mental condition and helps to go forward further step giving guidelines.
b. it increases the psychological relationship between students and teachers.
c. it helps them to develop occupational capacity.
d. it helps the teachers to measure the behavioural objectives.
e. to make interest over subject matter of teaching and learning subject and to remember the subject matter for long term in the memory learning theory is used.
From above mentioned things of points we can notice that learning theory is helping directly or indirectly in all round of own society or individuals, such theories are implemented in different subject teaching activities. some mathematical matters area complex and abstract but are very important, we can use different learning theories in practice. many mathematicians have implemented learning theories in mathematical problems. among them Jean Piaget, J.P. Dines, Gagne, R. Skemp are main mathematicians who implemented the learning theories and helped to make learning mathematics easier, faster and in good environment. mathematics learning theory has helped to develop new curriculum and to implement it. among them the mathematicians who help to improve the state and show the path way for the younger generations of mathematics.
Areas of learning mathematics
A. Programmed Learning
laboratory approach of learning is more effective way of learning. in this method teachers should have to prepare a model. a package of learning strategies for certain contents. there should be enough teaching materials and reference materials to expose the learner into content. content should be presented in simple to complex, particular to general, and bottom to top of learning.
B. Contents programme
topic for the programme can be designed to be unfamiliar to the students but that should be included related to previous knowledge in each and every case.
C. Measuring students' perfomance
after completion of teaching learning activities teachers have to evaluate the students to forward their relation. those types of evaluation may be test of performance.
- test of transfer
- test of subordinate knowledge
D. Variables in learning programme
E. There should be variety in teaching activities so teacher can compose different activities during his learning programme.
Skemp’s Psychological Learning Mathematics
Richard Skemp was born at Bristol of London in 1919. He had done post graduate in mathematics from Hartford Collage in 1939, and worked in Royal Signal from 1939 to 1945 as a mathematics teacher. During that period he was interested to solve psychological problems such as
i. How can students learn knowledge that is more mathematical?
ii. How can teacher teach to the students more effectively?
Skemp is mathematician cum psychologist. According to him, the principle of mathematics learning is the interaction between mathematics and psychology. The psychology of students plays a vital role in teaching mathematics. He was increasingly concerned with the problems of those pupils who, though intelligent and hard-working, could not do well in mathematics. Surely the main ability required for mathematics was the ability to form and to manipulate abstract ideas.
Habit Learning and Intelligent Learning
According to Skemp, there are two types of learning. They are :
a. Habit learning
b. Intelligent learning
These two types of learning differ from each other in qualitative point of view. Habit learning refers memorization of mathematical concepts by rote learning and intelligence refers understanding learning. Main principles of Skemp’s learning are based on the following three questions:
i. What is intelligence?
ii. What is understanding?
iii. How mathematics learning can be improved?
Understanding
The term understanding is used to mean the ways of interpreting, organizing and analyzing the experiences. This is done by means of concepts, conceptual structures and organizing principles. The concepts could be handled only through symbols. The interpretation and analysis have to be judged for their rightness, truth, and adequacy.
Factors Affecting Learning Mathematics
According to Skemp, six factors affect learning mathematics. If we properly use these factors in mathematics teaching, then students can easily understand the mathematical concepts and they can develop understanding capacity. The six factors are as follows:
Ø Formation of mathematical concepts
Ø The idea of schema
Ø Intuitive and reflexive intelligence
Ø Symbols
Ø Different kinds of imagery
Ø Interpersonal and emotional factors
1. The formation of mathematical concepts:
There are certain steps to the formation of mathematical concepts which are as follows:
a. Abstracting and classifying
b. Naming
Communication of Concepts
According to Skemp, there are two types of concepts. Primary concept is formed on the basis of sensory and motor experiences of outside world such as red, motorcar, heavy, hot, sweet are called primary concepts. Secondary concepts are the collection of primary concepts or those concepts which are abstracted from other concepts. Secondary concepts are of higher order than primary concepts.
Concept as a cultural heritage
A concept is a way of processing data that enables the users to bring past experiences in use.


The Learning of Mathematical Concepts:
i. The concepts of higher order than those that a person already has, cannot be communicated to him/her by a definition but only by arranging for him/her to encounter a suitable collection of examples.
ii. Mathematical concept is invariably ….than other concepts. It must first be ensured that these are already formed in the learners’ mind.
Learning and Teaching
Learning and teaching are interrelated to each other if both of them have a good combination then entire learning and teaching will be effective. For this purpose, teacher has to teach effectively by using different methods with the help of different teaching materials. And students have to bear proper attention to learn.
2. The idea of schema:
Schema is a mental structure which deals about how the concepts fit together to form conceptual structure. The formation of simple concepts based on formation of mathematical concept is the process of schema.
Functions of idea of schema:
- The integrative function of schema
- Schema as a mental tool for further learning
Steps of schema
- Understanding
- Implication for the learning of mathematics
3. Intuitive and reflexive intelligence:
4. Symbols:
The functions of symbols are as follows:
a. Communication
b. Recording of knowledge
c. Communication of new concept
d. Making multiple classification straightforward
e. Explanation
f. Making possible reflective activity
g. Helping to show structure
h. Making routine manipulation automatic
i. Recovering information and understanding
j. Creative mental activity
5. Different kinds of imagery:
- Visual and verbal symbols
- Visual symbols in geometry
6. Interpersonal and emotional factors:
Since each individual is different, they have to be treated accordingly. They have their own peculiar interpersonal and emotional characters which are to be addressed while teaching mathematics.
7. Implications of Skemp's Learning Theory in Mathematical Instruction
1. The concept of higher order then those which people already have cannot be communicated to them to encounter a suitable collection of examples. This means plenty of carefully selected examples should be used in the text books and definitions should be used only to consolidate a concept when that is already formed.
2. In a mathematical curriculum the logical priority of concepts should be clearly worked out and order of learning of concepts, where implied by a careful conceptual analysis, should be followed.
3.Since mathematical concepts are abstract there is a danger of their becoming mere symbols, there fore, in the early stage a lot of relevant experience should be provided for in the curriculum itself. At the same time, they should be formed in such a way that they can become free from reliance on the apparatus, then only shall they become genuinely mathematical in nature.
4. Intuitive intelligence may or may not be true because sometimes it may be wrong in the situation teacher should be responsible to correct the problems or errors done by students. As a result student know their mistake and they get a right chance to correct and from onwards and they do not repeat that mistake. In a way, they can solve the problems without any help of teacher.
5. A variety of examples should be chosen so that the concepts learnt can become free from the incident features of the examples.
6. To develop the intuitive intelligence of learners , teachers should applied the many distinct method. As it is impossible to find their intuitive intelligence for even thought it is even necessary to encourage towards true intuitive intelligence. Not only that but also the teacher should be capable to develop the intuitive intelligence by deep study . If the teacher does not have the knowledge of intuitive intelligence, he will not be success to give clear knowledge to the students.
7. The mathematical teacher should focus on the theory that "process is more important then the product" during teaching learning activities that helps the students to develop strong concepts, to prepare mentally ready for learning and to help further learning concepts by means of previous one. For example
12 = 4 + 4+ 4 adding 4 three times(previous learning)
12 = 4 x 3 multiplicative form with the help of additional process (new learning)
From the combination of these two, students understand that multiplication comes after addition operation.
8.Teracher must used multi techniques to solve problems of mathematics that helps students to increase the mental power so that learners able to search themselves different methods and choose appropriate process. At the result, students can make the scheme for further solution. For example, to find the HCF of x2-4x+4 and x3-8, we can use factorization method, Venn diagram , division method, etc.
9. Skemp learning theory focuses the leaner's imagery and motive the learners. If the learners are motivated through the teachers, they search the problems themselves, them thinks themselves, they solve themselves and finalize, and they derive the solution. In this way learner can learn.
10. Teacher should careful about individual differences of students in intelligence, logical, imagery, problem solving abilities, learning capacities etc. Therefore teacher should focus the individual learning based on interpersonal and emotional factors.
11. Teacher should create the environment of thinking, speculating and processing of many concepts so that they are able to make imagery themselves and use the imagery which helps to make mathematical concepts prolong and applicable in behavior.
12. Intuitive intelligence cannot always true. Teacher should correct the results carried out by students and if students are good in way then teacher should praise the students.
Bibliography
Pandit, Ramjee Prasad.2006. Foundation of Mathematics Education.
Budhathoki, Tara Bahadur & Ram, Surendra. 2007. Ganit Shikshako Aadhar.
Upadhyaya, Hari Prasad. 2005. New Trends in Mathematics Education.

social needs of mathematics

Manoj Subedi(2010)

1. Introduction
Simply speaking, mathematics is a science of numbers and their basic actions (addition, subtraction, multiplication, and division) and interaction between and among them. But this definition is not complete in how it is called the science of abstract terms as well. It plays vital role in modern scientific and body questions contribution.
Mathematics is the necessity of the modern civilization. It has been an important part of human society since Paleolithic period. The various branches of mathematics have vital roles to ascend the value, belief of the world. Their worthy practices have made mathematics proud. But in this paper, we are going to present the discussion about cultural and social issues of mathematics in the context of Nepal.
Cultural and Social Issues on Mathematics Education in Nepal
Any kind of development is affected by the society and culture. Because human being are cultural organisms. Their every activity must be affected by their own cultural patterns, such as religious, social stratification, etc.
Nepal is Hinduism country, so the mathematics development of Nepal is also devoted to Hinduism. Hindus are in high place for the development of arithmetic. They have developed number , number system and algebra. So Hindus are in front stage for the development of arithmetic then the western mathematicians.
Mathematics education is an applied discipline. The main aim of the mathematics education is to prepare qualified teacher in context of teacher methods. It is the synthesis of what to teach(content), and how to teach(methods).
We usually use the terms mathematics instructor, mathematics teacher or arithmetic education. Those individuals who are involved in mathematics teaching percept the mathematical knowledge to the mind of learners like other subject teacher with interesting and meaningful methods. Such kinds of deed can’t be a regular process. Which is not easy, so mathematics teacher cannot be trapped only on content or method but he should have fulfilled qualifications on both of them because both content and teaching methods are the two wheels of a cart. So content and teaching method can’t be separated in mathematics teaching.
Culture implies the values, belies and norms established b each society form which each individual of the society fulfils own need. And aims the factors of values, norms and knowledge can have given the place in culture of society in that time when they have vital impact on society. If we glance at the ancient history of mathematics or at present achievement and utilities of mathematics, we know that it has fulfilled the need of society directly or indirectly. In other words, it plays very vital role to develop the culture of any society.
Mathematics is called as the mirror of civilization. If we want to visualize the suitable feature of culture of society. We have to look at the mirror of mathematics of that society. Clearing about the cultural role of the mathematics, J.W. Young presents his own ideas ‘If we glance anywhere in this age of iron, vapour and electricity, we get mathematics as an inventor. If we reject this backbone, the physical civilization and culture will be damaged. If mathematics would not purified the various sciences modern ideas and beliefs would not have been completed. So the different scientific laws and devices are based on pure mathematics concepts. Astronomy and physics are pure sciences which are due to mathematical applications.
So we agree on this matter because mathematics plays an important role to develop our culture. So mathematics is the foundation stone of all sciences. Therefore, today we are proud of our mathematics in this way mathematics has decorated and furnished the new era.
Nepal is a Hindu country. So in the context of Nepal, mathematics has played an important role in various fields. If we glance at any field, either it is astronomy or other. For instance, geometric patterns and mathematics is used to predict for forecasting the future of man, nation, environment etc. even for forecasting the national events in future, astronomers apply it.
But formally, mathematics is not applied satisfactorily. Due to low literacy rate, educational report, data visualize that we are very poor in the utility of mathematics. Which are due to illiteracy, unconsciousness and without the any longitudinal formation of planning of our planners. So we backward to this present changing age. Therefore, it can be considered that the national process of Nepal is impossible till the complete development of mathematics education. And the planning should be began by heart.
Sociology of Nepalese Mathematics Education
Mathematics is a behavioural subject which is learnt by known or unknown in daily life. It is used to solve the daily problems. So there is impossible to find out such person who has not used it in his daily life. In society, there can be various types of people. Therefore, mathematical education differs from each member. If we glance at our society, we get that there are such persons who calculate mathematical problems folding their fingers and on the other hand, there’re other person s who calculate by scientific technology. Such type of image of mathematics education can be obtained in society.
The mathematics skills and knowledge can be used in various fields. It helps to forecast the climate. The knowledge of scientists, engineers, pilots is worthless without the utility of mathematics. All the goods of communication, travelling, etc may fail without its help. So mathematics education has the deep image in our society.
The mathematics education is related to the minimum needs to the great discoveries. So its image is deep and dense in our society. It is in the high place due to being the foundation stone of all constructions and scientific inventions in our society. That society is highly developed where the mathematics education is highly reputed.
But in context of Nepal, mathematics is supposed as tedious and hard subject. Our higher mathematical education is worthless. So we have no need of higher and analytical mathematics. Only the mathematics up to secondary level is essential and useful in our daily life. So Nepalese higher mathematical education is failed for solving our daily mathematical applications. So in Nepalese society, the mathematical education has negative impact on higher level. So we can have two types of people in the context of mathematical concepts. One kind of people are having the maximum advantages with mathematical knowledge, skills and concepts. So they have positive attitude towards mathematics education. Others have negative attitude with the usability to learn its concepts. So in total, the mathematics education has both positive and negative attitudes towards it in our society.
2. Need and Relation among Various Needs
Solving problem , searching problems and using mathematical knowledge to solve the problems are short-term needs. The needs of society , objectives of mathematics education and development of student’s logical power are long-term needs. The short-term needs should help to fulfill the long term needs. Mathematics education should be reformed according to the coordination between short term and long term needs.
Mathematics is the essential subject matter for every member of society. As though they are ‘finger folder’ or ‘computer users’. They all use it according to their needs. So mathematics is the supplementary subject for the society.
Let us discuss the need of mathematics in the following points.
Guidance of society: mathematics education is such kind of philosophy that directs the social, cultural norms, values and attitudes that society is highly developed and technological inventions always depend on pure mathematical facts. Therefore mathematics education is needed to guide the whole society.
Foundation stone of inventions: all the scientific technologies faced in front of this new modern era due to the mathematics. They all can be lame. Thus mathematics is the foundation stone of all scientific discoveries and inventions.
Determination of development: if the mathematics education is well furnished in any society and nation, the development process is rapid in such place. So, mathematics determines the development of all society and country.
Creativity and entertainment: mathematics is the creative subject through which development of new scientific attitudes and possibilities. Mathematics is an interesting and amusing subject.
Way of thinking: mathematics education is a philosophy which develops the anxiety power of people. So mathematics is a way to settle in the mind and habit of reasoning. Which creates the new scientific technologies.
Behavioural science: mathematics is the behavioural science. All the men use it for solving daily mathematical problems. So mathematics is needed in society.
3. Needs and Demands and Needs and Possibility
Relation between the needs and possibility: To make success mathematics education we must be careful with social and individual needs. It in one way needs and in other way curriculum then the curriculum should not be matched that’s way before launching the mathematics we must be careful about need of math education ability of student, teacher’s ability, school’s situation and appropriately resources.
4. Reforms in School Mathematics Education
School level’s mathematics education is suitable to uplift the society to some extent. But still to make it radical it needs to verify time and again. It must be developed with associating various social needs and desires, both short and long terms. It needs to fulfill the basic requirements of varying social structures. There are many societies with in a nation. Many political, social, economical and scientific factors affect them. So the need of every society also differs. That is why while planning its curriculum holistic approach must be adopted. Where the common mathematical needs get fulfilled. For this reasons, school level’s curriculum must be both flexible and associative.
Reforms in terms of policy
Policy is long term policy which is used in every field. We can’t get success without policy. So policy is also necessary in mathematics education. The reforms in terms of policy in mathematics education are as follows:
[ The government should make it easy and enjoyment subject.
[ The government should be increase the investment in mathematics education.
[ The government should mobilize the product of mathematics education in field projects, etc.
Reforms in curriculum of school mathematics education
a. The planners of curriculum must be of own nation’s scholars. If needed they could take suggestions from foreign scholars as well. Otherwise, the same bitter meaningless reality like that of roll, cannot be said will be unrepeated.
b. The evaluation and determination of various levels mathematics curriculum must be examined whether they are fulfilling the needs of time or not. The contents of curriculum may include all imported ones. The availabilities of teaching learning materials also should take care while drafting it. New and scholarly ways so teaching must be managed by implementing different principles. Students should be encouraged with more and more practical ways of learning.
c. To achieve the intended goals both easily and effectively, the traditional ways so teaching learning methods must be replaced by new ones. Teachers also should apply different kinds of methods so the students could get chances to develop their rational turn of mind both externally and internally in a meaningful ways.
Students in mathematics education reforms in terms of materials should be selected carefully.
? The materials should be selected and reformed by the experts of own country.
? For effective teaching learning activities it is necessary to select the suitable teaching materials.
? Objectives of mathematics education should be made certain.
Traditional methods of teaching are ineffective. So we should use new and psychological teaching methods to achieve the goals of education. Using proper method according to the nature of subject matter is necessary to obtain in the certain goal.
Finally, in the 21st century science and technology could not be changed in the absence of mathematics education. Therefore, mathematics education is important in every field of society.
In the context of Nepal, for effective teaching learning activities, there must be relation between different needs and reforms of mathematics education.
5. Problems in Reforms
Ø Poor economic condition
Ø Geographical factors
Ø Socio-cultural factors
Ø Political factors
Ø Lack of instruments of mathematics education
6. Summary
To sum up, mathematics is an important subject for the present society. Nobody can understand its implications where scientific and technological education is so rapidly increasing. Everywhere, mathematics is used in more or less. So the more mathematics is practiced the more the nation will get developed. The extreme use of mathematics thus means the fully developed nations. From solving simple social problems to exploring and inventing new things, mathematics is working , being one of the fundamental necessities. The beginning of such as implement subject is from the school level. So in every level it must be effectively developed by solving social needs and developing up to more higher and unless the advanced and true mathematical education is brought it to practice widely in social level, needless to even imagine to be developed ones for any nations. Because any society is still working with unscientific superstitions, beliefs. So mathematics education is equally important from local to global level for more developed world, enlightening the whole people and developing their rational way of thinking.
7. References
Budhathoki, T.B., Surendra Ram. (….). Foundations of Mathematics Education Kirtipur: Kshitiz Prakashan.
Maharjan, H.B., Upadhyaya, H.N. and Poudel, L.M. (….). Teaching Mathematics. Kathmandu: Ratna Pustak Bhandar.
Mathematics Education and Society. UNESCO Document.

Introducing myself

hi, everyone ever there! It's me, Manoj. All the way from Budhabare, Jhapa. I like what you don't and do what you think you can't. Jusk kidding!

Abu Abdullah Muhammad ibn Musa al-Khwarizmi

Abu Abdullah Muhammad ibn Musa al-Khwarizmi
(c. 780, – c. 850)

-- Manoj Subedi (2010)

Abu Abdullah Muhammad ibn Musa al-Khwarizmi was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.

His Kitab al-Jabr wa-l-Muqabala presented the first systematic solution of linear and quadratic equations. He is considered the founder of algebra, In the twelfth century, Latin translations of his work on the Indian numerals, introduced the decimal positional number system to the Western world. He revised Ptolemy's Geography and wrote on astronomy and astrology.
His contributions had a great impact on language on mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name. His name is the origin of Spanish meaning digit.

Life

Few details of Al-Khwarizmi’s life are known with certainty, even his birthplace is unsure. His name may indicate that he came from Khwarezm which occupied the eastern part of the Greater Iran, now in Uzbekistan.

Harun al-Rashid became the fifth Caliph of the Abbasid dynasty on 14 September 786, about the time that al-Khwarizmi was born. Harun ruled, from his court in the capital city of Baghdad, over the Islam empire which stretched from the Mediterranean to India. He brought culture to his court and tried to establish the intellectual disciplines which at that time were not flourishing in the Arabic world. He had two sons, the eldest was Al-Amin while the younger was Al-Mamun. Harun died in 809 and there was an armed conflict between the brothers.

Al-Mamun won the armed struggle and Al-Amin was defeated and killed in 813. Following this, Al-Mamun became Caliph and ruled the empire from Baghdad. He continued the patronage of learning started by his father and founded an academy called the House of Wisdom where Greek philosophical and scientific works were translated. He also built up a library of manuscripts, the first major library to be set up since that at Alexandria, collecting important works from Byzantium. In addition to the House of Wisdom, Al-Mamun set up observatories in which Muslim astronomers could build on the knowledge acquired by earlier peoples.

Al-Khwarizmi and his colleagues the Banu Musa were scholars at the House of Wisdom in Baghdad. Their tasks there involved the translation of Greek scientific manuscripts and they also studied, and wrote on, algebra, geometry and astronomy. Certainly al-Khwarizmi worked under the patronage of Al-Mamun and he dedicated two of his texts to the Caliph. These were his treatise on algebra and his treatise on astronomy. The algebra treatise Hisab al-jabr w'al-muqabala was the most famous and important of all of al-Khwarizmi's works. It is the title of this text that gives us the word "algebra" and, in a sense that we shall investigate more fully below, it is the first book to be written on algebra. Regarding Al-Khwarizmi’s religion, he was an orthodox Muslim.

Al-Khwarizmi accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia, Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as China and India traveled to this city, as did Al-Khwarizmi. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph Al-Mamun, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts.

Contributions

Algebra
Al-Kitab al-mukhtaSar fi ḥisab al-jabr wa-l-muqabala
“The Compendious Book on Calculation by Completion and Balancing”)
Arithmetic
Al-Khwarizmi on the Hindu Art of Reckoning.
Trigonometry
Zij al-Sindhind,( tables for the trigonometric functions sine, cosine and for the first time for tangent)
Astronomy (construction of sundials and quadrants)
Geography
Kitab ṣurat al-Arḍ ("Book on the appearance of the Earth" or "The image of the Earth" translated as Geography)
Jewish calendar
Al-Khwarizmi’s contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, "The Compendious Book on Calculation by Completion and Balancing" (Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala.
On the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Al-Khwarizmi rendered as (Latin) Algoritmi, led to the term "algorithm".

Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics.

Al-Khwarizmi systematized and corrected Ptolemy's data for Africa and the Middle east. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa.

He also wrote on mechanical devices like the astrolabe and sundial.

He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma-mun, the caliph, overseeing 70 geographers.

When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

Algebra

Al-Khwarizmi is sometimes called the “Father of Algebra”.Al-Khwarizmi’s most important work Hisab al-jabr w’al-muqabala written in 830 gives us the word algebra. This treatise classifies the solution of quadratic equations and gives geometric methods for completing the square. No symbols are used and no negative or zero coefficients were allowed.

Al-Kitab al-jabr wa-l-muqabala “The Compendious Book on Calculation by Completion and Balancing”) is a mathematical book written approximately 830 CE. The term algebra is derived from the name of one of the basic operations with equations (al-jabr, meaning completion, or, subtracting a number from both sides of the equation) described in this book.

The al-jabr is considered the foundational text of modern algebra. It provided an exhaustive account of solving polynomial equations up to the second degree, and introduced the fundamental methods of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.

His book Al-Kitab al-mukhtaSar fi ḥisab al-jabr wa-l-muqabala on algebra, was translated into Latin and used for generations in Europe.

Some featurers of his book Al-jabr wa-l-muqabala

• It is strictly rhetorical – even the numerals are expressed as words, and it is more elementary than Arithmetica by Diophantus.
• It is a practical work, by design, being concerned with straightforward solutions of deterministic problems, linear and especially quadratic.
• Chapters I–VI covers cases of all quadratics with a positive solution in a systematic and exhaustive way.
• It would have been easy for any student to master the solutions. Mostly he shows his methods using examples – as others have done.
• Al-Khwarizmi then establishes geometric proofs for the same solutions of these quadratics. However, the proofs are more in the Babylonnian style.
• He dealt with three types of quantities: the square of a number, the root of the square (i.e. the unknown), and absolute numbers.
• He then solves the equation using essentially a rhetorical form for the quadratic equation.
He notes six different types of quadratics:
ax2 = bx
ax2 = c
bx = c
ax2 + bx = c
ax2 + c = bx
ax2 = bx + c
The treatise Al-Kitab al-mukhtaSar fi ḥisab al-jabr wa-l-muqabala was the most famous and important of all of Al-Khwarizmi's works. In this book, which has givenus the word ‘algebra’, Al-khwarizmi gives a complete solution to all possible types of quadratic equation.
Here is Al-Khwarizmi's solution of the equation.
x2 + 21 = 10x.
What is most remarkable is that in this case he knows that the quadratic has two solutions
Halve the number of the roots. It is 5. Multiply this by itself and the product is 25. Subtract from this the 21 added to the square term and the remainder is 4. Extract its square root, 2, and subtract this from half the number of roots, 5. There remains 3. This is the root you wanted, whose square is 9. Alternatively, you may add the square root to half the number of roots and the sum is 7. This is then the root you wanted and the square is 49. The above discussion uses modern mathematical notation for the types of problems which the book discusses. However, in Al-Khwarizmi’s day, most of this notation had not yet been invented, so he had to use ordinary text to present problems and their solutions. For example, for one problem;
He writes,
You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times.
In modern notation this process, with 'x' the "thing" or "root” is given by the steps,
(10 − x)2 = 81x
or, x2 + 100 = 101x
Arithmetic
Al-Khwarizmi's second major work was on the subject of arithmetic, which survived in a Latin translation but was lost in the original Arabic.
Al-Khwarizmi also wrote on Hindu-Arabic numerals. The Arabic text is lost, but a Latin translation, Algoritmi de numero Indorum, which in English is Al-Khwarizmi on the Hindu Art of Reckoning, gave rise to the word algorithm deriving from his name in the title.
The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: Dixit algorizmi ("So said Al-Khwarizmi”), or Algoritmi de numero Indorum ("Al-Khwarizmi's on the Hindu Art of Reckoning").
Al-Khwarizmi's work on arithmetic was responsible for introducing the Arabic numerals, based on the Hindu-Arabic numeral system developed in Indian mathematics, to the Western world. The term "algorithm" is derived from the algorism, the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwarizmi. Both "algorithm" and "algorism" are derived from the Latinized forms of al-Khwarizmi's name, Algoritmi and Algorismi, respectively.
Trigonometry
In trigonometry, Al-Khwarizmi produced tables for the trigonometric functions of sine and cosine in the Zij al-Sindhind, alongside the first tables for tangents. He was also an early pioneer in spherical trigonometry, and wrote a treatise on the subject.
Astronomy
Al-Khwarizmi made several important improvements to the theory and construction of sundials, which he inherited from his Indian and Greek predecessors. He made tables for these instruments which considerably shortened the time needed to make specific calculations. His sundial was universal and could be observed from anywhere on the Earth. From then on, sundials were frequently placed on mosques to determine the time of prayer. The shadow square, to find the height of a body was also invented by Al-Khwarizmi in ninth-century Baghdad.
The first quadrant was invented by al-Khwarizmi in ninth century Baghdad. The sine quadrant, invented by Al-Khwarizmi was used for astronomical calculations. The first horary quadrant for specific latitudes, was also invented by Al-Khwarizmi in Baghdad, then center of the development of quadrants. It was used to determine time.
Geography
Al-Khwarizmi’s third major work is his Kitab ṣurat al-Arḍ ("Book on the appearance of the Earth" or "The image of the Earth" translated as Geography), which was finished in 833. It is a revised and completed version of Ptolemy's Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.
The book opens with the list of latitudes and longitudes, in order of "weather zones", that is to say in blocks of latitudes and, in each weather zone, by order of longitude
Jewish calendar
Al-Khwarizmi wrote several other works including a treatise on the Hebrew calendar "Extraction of the Jewish Era"). It describes the 19-year cycle, the rules for determining on what day of the week the first day of the month.
Honor and Tribute
He is sometime also known as father of Algebra.
The words Algebra and Algorithm are termed after his name.
Khwarizmi is a lunar impact crater located on the far side of the Moon named by NASA on his tribute.
The Khwarizmi International Award is given annually by the Iranian Research Organization for Science and Technology (IROST) to individuals who have made outstanding achievements in research, innovation and invention, in fields related to science and technology.
References
History of mathematics.
http://en.wikipedia.org/wiki/Khwarezm"
http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Khwarizmi.html
http://en.wikipedia.org/wiki/Muhammad_ibn_Mūsā_al-Khwārizmī