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Assessment of Math Education  in China Rongbao  Tu Nanjing Normal University, China   Xia Men 2009.4.
Outline The main types of  math education assessment school work-based assessment selection-aimed eleven-plus assessment competition-based  assistant assessment. Daily Assessment Period Assessment Final Assessment school work-based assessment Purpose:  don’t  aim at recording grades The main forms:  closed book tests and closed book examinations
Senior High School Entrance Exam ——  O’ level Selection-aimed  Eleven-plus Assessment College Entrance Examination ——  A’ level,  SAT&ACT
Selection-aimed Eleven-plus Assessment ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Selection-aimed Eleven-plus  Assessment   1. Zhong Kao  ( O’ level) (Math) ,[object Object],[object Object],[object Object],Characteristics of mathematics exam paper According to—— Curriculum Standard for Junior High  School Directions for Zhong Kao Time limit:  120 minutes.  Full mark:  120 points Format : altogether 20 ~ 25  test questions ,  including  MCQ,  blank-filling,   solution-seeking  or reasoning questions Score proportion:  easy /moderate /difficult = 7∶2∶1  The difficulty  of  the whole paper —— 0.60 ~ 0.75
this is a sample  of an exam paper. this is a sample for the standard solution of an exam paper.
this is a sample for a marked exam paper.
Change 1: basic knowledge   and basic skills to the test in the form of increasingly becoming diversified The mathematics questions designed    to test changes in trend analysis     in the past eight years of Nanjing City ,[object Object],[object Object]
senior high school entrance   Examinations  of Nanjing, China, 2006 Mathematics   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Change 2: contacting with facts of production and living,    designing problems of applying which have several kinds of    backgrounds, examining applying consciousness, reading    comprehension and information processing abilities of students. ,[object Object],[object Object],[object Object]
2 . The followed diagram is illustrated that the air temperature of  some place recorded the highest temperature and the lowest  temperature from January 1st for 4th in 2006. Date    1/1  1/2  1/3  1/4 The highest temperature  5℃   4℃   0℃   4℃ The lowest temperature    0℃   - 2℃  - 4℃  - 3℃ So the day that has the largest difference in temperature is (  ) (A)1/1  (B)1/2  (C)1/3  (D)1/4 Remark:   The subject puts the subtration of rational number into a real situation.
Change 3: The Questions Change  (Open title, innovation, and explore )  the increasingly prominent students of mathematics thinking process, the students focus on the comprehensive capacity study ,[object Object],[object Object],1.  Please write an irrational number which product with  is a  rational number .
(2)In picture (2), drawing a point  P  on the straight line  l , make the line which include  A ,  P  parallel to the straight line  l . You can only use compasses . (2) Remark: There are many solutions to this question, it is a typical Open-ended Question . 3.  There is a straight line  l  and a point  A  out of it .   Please draw two pictures according to the following request. Write the method of drawing and retain the track.   (1)In picture (1), drawing two points  B ,  C  in the straight line  l , which make  A , B , C   to constitute an  isosceles triangle.You can only use compasses . (1) 
Selection-aimed Eleven-plus  Assessment 2.   Gao Kao  ( A’ level,  SAT&ACT ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],1.  Multiple Choice (3)If vector  a =(1, 1) ,  b =(1,  - 1)  ,  then vector  (  ). A.  ( - 2,  - 1)  B.( - 2,  1)  C.( - 1,  0)  D.( - 1,  2)  Examples  of Test Questions in Gao Kao Paper  (1) (1)The focus of the parabola  y 2 =4 x  is  F , and  M  is a point on the parabola. The distance between  M  and  F  is 1. Then the  y -coordinate of  M  is (  ).  A. 17/16  B.  15/16  C.5/8  D. 0
[object Object],2. blank-filling (3) If  S n   is the sum of the first  n  terms of geometric series { a n } ,  and  S 1 , 2 S 2 , 3 S 3  forms an arithmetic series, the common ratio of  the arithmetic series  is  . (2) If  is an odd function,  then  a  =      . Examples  of Test Questions in Gao Kao Paper  (2)
3. solution-seeking Examples  of Test Questions in Gao Kao Paper  (3) (2) In a rectangular pyramid  P-ABCD ,  PA= 2,  the angle between line  PA  and base  ABCD  is 60°.   Calculate the volume of the  rectangular  pyramid  P-ABCD . (1) Let  f  ( x ) = e x   - e - x   .  (Ⅰ)Prove  f ′ ( x ) ≥ 2 . (Ⅱ)If  x  ≥ 0 for all  x , we can obtain  f  ( x ) ≥  ax ,  calculate the domain of  a .
Examples  of Test Questions in Gao Kao Paper  (4) 3. solution-seeking (3)The radius circle  O 1  and circle  O 2   are 1,  O 1 O 2  =4.  Tangent  PM  and  PN  (the point of contact are  M  and  N ) intersect on point  P ,  and  .  Form the frame of axes,  and find locus equation of  P .
[object Object],[object Object],[object Object],[object Object],4. problem sums Examples  of Test Questions in Gao Kao Paper  (5) O
[object Object],5. innovative  question Examples  of Test Questions in Gao Kao Paper  (6)
( 2)The figure is made up of two same  rectangular pyramids. It can be placed  in a cube.  The length of the cube is 1.  Let the bottom of the upper rectangular  pyramid ( ABCD ) parallel to a plane of  the cube, the vertexes of  the rectangular  pyramids are all on the surface of the cube.  Then, the probable value for the volume  of the geometry is (  ). A. 1  B. 2  C. 3  D. infinite
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Selection-aimed Eleven-plus  Assessment   Gao Kao  (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Selection-aimed Eleven-plus  Assessment   Gao Kao  (cont.)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Thank you  very mach  !
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Senior High School Entrance Exam The mathematics examination  of senior high school entrance examination is marked together by the marking group organized by local educational departments.  The styles of the exam paper is in clouding  multiple-choice,  blank-filling,  question answering and question proving. However, today i will only talk about Junior High School Elective Entrance Examination and College Entrance Examination
 
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],It was reported by BBC that Richard (the principal)  expressed a fact:
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Royal Chemistry Society of Britain compared the math examination papers in entrance examination in China and the exam papers in the first year of college in Britain.
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Diagnostic test set by an English university for first year students:
This is the end of my presentation.  Thanks for your appreciation!

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☆中高考综合报告[英]

  • 1. Assessment of Math Education in China Rongbao Tu Nanjing Normal University, China Xia Men 2009.4.
  • 2. Outline The main types of math education assessment school work-based assessment selection-aimed eleven-plus assessment competition-based assistant assessment. Daily Assessment Period Assessment Final Assessment school work-based assessment Purpose: don’t aim at recording grades The main forms: closed book tests and closed book examinations
  • 3. Senior High School Entrance Exam —— O’ level Selection-aimed Eleven-plus Assessment College Entrance Examination —— A’ level, SAT&ACT
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  • 6. this is a sample of an exam paper. this is a sample for the standard solution of an exam paper.
  • 7. this is a sample for a marked exam paper.
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  • 12. 2 . The followed diagram is illustrated that the air temperature of some place recorded the highest temperature and the lowest temperature from January 1st for 4th in 2006. Date 1/1 1/2 1/3 1/4 The highest temperature 5℃ 4℃ 0℃ 4℃ The lowest temperature 0℃ - 2℃ - 4℃ - 3℃ So the day that has the largest difference in temperature is ( ) (A)1/1 (B)1/2 (C)1/3 (D)1/4 Remark: The subject puts the subtration of rational number into a real situation.
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  • 14. (2)In picture (2), drawing a point P on the straight line l , make the line which include A , P parallel to the straight line l . You can only use compasses . (2) Remark: There are many solutions to this question, it is a typical Open-ended Question . 3. There is a straight line l and a point A out of it . Please draw two pictures according to the following request. Write the method of drawing and retain the track. (1)In picture (1), drawing two points B , C in the straight line l , which make A , B , C to constitute an isosceles triangle.You can only use compasses . (1) 
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  • 18. 3. solution-seeking Examples of Test Questions in Gao Kao Paper (3) (2) In a rectangular pyramid P-ABCD , PA= 2, the angle between line PA and base ABCD is 60°. Calculate the volume of the rectangular pyramid P-ABCD . (1) Let f ( x ) = e x - e - x . (Ⅰ)Prove f ′ ( x ) ≥ 2 . (Ⅱ)If x ≥ 0 for all x , we can obtain f ( x ) ≥ ax , calculate the domain of a .
  • 19. Examples of Test Questions in Gao Kao Paper (4) 3. solution-seeking (3)The radius circle O 1 and circle O 2 are 1, O 1 O 2 =4. Tangent PM and PN (the point of contact are M and N ) intersect on point P , and . Form the frame of axes, and find locus equation of P .
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  • 22. ( 2)The figure is made up of two same rectangular pyramids. It can be placed in a cube. The length of the cube is 1. Let the bottom of the upper rectangular pyramid ( ABCD ) parallel to a plane of the cube, the vertexes of the rectangular pyramids are all on the surface of the cube. Then, the probable value for the volume of the geometry is ( ). A. 1 B. 2 C. 3 D. infinite
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  • 27. Thank you very mach !
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  • 29. Senior High School Entrance Exam The mathematics examination of senior high school entrance examination is marked together by the marking group organized by local educational departments. The styles of the exam paper is in clouding multiple-choice, blank-filling, question answering and question proving. However, today i will only talk about Junior High School Elective Entrance Examination and College Entrance Examination
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  • 34. This is the end of my presentation. Thanks for your appreciation!