☆中高考综合报告[英]

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2009年4月21日下午,厦门大学嘉庚三215会议室,数学教育沙龙。

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  • Zhong kao is now equivalent to the GCSE in the UK- O-levels now written-off/gone it's a 1980s thing.
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☆中高考综合报告[英]

  1. 1. Assessment of Math Education in China Rongbao Tu Nanjing Normal University, China Xia Men 2009.4.
  2. 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. 3. Senior High School Entrance Exam —— O’ level Selection-aimed Eleven-plus Assessment College Entrance Examination —— A’ level, SAT&ACT
  4. 4. Selection-aimed Eleven-plus Assessment <ul><li>Important basis of selecting students into a higher level </li></ul><ul><li>Belongs to especial concluding assessment </li></ul><ul><li>Nanjing Normal University is in charge of the exam paper </li></ul><ul><li>setting and marking in Jiangsu Province. </li></ul><ul><li>Some of us are the team leader for the paper setting team, </li></ul><ul><li>while some is the team leader for the marking team. </li></ul><ul><li>Question-setting and exam papers-marking </li></ul><ul><li>Zhong Kao (O’ level)——Local educational departments </li></ul><ul><li>Gao Kao (A’ level)——National and provincial </li></ul><ul><li>educational administrative departments </li></ul>
  5. 5. Selection-aimed Eleven-plus Assessment 1. Zhong Kao ( O’ level) (Math) <ul><li>Main Purpose : </li></ul><ul><li>To select qualified students for Senior High School </li></ul><ul><li>based on the score of examination. </li></ul>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
  6. 6. this is a sample of an exam paper. this is a sample for the standard solution of an exam paper.
  7. 7. this is a sample for a marked exam paper.
  8. 8. 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 <ul><li>Between two sequential integers a and b , </li></ul><ul><li>if a < < b , then a = and b = . </li></ul>
  9. 9. senior high school entrance Examinations of Nanjing, China, 2006 Mathematics <ul><li>2. According to following figure, the </li></ul><ul><li>point M is (3,0). M on the line l , and </li></ul><ul><li>l is parallel with y -axis. </li></ul><ul><li>(1) △ABC is a triangle. The points A , </li></ul><ul><li>B and C are ( - 2, 0), ( - 1, 0) and </li></ul><ul><li>( - 1, 2) respectively. </li></ul><ul><li>△ A 1 B 1 C 1 is the symmetric figure of AB C with y -axis. △A 2 B 2 C 2 </li></ul><ul><li>is the symmetric figure of △A 1 B 1 C 1 with line l . </li></ul><ul><li>What is the coordinates of A 2 , B 2 and C 2 . </li></ul><ul><li>(2) If the point P is ( - a , 0), and a > 0. Point P 1 is the symmetric point of point P with y -axis. Point P 2 is the symmetric point of point P 1 with line l . </li></ul><ul><li>Then, please calculate the length of line segment PP 2 . </li></ul>
  10. 10. <ul><li>The following is solution: </li></ul><ul><li>(1)the three vertexes coordinates of </li></ul><ul><li>the △ A 2 B 2 C 2 are A 2 (4, 0), </li></ul><ul><li>B 2 (5, 0), </li></ul><ul><li>C 2 (5, 2). </li></ul><ul><li>(2) if 0< a ≤3, then P 1 is on segment OM . </li></ul><ul><li>PP 2 = PP 1 + P 1 P 2 =2 OP 1 +2 P 1 M </li></ul><ul><li>= 2( OP 1 +1 M )=2 OM = 6; </li></ul><ul><li>If a >3, then P 1 is on the right of M , </li></ul><ul><li>PP 2 = PP 1 - P 1 P 2 = 2 OP 1 - 2 P 1 M </li></ul><ul><li>=2( OP 1 - P 1 M ) = 2 OM = 6 </li></ul><ul><li>So the length of PP 2 is 6. </li></ul>
  11. 11. 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. <ul><li>1 . In the NanJing traffic map which has scale of 1:38000 there is a tunnel called XuanWu tunnel that ocuppy the length of 7 centimeters, so in fact the length of the tunnel is ( ) </li></ul><ul><li>(A)0.266 km (B)2.66 km (C)26.6 km (D)266 km </li></ul><ul><li>Remark: This subject examines the calculation of scale. </li></ul>
  12. 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.
  13. 13. 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 <ul><li>2. There are many quadratic function whose symmetry axis of their images are y -axis. Please write two different analytic expressions of quadratic function , which make the symmetry axis of their images are y- axis. </li></ul><ul><li>Remark: The most noticeable characteristic of the Open-ended Question is that the answer is not unique . </li></ul>1. Please write an irrational number which product with is a rational number .
  14. 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) 
  15. 15. Selection-aimed Eleven-plus Assessment 2. Gao Kao ( A’ level, SAT&ACT ) <ul><li>There is a big change of the College Entrance Examination in Jiangsu in 2008, which is the cancellation of the multiple choice questions, this is because MCQs cannot test students' thinking process and their real skills. </li></ul><ul><li>Characteristics of mathematics exam paper </li></ul><ul><li>Since 2004, 15 provinces have self-set the exam paper. </li></ul><ul><li>According to—— Curriculum Standard for Senior High school </li></ul><ul><li>Directions for Gao Kao </li></ul><ul><li>Time limit: 120 minutes. Full mark: 150 points </li></ul><ul><li>Format: same as Zhong Kao exam paper </li></ul><ul><li>Score proportion: easy /moderate /difficult = 3∶5∶2 </li></ul><ul><li>The score rate—— easy (score rate>0.7), </li></ul><ul><li>moderate (0.4<score rate<0.7), difficult (score rate<0.4). </li></ul><ul><li>The difficulty of the whole paper —— 0.55 ~ 0.60 </li></ul>
  16. 16. <ul><li>If a , b ∈R, and {1, a + b , a }={0, b / a, b }, </li></ul><ul><li>then b - a = ( ). </li></ul><ul><li>A. 1 B. - 1 C. 2 D. - 2 </li></ul>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
  17. 17. <ul><li>(1) If the graph of function and y = log 3 x ( x > 0) are symmetrical of line y = x , then f ( x ) = . </li></ul>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)
  18. 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. 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 .
  20. 20. <ul><li>(1) Please design a tent with its base a hexagonal prism and its height 1m. Its coping is a hexagonal pyramid with sideline 3m. To maximize the volume of the tent, </li></ul><ul><li>determine the distance from the </li></ul><ul><li>Peak O to the Center O 1 in the </li></ul><ul><li>undersurface. </li></ul>4. problem sums Examples of Test Questions in Gao Kao Paper (5) O
  21. 21. <ul><li>(1) In the following picture, point E and F are the center of ADD 1 A 1 and BCC 1 B 1 respectively. Then the projection of quadrilateral BFD 1 E on the any face of the cube may be ___________ (Fill the number of the graphics in the blank, if the graphics match the condition.) </li></ul>5. innovative question Examples of Test Questions in Gao Kao Paper (6)
  22. 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
  23. 23. <ul><li>Marking team for Gao Kao : </li></ul><ul><li>Markers: college teachers, </li></ul><ul><li>middle school teachers, </li></ul><ul><li>graduate students from math. department </li></ul><ul><li>Scale: markers: examinees =1.6 :1000 </li></ul><ul><li>e.g. 500,000 examinees VS 800 markers </li></ul><ul><li>(in ’07 in Jiangsu Province) </li></ul>Selection-aimed Eleven-plus Assessment Gao Kao (cont.)
  24. 24. <ul><li>The process of marking </li></ul><ul><li>Formulate standard- —preliminary marking by samples </li></ul><ul><li>Formal marking —after strict training and </li></ul><ul><li>the preliminary marking </li></ul><ul><li>Marking work can be completed within 10 days . </li></ul><ul><li>Marking for MCQ —operated by computers. </li></ul><ul><li>Other Questions — marked on-line by markers . </li></ul><ul><li>Each grader is responsible for only one question. </li></ul><ul><li>Each question is marked by two graders. </li></ul><ul><li>Reexamining by sampling, reduce the maximum 2-score </li></ul><ul><li>deviation to the ratio of 0.1‰. </li></ul>Selection-aimed Eleven-plus Assessment Gao Kao (cont.)
  25. 25. <ul><li>Although examinations in China are well-known, most </li></ul><ul><li>people don’t really understand the exam system in China. </li></ul><ul><li>Even we Chinese don’t clearly know the relationship </li></ul><ul><li>between assessment and examinations.  </li></ul><ul><li>Generally speaking , most people pay attention to the </li></ul><ul><li>entrance examinations in China, or they hold the opinion </li></ul><ul><li>that the assessment is solely instead by entrance exams. </li></ul><ul><li>However , the more valued, which go through the whole </li></ul><ul><li>education process is school work-based assessment. </li></ul><ul><li>In other words, the more valued in China are daily assessment, period assessment and final assessment. </li></ul><ul><li>Unfortunately , school work-based assessment has recently </li></ul><ul><li>been led to the wrong way. The more obvious change is that, </li></ul><ul><li>there are too much daily assessment and period assessment </li></ul><ul><li>which results in heavy workload for students. </li></ul>
  26. 26. <ul><li>As a whole , these examinations are useful for assessments, but for the long-time development, the demerits overweight the merits.  </li></ul><ul><li>However , only exams can maintain the fairness, and only in this way, people from lower class could obtain the opportunity to enter the upper class, otherwise no chances. </li></ul><ul><li>Large quantities and high level of difficulty are determined by Chinese cultural tradition, which requires students to work very hard. </li></ul><ul><li>on the other hand , There is an old saying in China, the one who achieves more must work much harder and all things beneath studying. </li></ul>
  27. 27. Thank you very mach !
  28. 28. <ul><li>Cancellation of Junior high school entrance examination </li></ul><ul><li>Reason: Compulsory Education </li></ul><ul><li>Children of the right age attend schools nearby </li></ul><ul><li>all of them enter junior high school. </li></ul><ul><li>I myself have been shouldering the role of team leader for the marking team for 15 years. </li></ul><ul><li>Main Purpose : To select qualified students for </li></ul><ul><li>Universities and Colleges based on the score of exam. </li></ul><ul><li>Marking for Gao Kao </li></ul><ul><li>Done by special marking team, which is </li></ul><ul><li>organized by the Provincial Education Department. </li></ul>
  29. 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
  30. 31. <ul><li>The number of the students who selected math as elective course decreased gradually. </li></ul><ul><li>This situation is fit for the other subject as difficult as math. </li></ul><ul><li>The new students of science in most of the college in Britain need taking math classes after school. </li></ul><ul><li>In China, students in middle schools must learn math till 18. </li></ul><ul><li>The situation in England will effect the future development </li></ul><ul><li>of technology and economics seriously. </li></ul><ul><li>It causes the great worries of the business circles and academic circles. </li></ul>It was reported by BBC that Richard (the principal) expressed a fact:
  31. 32. <ul><li>National test set by Chinese education authorities for pre-entry students: </li></ul><ul><li>As shown in the figure ABCD-A 1 B 1 C 1 D 1 , in square prism and foot of </li></ul><ul><li>perpendicular is E , </li></ul><ul><li>(ⅰ) Prove: </li></ul><ul><li>(ⅱ) Determine the angle between </li></ul><ul><li>the two planes </li></ul><ul><li>(ⅲ) Determine the angle between </li></ul><ul><li>formed by lines </li></ul><ul><li>which are in different planes. </li></ul>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.
  32. 33. <ul><li>In the diagram (not drawn to scale), angle ABC is a right angle, AC =4m, BC =3m. </li></ul><ul><li>(ⅰ) What is the length of AB ? </li></ul><ul><li>(ⅱ) What is the area of triangle ABC </li></ul><ul><li>(above)? </li></ul><ul><li>(ⅲ) What is the tan θ of the triangle </li></ul><ul><li>ABC (above) as a fraction ? </li></ul>Diagnostic test set by an English university for first year students:
  33. 34. This is the end of my presentation. Thanks for your appreciation!

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