Mathématiques

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Publié le : jeudi 21 juillet 2011
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This document contains assessment highlights from the 2008 Grade 9 French Mathematics Achievement Test.  Assessment highlights provide information about the overall test, the test blueprints, and student performance on the French form of the 2008 Grade 9 Mathematics Achievement Test. Also provided is commentary on student performance at the acceptable standard and the standard of excellence on the 2008 achievement test. This information is intended for teachers and is best used in conjunction with the multi-year and detailed school reports that are available to schools via the extranet. Assessment highlights reports for all achievement test subjects and grades (except Grade 9 Knowledge and Employability courses) will be posted on the Alberta Education website every year in the fall.  Released test items, which contained approximately 25 % of the total number of test items from previously secured achievement tests, were mailed to school administrators each fall from 2004 to 2006 and have been made available to teachers only in print form because of copyright limitations. Every second year , as of the fall of 2007, a complete test for all achievement test subjects and grades (except grades 6 and 9 Social Studies; grades 3, 6, and 9 Français/French Language Arts; and Grade 9 Knowledge and Employability courses) will be mailed to school administrators in conjunction with the assessment highlights report for that year. In this way, teachers will receive complete forms of achievement tests. The parts of those tests that are released in print form for which electronic copyright permission is received will subsequently be posted on the Alberta Education website. A test blueprint and an answer key that includes the difficulty, reporting category, test section, and item description for each test item will also be included. These materials, along with the Program of Studies and subject bulletin, provide information that can be used to inform instructional practice.  For further information, contact Kelly Rota, Grade 6 & 9 Mathematics Examination Manager, at Kelly.Rota@gov.ab.ca; Thomas Thompson, Grade6 & 9 Mathematics Examiner, at Thomas.Thompson@gov.ab.ca; or Jo-Anne Hug, Director, Achievement Testing, at Jo-Anne.Hug@gov.ab.ca at Learner Assessment, or call (780) 427-0010. To call toll-free from outside Edmonton, dial (780) 310-0000.  The Alberta Education Internet address is www.education.alberta.ca.               Copyright 2008, the Crown in Right of Alberta, as represented by the Minister of Education, Alberta Education, Learner Assessment, 44 Capital Boulevard, 10044 108 Street NW, Edmonton, Alberta T5J 5E6, and its licensors. All rights reserved.  Special permission is granted to Alberta educators only to reproduce, for educational purposes and on a non-profit basis, parts of this document that do not contain excerpted material.
 
Contents  
 The 2008 Grade 9 French Mathematics Achievement Test.........................................................................1  2008 Test Blueprint and Student Achievement ...........................................................................................2  2008 Mathematics 9 PAT Student Performance Commentary ....................................................................3  Achievement Testing Program Support Documents..................................................................................10          
 
The 2008 Grade 9 French Mathematics Achievement Test  This report provides teachers, school administrators, and the public with an overview of the performance of those students who wrote the French form of the 2008 Grade 9 Mathematics Achievement Test. It complements the detailed school and jurisdiction reports.  How Many Students Wrote the Test? Approximately 2 401 students wrote the French form of the 2008 Grade 9 Mathematics Achievement Test.  What Was the Test Like? The 2008 Grade 9 French Mathematics Achievement Test consisted of 44 multiple-choice items and 6 numerical-response items based on four strands: Number; Patterns and Relations; Shape and Space; and Statistics and Probability.  How Well Did Students Do? The percentages of students meeting the acceptable standard and the standard of excellence in 2008 compared with 2007 are shown in the graphs below. The results presented in this report are based on scores achieved by all students in French Immersion and Francophone programs who wrote the French form of the test; results for those students who wrote the English form of the test are reported separately. Out of a total score of 50 on the test, the provincial average was 34.3 (68.6 % ). Detailed provincial assessment results are provided in school and jurisdiction reports.  
100 100 90 90 80 80 70 70 60 60 % 50 % 50 40 40 30 30 20 20 10 10 0 0     2007 Achievement Standards: The percentage of students in the province who met the acceptable standard and the  standard of excellence on the 2007 Grade 9 French Mathematics Achievement Test (based on those who wrote). 2008 Achievement Standards: The percentage of students in the province who met the acceptable standard and the  standard of excellence on the 2008 Grade 9 French Mathematics Achievement Test (based on those who wrote).     
 
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Test Sections (Curricular Content Areas)  
2008 Test Blueprint and Student Achievement  In 2008, 87.0 % of students who wrote the French form of the test achieved the acceptable standard on the 2007 Grade 9 French Mathematics Achievement Test, and 29.4 % of students achieved the standard of excellence . Compared with the results from 2007, the percentage of students achieving the acceptable standard increased by 1 % , and the percentage of students achieving the standard of excellence increased by 2.7 % .  The blueprint below shows the reporting categories and test sections (curricular content areas) by which 2008 summary data are reported to schools and school authorities, and the provincial average of student achievement by both raw score and percentage. Reporting Category  Knowledge Skills Provincial Student Rceocnalcle fpatcst, s, Applyp rfoacctesd, concepts, Achievement procedures,andterminolougrye, sa, nd Average terminol gy relationships to solve Raw Score and o problems in a variety Percentage of situations  8.7/13  (66.9 % )  10.5/15  (70.0 % ) 9.5/14  (67.9 % ) 5.6/8  (70.0 % )  Total Test Raw Score  34.3/50  (68.6 % )  
  
  
Number  Number Concepts Number Operations  Patterns and Relations   Patterns  Variables and Equations  Relations and Functions Shape and Space  Measurement  3-D Objects and 2-D Shapes  Transformations Statistics and Probability  Data Analysis  Chance and Uncertainty  AvPerroavgien cRiaal wS tSucdoerne t aAncd hPieevrecemnetnatg  11.6/16 e For Students Who W the Tes rote t  (72.5 % )   
 
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 22.7/34  (66.8 % )  
2008 Mathematics 9 French PAT Student Performance Commentary  The following table provides a brief synopsis of student performance demonstrated on the 2008 Grade 9 Mathematics Achievement Test. The observations have been categorized in terms of student performance strengths and challenges in relation to outcomes that were tested in each of the four strands from the Alberta Program of Studies for K–9 Mathematics. Following the brief synopsis, four items that appeared on both the 2007 and 2008 tests have been provided to illustrate a few of the observations listed in the table below.  Strand Outcome Strengths Outcome Challenges r wers • Applying proper calculator keying sequences to  wAiptph liyning the expoonneenntts l aws fopoperform calculations involving rational Number Solvingt epgrroabl leexmps using rational numbers numbers  in meaningful contexts • Determining whether or not a number is rational  • Modeling situations that can be • Solving, algebraically, first-degree inequalities represented by first-degree expressions  rweiptrhe soennet avtairoina bolfe  tahne ds odleutteiromn ioninn ga  tnhue mcboerrr elicnt e  Patterns and • Solving first-degree, single-variable Relations equations • Evaluating polynomial expressions, given the value(s) of the variable(s) • Using trigonometric ratios in solving • Relating expressions for volumes of cones to right triangles volumes of cylinders • Applying the rate of area to perimeter to • Calculating and applying the rate of volume to solve design problems in two surface area to solve design problems in three dimensions dimensions • Recognizing why two triangles are  and Shape similar and using the properties of Space similar triangles to solve problems • Relating congruence to similarity in the context of triangles • Matching a 3-D object with its plan and elevation views • Determining the image of a 2-D shape as a result of a dilatation • Interpreting a report to determine the • Interpreting scatterplots to determine an Statistics relationship between two variables apparent relationship and volv  Probability  iSnodlevpinegn dpernotb elevemnst isningthe probability of    
 
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Items 1 and 2, which appeared on both the 2007 and 2008 Grade 9 French Mathematics PATs, are examples of performance strengths on two specific outcomes. Information about the relative strength of student performance from one year to the next is also given in terms of whether or not the difference was statistically significant.   Item 1   Quelle est la valeur de x  dans l’équation (2 a –3 )(6 a x ) = 12 a 15 ?  A. –18 B. –12 C. 12 D. 18           Statistical Data  Year of Administration Mean 2007 vs. 2008 Performance 22000087  8802..51 %%  Not statistically significant  Although a difference of 1.6 % was observed between 2007 and 2008, this difference was not statistically significant. Therefore, there was no meaningful difference in performance between these two administrations.   Outcome Competency   Students answering this question correctly were able to successfully apply the laws of exponents in order to simplify an algebraic expression and then to isolate and solve for the unknown variable. Although the algebra skill required to isolate the variable within the equation was relatively straight forward, students also needed to extract the equation from the exponents which may have been a difficult extension for some.    
 
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Item 2   Francis a un nombre égal de pièces de monnaie de 5 ¢, de 10 ¢ et de 25 ¢. S’il a 4,40 $ en pièces de monnaie, combien de pièces de 5 ¢ a-t-il au total?  A. 33 B. 30 C. 11 D. 10    Statistical Data  Year of Administration Mean 2007 vs. 2008 Performance 22000078  8858..93 %%  Statistically significant increase   In a statistical analysis of this item’s performance, an increase of 2.4 % ± 1.9 % was observed in the 2008 administration. The 95 % confidence interval for this increase ranged from 0.5 % (2.4 % –1.9 %) to 4.3 % (2.4 % + 1.9 % ).  Outcome Competency   Students answering this question correctly were most likely able to formulate an expression that represented the information within the question, and then carry out a series of algebraic steps to solve for the variable representing the total number of each coin. The remaining three choices were more or less split, with 3 % choosing A, and 4 % choosing ‘B’ or ‘D’. These responses may have been selected because each value, when combined with the coin values, could lead to a total value that satisfies the value criteria but not the number of coins criteria.  
 
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Items 3 and 4, which also appeared on the 2007 and 2008 Grade 9 French Mathematics PATs, are examples of performance challenges on two specific outcomes. While student performance may have increased from one year to the next, it is still relatively low in comparison to overall test performance. Information about the relative strength of student performance from one year to the next is also given in terms of whether or not the difference was statistically significant.   Item 3 Utilise l’information suivante pour répondre à la question 31.   Voici une roulette et un dé à six faces.
   Quelle est la probabilité que lorsqu’on fait tourner la roulette, l’aiguille s’arrête sur le rouge et qu’ensuite, lorsqu’on lance le dé, on obtient un 1 ou un 2?   Statistical Data  Year of Administration Mean 2007 vs. 2008 Performance 22000087  6655..43 %%  Not statistically significant   Although a difference of 0.1 % was observed between 2007 and 2008, this difference was not statistically significant. Therefore, there was no meaningful difference in performance between these two administrations.   A. 214 B 1 . 12 C. 81 D. 16   
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Outcome Competency   The majority of students answering this question correctly were most likely able to determine the probability of the desired outcome from each independent event and then multiply those values to determine the overall probability of the desired outcomes. Over 18 % chose ‘A’ as the correct answer, suggesting that they may not have determined the probability of the desired outcomes from the die before they calculated the overall probability. It may also be plausible that between 5 % and 10 % chose ‘C’ or ‘D’ because they recognized that the two desired outcomes from the die were important but were unable to determine the correct probability for the event. Therefore, they were unable to make a mathematically correct calculation to determine the overall probability of the desired outcomes.   
 
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Item 4  Utilise l’information suivante pour répondre à la question 8.   Le carré PQRS a subi une homothétie, ce qui a formé le carré P´Q´R´S´, comme le montre le plan cartésien suivant.  
  Quel est le rapport d’homothétie montré ci-dessus?  1 A. 6
B 1 . 5
C. 5
D. 5   
 
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