ASSESSING MATHS LITERACY IN GRADE 11 Jackie Scheiber RADMASTE Centre, Wits University
[email protected] Mathematical Literacy was introduced in Grade 10 in 2006. In 2007 teachers will have to assess Grade 11 Maths Literacy learners for the first time. During this workshop participants will • Answer a typical Grade 11 Maths Literacy question • Study the requirements for the Grade 11 Maths Literacy examination as listed in the Subject Assessment Guidelines MATHEMATICAL LITERACY (January 2007). • Study the Description of the Levels in the Mathematical Literacy Assessment Taxonomy • Analyse the Maths Literacy question in terms of the requirements and the taxonomy • Study the Assessment Frameworks for Papers 1 and 2 and complete a similar framework for the given question.
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A TYPICAL GRADE 11 MATHS LITERACY QUESTION QUESTION 1 Mrs Phumzile owns a taxi business. The table below shows a list of Mrs Phumzile's income and expenditure for her business, for the month of February 2007. INCOME EXPENDITURE Petrol R 1 065,70 Washing of taxi R 60,00 Servicing of taxi ( oil change, spark plugs et R 546,09 cetera) Fares paid by taxi commuters R7 842,00 Insurance for the taxi (in case of an accident) R 305, 45 Taxi-driver salary R 3 500,00 Taxi association fee R 200,00 (1)
1.1 Determine, for February 2007: 1.1.1 The total income 1.1.2 The total expenditure
(2)
1.2 Did Mrs Phumzile’s taxi business make a profit or a loss for the month (1) of February? 1.3 Calculate the profit or loss for this month
(2)
1.4 Hence determine the profit margin for the month Use the formula: Profit Margin =
Income − Expenses × 100% Expenses
(3)
1.5 Mandla works as a taxi driver for Mrs Phumzile. His basic salary is R35,00 per hour. On Monday 18 February he worked from 06:00 to 15:30 and had 1 hour off for lunch. (2) 1.5.1 How many hours did he work on that day? (2) 1.5.2 How much money did he earn on that day? Mrs Phumzile asks Mandla to transport passengers to a wedding 170 km away. Mandla drives the taxi at an average speed of 90 km/h. How many hours will the journey take? (Use the formula: Distance = Speed x Time to calculate your answer.) Write your answer correct to two (4) decimal places. [17]
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The requirements for the grade 11 mathematics literacy examination as listed in the subject assessment guidelines mathematical literacy (January 2007). According to the Subject Assessment Guidelines, the following the time allocations and number of papers is recommended for the final examinations for Grades 10, 11 and 12: GRADE 10 – one 3-hour paper of 150 marks GRADE 11 – two 2 ½ hour papers of 100 marks each GRADE 12 – two 3-hour papers of 150 marks According to the Subject Assessment Guidelines, an examination should • Give equal weighting to the four Learning Outcomes and should attempt to examine all of the Assessment Standards determined for the grade • Consist of questions which all focus on a context • Consist of questions which integrate Assessment Standards from more than one Learning Outcome • Be differentiated according to the Mathematics Literacy taxonomy with the following proportion of marks allocated to each of the levels: o 30% of the marks at the knowing level o 30% of the marks at the applying routine procedures in a variety of contexts level o 20% of the marks at the applying multi-step procedures in a variety of contexts level o 20% of the marks at the reasoning and reflecting level. TABLE 1 – REQUIREMENTS FOR GRADE 11 LEVEL 1 LEVEL 2 LEVEL 3 (30%) (30%) (20%) Knowing Applying routine Applying multiprocedures in step procedures familiar contexts in a variety of contexts
LEVEL (20%) Reasoning reflecting
4 and
LO1 PAPER 1 25% (2 ½ hours - 100 marks)
Paper 2 (2 ½ hours – 100 marks)
Paper 1 is intended to be a LO2 basic knowing and routine 25% application paper
Paper 2 is intended to be an applications and reasoning and reflecting paper
Consists of between 5 and 8 shorter questions
Consists of between 4 and 6 longer questions. These questions will require more
LO3 25%
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interpretation and application of the information provided
LO4 25%
Questions context
focus
on
a
60% on Level 1 and 40% on Level 2
Questions focus on a context
20% on Level 2, 40% on Level 3 and 40% on Level 4
TABLE 2 – DESCRIPTION OF THE LEVELS IN THE MATHEMATICAL LITERACY ASSESSMENT TAXONOMY LEVEL 1 (30%) LEVEL 2 (30%) LEVEL 3 (20%) LEVEL 4 (20%) Knowing Applying Routine Applying multi-step Reasoning and Procedures In procedures in a reflecting Familiar Contexts variety of contexts c) Performs h) Solve k) Pose and answer • Calculate using well-known problems using questions about the basic procedures in well-known what mathematics operations, familiar contexts. procedures. This they require to including: All the information required solve a problem -Algorithms for +, required to solve procedure is, and then to select –, x and ÷ the problem is however, not and use that -Appropriate immediately immediately mathematical rounding of available to the obvious from the content. numbers student way the problem k) Interpret the - Estimation d) Solves is posed. Learners solution they - Calculating a equations by will have to determine to a percentage of a means of trial and decide on the problem in the given amount error or algebraic most appropriate context of the - measurement processes procedure to solve problem and • Know and use e) Draw data the solution to the where necessary appropriate question and may to adjust the vocabulary such as graphs for provided data have to perform mathematical equation, formula, f) Draw one or more solution to make bar graph, pie algebraic graphs preliminary sense in the chart, Cartesian for given equations calculations context plane, table of g) Measure before l) Critique solutions values, mean, dimensions (e.g. determining a to problems and median and mode length, weight and solution statements about • Know and use i) Select the situations made formulae such as time) using appropriate most appropriate by others the area of a 59
rectangle, a triangle and a circle where each of the required dimensions is readily available Read information directly from a table (e.g. the time a particular bus departs from the terminal)
measuring instruments sensitive to levels of accuracy
data from options in a table of values to solve a problem j) Decide on the best way to represent data to create a particular impression
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m) Generalize patterns observed in situations, make predictions based on these patterns and/or other evidence and determine conditions that will lead to desired outcomes
TABLE 3 – EXAMPLE OF AN ASSESSMENT FRAMEWORK FOR PAPER 1 Learning Taxonomy Context SubOutcomes Level Q Item Total detail total LO LO LO LO 1 2 3 4 L1 60% L2 40% 1.1.1 1 1 1 1.1.2 2 2 2 1,2 1 1 1 2 2 Buying a 1,3 2 1 17 cell phone 1,4 3 3 3 1.5.1 2 2 2 1.5.2 2 2 2 1,6 4 4 4 2.1.1a 2 2 2 2.1.1b 2 2 2 2.1.2 4 2 2 4 2.1.3 2 2 2 2.1.4 2 2 2 2.1.5 4 2 2 4 2.1.6 2 2 2 Building a 2 29 2.1.7a 2 2 2 house 2.1.7b 3 3 3 2.2.1 1 1 1 2.2.2 1 1 1 2.2.3a 1 1 1 2.2.3b 1 1 1 2.2.3c 1 1 1 2.2.4 1 1 1 3.1.1a 1 1 1 3.1.1b 1 1 1 3.1.2a 1 1 1 3.1.2b 2 1 1 2 Buying a 3,2 1 1 1 3 21 new car 3,3 2 1 3 3 3,4 2 2 2 3.5.1 5 5 5 3.5.2 1 1 1 3.5.3 4 3 1 4
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4.1.1 1 1 1 4.1.2 2 2 2 4.1.3 3 2 1 3 4.1.4 2 2 2 4.1.5 2 1 1 2 Global 4 25 warming 4.2.1a 3 3 3 4.2.1b 2 1 1 2 4.2.2 5 3 2 5 4.3.1 2 2 2 4.3.2 3 3 3 5.1.1 2 2 2 Consumer 5.1.2 1 1 1 5 8 Price Index 5.1.3 2 2 2 5,2 3 2 1 3 22 29 26 23 56 44 100 100 TABLE 4 – EXAMPLE OF AN ASSESSMENT FRAMEWORK FOR PAPER 2 Learning Taxonomy SubOutcomes Level Context Total Q Item detail LO LO LO LO L2 L3 L4 tot 1 2 3 4 20% 40% 40% 1.1.1 1 1 1 1.1.2 1 1 1 1.2.1a 2 2 2 1.2.1b 2 2 2 1.2.1c 4 4 4 1.2.1d 5 5 5 1.2.1e 2 2 2 1.2.2 3 3 3 Buying a 1.2.3 4 4 4 1 washing 46 1.3.1 4 4 4 machine 1.3.2a 2 1 1 2 1.3.2b 2 1 1 2 1.3.3 2 2 2 1.4.1 3 3 3 1.4.2 2 2 2 1.4.3a 2 2 2 1.4.3b 2 2 2 1,5 3 1 2 3 2 Plan of 2.1.2 1 1 1 22
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3
4
the school 2.1.2 building 2.1.3 2.2.1 3 2.2.2 4 2.3.1 2.3.2 2.3.3a 2.3.3b 3,1 3,2 2 3.3.1 4 3.3.2a 2 Global warming 3.3.2b 2 3.3.3a 3.3.3b 3.3.4 4,1 Crime 4,2 Statistics 4.3.1 4.3.2 27
3 2
3
2 1 5 1 2
1 5 1 2 2 2 1
21
2 3 2
2 2 2 2 3 2 4 30 22
63
2 4 5 2 2 2 2 2 2 3
22
39
2 4 39
3 2 3 4 1 5 1 2 2 4 5 2 2 2 2 2 2 3 2 4 100
21
11 100
