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Patterns and Trends in NCEA Mathematics/Statistics
Eldon Paki
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Level 3 Calculus has three externally-assessed achievement standards
Patterns/Trends Level 3 Calculus has three externally-assessed achievement standards 91577 – Apply the algebra of complex numbers in solving problems 91578 – Apply differentiation methods in solving problems 91579 – Apply integration methods in solving problems
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2018 Data N = 9,553 students with at least one result in externally-assessed achievement standards 91577 (Complex Nos.) 91578 (Differentiation) 91579 (Integration) By result, I mean grade, i.e. an N, A, M, or E grade
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2018 Data N = 9,553 students with at least one result in externally-assessed achievement standards 91577 (Complex Nos.) = 6, % Least Popular 91578 (Differentiation) = 8, % Most Popular 91579 (Integration) = 7, %
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Results: Venn diagram (%) N = 9,553 students
2018 Data 91577 3 91579 1 91578 8 Results: Venn diagram (%) N = 9,553 students 8 2 57 21 In the trends that follow I group results into three categories Percentage of students with results in one standard only Percentage of students with results in two standards Percentage of students with results in three standards
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Data What do you see? Results in all three standards trending downward from 67 percent in 2014 to 57 percent in 2018 Results in two standards trending upward from 22 percent in 2014 to 31 percent in 2018
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2014-2018 Data Maori What do you see?
Results in all three standards trending downward from 49 percent in 2014 to 40 percent in 2018 Results in two standards bouncing around from 31 percent in 2014 to 38 percent in 2018
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Data Pasifika
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Level 3 Statistics has three externally-assessed achievement standards
Patterns/Trends Level 3 Statistics has three externally-assessed achievement standards 91584 – Evaluate statistically based reports 91585 – Apply probability concepts in solving problems 91586 – Apply probability distributions in solving problems
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2018 Data N = 13,021 students with at least one result in externally-assessed achievement standards 91584 (Stat. Report) 91585 (Prob. Concepts) 91586 (Prob. Distns.)
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2018 Data N = 13,021 students with at least one result in externally-assessed achievement standards 91584 (Stat. Report) = 4, % Least Popular 91585 (Prob. Concepts) = 8, % Most Popular 91586 (Prob. Distns.) = 7, %
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2018 Data 91584 14 91586 15 91585 25 Results: Venn diagram (%) N = 13,021 students 7 4 6 30
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Data What do you see? Results in all three standards trending downward from 16 percent in 2014 to 6 percent in 2018 Results in one standard only trending upward from 34 percent in 2014 to over half (53 percent) in 2018
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2014-2018 Data Maori What do you see?
Results in all three standards trending downward from 11 percent in 2014 to 3 percent in 2018 Results in one standard only trending upward from 46 percent in 2014 to 66 percent (i.e. two-thirds) in 2018
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2014-2018 Data Pasifika What do you see?
Results in all three standards trending downward from 10 percent in 2014 to 3 percent in 2018 Results in one standard only trending upward from 50 percent (half) in 2014 to 74 percent (i.e. almost three-quarters) in 2018
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Level 2 Math has three externally-assessed achievement standards
Patterns/Trends Level 2 Math has three externally-assessed achievement standards 91261 – Apply algebraic methods in solving problems 91262 – Apply calculus methods in solving problems 91267 – Apply probability methods in solving problems
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2018 Data N = 30,889 students with at least one result in externally-assessed achievement standards 91261 (Algebra) 91262 (Calculus) 91267 (Probability)
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2018 Data N = 30,889 students with at least one result in externally-assessed achievement standards 91261 (Algebra) = 14, % Least Popular 91262 (Calculus) = 15, % 91267 (Probability) = 23, % Most Popular
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2018 Data 91261 2 91267 44 91262 3 Results: Venn diagram (%) N = 30,889 students 18 3 23 7
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Data What do you see? Results in all three standards trending downward from 37 percent in 2014 to 23 percent in 2018 Results in one standard only trending upward from 39 percent in 2014 to 49 percent in 2018
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2014-2018 Data Maori What do you see?
Results in all three standards trending downward from 23 percent in 2014 to 15 percent in 2018 Results in one standard only trending upward from 54 percent in 2014 to 64 percent in 2018
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2014-2018 Data Pasifika What do you see?
Results in all three standards trending downward from 21 percent in 2014 to 10 percent in 2018 Results in one standard only trending upward from 52 percent in 2014 to 64 percent in 2018
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Patterns/Trends Level 1 Math focused on end-of-year three externally-assessed achievement standards 91028 – Investigate relationships between tables, equations and graphs 91031 – Apply geometric reasoning in solving problems 91037 – Demonstrate understanding of chance and data
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2018 Data N = 35,418 students with at least one result in end-of-year externally-assessed achievement standards 91028 (Tables) 91031 (Geo. Reasoning) 91037 (Chance)
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2018 Data N = 35,418 students with at least one result in end-of-year externally-assessed achievement standards 91028 (Tables) = 22, % 91031 (Geo. Reasoning) = 12, % Least Popular 91037 (Chance) = 23, % Most Popular
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2018 Data 91028 11 91037 28 91031 6 Results: Venn diagram (%) N = 35,418 students 17 25 9 4
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Data What do you see? Results in all three standards trending downward from 36 percent in 2014 to 9 percent in 2018 Results in one standard only trending upward from 25 percent in 2014 to 45 percent in 2018
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2014-2018 Data Maori What do you see?
Results in all three standards trending downward from 23 percent in 2014 to 5 percent in 2018 Results in one standard only trending upward from 38 percent in 2014 to 60 percent in 2018
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2014-2018 Data Pasifika What do you see?
Results in all three standards trending downward from 21 percent in 2014 to 4 percent in 2018 Results in one standard only trending upward from 43 percent in 2014 to 63 percent in 2018
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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Level 2 Achievement Standards Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Using 2018 data
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Most Popular 2-Standard Course Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Order doesn’t matter so 14 Choose 2 = 91 possibilities 92 instances of a 2-Standard Course 9 of the 92 instances have this configuration Configuration represents 5 credits
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Most Popular 3-Standard Course Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Order doesn’t matter so 14 Choose 3 = 364 possibilities 115 instances of a 3-Standard Course 8 of the 115 instances have this configuration Configuration represents 9 credits
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Most Popular 4-Standard Course Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Order doesn’t matter so 14 Choose 4 = 1,001 possibilities 224 instances of a 4-Standard Course 8 of the 224 instances have this configuration Configuration represents 17 credits
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Most Popular 5-Standard Course Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Order doesn’t matter so 14 Choose 5 = 2,002 possibilities 388 instances of a 5-Standard Course 24 of the 388 instances have this configuration Configuration represents 20 credits
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Most Popular 6-Standard Course Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Order doesn’t matter so 14 Choose 6 = 3,003 possibilities 474 instances of a 6-Standard Course 24 of the 474 instances have this configuration Configuration represents 20 credits
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Most Popular 7-Standard Course Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Order doesn’t matter so 14 Choose 7 = 3,432 possibilities 173 instances of a 7-Standard Course 17 of the 173 instances have this configuration Configuration represents 19 credits
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Most Popular 8-Standard Course Std. Cr. Description
91261 4 Apply algebraic methods in solving problems 91262 5 Apply calculus methods in solving problems 91267 Apply probability methods in solving problems 91256 2 Apply co-ordinate geometry methods in solving problems 91257 Apply graphical methods in solving problems 91258 Apply sequences and series in solving problems 91259 3 Apply trigonometric relationships in solving problems 91260 Apply network methods in solving problems 91263 Design a questionnaire 91264 Use statistical methods to make an inference 91265 Conduct an experiment to investigate a situation using statistical methods 91266 Evaluate a statistically based report 91268 Investigate a situation involving elements of chance using a simulation 91269 Apply systems of equations in solving problems Order doesn’t matter so 14 Choose 8 = 3,003 possibilities 28 instances of a 8-Standard Course 2 of the 28 instances have this configuration Configuration represents 27 credits
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Outline Pattern – Level 3 Calculus externally-assessed achievement standards Trend – Level 3 Calculus externally-assessed achievement standards Pattern – Level 3 Statistics externally-assessed achievement standards Trend – Level 3 Statistics externally-assessed achievement standards Pattern – Level 2 Math externally-assessed achievement standards Trend – Level 2 Math externally-assessed achievement standards Pattern – Level 1 Math end-of-year externally-assessed achievement standards Trend – Level 1 Math end-of-year externally-assessed achievement standards Level 2 Math Courses
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