1. NCEA
What on earth is it?
Robin Tiffen Teaching Fellow

2. Secondary School in NZ is typically years 9 to 13 i.e. ages 13 -18
Level 1
Level 2
Level 3

3. National Certificate of Educational Achievement
Credits are the currency of the NCEA qualification.
Students need a total of 80 credits for each NCEA qualification:
Generally speaking one credit represents ten hours of learning and assessment. This includes teaching time, homework and assessment time.
NCEA Level 1 – 80 credits at any Level, including credits in literacy(10) and numeracy(10).
NCEA Level 2 – 60 credits at Level 2 or above, plus 20 credits
from Level 1 or above.
NCEA Level 3 – 60 credits at Level 3 or above, plus 20 credits from Level 2 or above.
Introduction ( facts/factsheet-4/)

4. How many credits do students need?
Note - Students do not have to complete NCEA qualifications within a single school year - they can accumulate credits towards qualifications over any number of years.
A typical course generates between 18 and 24 credits – so over five subjects, a typical student could aim for up to 120 credits.
But schools can and do run courses that assess standards totalling as few as 12 credits, with others assessing 30 credits or more.

5. How many credits do students achieve?
The chart below shows the distribution of credits gained during 2010 by year 11, 12 and 13 students.

6. University Entrance
University Entrance (UE) is the minimum requirement to go to a New Zealand university.
To qualify you will need:
Approved subjects - 42 credits at Level 3 or higher, made up of:
14 credits in one approved subject
14 credits in another approved subject
14 credits from one or two additional domains or approved subjects
Literacy requirements - 10 credits in English or te reo Maori at Level 2 or higher, made up of: 4 credits in reading and 4 credits in writing
Numeracy requirements - 10 credits in Numeracy at Level 1 or higher, made up of credits in Mathematics or Statistics and Probability

7. Realignment of standards
Achievement standards and unit standards are being reviewed. The review affected Level 1 in 2011, Level 2 in 2012, and will affect Level 3 in Some of the changes will impact on the mix of internal and external assessment.
Achievement standards only will be used to assess curriculum linked knowledge and skills.
Unit standards will cover other skills and knowledge.
Unit standards derived from the New Zealand Curriculum will be phased out, starting in 2011, and replaced with Achievement standards which are internally assessed.
In each subject there will be a maximum of three externally assessed standards. This will change the ratio of internally and externally assessed standards that are available in some subjects.

8. How do students gain credits?
Achievement standards
Achievement Criteria
Subject Reference
Mathematics and Statistics
Title
Apply xxxxxxxx in solving problems.
Level
Credits
Assessment
Internal/external
Achievement
Achievement with Merit
Achievement with Excellence
Apply xxxxxxxx in solving problems.
Apply xxxxxxxxxxx, using relational thinking, in solving problems.
Apply xxxxxxxxxxx, using extended abstract thinking, in solving problems.
Explanatory Notes
This achievement standard involves applying xxxxxxxxxxxx in solving problems.
This achievement standard is derived from Level 8 of The New Zealand Curriculum, Learning Media,
Ministry of Education, 2007;
and is related to the achievement objectives:

9. External Standards
There will be an examination for each externally assessed standard. Three externally assessed standards will be examined in a three hour examination. This will give students sufficient time to complete the examination and ensure assessment is reliable.
Previously, in some subjects up to six standards were assessed in a three hour examination. This often resulted in students running out of time and leaving out important parts of the examination.

10. Course endorsement
Course endorsement was introduced in 2011 to recognise
exceptional achievement in an individual course.
To gain a course endorsement:
Students must gain 14 or more credits at Merit and/or Excellence within a school course.
There must be a mix of internally and externally assessed credits
– at least 3 credits from each (except in Physical Education, Religious Studies and Level 3 Visual Arts where there is no external assessment).

11. How are grades obtained? The SOLO taxonomy
SOLO stands for the Structure of Observed Learning Outcomes. It was developed by Biggs and Collis (1982). Biggs describes SOLO as “a framework for understanding”. (1999, p.37)
SOLO identifies five stages of thinking. Each stage embraces the previous level but adds something more in terms of the level of thinking.

12. A change of focus in mathematics
The SOLO hierarchy shifts us from the situation in maths of “doing more” and “ doing longer tasks” to qualify for a higher grade.
This change recognises and rewards deeper and more complex thinking along with more effective communication of mathematical ideas and outcomes.
It is these that are fundamental competencies to mathematics.

13. The stages of SOLO
Prestructural the student acquires bits of unconnected information that have no organisation and make no sense.
Unistructural and Multistructural = Achieved students make connections between pieces of information using a known pattern
Relational = Merit the students sees the significance of how various pieces of information relate to one another and know how and when to use strategies.
Extended abstract = Excellence students make connections beyond the scope of the problem or question, to generalise or transfer learning into a new situation

14. An example of SOLO at level 3 trigonometry

17. The curriculum
Remember this?

23. Achievement standard matrix for the realigned standards.
Assessment
Achievement standard matrix for the realigned standards.

24. Apply trigonometric methods in solving problems 4 credits Internal
Level 1
Level 2
Level 3 AS
Apply numeric reasoning in solving problems
4 credits Internal AS
Apply co-ordinate geometry methods in solving problems
2 credits Internal
3.1
Apply the geometry of conic sections in solving problems
3 credits Internal AS
Apply algebraic procedures in solving problems
4 credits External (CAT) AS
Apply graphical methods in solving problems
3.2
Apply linear programming methods in solving problems AS
Investigate relationships between tables, equations and graphs
4 credits External AS
Apply sequences and series in solving problems AS
Apply linear algebra in solving problems AS
Apply trigonometric relationships in solving problems
3.3
Apply trigonometric methods in solving problems AS
Apply measurement in solving problems AS
Apply network methods in solving problems
3.4
Use critical path analysis in solving problems
2 credits Internal AS
Apply geometric reasoning in solving problems AS
Apply algebraic methods in solving problems
3.5
Apply algebraic methods in solving problems
5 credits External AS
Apply right-angled triangles in solving measurement problems AS
Apply calculus methods in solving problems
3.6
Apply differentiation methods in solving problems
6 credits External
3.7
Apply integration methods in solving problems
3.3
Apply trigonometric methods in solving problems   
4 credits
Internal

25. AS
Apply knowledge of geometric representations in solving problems
3 credits Internal AS
Design a questionnaire
3.8
Investigate times series data
4 credits Internal
3.9
Investigate bivariate measurement data
4 credits Internal AS
Apply transformation geometry in solving problems
2 credits Internal AS
Use statistical methods to make an inference
3.10
Use statistical methods to make a comparison
5 credits Internal AS
Investigate a given multivariate data set using the statistical enquiry cycle AS
Conduct an experiment to investigate a situation using statistical methods
3.11
Conduct an experiment using experimental design principles AS
Investigate bivariate numerical data using the statistical enquiry cycle AS
Evaluate a statistically based report
3.12
Critically evaluate statistically based reports
4 credits External AS
Demonstrate understanding of chance and data AS
Apply probability methods in solving problems
3.13
Apply probability concepts in solving problems AS
Investigate a situation involving elements of chance AS
Investigate a situation involving elements of chance using a simulation
3.14
Apply probability distributions in solving problems AS
Apply systems of equations in solving problems
2 credits Internal
3.15
Apply linear systems in solving problems

26. Typical course structure
Year 13 Calculus
Typical course structure
3.1 Conics credits
3.3 Trigonometry 4 credits
3.5 Algebra 5 credits
3.6 Differentiation 6 credits
3.7 Integration 6 credits
Total credits

27. What is Achieved? Merit? Excellence? e.g. Integration 2011
2 questions
Integrate functions
Integrate functions to solve problems
Achieved (and 6 credits) is 2 out of 3 in Q1
and 1 out of 2 in Q2
Merit is 1 out of 2 in Q1 and 1 out of 2 in Q2
Excellence is 1 of Q1 or Q2

28. Achieved =2 out of 3

29. And 1 out of 2

30. Merit=
1 out of 2

31. And 1 out of 2

32. Excellence = merit + 1 of the 2 parts
i.e. this …

33. … Or this

34. Profiles of expected performance

35. Year 13 Statistics and Modeling
Typical course structure
Time Series 3 credits
3.2 Confidence intervals* 3 credits
3.3 Probability 4 credits(5new)
3.4 Equations 4 credits
3.5 Bivariate Data 3 credits(4new)
3.6 Probability Distributions 4 credits
3.7 Modeling* 3 credits
Total credits
*expiring 2013 being replaced by:-
3.10 Inference 4 credits
3.11 Expt. Design 4 credits
3.12 Evaluate statistical reports 4 credits

36. What is Achieved? Merit? Excellence? e.g. Probability
3 questions
Achieved (and 4 credits) is 2 out of 3 part (a)’s
Merit is 2 out of 3 part (b)’s
Excellence is 2 out of 3 part (c)’s

37. Achieved is 2 out of 3
A New Zealand tour company collected data over a period of a year to investigate information about its passengers.
(a) It found that:
• 48% of its passengers were male
• 63% of its female passengers came from overseas
• 21% of all passengers were males from overseas.
You may assume that the event that a passenger is male and the event that a passenger is from overseas are independent.
Find the probability that a randomly selected male passenger was from overseas.
The tour company decides to analyse its data in more depth.
(a) It finds that:
• the probability of an overseas passenger coming from Australia is 2/3
• the probability of an overseas passenger coming from Australia or aged over 30 is 3/4
• the probability of an overseas passenger coming from Australia and aged over 30 is 1/10.
Find the probability that an overseas passenger is aged over 30.
In 2006, a survey was conducted on households in Hamilton, Canada.
(a) Let the random variable X represent the number of cars in a randomly chosen household at the time of the survey. The survey gave the following probability distribution for X. x
P(X = x)
Find the expected value of X.

38. In summary
A student enrolling at UC who sat level 3 NCEA Calculus or Statistics and Modeling will have at least:-
14 credits in 3 (or 4) approved subjects for UE+ literacy + 10 credits in mathematics at level 1 or better for numeracy
sat achievement standards for 18 – 24 credits in calculus or stats and modeling
Achieving 14 credits in calculus means basic competence in at least two of differentiation, integration and algebra