NCEA What on earth is it? Robin Tiffen Teaching Fellow

Secondary School in NZ is typically years 9 to 13 i.e. ages 13 -18 Level 1 Level 2 Level 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 (http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/understanding-ncea/the facts/factsheet-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.

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

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

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 2013. 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.

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:

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.

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).

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.

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.

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

An example of SOLO at level 3 trigonometry

The curriculum Remember this?

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

Apply trigonometric methods in solving problems 4 credits Internal Level 1 Level 2 Level 3 AS91026 1.1 Apply numeric reasoning in solving problems   4 credits Internal AS91256 2.1 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 AS91027 1.2 Apply algebraic procedures in solving problems 4 credits External (CAT) AS91257 2.2 Apply graphical methods in solving problems 3.2 Apply linear programming methods in solving problems AS91028 1.3 Investigate relationships between tables, equations and graphs 4 credits External AS91258 2.3 Apply sequences and series in solving problems AS91029 1.4 Apply linear algebra in solving problems AS91259 2.4 Apply trigonometric relationships in solving problems 3.3 Apply trigonometric methods in solving problems AS91030 1.5 Apply measurement in solving problems AS91260 2.5 Apply network methods in solving problems 3.4 Use critical path analysis in solving problems 2 credits Internal AS91031 1.6 Apply geometric reasoning in solving problems AS91261 2.6 Apply algebraic methods in solving problems 3.5 Apply algebraic methods in solving problems 5 credits External AS91032 1.7 Apply right-angled triangles in solving measurement problems AS91262 2.7 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

AS91033 1.8 Apply knowledge of geometric representations in solving problems   3 credits Internal AS91263 2.8 Design a questionnaire 3.8 Investigate times series data 4 credits Internal 3.9 Investigate bivariate measurement data 4 credits Internal AS91034 1.9 Apply transformation geometry in solving problems 2 credits Internal AS91264 2.9 Use statistical methods to make an inference 3.10 Use statistical methods to make a comparison 5 credits Internal AS91035 1.10 Investigate a given multivariate data set using the statistical enquiry cycle AS91265 2.10 Conduct an experiment to investigate a situation using statistical methods 3.11 Conduct an experiment using experimental design principles AS91036 1.11 Investigate bivariate numerical data using the statistical enquiry cycle AS91266 2.11 Evaluate a statistically based report 3.12 Critically evaluate statistically based reports 4 credits External AS91037 1.12 Demonstrate understanding of chance and data AS91267 2.12 Apply probability methods in solving problems 3.13 Apply probability concepts in solving problems AS91038 1.13 Investigate a situation involving elements of chance AS91268 2.13 Investigate a situation involving elements of chance using a simulation 3.14 Apply probability distributions in solving problems AS91269 2.14 Apply systems of equations in solving problems 2 credits Internal 3.15 Apply linear systems in solving problems

Typical course structure Year 13 Calculus Typical course structure 3.1 Conics 3 credits 3.3 Trigonometry 4 credits 3.5 Algebra 5 credits 3.6 Differentiation 6 credits 3.7 Integration 6 credits Total 24 credits

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

Achieved =2 out of 3

And 1 out of 2

Merit= 1 out of 2

And 1 out of 2

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

… Or this

Profiles of expected performance

Year 13 Statistics and Modeling Typical course structure 3.1 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 24 credits *expiring 2013 being replaced by:- 3.10 Inference 4 credits 3.11 Expt. Design 4 credits 3.12 Evaluate statistical reports 4 credits

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

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 0 1 2 3 4 P(X = x) 0.059 0.383 0.377 0.153 0.028 Find the expected value of X.

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