FIELD                        SCIENCES

 

Review, Rollover, Revision and AMAP Change of Mathematics and Statistics and Probability unit standards

 

Subfield

Domain

Id

Mathematics

Algebra

5246, 5267, 5272, 11102, 11106, 11107, 11108, 11112, 11117, 12337-12345

Calculus

5244, 5260, 5261, 5265, 5266, 11104, 11105, 11109-11111, 11113-11116

Geometry

5231, 5245, 5252, 5269

Mathematical Studies

12318-12330

Measurement

5228, 5241, 8492

Number

5224, 5225, 5227, 5234, 5235, 8489 - 8491, 12331, 12346

Trigonometry

5236, 5251, 5255, 5268, 11103

Statistics and Probability

Probability

5250, 7571, 12347

Statistics

5230, 5257, 11118-11130, 12332-12335

 

The NZQA National Qualifications Services (NQS) has completed the review, revision and rollover of the unit standards listed above that were registered in August 1995, May 1996, August and September 1997, and November 1999.

 

This report is in two sections:

·          The first deals with the unit standards that have been reviewed, and the new unit standards that arose out of the review process.

·          The second deals with the rollover and revision of the remaining unit standards.

 

Section 1            Reviewed unit standards

 

The following unit standards were reviewed.

 

Subfield

Domain

Id

Mathematics

Algebra

5246, 5267, 5272

Calculus

5244, 5260, 5261, 5265, 5266, 11104, 11105

Geometry

5231, 5245, 5252, 5269

Mathematical Studies

12328-12330

Measurement

5228, 5241, 8492

Number

5224, 5225, 5227, 5234, 5235, 8489-8491, 12331, 12346

Trigonometry

5236, 5251, 5255, 5268

Statistics and Probability

Probability

5250, 7571

Statistics

5230, 5257, 11119, 11122, 11123, 12335

 

Date new versions published                        June 2004

 

New comments by date                        June 2008

 

Expiry date of new versions of the unit standards                        December 2009

 

Summary of review and consultation process

 

NQS decided in late 2002 that a review of unit standards in these two subfields was necessary because

·          feedback through the moderation process had indicated the need for changes to a number of the unit standards, and

·          a number of the unit standards, some of which did not meet technical quality criteria, reached their expiry date in December 2002.

Some further recommendations for change came through the consultation process when NQS notified stakeholders of the review and invited feedback.

 

A review panel with secondary school and tertiary provider representation met on 30 April and 1 May 2003 to consider the proposed changes.  Overlaps with achievement standards were also considered.  Review outcomes were subsequently circulated widely to schools and tertiary providers, with drafts of the reviewed unit standards provided on request and also placed on the New Zealand Association of Mathematics Teachers website.  Industry training organisations whose qualifications may have been affected by the review were also invited to respond, as was anyone who had indicated an interest in the review when it was first initiated.  The provider who had reported results for the unit standard designated Category D was also consulted. 

 

Feedback from this consultation was considered by the panel and has informed the new versions of the unit standards.  In all, 42 unit standards were reviewed, 5 new unit standards were developed, and 47 unit standards were rolled over and revised.

 

Main changes resulting from the review

 

Levels and credits were reviewed in the light of their outcomes and content, and any overlaps with achievement standards were identified.  The exclusions list on the NCEA website (http://www.nzqa.govt.nz/ncea/acrp/secondary/7/731.html) has been updated.  Relationships with Mathematics in the New Zealand Curriculum objectives were confirmed.  The following changes were made.

·          Unit standards 5228, 5246, 5257, 5265, 11104, 11105 increased in credits.

·          Unit standards 5267 and 12329 decreased in credits.

·          Unit standards 5252, 5255, 5260, 5261, 5265, 5267, 5268, 5272, 11119, 11122, and 11123 decreased in level.

 

Other changes include the following.

·          Unit standards 5227, 5228, 5231,5236, 5245, 5251, 5255, 5261, 5265, 5268, 5269, 5272, 11123, 12335, and 12328-12330 have had changes in title.

·          Unit standard 5266 was designated Category C and has been replaced by unit standards 20660 and 20905.

·          Unit standard 12346 was designated Category D and will expire.

·          Estimation requirements have been removed from unit standard 8492, and two new unit standards for estimation have been developed (20662 and 20663).

·          Many unit standards have had changes to assessment notes, elements and/or performance criteria in order to make them more flexible, to clarify assessment requirements, to avoid overlap with other unit standards, and/or to achieve consistency with the stated level.

·          Unit standards 8491, 8492, 11105 and 11119 now include a special note showing the relationship between each unit standard’s outcomes and Mathematics in the New Zealand Curriculum objectives.  This is in keeping with other curriculum-based Mathematics unit standards.

·          Definitions of ‘problem’ and ‘strategy’ have been included (or referenced), where appropriate.

·          Relationships between some of the level one unit standards have been clarified in a special note.

·          Recommended competency advice has been moved from entry requirements to special notes.

·          Minor corrections and editorial amendments have been made.

 

Unit standards 20659, 20660, 20661, 20662 and 20663 have been developed to fill identified gaps.

 

Unit standards categorised as category C or D expire at the end of December 2005.

 

Unit standard 5266 has been designated Category C.

Unit standard 12346 has been designated Category D.

 

Impact on existing provider accreditations

 

None.

 

Impact on Accreditation and Moderation Action Plan (AMAP)

 

Apart from unit standard 12346, designated review category D, all of the reviewed unit standards are now included on Accreditation and Moderation Action Plan (AMAP) 0226, which covers domains designated as Base Scope of Accreditation for Schools (BSAS)[1].  This AMAP now includes all Mathematics and Statistics and Probability unit standards from levels 1-4.

 

Impact on existing qualifications

 

The following National Qualifications Services qualifications are affected by the outcome of this review.  Because attainability of the qualifications is not affected, the changes to the mathematics unit standards will be taken into account at the next review/revision of the qualifications.

 

Qualification Title

Id

National Certificate in Rigging with strands in Basic Rigging, Intermediate Rigging, and Advanced Rigging [Ref: 0111]

5228, 5236

National Certificate in Scaffolding with strands in Advanced Scaffolding, Basic Scaffolding, and Suspended Scaffolding [Ref: 0110]

5228

 

The following qualification is also affected by the outcome of this review.  The standard setting body (SSB) has been advised that it requires revision.

 

Qualification Title

Id

SSB Name

National Diploma in Civil Engineering [Ref: 0881]

5265, 5268, 5269, 5272, 11104, 11105, 11112

InfraTrain New Zealand

 

The following qualifications are not materially affected by the changes.  They will be updated when they are next reviewed or revised.

 

Qualification Title

Id

SSB Name

National Certificate in Cranes (Mobile Crane Dispatch Supervision) [Ref: 0119]

5228, 5236

Power Crane Association ITO

National Certificate in Cranes (Mobile Crane Supervision) [Ref: 0118]

5228, 5236

Power Crane Association ITO

National Certificate in Cranes (Tower Crane Supervision) [Ref: 0120]

5228, 5236

Power Crane Association ITO

National Certificate in Elementary Construction Skills with strands in Entry Level, and Advanced Level [Ref: 0751]

5228, 5241

Building and Construction ITO

National Certificate in Engineering Machining and Toolmaking (Level 4) [Ref: 0123]

5228, 5251

Competenz

National Certificate in Engineering and Technology (for the Design and Construction Sector) [Ref: 0672]

5260, 5261, 5244

InfraTrain New Zealand

National Certificate in Engineering and Technology (Glass Containers) (Level 2) [Ref: 0947]

5228

PaMPITO

National Certificate in Furniture Finishing (Level 2) [Ref: 0790]

5228, 5225

NZ Furniture ITO

National Certificate in Furniture Finishing (Level 4) [Ref: 0092]

5228, 5225

NZ Furniture ITO

National Certificate in Maintenance and Diagnostics in Mechanical Engineering (Level 4)[Ref: 0125]

5228, 5251

Competenz

National Certificate in Metal Casting (Technology) (Level 4) [Ref: 0129]

5228, 5251

Competenz

National Certificate in Wastewater Treatment (Site Operator) [Ref: 0879]

5228, 5241

Agriculture ITO

National Certificate in Water Treatment (Site Operator) [Ref: 0880]

5228, 5241

Agriculture ITO

 

Summary of main changes to standards’ Ids, classification, titles, levels, and credits

 

The following summary shows the changes made to the standards as a result of the review.  All changes are in bold.

 

Key to review category

 

A

Dates changed, but no other changes are made - the replacement standard carries the same Id and a new version number

B

Changes made, but the overall outcome remains the same - the replacement standard carries the same Id and a new version number

C

Major changes that necessitate the registration of a replacement standard with a new Id

D

Standard will expire and not be replaced

 

Subfield                        Mathematics

Domain                        Algebra

Id

Title

Level

Credit

Review category

5246

Manipulate algebraic expressions and use algebraic methods to solve problems

2

3

4

B

5267

Use complex numbers to solve problems

4

3

4

3

B

5272

Use functions and their graphs to model situations

Use functions and their graphs to model situations and solve problems

4

3

4

B

 

Domain                        Calculus

Id

Title

Level

Credit

Review category

5244

Demonstrate calculus skills

2

2

B

5260

Find and use derivatives to solve problems involving rate of change

3

2

2

B

5261

Use integral calculus to solve problems

Find and use integrals to solve problems

3

2

2

B

5265

Differentiate functions and use calculus to solve problems

Differentiate functions and use differentiation to solve problems

4

3

5

6

B

5266

Use calculus to solve problems in integration and differential equations

4

7

C

20905

Integrate functions and use integration to solve problems

3

5

 

11104

Use integration techniques to model and solve problems

4

 

2

3

B

11105

Use differential equations to model, solve, and interpret physical situations

4

2

B

 

Use differential equations to model, solve and interpret physical situations

 

3

 

 

Domain                        Geometry

Id

Title

Level

Credit

Review category

5231

Use constructions and drawings

Use constructions and make drawings for geometrical situations

1

2

B

5245

Solve problems involving lines and points

Solve coordinate geometry problems

2

2

B

5252

Derive angle properties of circles and use them to solve mathematical problems

2

1

3

B

5269

Investigate and use the mathematics of conic sections and other curves

Apply mathematics to conic sections and other curves

4

4

B

 

Domain                        Mathematical Studies

Id

Title

Level

Credit

Review category

12328

Describe the history of a mathematical topic or mathematician

Demonstrate knowledge of the history of a mathematical topic or mathematician

1

2

B

12329

Research and report on an aspect of the history of a topic in mathematics

Investigate an aspect of the history of a mathematics topic or mathematician and present results

2

3

 

2

B

12330

Research and analyse an aspect of the history of mathematics

Plan and analyse research on an aspect of mathematics

3

3

B

 

Domain                        Measurement

Id

Title

Level

Credit

Review category

5228

Take measurements and use them in calculations to solve problems

1

2

B

 

Take measurements and use calculations to solve measurement problems

 

3

 

5241

Use strategies to solve measurement problems

1

3

B

8492

Use standard units of measurement

1

3

B

 

Domain                        Number

Id

Title

Level

Credit

Review category

5224

Use decimals and percentages to solve problems

1

2

B

5225

Use fractions, ratio, and proportion to solve problems

1

2

B

5227

Solve problems involving time and money

Solve problems involving money

1

3

B

5234

Use calculations in money situations

1

3

B

5235

Use strategies to solve number problems

1

2

B

8489

Solve problems which require calculation with whole numbers

1

2

B

8490

Solve problems using calculations with numbers expressed in different forms

1

2

B

8491

Read and interpret information presented in tables and graphs

1

2

B

12331

Investigate and report on the mathematics of a given project

2

3

B

12346

Represent numbers and carry out calculations in different number systems

5

3

D

 

Domain                        Trigonometry

Id

Title

Level

Credit

Review category

5236

Use Pythagoras' Theorem and trigonometry to solve problems involving right-angled triangles

Use Pythagoras’ Theorem and trigonometry to find unknowns in right-angled triangles

1

2

B

5251

Solve problems modelled by triangles

Choose and apply trigonometric methods to solve problems involving lengths and angles

2

3

B

5255

Use trigonometry to solve problems

Use trigonometry and trigonometrical graphs to solve equations and problems

3

2

3

B

5268

Manipulate trigonometric expressions, solve equations and sketch graphs

Manipulate trigonometric expressions, sketch graphs of trigonometric functions, and solve equations

4

 

3

4

B

 

Subfield                        Statistics and Probability

Domain                        Probability

Id

Title

Level

Credit

Review category

5250

Use probability techniques to solve problems

2

2

B

7571

Use simulation techniques to determine probability and solve problems

1

2

B

 

Domain                        Statistics

Id

Title

Level

Credit

Review category

5230

Carry out a statistical investigation and interpret data

1

3

B

5257

Investigate time series

3

2

3

B

11119

Investigate relationships between pairs of quantitative variables

4

3

4

B

11122

Explain sampling distributions and estimate population parameters from large simple random samples

5

 

4

3

B

11123

Explain sampling distributions and estimate population parameters from small simple random samples

5

3

B

 

Make point estimates from population parameters using small samples and find confidence intervals

4

 

 

12335

Demonstrate understanding of hypothesis testing and its use in different contexts

Use hypothesis testing on means or proportions and draw conclusions

4

3

B

 

New unit standards

 

The following new unit standards were developed to fill gaps identified by the review process.

 

Subfield                        Mathematics

Domain                        Algebra

id

Title

Level

Credit

20659

Demonstrate basic algebra skills

1

2

 

Domain                        Calculus

Id

Title

Level

Credit

20660

Use integral calculus to solve differential equation problems

3

2

 

Domain                        Geometry

Id

Title

Level

Credit

20661

Sketch, describe and find equations of graphs

3

2

 

Domain                        Measurement

Id

Title

Level

Credit

20662

Make estimates of measurements with common units

1

2

 

Domain                        Number

Id

Title

Level

Credit

20663

Use a strategy to estimate the solution to number problems

1

2

 

Section 2            Revised and rolled over unit standards

 

The following unit standards, which were not included in the review, have been revised and rolled over.

 

Subfield

Domain

Id

Mathematics

Algebra

11102, 11106, 11107, 11108, 11112, 11117, 12337-12345

Calculus

11109-11111, 11113-11116

Mathematical Studies

12318-12327

Trigonometry

11103

Statistics and Probability

Probability

12347

Statistics

11118, 11120, 11121, 11124-11130, 12332, 12333, 12334

 

The NZQA National Qualifications Services decided that the unit standards should have their period of registration extended because they have not been used sufficiently to warrant a review at this stage.

 

A review of these unit standards is expected to take place during 2007.

 

Date new versions published                        June 2004

 

New comments by date                        December 2006

 

Expiry date of new versions of the unit standards                        December 2007

 

Main changes resulting from the revision

 

·          Minor amendments to some unit standards were made to correct errors and inconsistencies and update references to other unit standard titles.

·          Minor editorial amendments were made to most unit standards.

·          The accreditation and moderation options were updated.

 

Impact on existing provider accreditations

 

None.

 

Impact on Accreditation and Moderation Action Plan (AMAP)

 

The following unit standards are now included on Accreditation and Moderation Action Plan (AMAP) 0226, which covers domains designated as Base Scope of Accreditation for Schools (BSAS) for which NZQA is the standard setter.  This AMAP now includes all Mathematics and Statistics and Probability unit standards from levels 1-4.

 

Subfield

Domain

Id

Mathematics

Algebra

11102, 12344

Mathematical Studies

12318-12327

Trigonometry

11103

Statistics and Probability

Statistics

11118, 12332, 12333, 12334

 

Unit standards from levels 5-6 are covered by AMAP 0153.

 


[1]Base Scope of Accreditation for Schools (BSAS) was formerly known as ‘Conventional School Subjects’ (CSS).