Numeracy Unit Standards.

Numeracy Requirements for NCEA Level 1

The numeracy requirement for NCEA Level 1 changes from the current 8 credits to 10 credits from 2012.

Numeracy can be acquired through:

Either Unit standards.Three numeracy unit standards (all 3 needed)

Or Achievement standards.Any AS in mathematics and statistics ORSpecific AS available in a range of subjects

Transition for 2011

There will be a transition year in 2011 before adopting the new requirements for level one NCEA in 2012. This will give schools time to adjust to the new requirements and the two methods of achieving the requirements for numeracy.

In 2011 the numeracy requirement for NCEA Level 1 can be met through either: •the current numeracy requirement using current specified unit and internally assessed achievement standards OR •the new numeracy requirements.

Note: A student cannot mix and match between the new and current requirement within the numeracy requirement.

Numeracy requirements through Achievement Standards

The standards have been selected using the following definition:

Numeracy to meet the demands of the New Zealand Curriculum at Level 6. These standards provide the scope for students to demonstrate number, measurement and statistical skills.

Numeracy Unit Standards•To be used in schools, tertiary and workplace programmes •To support the principle of embedded numeracy. •Appropriate for students working below NZC level 6.

Designed using the following definition:

Numeracy is the bridge between mathematics and daily life. It includes the knowledge and skills needed to apply mathematics to everyday family and financial matters, work and community tasks.

Reporting achievement of the Numeracy Requirement

The reports showing that students have achieved the numeracy requirement will indicate how they were achieved. That is through achievement standards at level 6 of the curriculum or through the numeracy unit standards.

The School Results Summary and the Results Notice will state: Either 'Numeracy requirement met by achievement standards' Or 'Numeracy requirement met by unit standards'

If a student has met the requirements through both the unit and achievement standards methods, the statement will show that the requirement was met by achievement standards.

Three Numeracy Unit Standards (Draft titles):

Number•Use number to solve problems

Measurement•Use measurement to solve problems

Statistics•Interpret statistical information in solving a problem

Environment : the place where learning takes place, the setting; eg: classroom, sports field, gym, home, place of work...

Context: the area of interest; eg: playing netball/rugby/hockey, kapa haka, part-time job, building a shed, mountain biking, organising a powhiri, redecorating

Objective : The aim of the work - why we are interested in doing something; eg: wanting to get better at a sport.

Problem: A specific question within the context that the student wants to solve; eg: How long should I train each week to get better at my sport?

Solution: The answer to the problem – it should have meaning in terms of the context.

Terminology

Structuring the learning

The following diagram was created to emphasise the embed nature of the environment, context, objective, problem and solution.

Key ideas: •The objective motivates learning in the context. •The problem(s)/question(s) flow from the objective.•The solution can be related back to the problem, objective and the context to support the achievement of the objective.

The focus of learning is to achieve the objective in context, rather than to ‘pass’ the standard.

Evidence for Numeracy is located inside the learning

EnvironmentThe place where the student is learning.

Context The general activity under consideration.

Objective The aim of the learning

ProblemSpecific questionrequiring solution

Solution

Naturally Occurring Evidence

Students will be engaged in solving many problems within the learning contexts and objectives. Authentic problems: •are realistic and meaningful to students, •engage students, and •induce a desire to want to know and use the solutions for further meaningful work in order to achieve the objective in the context.

Problems should be solved as they are met. This is a natural part of investigating how to solve problems relating to the objective/context. As problems are solved, evidence may be produced that can be used to meet the standard.

Verifying and Assessing

Evidence that comes from learning areas other than mathematics/statistics needs to be: – verified as authentic work of the student and – assessed by the person in charge of the numeracy

programme.

Collecting the Evidence

•Evidence will be collected from students as and when they solve problems during the course of their learning.

•Evidence could be photocopies, scans or photographs of pages from student work books, video/audio recordings, Powerpoints/presentations or other verified records. Digital records offer advantages in terms of searching and storage.

•Assessment events can be organised to generate evidence at certain times and under conditions that ensure authentic student work. It is important that these are not designed specifically to award credits for the standard and/or unrelated to the objectives of the learning programme.

Use Number to Solve Problems

Focuses on students using a variety of types of numbers and operations in a meaningful way to solve a problem that has currency in the context of the learning.

The result of the calculation must contribute to solving a meaningful problem. This involves more than simply doing calculations just to demonstrate mastery of a skill or procedure.

For example: The learning context is ‘budgeting for my holiday’. A student calculates expenditure and income for a week to determine whether they have enough money to go on a trip at the weekend.

Element 1 ( This is one element standard)Use number to solve problems.

Performance Criteria

1.1 Effective strategies are used to solve problems.

1.2 The methods used are described in terms of their appropriateness to the problems.

Use Number to Solve Problems

•Linked to step 3 of adult numeracy progressions not NZC.

•How do we decide on level of difficulty without NZC?

•One step problems as per the tasks for the old 8489

•Calculators and technology

Use Number to Solve Problems - Issues

•What does a strategy mean?

•Three contexts (What is a different context?)

•Domain is not mathematics – what are the implications of this?

•How will we collect evidence?

•How many assessments?  

Use Number to Solve Problems - Issues

Use Measurement to Solve Problems

Focuses on students taking their own measurements, using them in simple calculations and using the result in a meaningful way to solve a problem relevant to the context.

This involves more than just taking a measurement and calculating a result from it.

For example: The learning context is ‘redecorating my bedroom’. A student measures the dimensions of a wall, calculates the area then decides how much paint to buy in order to paint the wall.

Element 1 ( This is one element standard)Use measurements to solve problems.

Range: measurements include at least four of - length, capacity, mass, angle, time, temperature

Performance Criteria1.1 Effective methods are selected and used to solve problems.

1.2 The methods used are described in terms of their appropriateness to the problems.

Use Measurement to Solve Problems

Use Measurement to Solve Problems - Issues

Interpret Statistical Information in Solving a Problem

Focuses on interpreting statistical information to draw conclusions that contribute to answering a question related to the overall objective of the learning.

Note:Data may be supplied to the students. Students may use data they have collected.

Element 1 ( This is one element standard)Interpret statistical information in solving a problem

Performance Criteria1.1 The general features of the information are identifiedRange: general features may include but are not limited to

-measures of centre (mean, median, mode)-measures of spread -trends-unusual features ( eg extreme values)

1.2 Conclusions are drawn based on the evidence from the statistical information1.3 The conclusions drawn are appropriate and reasonable in terms of the information provided and the problem.

Interpret Statistical Information in Solving a Problem

Interpret Statistical Information in Solving a Problem - Issues

Example for the statistics unit standard

A student is interested in athletics. As part of a statistical investigation, she:• gathers statistical information for world record times for the

men’s 100m, • identifies features and trends in the data, and• makes tentative suggestions about when the record might

reach 9.5s.Evidence for statistics standard may be gathered from the second two bullet points.