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The Achievement Standards
The Achievement Standards
Please note:
Different Achievement Standards (AS) for years eleven and twelve.
They reflect equivalence of achievement across subjects.
AS are not a rubric in themselves. Rubrics will be drawn from some of the AS suitable for the intended task. All AS will be covered over the the suite of tasks.
The Mathematics Framework Panel wrote the Achievement Standards considering key knowledge, understand and skills required by Mathematics students in years eleven and twelve.
The grade bands are differentiated using Bloom's Taxonomy and the scope of the learning demonstrated in the piece of work
Years eleven and twelve have distinct AS, as after one year of college education, by year twelve, students will have enhanced skills and knowledge that are acknowledged by assessment expectations and the AS.
The AS are the means for providing equity as all students will have the same expectations placed upon their performance regardless of the details of the task.
The Achievement Standards describe grade bands, not scores. There is no fixed relationship between marks and grades. Internal moderation between classes may change raw scores.
AS are based on ACARA design specifications.
Activity 2.1
Activity 2.1
Achievement Standards
Map the AS to three tasks that would address the AS over a semester. What tasks are needed to address all the AS?
Repeat the mapping using different tasks types.
Record the mapping.
Applying Achievement Standards to Different Levels of Math
Applying Achievement Standards to Different Levels of Math
Consider the reasoning recorded to the left.
If you were applying the AS to this work for a Mathematical Applications student or a Specialist Methods students, how would the grade vary? How are the AS interpreted differently for the different levels of Mathematics?
The Task Type Table
The Task Type Table
The task type table guides the development of assessment tasks within a school.
The task type table makes provision for a diverse range of pedagogical approaches to engage all students. This enables schools to make decisions about assessment that address the needs of their students. Schools will decide how to guide students to meet the Achievement Standards.
These are decisions for teachers and schools to make in regard to their context, their students and the intended task. Schools will set word limits and assessment conditions as is appropriate to the tasks and will allow students to meet the Achievement Standards.
Consider the additional parameters are added by this section 'Additional Assessment Information for A/T/M courses"?
Note:
the requirements for a problem solving investigation
the limit to the number of tasks
the requirement for varied task types over a course
the requirement for tasks to cover all Achievement Standards and Content Descriptions
a recommendation for unsupervised tasks
the requirement to have systems to maintain academic integrity- see resources here.
Note that the requirement to maintain academic integrity also includes ethical research considerations see the workshop- Introduction to BSSS Ethical Research Principles and Guidelines (Online Course)
Considering Generative AI
The advent of sophisticated generative AI that is freely available may allow students to submit work that is not their own with very little chance of detection. This may prevent accurate measurement of student capacity. You should assume that if students take a task home that they will have used AI to assist them. You should also assume you cannot distinguish AI generated work from student work.
Currently, attempts to develop detection software have not been successful. Any detection software results can only be suggestive, conversations with students and procedural fair processes would have to follow.
Consequently you need to consider what aspect of the discipline are you trying to assess and how generative AI might impact on it. Then you can try to design tasks that focus on what you want to know about student performance while limiting interference from AI.
Teach students to keep their research notes and submit a record of prompts used so that they can provide evidence of process and composition if required.
Explicitly define the appropriate use of AI in a task and accommodate this in your rubric, e.g. AI use might mean the expectation of perfect spelling as the minimum standard.
Consider increasing the weighting of supervised in-class tasks without digital tools or with lock down browsers- in this context a prepared oral presentation is not an in-class task.
If you are interested in exploring the implications of generative AI further, you could undertake this BSSS Professional Learning online workshop- Introduction to to AI in the ACT Senior Secondary System.
Activity 2.2
Activity 2.2
Write a paragraph on what assessment possibilities are suitable for your school context.
Activity 2.3
Activity 2.3
Curriculum Coverage
Examine this suite of tasks below. This is not intended to be a perfect suite of tasks. There are problems.
Consider the coverage of the unit's Content Descriptions. Do the tasks indicate engagement with the content?
Would the suite of tasks have allowed students to achieve all of the Achievement Standards of the 2021 Framework? Do the questions direct students to the level of analysis required to achieve an A? What is missing? Does the package raise any issues? Write a paragraph in answer.
Write a paragraph.
Suite of Mathematics Tasks: Maths Methods: Unit 1: Mathematical Methods
Task One Test 30%
(Questions from https://www.transum.org's adaptation of IB and IGCSE questions)
Consider a right-angled triangle, ABC, with the right angle at vertex C and where sin A=12/13
(a) Show that cos A=5/13
(b) Find sin 2A
The cosine of acute angle α is 1/√5
The angle β is obtuse and sinβ= √2/3
(a) Find exact values of tan α tanβ
(b) Hence show that tan(α−β)tan(α−β)
can be written as a+b √2 where a and b are rational numbers
Strat drove from Wolverhampton to London via Coventry.
The distance from Wolverhampton to Coventry is 56 km.
The distance from Coventry to London is 156 km.
Strat's average speed from Wolverhampton to Coventry was 63 km/h.
Strat took 90 minutes to drive from Coventry to London.
(a) Work out Strat's average speed for his total drive from Wolverhampton to London.
Raven drove from Bedrock to Springfield via South Park.
Raven's average speed from Bedrock to South Park was 70 km/h.
Her average speed from South Park to Springfield was 50 km/h.
Raven says that the average speed from Bedrock to Springfield can be found by working out the mean of 70 km/h and 50 km/h.
(b) If Raven is correct, what does this tell you about the two parts of Raven's journey?
The line L is parallel to the vector (2, 5)
(a) Find the gradient of the line L .
The line L passes through the point (11, 3).
(b) Write down the equation of the line L in the form y=ax+b
(c) Find a vector equation for the line L.
In triangle ABC, AB = 7cm and AC = 9cm. The area of the triangle is 20cm2.
(a) Find the two possible values for the angle A.
(b) Given that A is obtuse, find the length of the side BC
Christine owns a four sided piece of land, ABCD. The length of BC is 180 m, the length of CD is 70 m, the length of AD is 90 m, the size of angle BCD is 82° and the size of angle BAD is 102°.
(a) Calculate the length of the fence.
The fence costs 19 USD per metre to build.
(b) Calculate the cost of building the fence. Give your answer correct to the nearest USD.
(c) Show that the size of angle ABD is 28.6°, correct to three significant figures.
(d) Calculate the area of triangle ABD.
She sells the land for 110 USD per square metre.
(e) Calculate the value of the land that Christine sells. Give your answer correct to the nearest USD.
Christine invests 200 000 USD from the sale of the land in a bank that pays compound interest compounded annually.
(f) Find the interest rate that the bank pays so that the investment will double in value in 12 years.
A drone flying test course is in the shape of a triangle, ABC, with AB = 400m , BC = 600m and angle ABC = 44o. The course starts and finishes at point A.
(a) Calculate the total length of the course to the nearest metre.
It is estimated that a drone can travel at an average speed of 4.5ms–1.
(b) Calculate an estimate of the time taken to fly around the course. Give your answer to the nearest minute.
(c) Find the size of angle ACB.
To comply with safety regulations, the area inside the triangular course must be kept clear of people, and the shortest distance from B to AC must be greater than 275 metres.
(d) Calculate the area that must be kept clear of people.
(e) Determine, giving a reason, whether the course complies with the safety regulations.
The course is viewed from a tower which rises vertically from point A. The top of the tower is point T. The angle of elevation of T from B is 8o.
(f) Calculate the vertical height, AT , of the tower.
Task Two- Group Work Problem Solving In-class 40%
(Questions from https://www.transum.org)
Solve the problems in assigned groups and write out the method and solution on a poster. Reference sources that supported finding the answer.
The Group presents the method and solutions to the class in a five minute presentation and takes questions.
Write a five hundred word reflection on the method for finding the solution, the group work process, your contributions to the group, and your learning.
Team A and Team B are perennial football rivals. Every year they meet for a series of games. The first team to win four games gets to take home the Golden Teapot and keep it for a year. The teams are evenly matched except for a small home advantage. When playing at home, each team has a 51 per cent chance of winning. (And a 49 per cent chance of losing. No ties are allowed.) Every year, the first three games are played at the home of Team A, and the rest at the home of Team B. Which team is more likely to win the Golden Teapot?
A coin is tossed repeatedly. If it comes up heads Pascal gets a point but if it comes up tails Fermat wins a point. The first person to win three points is the winner and receives the prize of £12. Unfortunately the game had to end abruptly after three tosses of the coin. Pascal had two points and Fermat had one point. They decided to share the £12 in a ratio that matched the probability of them winning the game if it had continued. How should they divide the £12?
Driving test has two sections, practical(p) and theory(t). One day everyone who took the test passed at least one section. 77% passed the practical section and 81% passed the theory section.
(a) Represent this information on a Venn diagram showing the percentage of candidates in each section of the diagram.
One person is chosen at random from all the people who took the test that day. What is the probability that this person:
(b) passed the practical section, given that they passed the theory section,
(c) passed the theory section, given that they passed only one section?
4. Propose a solution to Bertrand's Box Paradox
There are three boxes:
(1) a box containing two gold coins,
(2) a box containing two silver coins,
(3) box containing one gold coin and a silver coin.
You randomly choose a box, then randomly pull a coin from that box. The coin is gold. You don’t put the coin back in the box. What’s the probability the second coin you pull from that same box is also gold?
Task Three -Assignment 30%
(Questions from https://www.transum.org's adaptation of IB and IGCSE questions)
Answer each of the questions with full working. Reference research that helped to find solutions. Show failed and successful working.
Write 200 words reflecting on which techniques helped you to learn the principles behind these questions.
Question One
Question One
Question Two
Question Two
Question Three
Question Three
Question Four
Question Four
Question Five
Question Five
Question Six
Question Six
Question Seven
Question Seven
Learning and Assessment Ideas
Learning and Assessment Ideas
Try searching the Irish curriculum site for ideas for scope and sequences, studies, resources and assessment. They also have work in Irish Gaelic if you would like an extra challenge.
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