1. Breadth, Challenge & Application
Jaclyn Andrews
November 2018
Resources required: Printed copies of allocated Es and Os
Experiences and Outcomes across the curriculum
Copies of Moderation Cycle
Copies of Self-evaluation grids
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2. Purpose of the training
Further develop understanding of how to ensure breadth within their classrooms
Further develop understanding of how to ensure challenge within their classrooms
Further develop understanding of the definition of application and how to ensure it within their classrooms
Look at practical examples
Self-evaluate in relation to breadth, challenge and application
Through moderation and school visits, we have found that there has been a good level of breadth evident and some level of challenge, however, we have not seen as much evidence of application and Education Scotland have said the same at a national level.
Therefore, we thought it would be beneficial to provide further training on this.
We will look briefly at breadth, before moving on and spending more time looking at challenge and application.
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3. You will now be much more familiar with the Moderation Cycle.
A key part of this is that evidence gathered should demonstrate breadth, challenge and application.
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4. can apply what they have learned in new and unfamiliar situations
For learners to demonstrate that their progress is secure and that they have achieved a level, they will need opportunities to show that they:
have achieved a breadth of learning across the experiences and outcomes for an aspect of the curriculum
can respond to the level of challenge set out in the experiences and outcomes and are moving forward to more challenging learning in some aspects
can apply what they have learned in new and unfamiliar situations
You will find as we go along that actually, the three area often overlap.
Building the curriculum 5
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5. What is meant by breadth of learning?
Breadth refers to the number and range of experiences and outcomes encountered by learners.
CfE Briefing 2
Curriculum for Excellence: Assessing progress and achievement in the 3-15 broad general education
This means that assessment needs to make use of a broader range of approaches which match the nature of that learning and the way it was encountered. This will ensure that learners can show more accurately what they know, understand and can do. Assessment should not constrain learning but reflect and be driven by it, thereby giving responsibility and considerable scope for learners and those that guide them to design together how best to do it. A carefully planned blend of approaches to the kinds of evidence used, and the ways in which it is gathered, can give validity and show an accurate picture of progress in learning over time.

6. What is meant by breadth of learning?
Examples of where an increase in breadth can show that a learner is progressing include:
• A growing confidence and competence in skills for learning, life and work
• A broadening range of texts, performances or presentations
• An improving range and competence in skills and concepts
• A broadening use of more advanced language, formulae and equations
• A broadening amount of detail in the descriptions and explanations they give
There should also be a breadth of experiences offered to learners.
CfE Briefing 2

7. Breadth is not ‘coverage’ or ticking off lots of boxes.
Ensuring Breadth
Varied approach for:
Learning and teaching
Assessment approaches (say/make/write/do)
Breadth is not ‘coverage’ or ticking off lots of boxes.
Pupils all learn in different ways. I’m sure we are all aware of the different learning styles, it’s likely we all covered this at university/college. It’s important that we not only give learning a range of different assessment approaches but that we use a breadth of teaching approaches. It also keeps the learning process interesting and fresh.
At local level and national level, the message is that we are generally quite good at ensuring breadth, therefore we are not going to spend too much time looking at that. We will now move onto look at challenge.

8. Breadth in Numeracy & Mathematics
Work confidently with an increasing number of connected experiences and outcomes
Identify mathematical ideas and concepts required to interpret questions
Use an increasing range of mathematical language and notation, formulae and equations
Use an increasing range of mathematical tools
Opportunities for breadth can be provided by planning a range of activities to bring together and use numeracy and mathematical knowledge and understanding developed in various contexts: for example, using money as a context for learning about number or using knowledge of decimal fractions within area and perimeter calculations.

9. What is meant by challenge in learning?
Challenge refers to the attributes, capabilities and skills, including higher order thinking skills which are embedded in learning. For example, many of the Experiences and Outcomes include skills such as analysing, evaluating and creating.
Notes to presenter:
This slide provides clarification on what exactly is meant by the term ‘challenge’ in the context of assessing progress and achievement.
CfE Briefing 2

10. Examples in Numeracy & Mathematics
Early
I have explored numbers, understanding that they represent quantities, and I can use them to count, create sequences and describe order. MNU 0-02a
I have spotted and explored patterns in my own and the wider environment and can copy and continue these and create my own patterns. MTH 0-13a
First
I can explore and discuss how and why different shapes fit together and create a tiling pattern with them. MTH 1-16b
I have explored symmetry in my own and the wider environment and can create and recognise symmetrical pictures, patterns and shapes. MTH 1-19a
Second
I have investigated how a set of equivalent fractions can be created, understanding the meaning of simplest form, and can apply my knowledge to compare and order the most commonly used fractions. MTH 2-07c
I can show the equivalent forms of simple fractions, decimal fractions and percentages and can choose my preferred form when solving a problem, explaining my choice of method. MNU 2-07b
Third
Having explored the notation and vocabulary associated with whole number powers and the advantages of writing numbers in this form, I can evaluate powers of whole numbers mentally or using technology. MTH 3-06a
I can collect like algebraic terms, simplify expressions and evaluate using substitution. MTH 3-14a
I can create and evaluate a simple formula representing information contained in a diagram, problem or statement. MTH 3-15b
Here are a few examples of these challenge words in a selection of Numeracy and Maths Experiences and Outcomes.

11. What is meant by challenge in learning?
Examples of where an increase in challenge can show that a learner is progressing include:
Learning in more complex contexts
Using and/or presenting increasingly complex texts in terms of length, structure, vocabulary, ideas, and/or concepts
Responding to and producing increasingly complex pieces of work, information and concepts
Responding accurately and confidently to more complex contexts
Learners becoming more adept at evaluating their own and other’s learning
Demonstrating increasing responsibility and independence in learning
Notes to presenter:
This slide provides clarification on what exactly is meant by the term ‘challenge’ in the context of assessing progress and achievement.
You’ll notice the word ‘complex’ comes up in many of these. The level of ‘complexity’ will vary from learner to learner. What will be complex to some will not be complex to others.

12. This has been around for a while and I am sure we have all seen it at some point in our careers.
As teachers we need to ensure that we are providing experiences in all of these areas and not just at the bottom end of the arrow. Some of these are harder to facilitate and require us pushing ourselves out of our comfort zones and letting control a little.
In 1956, Benjamin Bloom headed a group of educational psychologists who developed a classification of levels of intellectual behaviour important in learning. Bloom found that over 95 % of the test questions students encounter required them to think only at the lowest possible level...the recall of information. Bloom identified six levels within the cognitive domain, from the simple recall or recognition of facts, as the lowest level, through increasingly more complex and abstract mental levels, to the highest order which is classified as evaluation. ​ ​
This taxonomy helps teachers pose questions in such a way to determine the level of understanding that a pupil possesses. For example, based upon the type of question asked, a teacher can determine that a pupil is competent in content knowledge, comprehension, application, analysis, synthesis and/or evaluation. This taxonomy is organised in a hierarchal way to organize information from basic factual recall to higher order thinking. Bloom’s taxonomy helps teachers better prepare questions that would foster basic knowledge recall all the way to questioning styles that foster synthesis and evaluation. By structuring the questioning format, teachers will be able to better understand what a child’s weaknesses and strengths are and determine ways to help students think at a higher-level.​
o of ‘control’ at times but they are essential in ensuring that learners are truly challenged.
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13. Challenge is not something that should be provided for only high achievers
It is an important balance. That balance is that you’re providing a learning experience that is challenging without becoming frustrating.
Challenge is important for students because it forces them to grow.
Not too easy/not too difficult
That balance is that you’re providing a learning experience that is challenging without becoming frustrating.
An “easy” learning environment is hardly one that encourages appropriate development – it may rather lead to boredom. When a particular course is easy, it may mean that the standards are too low.
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14. The importance of ‘struggle’
Professor Jo Boaler
Stanford University
‘Mistakes are powerful’
It is important to share the message with our pupils that it is part of the learning process to make mistakes
As teachers it can be difficult to stand back and let them make mistakes or have struggle time. However, it is an absolute essential part of the learning process.
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15. Pace Moving at a brisk pace keeps learners focused
It is not ‘rushing’ through everything at speed
Getting pace correct is essential. You want to make sure that you set enough time to complete tasks without leaving extra time. It is likely we have all been in sessions like this and we have been set a task to complete in small groups. Sometimes we are given too long and we drift off topic and start chatting about other things not related to the task. This happens with pupils too.
Additionally, we need to ensure that they do actually have time to complete set tasks or they will end up frustrated.
Many learners have the perception that getting through work quickly demonstrates intelligence and we really need to shift that mind set. This clip is a great one to share with our learners.
We have to be mindful of giving slower thinkers time to process and develop as well as challenging faster thinkers. A good example for faster thinkers is to ask them to think of ‘another way of getting the same answer’ e.g. using different approaches. Or to get them to persuade someone else of the method they have used.
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16. Ensuring challenge in the classroom Awareness of previous knowledge/skills is essential. Learners are working on appropriate tasks and the teacher is responsive to the ability and interests of the pupils or group. Learning intentions and Success Criteria are expressed overtly. Learners are clear about how to use their learning.
In order to pitch the lesson correctly you must be aware of their previous knowledge, skills.
You will do this through your transition dialogue, looking at previous assessments, discussions with learners. You may carry out an assessment before you carry out your planning to see where they are.
Learners are aware of what they need to do to improve culture of peer and self-evaluation – constantly talking about what they have learned and how to use their learning.
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17. Ensuring challenge in the classroom A balance of active, collaborative, and independent learning is within the classroom/school learning areas. All pupils are involved – everyone has something to say or do to contribute to their learning.  Sound knowledge of prior learning is essential. Don’t complete pages and pages of work just to keep them busy. Don’t give the answers away too readily – take a step back!
Learners are aware of what they need to do to improve culture of peer and self-evaluation – constantly talking about what they have learned and how to use their learning.
You should not assume that pupils do not know it because you haven’t taught it. On the other side, you can’t make assumptions about what you think they should know. Therefore it is essential that you assess prior knowledge/skill developed.
We have all had those pupils that zoom through work and I am sure at some point we have all been guilty of giving them more pages to complete. This is not effectively allowing them to develop. Think of problem solving activities that will develop the skill they are working on. Problem solving is an area that traditionally learners don’t always perform well in, ensuring they have more and more opportunities will enable these skills to progress and develop.
Sound knowledge of prior learning is essential has now been mentioned twice but it really is a huge factor in ensuring appropriate level of challenge.
In your handouts you have been given a list of strategies that can ensure challenge within a classroom.
Remember – teachers should not be the sole source of illumination.
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18. Higher order questions help pupils explore ideas and make connections.
Questioning
Questions can help pupils to develop their thinking from the concrete and factual to the analytical and evaluative.
Higher order questions help pupils explore ideas and make connections.
Questions prompt pupils to inspect their existing knowledge and experience to create new understandings.
It is therefore essential that you plan high quality questions before carrying out your lessons.
The next slide shows us some examples of different levels of questioning.
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19. Questioning Ask fewer but better questions Use more ‘open’ questions
Reframe questions
Prepare key questions before the lesson
Allow proper ‘thinking time’
Allow time for learners to discuss
Questions such as ‘Would you line up please?’ ‘Do you think I didn’t see that?’ should be eliminated. These are unnecessary.
Open – ‘Why do you think…? Can you tell me more about….?’
Reframe – Instead of saying what is 7 + 8, ask ‘How many ways can we make 15?’
Allowing learners to discuss the question gives them longer to process it and will result in better engagement from more pupils.
Try to get pupils to answer other pupils’ questions.
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20. Interactive Oral Mental Mathematics
What is 6 - 4? Show me two numbers with a difference of two.
Is 16 an even number? What even numbers lie between 10 and 20?
What are four threes? Show me two numbers with a product of 12.
How many centimetres in a metre? Tell me two lengths that together make a metre.
Continue this sequence: 1, 2, 4, Find different ways to continue this sequence: 1, 2, 4, ...
How do we change closed questions to open questions? Examples like these can be used with the “show me” digit cards, so that every child has the opportunity to answer. Opportunities to discuss answers can be taken, with wrong answers being used as positive teaching points. Explore the pupils thinking behind their answers…

21. The Answer Is… What is the Question?x + 7 – 
The next few slides highlight a couple of ways you could ask open questions which would lend themselves to discussion and help pupils explore different strategies.
Using one of the strategies mentioned earlier - one way of encouraging this flexible thinking is to select a number as the “answer” and then ask for questions.

22. The Answer Is… What is the Question?x
7 x 1
3·5 x 2
1·75 x 4 +
3 + 4
1·2 + 5·8
-1 + 8 7 –
8 – 1
10 – 3
29 – 22 
35  5
63  9
77  11
This takes children out of the narrow range often determined by the resource and also encourages the pupils to identify more and more challenging algorithms.

23. What Else Do You Know?
12 x 5 = 60
Another way of encouraging this type of thinking is to identify “what else do you know” as a result of knowing one fact. This could be done in pairs, as indicated earlier, then shared with the whole group.

24. What Else Do You Know? 60 12 = 5 60  5 = 12 6 x 5 = 30 5 x 12 = 60
This can be extended to include decimal, fraction and percentage links.
11 x 5 = 55

25. What Else Do You Know? 60 12 = 5 3 x 5 = 15 60  5 = 12 6 x 5 = 30
This can be extended to include decimal, fraction and percentage links.
12 x 05 = 06
11 x 5 = 55
10 x 5 = 50

26. What Else Do You Know? 20% of 60 = 12 of 60 = 5 of 60 = 12 60 12 = 5
3 x 5 = 15
60  5 = 12
6 x 5 = 30
12 x 25 = 30
5 x 12 = 60
12 x 5 = 60
12 x 10 = 120
24 x 5 = 120
1·2 x 5 = 6
This can be extended to include decimal, fraction and percentage links.
12 x 05 = 06
11 x 5 = 55
10 x 5 = 50

27. This is a really useful tool in helping you to form questions that will encourage more higher order thinking skills. I kept my cope next to where I would carry out my planning each week and I found it invaluable.
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28. Challenge in Numeracy & Mathematics
work with increasingly complex questions involving more steps and operations
work with open-ended questions and tasks
use an extended range of mathematical knowledge in tasks
interpret increasingly complex numerical information and use this to draw conclusions, assess risk, make reasoned evaluations and informed decisions
communicate understanding by articulating ideas, approaches and processes with increasing clarity, both orally and in written form.
Challenge can be provided through planning an appropriate range of opportunities within tasks and activities. These tasks and activities should increase in complexity and require a greater number of processes to complete them: for example, learners may be asked to sort a range of shapes and objects using their own criteria or to work out the cost and risks of various forms of loans and justify their choices. Using open ended tasks allows learners the opportunity to clearly explain their approach to the question.

29. What is meant by application of learning?
Overlapping with both breadth and challenge, application refers to how knowledge and understanding, attributes, capabilities and skills, including higher order thinking skills, are used in new and unfamiliar contexts so that they become transferable. This is about learners becoming flexible and adaptable in the way they apply their learning.
Notes to presenter:
This slide provides clarification on what exactly is meant by the term ‘application’ in the context of assessing progress and achievement.
CfE Briefing 2

30. What is meant by application of learning?
Examples of progress in application of learning include:
Using skills and knowledge in different situations
Using skills and knowledge in creative and innovative ways
Finding, selecting, sorting and linking information from a variety of sources
Using information for different purposes
Creating texts to persuade, argue and explore ideas
Presenting, analysing and interpreting evidence to draw conclusions
We are all aware that in order for us to be able to say that has learner has met the standard, they must be able to demonstrate that they can apply their learning in a new or unfamiliar context.
CfE Briefing 2

31. Summarised Inspection Findings
‘Across the school, children have regular opportunities to write, often linked to the current class theme or topic. This gives the children opportunities to practise and apply their writing skills in a meaningful context.’
‘Staff recognise the need to ensure children have regular opportunities to revisit topics and offer children more opportunities to demonstrate and apply their learning.’
Bothwell Primary - Summary Inspection Findings 22/5/18
It is useful to know what is actually expected of us. I went through a number of inspection reports where the ‘Learning, Teaching and Assessment’ came out with a high standard. It is worth us having a look at a few of these just now.
Many of us will do this naturally without thinking about it.
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32. Summarised Inspection Findings
‘Teachers use a range of assessments to monitor children’s progress and plan next steps for individuals and groups. Commendably, this includes a holistic approach to assessing children’s application of learning in new and unfamiliar contexts. ‘
‘They can also talk about a range of real-life contexts and occupations were the application of numeracy and mathematics is a key skill. ‘
Corsehill Primary – North Ayrshire 12/03/18
We need to ensure that learners know how they can apply their learning in real life contexts, this will help to ensure depth of learning.
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33. Application of Learning
Swedish Example
This was evident in a study of some Swedish 12- and 13-year-olds who were accomplished at basic mathematics(Säljö and Wyndhamn 1990). In this study the pupils were asked to find the cost of posting a letter. They were given the letter (which weighed120 grams), some scales and a simple post office chart showing rates ofpostage. For example, letters up to 100 grams would cost 4 kronor, while letters up to 250 grams would cost 7.5 kronor. This is in fact a very simple problem, requiring only that the letter be weighed and the appropriate rate read off from the chart. However, many of the pupils failed to find the correct cost of postage and most of those who succeeded did so after a great deal of trouble. The higher the mathematical attainment of the pupils, the more roundabout were their problem-solving procedures.
These pupils, it seemed, had considerable difficulty in knowing which aspect of their classroom knowledge to apply to this ‘real world’ problem. Even these accomplished youngsters showed severe limitations in their capacity to use or apply their mathematical knowledge and skills from one setting to another.
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34. A major goal of schooling is to prepare students for flexible adaptation to new problems and settings. The ability of students to transfer provides an important index of learning that can help teachers evaluate and improve their instruction.
How People Learn: Brain, Mind, Experience, and School: Expanded Edition (2000)
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35. Examples of Application
Outdoor learning
Problem solving
Using their learning in another curricular area, e.g.
- report writing in science
- talking and listening in health and wellbeing
- numeracy in science
- ICT across all areas
- many, many more…
Often Outdoor learning and problem solving are used as ways of allowing learners to apply their learning, however, these can also be used at the start of a process, at the investigative part of the learning process. Learners will be more engaged if you manage to provide something ‘real’ that they have to investigate.
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36. Application in Numeracy & Mathematics
make connections and apply knowledge, understanding and skills across the numeracy and mathematics experiences and outcomes
use numeracy and mathematical skills in other curricular areas
understand and explain how numeracy and mathematics impacts on the world of learning, life and work.
Learners should be provided with opportunities to use a wide range of numeracy and mathematical skills to address tasks in new and unfamiliar contexts. These will include planned opportunities for learners to use their mathematical skills in other curriculum areas: for example, designing and creating a new board game or working out the electrical consumption of a house and calculating the most effective way to save money. Practitioners should provide opportunities for children and young people to develop an awareness and increasing understanding of the importance of numeracy in society, the economy and the world of work. As a result, learners should better understand how learning in numeracy develops important transferable skills for learning, life and work. Practitioners can provide a wide range of opportunities for learners to use and develop digital competencies as they apply their learning in numeracy and mathematics.

37. Numeracy Example – St Columba’s
In June, P7/6 will be going to Iona for a day trip to learn about St Columba. There will be 23 children going and 3 adults. We must travel from Oban to Mull by ferry and then when we arrive on Mull, we must travel by bus from Craignure to Fionnphort before getting the ferry from Fionnphort to Iona. We must also have time to explore the Iona Abbey before returning to Oban.
You must plan our day. This should include when you get up, what time you need to leave your own house and you must ensure that we leave on the ferry from Oban no earlier that 8am and that we are back in Oban by 6pm. You must also calculate the average cost per person.
Relevant context – a trip that is happening
Elements of the question will have been covered previously but this format/combination will be new and unfamiliar.
Application of key number skills but without explicit instruction
You may find that many children struggle with this. It is important that we don’t avoid these things because they are too hard. The more we do this type of thing, the better they will become.
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38. Examples of holistic assessments Literacy
End of 1st Level
Create a game for the Christmas Fayre and write a clear set of instructions to help others play the game.
Design a poster to persuade visitors to the fayre that your game is worth playing!
Try each other’s games by reading the instructions provided and choose your favourite, giving a reason for your choice.
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39. Examples of Application
Work in small groups to share examples of where you or a colleague have provided opportunities for learners to apply their learning.
Make brief notes on the paper provided.
Allow 10 minutes to do this and then take an example from each group.
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40. Self-evaluation Template provided
Allow 10 minutes to do this and then take an example from each group.
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