1. The Maths Pipeline Programme for the FE and Skills Sector

2. Welcome to our session on The session will start shortly.
Formative assessment.
Your session leader is
Rita Farrell.
The session will start shortly.

3. FORMATIVE ASSESSMENT.
“When the cook tastes the soup that is formative assessment, when the customer tastes the soup that is summative assessment”. (Prof. Paul Black)

4. What is Formative Assessment?
Formative assessment is not defined by a particular assessment activity.
It is how we use assessments which determines whether or not the assessments are formative.
What is formative assessment? Why is it distinguished from summative assessment? It is important to understand that formative assessment is not a particular type or style of assessment. An assessment is formative because of how we use it. It is possible for any assessment to serve either formative or summative purposes, so when we think about formative assessment we must think about the purpose of the assessment. Why are we using that assessment, what information are we hoping to gather from it.

5. Why do we assess our students?
Think about your classroom practice. ……………………how much of the time are you assessing your students?
Why are you assessing?
How are you assessing?/What does the assessment look like?/What are you checking?
Before we explore formative assessment any further, let us think about assessments in general. In particular – why do we assess our students? Really allow yourself to visualise your classroom practice….how often do you check on learning, how often do you check on understanding, how do you do this?
What kind of feedback do you give to your students during such learning checks? Do your classroom assessments ever cause you to divert from your lesson plan and spend more or less time on a particular concept of topic?

6. Why do we assess our students?
Find out how much students have learnt
Gather information about the students level of understanding.
To control and guide the learning.
To focus attention on key concepts.
To help students to monitor their progress.
So we can identify areas where students need further guidance/support.
To expose misconceptions and misunderstandings.
So we can give students feedback and help them improve.
To encourage and motivate students to learn.
As a way of indicating what’s important in a particular topic.
Good teachers regularly assess their students progress and understanding during class time. So why do we do this? Assessments provide information to the teacher and the learner about the current level of understanding We assess our students in lessons to:
You can probably think of many more reasons? All of the outlined reasons for assessing students are equally important.

7. Formative: assessment for learning. Summative: assessment of learning.
‘… often means no more than that the assessment is carried out frequently and is planned at the same time as teaching.’ (Black and Wiliam, 1999)
‘… provides feedback which leads to students recognising the (learning) gap and closing it … it is forward looking …’ (Harlen, 1998)
‘ … includes both feedback and self-monitoring.’ (Sadler, 1989)
‘… is used essentially to feed back into the teaching and learning process.’ (Tunstall and Gipps, 1996)
Summative: assessment of learning.
‘…assessment (that) has increasingly been used to sum up learning…’(Black and Wiliam, 1999)
‘… looks at past achievements … adds procedures or tests to existing work ... involves only marking and feedback grades to student … is separated from teaching … is carried out at intervals when achievement has to be summarized and reported.’ (Harlen, 1998)
Formative assessments are assessments which we build into our lesson plan and which we carry out frequently during our lesson. The formative assessment provides feedback to the students. This is probably the single most important factor of formative assessment. It is crucial that such learning checks are followed up with immediate feedback to the learning which sums up their existing level of understanding and tells them how to improve or move to the next level of understanding. Formative assessments provide feedback to the teachers and the student on what is understood and what has to change and how to change it. Summative assessments are of course the more traditional view of assessment. Summative assessments are carried out at the end of a unit or course and measure levels of competency which leads to grades. Summative assessments are unlikely to involve much feedback. Summative assessments do of course have an important role to play in education. But as teachers, in our day to day practice we need to be mindful of formative assessment.

8. Assessments: formative or summative?
Formative and summative assessments are separated by their purpose. Summative assessments give final judgements on a students competency, such as end of year or end of unit exams. Formative assessments provide lots of feedback in real-time to the teacher and students on where they are now. Teachers may change the lesson content or differentiation strategies as a result of formative assessment. Effective formative assessment will inform what the teacher and students do next.
To recap……any questions at this point?

9. Formative assessment cycle.
Where the learner is going.
Within lessons this means, sharing lesson objectives and clarifying lesson objectives.
Where the learner is Planning effective tasks, activities and discussions which demonstrate the current level of learner understanding.
How to get there. Provision of descriptive feedback which includes guidance on how to improve understanding during the lesson and what to do next.
In order for formative assessments to be effective, it is important that the learners are fully aware of the lessons objectives. Formative assessment involves a high level of collaboration between the teacher and student(s), it is a cooperative approach to learning. The learners are fully aware of their starting point and where they are aiming to get to.

10. Who is and is not understanding the lesson?
Formative Assessment can help teachers to answer the following questions:
Who is and is not understanding the lesson?
What are this student’s strengths and needs?
What misconceptions do I need to address?
What feedback should I give students?
What adjustments should I make to my teaching/instructions?
How should I group students?
What differentiation do I need to prepare?
Formative assessments (in class assessments) provide information and feedback for the teacher and student(s). The teacher will be gathering information about…………………..

11. Practical strategies for Formative Assessment.
3 things!
List 3 things which a fellow student might misunderstand or get wrong in this topic.
Lets now look at activities which provide opportunities for gathering evidence of understanding and opportunities for giving feedback. This activity will highlight which aspects of a topic individual students find difficult to grasp. This can lead onto discussions about those aspects. We can delve deeper into this by asking students to explain why someone might misunderstand those specific things.

12. Practical strategies for Formative Assessment.
Venn diagrams!
Give the students mathematical statements to be sorted as true, sometimes true or never true.
true
Good for promoting discussion, good for group work can be printed on A3. Students will need to reason, sort and organise their thinking. It is useful to encourage students to give examples of when something is sometimes true, true or never true.
Never true.
Sometimes true.

13. Practical strategies for Formative Assessment.
Ask open questions!
Ask questions which allow for a variety of responses rather than one correct answer.
Open questions are useful for promoting class discussion.
Closed question
Open question
What is ¼ of 16?
4 is a fraction of a number. What fraction of what number? Give examples.
What are the factors of 8?
Give some examples of numbers with four factors and explain what else they have in common.
The NCETM have a very useful department training resource on Questioning. There are lots of examples given of changing maths questions from closed to open. Allowing for a range of answers will allow students to demonstrate all that they know and understand about that particular topic. .

14. Practical strategies for Formative Assessment.
Comparing and organising!
What is the same and what is different about……………..
y=2x+1 and y=-2x+1.
y=x2 and y=x2 -2.
Perimeter and area.
This requires learners to articulate their thinking, to organise their thinking and to justify their answers. You can do this with diagrams (two bar charts, two pie charts, two line graphs). .

15. Practical strategies for Formative Assessment.
Students create examples!
Show me an example of………………
An equation of a straight line with a negative gradient.
A bodmas calculation with a negative answer.
A percentage question with an answer less than 50.
For other information on good questioning in maths look at
This requires learners to articulate their thinking, to organise their thinking and to justify their answers. This moves students away from questions with just one correct answers. A whole host of answers can be given & shared with the class, discussions about how to solve some of the examples can be had. This is a good way of assessing how much they know, the complexity of their examples will demonstrate their current level of understanding. .

16. Practical strategies for Formative Assessment.
Exemplar work!
Ask students to mark a piece of exemplar work using the marking criteria. This will not only give them an insight into the assessment process and what a good piece of work looks like but it will also provide valuable insight into the students understanding of that particular topic. .

17. Practical strategies for Formative Assessment.
Use graphic organisers to help students to self-assess!
VAK: visual, auditory or kinaesthetic These activities provide insight into how our students learn, this informs our lesson planning and our assessment planning. .

18. Practical strategies for Formative Assessment.
Muddiest point!
Students write down the one or two aspects of a topic or concept of which they are least clear.
The teacher and students can then work at clearing up these misunderstandings and misconceptions.
Here the student are identifying their individual weaknesses. This is useful in encouraging students to monitor their own progress and to self-assess. .

19. Practical strategies for Formative Assessment.
Comment only marking!
Rather than just ticking questions as correct or incorrect, try writing comments such as
“you got 3 of the questions wrong, find the errors and fix them”
Students often get hung up on grades, and sometimes they don’t even read the feedback. In the absence of a grade they will focus on the feedback. Comment only feedback can be difficult in maths, but you can make suggestions like the one above which requires the student to check & self-assess their work. We can also give comments on techniques used. .

20. Practical strategies for Formative Assessment.
Wait time!
Wait time allows students time to think and organise their thoughts and ideas.
Wait time can take two forms:
Teacher asks a question, and then pauses before taking any responses.
Student response ends and the teacher waits before responding. This gives the student time to elaborate and expand on their original response.
Wait time is an important technique for formative assessment. We can’t fully assess our students understanding if we don’t give them time to really think it through. Quickly moving on after asking a question can sometimes make our students lazy. But if they know that the teacher will wait while they come up with a reasoned well thought through answer they will take more responsibility for their answer. We all know that we can answer questions better if we are given time to think. Think of the last time you did an interview, how many of your answers were better after you thought the questions through in the car on the way home! .

21. Practical strategies for Formative Assessment.
Lesson review!
Teacher leads a review of the session or topic, using questions to elicit understanding from students.
Students could review the lesson or topic in terms of how the teaching & learning tasks could have been altered to improve on understanding.
We (the teachers) need feedback too. Let the students review a topic in terms of how the teaching and learning helped them to understand. What would they change about the session? Would they have done the activities in that order? Did they need more time (or less) for some activities. This tells us a lot about what they do and don’t understand. .

22. Practical strategies for Formative Assessment.
Peer assessment!
Students are asked to assess a peer’s work. The focus should be on comment only marking in which the student lists two things which have been done well and one thing to improve on.
This requires the students to really analyse the work. It is not a ticking exercise, but an analytical one. It is important to stress to the students that the quality of the feedback is important, they must give details of what is good and why, what is not so good and why. This is quite a grown up exercise, and will inform the students (both the assessor and the assessed ) of how much they really understand. .

23. Practical strategies for Formative Assessment.
Bouncing!
Bounce answers around the room to build on understanding.
e.g.
Hassan what do you think of Linda’s answer?
Sundus can you add another comment or idea to Hassan’s answer?
Disha can you summarise all you have heard into one answer?
Don’t let the students get lazy. Get them into the habit of really listening to each others answers and thinking about what else could be added. This will help them to be more analytical and it encourages them to be active listeners. .

24. Practical strategies for Formative Assessment.
Use mistakes and misconceptions!
Use common mistakes and misconceptions to elicit understanding from students.
Common misconception: 2(x+3)=2x+3
Why is this wrong?
Begin a classroom discussion, asking students to explain why this is wrong.
If this is the answer, what is the question.
In this case give the answer 2x+6 and ask pupils to come up with the answer.
If this is the question, what is the most common incorrect answer.
Invite students to generate wrong answers and explain why there are wrong.
The NCETM have a fantastic departmental training package on using mistakes and misconceptions to deepen understanding. This can be found under departmental workshops. .

25. Practical strategies for Formative Assessment.
All you know!
Instruct students to write down everything they know about a particular topic. This could be done in groups creating mind maps of posters.
The teaching can then be planned accordingly making use of existing knowledge and understanding.
This is a great way of getting an overall view of current understanding. It is also very useful for planning the next steps in your lesson, or course. You can always extend on this by asking the students to add a section on what else they would like to know or find out more about. .

26. Practical strategies for Formative Assessment.
Post it!
Use post it notes to evaluate learning during or at the end of the lesson.
Students can answer:
What have I learnt?
What did I find easy?
What did I find difficult?
What would I like to know now?
Again this really sums up the students understanding. Planning the next steps can be done collaboratively between the teacher and students. .

27. Further reading & resources.
Embedded Formative Assessment, Dylan Williams.
Inside the Black Box, Dylan William & Paul Black.
Perfect Assessment for Learning, Claire Gadsby.
Embedding Formative Assessment, Dylan Williams & Siobhan Leahy.
Standards Unit: Improving Learning in Maths (unit PD6).
Formative Assessment for Teaching and Learning, Bill Boyle & Marie Charles.
Formative assessment is a BIG topic. There is so much information out there. I have put together a reading/resource list of books and resources which I have found to be good. The standards units module would be a great departmental workshop in which you can further explore formative assessment with your own team. Dylan Williams is considered to be one of the most knowledgeable people when it comes to formative assessment. I use his book all the time. .

28. Questions.
Formative assessment is a BIG topic. There is so much information out there. I have put together a reading/resource list of books and resources which I have found to be good. The standards units module would be a great departmental workshop in which you can further explore formative assessment with your own team. Dylan Williams is considered to be one of the most knowledgeable people when it comes to formative assessment. I use his book all the time. .