assessment & feedback in mathematics colleen young
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Assessment & Feedback in MathematicsColleen Young
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Contents
3 16 32 39 46page page page page page
50 54 71 74 76page page page page page
Assessment for Learning
Relationships Learning Activities Questions Retrieval Practice
Homework Marking Research Assessment for Learning - Summary
Further Reading
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Assessment for Learning
Assessment for learning, also known as formative assessment, is about:
checking learning and giving constructive feedback that informs subsequent learning.
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Assessment for Learning
The Assessment Reform Group (ARG) defines it as:
“…the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go, and how best to get there.” (ARG, 2002).
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Assessment for Learning
Research (Hattie, 2002) shows that giving learners feedback on their learning errors and omissions, and getting them to correct them or work towards improving future work, is one of the most significant methods of improving their performance.
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Assessment for Learning
Constructive feedback also has a profound influence on learners’ motivation and self-esteem
(Black and Wiliam, 1999).
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Is the Feedback You’re Giving Students Helping or Hindering?
(Dylan Wiliam, 2014).
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Is the Feedback You’re Giving Students Helping or Hindering?
What the Studies SayIn their review of feedback studies conducted between 1905 and 1995, Kluger and DeNisi (1996) found that in 38% of well-designed studies, feedback actually made performance worse—one of the most counterintuitive results in all of psychology.
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Is the Feedback You’re Giving Students Helping or Hindering?If there’s a single principle teachers need to digest about classroom feedback, it’s this: The only thing that matters is what students do with it. No matter how well the feedback is designed, if students do not use the feedback to move their own learning forward, it’s a waste of time.
(Wiliam, 2014).
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Add to that concept a second related principle: Feedback should be more work for the student than it is for the teacher. Teachers who internalize and practice feedback based on these precepts will be well on their way to teaching that improves learning.
(Wiliam, 2014).
Is the Feedback You’re Giving Students Helping or Hindering?
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Assessment for Learning is not about
assessing quantity rather than quality
marking and grading, rather than providing guidance for improvement
comparing individual learners
social and management purposes rather than support for learning.
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Assessment for Learning
Assessment and feedback is built in to all successful teaching and learning activities.
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“An assessment activity can help learning if it provides information to be used as feedback by teachers, and by their pupils in assessing themselves and each other, to modify the teaching and learning activities in which they are engaged.” Black and Wiliam 2002
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What Makes Great Teaching?1. (Pedagogical) content
knowledge As well as a strong understanding of the material being taught, teachers must also understand the ways students think about the content, be able to evaluate the thinking behind students’ own methods, and identify students’ common misconceptions.
What makes great teaching? Review of the underpinning research.Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major October 2014
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What Makes Great Teaching?2. Quality of instruction Includes elements such as effective questioning and use of assessment by teachers. Specific practices, like reviewing previous learning, providing model responses for students, giving adequate time for practice to embed skills securely and progressively introducing new learning (scaffolding) are also elements of high quality instruction.
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Student/TeacherrelationshipsRelationships
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Assessment for Learning However, the thing that really matters in feedback is the relationship between the student and the teacher.
When teachers know their students well, they know when to push and when to back off.
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Assessment for Learning Moreover, if students don’t believe their teachers know what they’re talking about or don’t have the students’ best interests at heart, they won’t invest the time to process and put to work the feedback teachers give them.
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Assessment for Learning Ultimately, when you know your students and your students trust you, you can ignore all the “rules” of feedback.
Without that relationship, all the research in the world won’t matter.
(Wiliam, 2014).
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What Makes Great Teaching?Classroom climate (Moderate evidence of impact on student outcomes)
“Covers quality of interactions between teachers and students, and teacher expectations.”What makes great teaching? Review of the underpinning research.Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major October 2014
Should be passionate and enthusiastic.Patient.Understanding.Approachable.Firm but kind.Someone you can feel comfortable with.Recognises achievements.Genuinely caring about the students.Someone who knows who you are.
Good Teachers...
Someone who you know won’t judge you. Expect the best out of your students, but don’t be angry if they don’t always achieve it.
Check with students individually if they are stuck.
They should be able to cater to all abilities.
Good Teachers...
Lets you talk about the work in class.
Praises students.
Good Teachers...
More on good teachers…
A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.
Tests that don’t have further impact on levels / grades. Just there for you to know what you don’t know.
What helps students learn?
Low stakes tests are really good because there is not much pressure and at the end of them I can see how I’m doing and what I need to improve on for later formal tests.
Going through and marking tests / homework.
What helps students learn?
Practice exam papers.
Mark schemes (train them in marking!)
Remember that we have a lot of subjects.
Post tests (test after a formal test with questions the students found the most difficult)
What helps students learn?
Diagrams and other visual aids.
Online resources.
Worked examples. Good notes
Detailed explanations.
Regular checking of answers.
What helps students learn?
In the classroom–an example
Year 11“5-a-day”
Following a mock examination I used these regularly
”Five-a-day” Year 11 Responses
Students completed a short questionnaire where they rated the usefulness of the 5-a-day resources.
I Can …
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Day to activities in the classroomLearning
activities
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Bob’s homeworkMark this, correcting wrong answers and telling him why he’s right or wrong
1) Simplify the following ratios:a) 4g:4kg
b) 13g:52g
c) 60cm:10m
d) 150ml:50ml
2) Share £42 between Henry and Rhiannon in the ratio 3:4
3)If Jack shares some sweets with Charlotte in the ratio 3:2 and Charlotte gets 18, how many does Jack get?
4)Grandma’s cake recipe3 eggs165g flour165g butter165g sugar
I’ve got smaller cake tins, so I’m going to use 2 eggs. How much of the other ingredients do I need?
÷4 1:1
÷13 1:4
÷10 6:1
÷10 15:5
3+4 = 7Henry gets 7x3 = 21Rhiannon gets 7x4 = 28
18÷3=6Jack gets 6x2=12
165g÷3 = 55g2x55g = 110g110g of each of the other ingredients Spot the Mistake
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Bob’s homeworkMark this, correcting wrong answers and telling him why he’s right or wrong
1) Simplify the following ratios:a) 4g:4kg
b) 13g:52g
c) 60cm:10m
d) 150ml:50ml
2) Share £42 between Henry and Rhiannon in the ratio 3:4
3)If Jack shares some sweets with Charlotte in the ratio 3:2 and Charlotte gets 18, how many does Jack get?
4)Grandma’s cake recipe3 eggs165g flour165g butter165g sugar
I’ve got smaller cake tins, so I’m going to use 2 eggs. How much of the other ingredients do I need?
÷4 1:1
÷13 1:4
÷10 6:1
÷10 15:5
3+4 = 7Henry gets 7x3 = 21Rhiannon gets 7x4 = 28
18÷3=6Jack gets 6x2=12
165g÷3 = 55g2x55g = 110g110g of each of the other ingredients
Units are different 1:1000 Units are different 3:50 Not finished 3:1
There are 7 shares. Each share is worth £42÷7=£6Henry gets 3x£6=£18Rhiannon gets 4x£6=£24
Jack to Charlotte is 3:2, so Charlotte gets 2 shares each worth 18÷2=9So Jack gets 3x9 = 27
Start with weights for 3 eggs so divide to get weights for 1 egg then multiply to get weights for 2 eggs
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Revision Activities The resource above is from Tom Riley on TES, exam questions and solutions but also with clues! Students match up the clues to a collection of exam questions on 10 higher topics, then use the clues to answer the questions.
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Questionstogetyourstudentsthinkingandexercisestosecureskills
Questions
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Questions
Weshouldplanforquestionscarefullyinourlessons,weneedquestionstoreallymakeourstudentsthinkandweneedquestionstohelpthempractiseskills.
References
Questions worth asking–theBrighton&HoveAssessmentforLearningProject
AssessmentwithoutLevels,noteDaisy Christodoulou onusingmultiplechoicequestions.
DiagnosticQuestions
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Revision Activities Here’s the diagram – what’s the question?
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Algebra Snippetts What’s the question? Discuss question paper terminology
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Thepracticeofretrievinginformationfrommemory.
RetrievalPractice
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Students need to recall information and the evidence suggests that testing is a better way of doing this than simply rereading material, a method often favoured by students. Mini-tests are low stakes ‘Self-checks’ ,a learning tool, not something to be stressed by.
Aristotle apparently wrote“exercise in repeatedly recalling a thing strengthens the memory.”
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Mini Tests
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How do we make it meaningful?
How do we make sure we build in time for review and to act on feedback?
Homework
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Homework
some ideas…
Homeworkdoesnotnecessarilyhavetobeonthetopicyouarecurrentlystudyingandcanofferthechancetoreviewprevioustopicsorlookaheadtoatopicyouwillbestudying.
Somealternativestothetextbook:
Set somequestionswithsolutionsandmarkschemes
Studentswritequestionsonagiventopicandalsoprovidesolutionsandamarkscheme.Inclasstheirpeerscantrythequestions.Thisoffersthechanceforsomeexcellentclassdiscussiononwhystudentsthinkaquestionisagoodquestion,thedifficultyofaquestionandhowitshouldbemarked.
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Homework
some ideas…
Homeworkdoesnotnecessarilyhavetobeonthetopicyouarecurrentlystudyingandcanofferthechancetoreviewprevioustopicsorlookaheadtoatopicyouwillbestudying.
Askthemtowritesome diagnostic questions withmultiplechoiceanswers.Askthemtoprovidethequestionwithfourpossibleanswers.Theyshouldindicatewhichansweriscorrectandexplaintheirreasoningbehindtheoptionstheyhavegiven.
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Homework
some ideas…
ReviseandRecallHelpstudentsrecallmaterialbysettingahomeworktoreviewatopicortopicsandthengivea mini-testinclass.Itendtocallthem‘Self-checks’forthestudentstoemphasizetheideatheyarejustcheckingwhattheyknowandwhattheymayneedfurtherhelpwith.
Dotwo!Givetwofairly/ verysimilarhomeworksinarow,thesecondbeingachancetoactonallthefabulousfeedbackyougaveforthefirstattempt!
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How do we make it meaningful?Marking
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Test Analysis
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Use Examiners’ Reports
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Main findings
The quality of existing evidence focused specifically on written marking is low.
April 2016
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Some findings do, however, emerge from the evidence
Careless mistakes should be marked differently to errors resulting from misunderstanding. The latter may bebest addressed by providing hints or questions which lead pupils to underlying principles; the former by simply marking the mistake as incorrect, without giving the right answer.
No matter how well the feedback is designed, if students do not use the feedback to move their own learning forward, it’s a waste of time.
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Some findings do, however, emerge from the evidence
Awarding grades for every piece of work may reduce the impact of marking, particularly if pupils becomepreoccupied with grades at the expense of a consideration of teachers’ formative comments.
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Some findings do, however, emerge from the evidence
The use of targets to make marking as specific and actionable as possible is likely to increase pupil progress
Pupils are unlikely to benefit from marking unless some time is set aside to enable pupils to consider and respondto marking
No matter how well the feedback is designed, if students do not use the feedback to move their own learning forward, it’s a waste of time.
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Some findings do, however, emerge from the evidence
Some forms of marking, including acknowledgement marking, are unlikely to enhance pupil progress.
A mantra might be that schools should mark less in terms of the number of pieces of work marked, but mark better.
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The 5 Minute Marking/Feedback Plan
The big picture?(The purpose of marking for this
work?)
Key marking points to share
with students?
Common Errors?!
Formative marking:
Re-teach?
Summative marking:
….print and scribble your way to focus on helping students to progress!
What? When?
How?Why?
Grading system:
Directed Improvement and Reflection Time?What?When?How?
Student response to feedback required?
Peer/Self assessment
opportunities?
to improve student learning
What is mastery for this work?
Follow up
Intervention?
Below?On?Above?
Plan for marking
#5 minute plan series, Ross Morrison McGill, @TeacherToolkit
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What do ou tell parents about students’ engagement with learning?
Reporting
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The best learners at Newstead have these qualities
growth mindset, resilient, curious, proactive, imaginative, creative, innovative, perseverance, determined
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Researchin100words
ChrisMoyse
Research
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SummaryAssessmentFor Learning
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Assessment for Learning
Return tocontents
© The Quality Improvement Agency for Lifelong Learning (QIA) 2008
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Blogs – Learning & TeachingAs always – these are my favourites (see Emily Nussbaum writing for The New Yorker on why she hates Top Ten Lists!); blogs I find thought provoking that I believe will be of interest to any teacher / senior leader. It’s a short list, I read from many sources but these are the blogs that I always check when I am alerted to a post.The Learning Spy by David Didau. You can search for posts by category at the foot of the blog. Every time I think I have something sorted out, David comes along and challenges my thinking!headguruteacher by Tom Sherrington. Note the top posts and pages, also the categories.@Leading Learner by Stephen Tierney. Note the Top Posts and (further down the page) Categories@TeacherToolkit by Ross Morrison McGill who is the author of the 5 minute lesson plan you will find many references to on my own blog. Ross has a very clear index here.Class Teaching by Shaun Allison and the chosen blog of the week alsojohntomsett by, unsurprisingly – John Tomsett!Hunting English by Alex QuiglyPragmatic Education by Joe KirbyThoughts on managing variability by Kev Lister
Further Reading
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Colleen Young
https://twitter.com/ColleenYoung
Mathematics, Learning & Technology
Mathematics for Students
Mathematics for Students Mathematics, Learning and Technology
Colleen Young