Formative Assessment - Mathshell
Formative AssessmentHow can I respond to students in ways that improve their learning?A PROFESSIONAL DEVELOPMENT MODULEIntroductionMathematics teaching assumes that students do not arrive at sessions as ‘blank slates’, but as activelythinking people with a wide variety of skills and conceptions. Research shows that teaching is moreeffective when it assesses and uses prior learning so that the teaching may be adapted to the needs ofstudents (Black & Wiliam, 1998). Prior learning may be uncovered through any activity that offersstudents opportunities to express their understanding and reasoning. It does not require more testing. Forexample, it can take the form of a single written question given at the beginning of a session to elicit arange of explanations that may then be discussed. This process, often referred to as formative assessment,may be defined as: all those activities undertaken by teachers, and by their students in assessing themselves, whichprovide information to be used as feedback to modify the teaching and learning activities in whichthey are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actuallyused to adapt the teaching work to meet the needs. (Black & Wiliam, 1998)This module considers the different ways this can be done and focuses on the following questions: How can problems be used to assess performance?How can this assessment be used to promote learning?What kinds of feedback are most helpful for students and which are unhelpful?How can students become engaged in the assessment process?ActivitiesActivity A: Introducing formative assessment. 3Activity B: Teachers’ own experiences of formative assessment . 4Activity C: Principles for formative assessment . 6Activity D: Analyze students’ responses to problem-solving tasks . 8Activity E: Observe formative assessment in action . 10Activity F: Plan and report back on an assessment lesson . 11Activity G: Consider the effects of feedback on student learning . 12Further Materials: MAP Formative Assessment Lessons . 14Acknowledgement:In preparing this material, we acknowledge the permissions given by the Bowland Charitable Trust to adapt the professionaldevelopment resources, Bowland Maths, that they had previously funded us to produce for the UK. This includes many of thehandouts and most of the video extracts. Additional resources were also adapted from Improving Learning in Mathematics, agovernment funded program in the UK. The original sources are:Swan, M; Pead, D (2008). Professional development resources. Bowland Maths Key Stage 3, Bowland Trust/ Department forChildren, Schools and Families. Obtainable in the UK from: http://www.bowlandmaths.org.uk.Swan, M; (2005). Improving Learning in Mathematics, challenges and strategies, Department for Education and Skills StandardsUnit. Obtainable in the UK from http://tlp.excellencegateway.org.uk/pdf/Improving learning in maths.pdfDraft Feb 2012 2012 MARS, Shell Centre, University of Nottingham
Related research to help your planning for this module.Black, P., & Wiliam, D. (1998). Inside the black box: raising standardsthrough classroom assessment. King’s College London School ofEducation.Now published by GL Assessment: http://shop.gl-assessment.co.ukThis short booklet offers a summary of the extensive researchliterature into formative assessment. It shows that there is clearevidence that improving formative assessment raises standards, andoffers evidence showing how formative assessment may beimproved. This booklet is essential reading for all teachers.Black, P., & Harrison, C. (2002). Working inside the black box: Assessmentfor learning in the classroom. King’s College London School ofEducation.Now published by GL Assessment: http://shop.gl-assessment.co.ukIn this booklet, the authors describe a project with teachers in whichthey studied practical ways of implementing formative assessmentstrategies and the effect this had on learning. The section onfeedback and marking (pp. 8-9) are particularly relevant to thismodule.Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2003).Assessment for learning: Putting it into practice. Buckingham: OpenUniversity Press.This book gives a fuller account of the earlier booklets Inside theblack box and Working inside the black box. It discusses four typesof action: questioning, feedback by marking, peer- and selfassessment and the formative use of summative tests. The section onfeedback and marking (pp. 42-49) is particularly relevant to thismodule, while the section on peer and self-assessment (pp. 49-53) isrelevant for the next CPD module.Hodgen, J., & Wiliam, D. (2006). Mathematics inside the black box. King’sCollege London School of Education. Now published by GLAssessment: http://shop.gl-assessment.co.ukThis booklet applies the above findings specifically to Mathematics.It considers some principles for Mathematics learning, choice ofactivities that promote challenge and dialogue, questioning andlistening, peer discussion, feedback and marking, and self and peerassessment. This booklet is essential reading for all mathematicsteachers.PD Module GuideFormative Assessment2
Activity A: Introducing formative assessmentMinimum time needed: 10 minutes.The different types and purposes of assessment.Invite participants to discuss the following issues: Why do you assess students?What different purposes do your assessments serve? Make a list.Their list of reasons might include: to diagnose difficulties; to celebrate achievement; to motivatestudents; to select students for classes; to maintain records to keep teachers and parents informed ofprogress; to assess teaching methods.To summarize, there are two main purposes of assessment: Summative assessment – to summarize and record overall achievement at the end of a course, forpromotion and certification. Most ‘high stakes’ tests and external examinations are designed forthis purpose. Summative assessment is also used to evaluate the relative effectiveness of aparticular course, teaching method, or even an institution. Formative assessment – to recognize achievements and difficulties at the beginning or during acourse, so that teachers and students can take appropriate action. This type of assessment formsan integral part of all learning.The potential of formative assessment to improve learning.Briefly mention the research evidence that sets out the case for formative assessment. This is summarizedby Black and Wiliam in several accessible publications for teachers (see p. 2). These researchers set out tofind out whether or not improving formative assessment improves learning.We checked many books and nine years’ worth of more than 160 journals, and earlier reviews ofresearch. This process yielded 580 articles or chapters to study. We prepared a review using materialfrom 250 of these sources. All studies show that strengthening formative assessment producessignificant, and often substantial, learning gains. These studies range over ages, across severalschool subjects, and over several countries (Black and Wiliam, 1998).1This module will examine the implementation of formative assessment, based on this and other research.1 Black , P., & and Wiliam, D. (1998). ‘Assessment and Classroom Learning, Assessment in Education, March 1998, pp. 7-74.PD Module GuideFormative Assessment3
Activity B: Teachers’ own experiences of formative assessmentMinimum time needed: 10 minutes.What do teachers know about their students and what consequentialaction do they take?Ask participants to work in pairs, considering the following questions. Think of two students in your class, one who is particularly strong and one who is finding thework very difficult. Take it in turns to describe the students’ strengths and difficulties to yourpartner, in as much detail as possible.How did you become aware of these strengths and difficulties? On what evidence do you baseyour judgments? Test results? Memories of oral responses during lessons? Observations ofthe student working? Written work?In what ways do your assessments of these students affect your lesson planning?Give examples.What difficulties do teachers encounter?Issue participants with copies of Handout 1. How far are the criticisms on the handout valid in your context?If any are, then what may be done about them?PD Module GuideFormative Assessment4
Handout 1: Difficulties in formative assessmentDraft Feb 2012Handout 1: Difficulties in formative assessment!"# %#&#'%(" )* #%' ,%# &,--#& & "' ./%0' *1# '&&#&&0#2 3%'( *(#& '%# 4#&# 5* " 3%/4)#0& '26 6*.*(,) *#&7 !"#&# '%# &,00'%*8#6 *2 "# #9 #2&*1# %#1*#5 4: ;)'( '26 *)*'0 ?@@AB? '& ./))/5&C Effectiveness of learning: !#'("#%&D #& & #2(/,%'-# %/ # '26 &,3#%.*(*') )#'%2*2-7 !"# E,#& */2& '26 0# "/6& , '%# 2/ &"'%#6 4# 5##2 #'("#%&F '26 "#: '%# 2/ (%* *(')): %#1*#5#6 *2 %#)' */2 / 5"' "#: '( ,')): '&&#&&7 !"#%# *& ' #26#2(: / #03"'&*8# E,'2 * : /. 5/% '26 / 2#-)#( * & E,')* : *2 %#)' */2 / )#'%2*2-7 Impact of assessment !"# -*1*2- /. &(/%#& '26 "# -%'6*2- .,2( */2 '%# /1#%#03"'&*8#6F 5"*)# "# -*1*2- /. ,&#.,) '61*(# '26 "# )#'%2*2- .,2( */2 '%# ,26#%#03"'&*8#67 G33%/'("#& '%# , *2 5"*(" & ,6#2 & '%# (/03'%#6 5* " /2# '2/ "#%F "# 3%*0# 3,%3/&# /. 5"*(" &##0& / "#0 / 4# (/03# * */2 %' "#% "'2 3#%&/2') *03%/1#0#2 H *2 (/2&#E,#2(#F '&&#&&0#2 .##64'( #'("#& )/5I'("*#1*2- & ,6#2 & "' "#: )'( J'4*)* :FK (',&*2- "#0 / (/0# / 4#)*#1# "' "#: '%# 2/ '4)# / )#'%27 Managerial role of assessment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lack, P., & Wiliam, D. (1998). Inside the black box: raising standards through classroom assessment. London: King’sCollege London School of Education.Handouts for TeachersPD Module GuideFormative AssessmentFormative AssessmentH-25
Activity C: Principles for formative assessmentMinimum time needed: 20 minutes.Issue participants with a copy of Handout 2. The ideas presented here are all drawn from research intoformative assessment. Bearing in mind the difficulties discussed in Activity B, how would you suggest that yourformative assessment practices be improved?Discuss the principles outlined on Handout 2.o Which of these do you currently use in your own teaching?o Which do you find most difficult? Why?What other principles do you think are important?Issue copies of Handout 3."It's all very well telling us to assess our students, but how cana busy teacher know what is going on inside 30 individualheads?" How would you answer this teacher? What strategies do you have for finding out whatstudents are thinking in your lessons? Discuss the two suggestions shown on Handout 3,and watch the two Activity C Videos: ‘MiniWhiteboards’ and ‘Posters’ to see these in action. Suggest some further strategies for making reasoningmore evident.The two strategies described on Handout 3 and illustrated in the Activity C Videos may help to makereasoning more ‘visible’.Mini-whiteboards are an indispensable resource for the following reasons: When students hold their ideas up to the teacher, it is possible to see at a glance what everystudent thinks. During whole class discussions, they allow the teacher to ask new kinds of question (typicallybeginning: ‘Show me an example of.’). They allow students to, simultaneously, present a range of written and/or drawn responses to theteacher and to each other.Posters are also a powerful way of helping students to externalize their thinking. This use does notrequire ‘polished’, ‘complete’, ‘attractive’ products but rather they should be seen as working documents.Perhaps the simplest way of using a poster is for students to solve a problem collaboratively, explainingthe thought processes involved at every step. A second use of posters is to find out what they alreadyknow about a given topic. In the diagram shown on Handout 2, the teacher asked students to write downall they knew about y 2x 6. As a class, the diagram was developed on the whiteboard. Students werethen given a variety of equations (the level of challenge was varied appropriately) and were asked toproduce their own poster. The discussion enabled the teacher to assess how much learners knew aboutequations and how well they were able to link the ideas together.PD Module GuideFormative Assessment6
Handout 2: Principles for formative assessmentDraft Feb 2012Handout 2: Principles for formative assessmentFormative assessment may be defined as:! all those activities undertaken by teachers, and by their students in assessing themselves, whichprovide information to be used as feedback to modify the teaching and learning activities in which theyare engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used toadapt the teaching work to meet the needs. (Black & Wiliam, 1998)Make the objectives of the lesson explicit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ssess groups as well as individual students@ (06&# ',-,',%.c(/&4#27&(66( '02,',%.&'(&().% -%;&9,.'%2;&A0%.',(2&.'01%2'.8&B"%7&"%96&'(&% '% 2#9,C%& %#.(2,2:c(/&'"%&'%# "% &'(&.%%&A0, 597&/"% %&1,33, 09',%.&"#-%&# ,.%28&&Watch and listen before interveningD%3( %&,2'% -%2,2:&,2&#&: (06&1,. 0.,(2;&/#,'&9,.'%28&B 7&'(&3(99(/&'"%&9,2%&(3& %#.(2,2:&'"#'&.'01%2'.&# %&'#5,2:8&E"%2&7(0&1(&,2'% -%2%;&)%:,2&)7&#.5,2:&'"%4&'(&% 69#,2&.(4%'",2:8&?3&'"%7&# %&02.0 %.309&'"%2&#.5('"% &.'01%2'&'(&"%968&Use divergent assessment methods (“Show me what you know about .”).F(2-% :%2'&#.%.4%2'&.' #'%:,%.&# %& "# # '% ,C%1&)7&', 5&9,.'.& #2G1(&.'#'%4%2'.8&B"%&'%# "% &#.5.& 9(.%1&A0%.',(2.&,2&( 1% &'(&#. % '#,2&/"%'"% &( &2('&'"%&.'01%2'&52(/.;&021% .'#21.&( & #2&1(&#&6 %1%'% 1&,2&/ ,''%2&'%.'.8&&H,-% :%2'&#.%.4%2';&,2& (2' 1%2'.&(66( '02,',%.&'(&1%. ,)%&% 69#,2&'"%, &'",25,2:& %#.(2,2:8&B"%.%&A0%.',(2.c(/&.'01%2'.&'(&.0 6 ,.%&0.&G&'"%&(0' (4%&,.&2('&6 %1%'% 4,2%18&&Draft Feb 2012Handout3: Making reasoning visibleHandout 3: Making reasoningvisible.Usequestioningwith mini-whiteboardsHandoutsfor TeachersFormative Assessment!"# %&''&()* , -& . "/012* (*2330//1 4)#3 &/"&"5 &3 .2 3/1# 3 )%#" 3 %/1&"2 # -.&*# / .#03 20# // 2'02&% / 620 &(&62 #7 8" .&3 3 02 #5,9 #:#0, 3 )%#" 60#3#" 3 2 0#36/"3# 3&1)* 2"#/)3*,7 ;.#" /6#" 4)#3 &/"3 20# )3#%9 3 )%#" 3 20# 2 *# / 5&:# %&''#0#" 0#36/"3#3 / ./3# 20/)"% .#17 .# #2(.#0 &3 2 *# / &11#%&2 #*, 233#33 -.&(. 3 )%#" 3 )"%#03 2"% .# &%#23 2"% -.&(. 20# 3 0)55*&"57 H-3 Ask students to produce posters 3? #2(. 312** 50/)6 /' 3 )%#" 3 / -/0? /5# .#0 / 60/%)(# 2 6/3 #0@ 3./-&"5 .#&0 A/&" 3/*) &/" / 2 60/ *#1 3)1120&B&"5 -.2 .#, ?"/- 2 /) 2 5&:#" /6&(9 /0 3./-&"5 -/ %&''#0#" -2,3 / 3/*:# 2 5&:#" 60/ *#1 3./-&"5 .# (/""#( &/"3 # -##" 2 12 .#12 &(2* &%#2 2"% / .#0 0#*2 #% &%#237 !"# %&"'()* ,''- )*./01'2&#)0/01'/0'3#%4& #%/567'8& #)% &0%'(*)'9":5#%/*0'#0"'; / 67' ?@A' Handouts for TeachersPD Module GuideFormative AssessmentFormative AssessmentH-57
Activity D: Analyze students’ responses to problem-solving tasksMinimum time needed: 20 minutesHandout 4 presents three problems together with four student responses on each. The tasks are: CountingTrees, Cats and Kittens, Security Cameras.These tasks use a variety of mathematical content, but all three focus on the problem solving andmodeling skills described in the Common Core Standards for Mathematical Practice. Often, such tasksprove more difficult than the individual elements of mathematical content would suggest, as students arerequired to choose and combine techniques in non-routine ways. Traditional summative assessments oftenfocus on isolated content standards and fail to test these ‘process skills’. Formative assessment is aneffective way to ensure that students are developing these practices.The following phases of problem solving are a useful tool to analyze students’ work on these tasks:A. Formulate questions, choose appropriate representations and techniques.B. Reason logically, construct hypotheses and arguments,compute accurately.C. Interpret and evaluate results obtained.D. Communicate and reflect.These are closely related to the phases of the modeling cycle described in the CCSS High Schoolstandards for modeling, but also relate to language found throughout the practices and are generallyapplicable to most problem-solving activities. Read through all three tasks then choose one task that will be most suitable for a class youwill soon teach. If you are working on this module in a group, it will be helpful if eachparticipant chooses the same problem, as this will facilitate the follow-up discussion. Consider the four student responses. What does each student’s response tell you about his orher capacity to use each of the phases of problem-solving: formulate, reason, interpret andevaluate, communicate and reflect?Handout 5 offers some comments on students’ responses to each of the tasks. If you were the teacher of these students, what feedbackwould you give them to help them improve theirresponses? Try to frame this help in the form of oralquestions you could ask in the classroom. You may find ithelpful to refer to the generic questions given onHandout 6. Watch Activity D Video: ‘Teachers DiscussingFeedback.’ This shows three teachers discussing thefeedback they gave on the three problems.PD Module GuideFormative Assessment8
Handout 4: Assessment tasks andsample responsesHandout 4: Assessment tasks and sample responsesDraft Feb 2012Handout 5: Improving students’responses through questioningDraft Feb 2012Handout 5: Improving students’ responses through questioningCounting TreesCounting Trees!!"!"!!!!!""!!"!"!!!!""!!!!!!!!!"!!!!"!"! !"! !! "" "! "! !" !!" !! !!"! !""! !!" !" !! "!! "!! !"" !!! "!!! "" !"!! "! "! !! !!! !! !! !" !! !! "!! !" !"!!! ! "" " !!""!!! ! !! !! " !" ! !! !! ""!! !! " "" !"!! ! !! !! !!"" " """! " !" " "! " !! !! ! !" " "" "! "! ! !! ! !! !"!! !" ! !!!! " "! " !!
The potential of formative assessment to improve learning. Briefly mention the research evidence that sets out the case for formative assessment. This is summarized by Black and Wiliam in several accessible publications for teachers (see p. 2). These researchers set out to find out whether or not improving
--1-- Embedded Formative Assessment By Dylan Wiliam _ Study Guide This study guide is a companion to the book Embedded Formative Assessment by Dylan Wiliam. Embedded Formative Assessment outlines what formative assessment is, what it is not, and presents the five key strategies of formative assessment for teachers to incorporate into their
Performance Assessment Score Feedback Formative 1 Date . Formative 2 Date : Formative 3 Date . Formative 4 Date : Formative 5 Date . Formative 6 Date : Summative Date Implements learning activities aligned to chosen standards and incorporates embedded formative assessment. Clearly conveys objectives in student-friendly language so that the
assessment. In addition, several other educational assessment terms are defined: diagnostic assessment, curriculum-embedded assessment, universal screening assessment, and progress-monitoring assessment. I. FORMATIVE ASSESSMENT . The FAST SCASS definition of formative assessment developed in 2006 is “Formative assessment is a process used
Formative Assessment Best Practices Part I H Gary Cook, Ph.D., WIDA Consortium Elluminate Session, Pennsylvania Department of Education April 28, 2009 WIDA Consortium ELL Formative Assessment 2 Overview Definitions Balanced Assessment Systems Formative Assessment Best Practices ELL Formative Assessment 3 Definitions
assessment professional learning system. They are stepping stones along the path. Part I. Learn About Formative Assessment 1.1 Inventory your comprehensive assessment system. 1.2 Clear up misconceptions about formative assessment. Part II. Plan For Formative Assessment 2.1 Identify elements of formative practice that you do well and those you
FORMATIVE ASSESSMENT Formative assessment is any assessment that is used to improve teaching and learning. Assessment is a three-step process by which evidence is collected, interpreted and used. Best-practice formative assessment uses a rigorous approach in which each step of the
An assessment practice is only truly “formative” if the data is used to inform instructional practice and provide support to ensure student success. To learn more about formative assessment practices, visit the D PI Formative Assessment website, or utilize the Formative Assessment Professional Learning Modules .
Age group: 5–18 Published: September 2014 Reference no: 140157 Her Majesty’s Chief Inspector (HMCI) raised concerns about low-level disruption in schools in his Annual Report 2012/13. As a consequence, guidance to inspectors was tightened to place greater emphasis on this issue in routine inspections. In addition, HMCI commissioned a survey to ascertain the nature and extent of low-level .
