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Related research to help your planning for this module. Black P Wiliam D 1998 Inside the black box raising standards. through classroom assessment King s College London School of. Now published by GL Assessment http shop gl assessment co uk. This short booklet offers a summary of the extensive research. literature into formative assessment It shows that there is clear. evidence that improving formative assessment raises standards and. offers evidence showing how formative assessment may be. improved This booklet is essential reading for all teachers. Black P Harrison C 2002 Working inside the black box Assessment. for learning in the classroom King s College London School of. Now published by GL Assessment http shop gl assessment co uk. In this booklet the authors describe a project with teachers in which. they studied practical ways of implementing formative assessment. strategies and the effect this had on learning The section on. feedback and marking pp 8 9 are particularly relevant to this. Black P Harrison C Lee C Marshall B Wiliam D 2003, Assessment for learning Putting it into practice Buckingham Open. University Press, This book gives a fuller account of the earlier booklets Inside the. black box and Working inside the black box It discusses four types. of action questioning feedback by marking peer and self. assessment and the formative use of summative tests The section on. feedback and marking pp 42 49 is particularly relevant to this. module while the section on peer and self assessment pp 49 53 is. relevant for the next CPD module, Hodgen J Wiliam D 2006 Mathematics inside the black box King s. College London School of Education Now published by GL. Assessment http shop gl assessment co uk, This booklet applies the above findings specifically to Mathematics. It considers some principles for Mathematics learning choice of. activities that promote challenge and dialogue questioning and. listening peer discussion feedback and marking and self and peer. assessment This booklet is essential reading for all mathematics. PD Module Guide Formative Assessment 2,Activity A Introducing formative assessment.
Minimum 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 motivate. students to select students for classes to maintain records to keep teachers and parents informed of. progress 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 for. promotion and certification Most high stakes tests and external examinations are designed for. this purpose Summative assessment is also used to evaluate the relative effectiveness of a. particular course teaching method or even an institution. Formative assessment to recognize achievements and difficulties at the beginning or during a. course so that teachers and students can take appropriate action This type of assessment forms. an 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 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 formative assessment improves learning. We checked many books and nine years worth of more than 160 journals and earlier reviews of. research This process yielded 580 articles or chapters to study We prepared a review using material. from 250 of these sources All studies show that strengthening formative assessment produces. significant and often substantial learning gains These studies range over ages across several. school subjects and over several countries Black and Wiliam 1998 1. This 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 Guide Formative Assessment 3, Activity B Teachers own experiences of formative assessment.
Minimum time needed 10 minutes, What do teachers know about their students and what consequential. action 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 the. work very difficult Take it in turns to describe the students strengths and difficulties to your. partner in as much detail as possible, How did you become aware of these strengths and difficulties On what evidence do you base. your judgments Test results Memories of oral responses during lessons Observations of. the 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 Guide Formative Assessment 4. Handout 1 Difficulties in formative assessment Draft Feb 2012. Handout 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 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,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 6 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,D 64 6 2 0 1 26 0 2 2 2 F 2. 93 2 2 2 2 27,2 4 3 6 6 2 D 2 9 2 4 52,0 0F 4 0 0 2 5 4 2 2 2 6 7.
2 0 2 6 1 2 3 2 2 6 2 D,5 6 2 2 2 2 6 H 0 F 0 3 2 2 2 0 2. 6 6 2 D 3 1 7, 1 Black P Wiliam D 1998 Inside the black box raising standards through classroom assessment London King s. College London School of Education,Handouts for Teachers Formative Assessment H 2. PD Module Guide Formative Assessment 5,Activity C Principles for formative assessment. Minimum time needed 20 minutes, Issue participants with a copy of Handout 2 The ideas presented here are all drawn from research into.
formative assessment, Bearing in mind the difficulties discussed in Activity B how would you suggest that your. formative 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 can. a busy teacher know what is going on inside 30 individual. How would you answer this teacher,What strategies do you have for finding out what.
students are thinking in your lessons,Discuss the two suggestions shown on Handout 3. and watch the two Activity C Videos Mini,Whiteboards and Posters to see these in action. Suggest some further strategies for making reasoning. more evident, The two strategies described on Handout 3 and illustrated in the Activity C Videos may help to make. reasoning 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 every. student thinks, During whole class discussions they allow the teacher to ask new kinds of question typically.
beginning Show me an example of, They allow students to simultaneously present a range of written and or drawn responses to the. teacher and to each other, Posters are also a powerful way of helping students to externalize their thinking This use does not. require 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 explaining. the thought processes involved at every step A second use of posters is to find out what they already. know about a given topic In the diagram shown on Handout 2 the teacher asked students to write down. all they knew about y 2x 6 As a class the diagram was developed on the whiteboard Students were. then given a variety of equations the level of challenge was varied appropriately and were asked to. produce their own poster The discussion enabled the teacher to assess how much learners knew about. equations and how well they were able to link the ideas together. PD Module Guide Formative Assessment 6, Handout 2 Principles for formative assessment Draft Feb 2012. Handout 2 Principles for formative assessment,Formative assessment may be defined as. all those activities undertaken by teachers and by their students in assessing themselves which. provide information to be used as feedback to modify the teaching and learning activities in which they. are engaged Such assessment becomes formative assessment when the evidence is actually used to. adapt the teaching work to meet the needs Black Wiliam 1998. Make the objectives of the lesson explicit,01 2 21 3 4 4 4 5 01 2 6 10 1 2 7 2.
0 1 0 2 1 3 3 4 3 52 0 6 4 7 0 4 8,90 1 2 3 3 6 10 0 3 8 0 1 10 4 2 3 3 0 8. 01 2 4 7 3 21 1 33 09 66 4 9 2 2 2 1 021 21 2 2 6,9 4 2 2 1 1 9 6 2 4 4 9 6 8 5 2 69 1 2. 4 2 2 4 2 1 22 2 3 9 2 0 3 2 4 69 97 9,01 2 5 2 8 3 1 9 6 4 4 9 6 2 2 69 2 7 2 5. 01 2 21 46 66 2 2 8,Assess groups as well as individual students. 06 99 4 27 66 02 9 2 21 A0 2 01 2 8 B 7 96 2 9 C,2 2 21 99 A0 597 1 33 09 28.
Watch and listen before intervening, D 3 2 2 2 2 06 1 0 2 21 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. 2 01 2 968, Use divergent assessment methods Show me what you know about. F 2 2 4 2 C 1 7 5 9 21 2G1 4 2 8 B 5,9 1 A0 2 2 1 2 2 01 2 52 021 21 2 1. 6 1 4 2 1 2 8 B 76 3 4 2 4 0 1 2 2 8,H 2 4 2 2 2 2 9 5 2 6 2 A0 2 99 01 2 66 02. 1 21 69 2 25 2 21 2 2 8 B A0 2 99 01 2 0 6 0 G 0 4. 2 6 1 4 2 18,Draft Feb 2012,Handout 3 Making reasoning visible.
Handout 3 Making reasoning visible,Use questioning. Handouts for Teachers with mini whiteboards,Formative Assessment H 3. 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.
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 Teachers Formative Assessment H 5. PD Module Guide Formative Assessment 7, Activity D Analyze students responses to problem solving tasks.
Minimum time needed 20 minutes, Handout 4 presents three problems together with four student responses on each The tasks are Counting. Trees Cats and Kittens Security Cameras, These tasks use a variety of mathematical content but all three focus on the problem solving and. modeling skills described in the Common Core Standards for Mathematical Practice Often such tasks. prove more difficult than the individual elements of mathematical content would suggest as students are. required to choose and combine techniques in non routine ways Traditional summative assessments often. focus on isolated content standards and fail to test these process skills Formative assessment is an. effective 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 School. standards for modeling but also relate to language found throughout the practices and are generally. applicable to most problem solving activities, Read through all three tasks then choose one task that will be most suitable for a class you.
will soon teach If you are working on this module in a group it will be helpful if each. participant 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 or. her capacity to use each of the phases of problem solving formulate reason interpret and. evaluate 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 feedback. would you give them to help them improve their, responses Try to frame this help in the form of oral. questions you could ask in the classroom You may find it. helpful to refer to the generic questions given on. Watch Activity D Video Teachers Discussing,Feedback This shows three teachers discussing the. feedback they gave on the three problems,PD Module Guide Formative Assessment 8. Handout 4 Assessment tasks and Handout 5 Improving students. sample responses,Handout 4 Assessment tasks and sample responses.
Draft Feb 2012,responses through questioning Draft Feb 2012. Handout 5 Improving students responses through questioning. Counting Trees Counting Trees,Sample response Laura. 0 12 2 3 4 1 14 5 1 5 6 2 0 3 1,2 5 2 17 58 9 2 66 0 5 2 1 1 0. What questions could you ask Laura that would help her improve her response. Sample response Jenny,4 1 1 5 2 2 1 1 0 4 5 2 12 1 0 2. 6 1 4 0 38 9 5 6 1 3 3,2 2 1 0 8 9 2 3 7 66 0 2 00 0 12 2.
What questions could you ask Jenny that would help her improve her response. 2 23 3 3 4 5 1, 6 4 0 2 47 8 95 4 53 6 3 2 5 338 Sample response Woody. 94 1 24 1 0 3 6 1 2 6 0 12 2 4 5 8 1 1 4 AB C 10 0 BD. 6 1 E 0 2 0 1 8,1 2 53 5 5 9 0 0 2 47, 73 4 5 053341 What questions could you ask Woody that would help him improve his response. 1 A 4 5 6 8 5 4 5 5 9 0B,Sample response Amber,F 6 7 1 2 6 5 3 5 1 3 8 9 6 6 14. 1 58 9 6 6 3 5 1 5 4 6 5 5 8 3 61 2,Handouts for Teachers Formative Assessment H 6. What questions could you ask Amber that would help her improve her response. Handouts for Teachers Formative Assessment H 16,6 Suggestions.
for questions,6 Suggestions for questions,012 3422 5 6 74 50 1. 8 23 05 3 9078 45 3 A5 803 30 05 B,8 4 5 94 50 1 5C D 45 72 3 2E 5 803 F 5AG29B. 0 5 8 2D8 0 23 9078 A2 32 G 82 2B,15 50 1 16 8 35 5 E0 7 9 9078 A2 82GF GB. 5 1094 H 45 0 12 309FG2 5 05 5 803B,5C D 45 309FG0 4 803 F 5AG29B. 01 2 8 03 5C E C8 03 5C B,8 33 9F 05 3 9078 45 9 2B.
82 2 8 12 45 322 3592 80 7 G0 2 803 A2 5 2B,8 03 0I2E 82 2J E C8 D 45 D8 72B. 8 03 82 3 92 E C8 03 E0 2 2 82 2B,8 C5 GE 8 FF2 0 K D8 72E 803LL 5 803LLLB. K3 803 FF 5 D8 750 7 4C82 2B,1 20 1 5 4 5,8 C0GG 45 E5 C82 45 72 8 3C2 B. 5 16 24 15,M803 03 N 3 3F2D0 G D 32 5 LLL C8 B,H 45 5 9 4 84F5 82323B. H 45 80 5 4 D5 2 2I 9FG23B,01 31 21 4,8 903 23 8 12 45 9 E2B.
H 45 3 7723 E0 2 2 C 4 5 E50 7 803B,8 D5 DG 305 3 D 45 9 2 59 803 E B. 5C D 45 D82D 803 D GD G 05 C0 85 E50 7 0 GG 7 0 B,8 03 32 30AG2 C 4 5 2D5 E 803B. 5C D 45 A23 E03FG 4 45 E B,K3 0 A2 2 5 32 803 4F2 5 D8 5 8 5 2B 84B. 15 5 16 4 5 8 F 2 3 D 45 322 0 803 E B,4 5 5 01 6 8 2 35 3 9078 82 2 A2 5 8232 F 2 3B. H 45 7012 92 D5 10 D0 7 7 92 5 8 3 292 B,01 51 21 41 61 5 45 80 8 3C2 03 2 35 AG2B 84B.
7 5C D 45 A2 O 3 2 8 03 2B H5 10 D2 92P,8 E5 45 80 5 Q 2R3 7 92 B 84B. 80D8 92 85E 9078 A2 A23 5 32 82 2B 84B,8 92 85E E0E 45 32B. 8 5 82 92 85E3 8 12 45 D5 30E2 2EB,80D8 5 45 92 85E3 C 3 82 A23 B 84B. 410 5 16 5,80D8 92 85E C 3 82 0D 23 B,82 2 8 12 45 322 F 5AG29 G0 2 803 A2 5 2B. 8 92 85E3 E0E 45 32 G 3 092B 5 GE 824 8 12 C5 2E,8 82GF G 3 27023 8 12 45 G2 2E 5 2I 092B.
012 30 4 5 65 0 78 9,PD Module Guide Formative Assessment 9. Activity E Observe formative assessment in action,Time needed 15 minutes. In this activity you are provided with video extracts of Andrew Dominic and Amy exploring how. formative assessment may be used to promote students learning They are using the three tasks from. Activity D, In an earlier lesson these teachers had asked students to sit in different places and attempt one of the tasks. individually with no help They then collected in their students responses assessed the work. qualitatively and prepared written feedback in the form of questions The film clips you are about to see. are taken from the follow up lesson Students have returned to their normal places and most have. solutions that are different to those of their partners. Watch Activity E Video Observing Formative Assessment. and consider,What different kinds of assessment can you see. What is the purpose of each kind of assessment,What do both the teachers and students learn.
In the video you will see, Andrew exploring how students respond to his feedback on the counting trees problem. Amy listening to then questioning individuals as they try to share their ideas and produce joint. solutions to the security camera problem, Dominic listening to presentations from students on their methods and reasoning for the cats and. kittens problem, Amy concluding her lesson by asking students to describe how they have used her feedback to. improve their work,PD Module Guide Formative Assessment 10. Activity F Plan and report back on an assessment lesson. Minimum time needed 30 minutes before the lesson,20 minutes for the pre lesson assessment.
30 minutes to prepare feedback,60 minutes for the lesson. 15 minutes for reporting back,Planning the lesson,Plan your own lesson using one of the problems. Plan a time for students to tackle the problem on their own. without help, Plan how you will assess this work give feedback and. Andrew s lesson,conduct a follow up lesson, Collect samples of students work to show how their. thinking has changed These will be discussed during the. follow up session, To help with your planning you may now like to watch one of the Dominic s lesson.
three 10 minute Activity F Videos showing Andrew Dominic and. Amy teaching the three problems from Activity D They are each. following the lesson plan on Handout 7,Amy s lesson. The pattern of activities on Handout 7 is as follows. Give the problem before the lesson and ask students to attempt it Handout 7 A formative. 20 minutes assessment lesson plan Draft Feb 2012,Handout 7 A formative assessment lesson plan. Collect in the work and prepare some constructive qualitative 01 2 3 2 4331 40 4 154 6 4 5 31 2 5. 6 7 8 41 6 4 0 4 0 409 4 31 2 5 4 2 7 6 4 0 4 0,4 1 9 4 4 37 2 4 154 6 0. feedback 0 42 14 1 0 1 19 4 1 531 6 7,Before the lesson 20 minutes. In the follow up lesson reintroduce the problem to the class. 1 3 1 43 4 4 31 6 4 9 4 53 4 5,4 9 0 1 1 2 3 4 1 7 8 54 04 0 4 1.
3 0 1 1 4 41 343 17,5 minutes 5 4 5 6 78 3 298 78 4 6 5 43 5 8. 6 88 7 8 65 25 7 4 5,5 4 3 6 3 298 5 78 4 3 25,5 4 3 7 4 5 5 6. Students work alone responding to the feedback using mini. A 6 3 3 2 B 3 5 7 2 C 4 8 25 8 5,49 1 4 41 45 41 0 31 2 57. whiteboards 5 minutes,A 3 9 6 65 8 E,F 6 8 4 8 E, Students work in pairs to improve their solutions 10 minutes F 6 4 5 5 4 8 4 5 8 E. 5 4 73 2 25 3 2 8 5 B 5 2 3 5 3 2 5 B, Students share their approaches with the class 15 minutes 9 5 2 B 3 7 65 5 3 5 B 3 2 3 65 5 5 4.
C 8 2 5 4 8 2 6 8 2 GHHH 2 IJ 4 5 E,B 4 2 7 2 9 5 6 88 5 8 3 2. Students continue with the problem or extend the problem 20 0 1 2 3. F B 3 B 2 3 2 4 5 7 E K5 8 9 8 9 E, 1 4 4 3 8 9 8 9 2 4 88 7 5 8 9 4 88 5 4 5 5 3 4 3 7 D 7 4 3. 6 B 8 5 2 4 5 78 4 2 5 5 5 LMHN,minutes 5 6 5 6 8 B 6 5. 5 4 6 8 9 6 5 5 4 7 B,5 8 8 2 28 8 5 5,O 4 47 5 6 3 6 9 C 2 65 3 653. 0 1 19 4 31 6 0 1 0 6 4 4 6 2409 7 0,Reporting back on the lesson.
9 4 1 4 A 4 P 5 4 2 8 Q 2 2 4 47 B C 6 14 0 1 1 6 D E1. 83 2 1 197 F 0 2409 0 4 G,Handouts for Teachers Formative Assessment H 20. After you have taught the lesson reflect on what happened with a group of colleagues. Take it in turns to share stories of the assessment strategies you used. How did you collect and assess evidence of your students work. What did you learn from this evidence,What did students learn from the follow up lesson. What are the more general implications for your Mathematics teaching. PD Module Guide Formative Assessment 11, Activity G Consider the effects of feedback on student learning. Time needed 20 minutes, So far we have focused on the teachers role in providing assessment feedback to students In this activity. we will consider the use students make of different types of feedback and the impact this has on their. Watch Activity G Video Student s Views showing, Andrew s students as they discuss the impact of assessment.
feedback on their learning, Which of their comments strike you as particularly. perceptive and important,What are the implications of their comments. Handout 8 presents some results of research from Black and Wiliam into the relative merits of feeding. back assessment information to students in different forms In particular it compares the effects of feeding. back quantitative information in the form of marks levels and rankings with the effects of offering. qualitative information in the form of specific content focused feedback. Compare the students comments with the research quotes given on Handout 8. The dangers of giving marks levels rewards and rankings. What are the implications of this for your practice. What would happen if you stopped giving marks or levels on pupils work. Why are so many teachers resistant to making this change. The advantages of giving clear specific content focused feedback. What are the implications of this for your practice. Does this kind of feedback necessarily take much longer to give. Research shows that students benefit most from feedback that. Focuses on the task not on grades or scores,Is detailed rather than general. Explains why something is right or wrong,Is related to objectives. Makes clear what has been achieved and what has not. Suggests what the student may do next,Offers specific strategies for improvement.
Conclude this module by discussing some ways of applying what you have learned in this PD module. to the other mathematics lessons that you teach, How could you involve pupils in improving your assessment practices. PD Module Guide Formative Assessment 12, Handout 8 The effects of feedback on student learning Draft Feb 2012. Handout 8 The effects of feedback on students learning. 0 1 2 0 3 4 15 6 3 0 27 89 2 2, The dangers of giving marks levels rewards and rankings. 0 1 2 34 1 52 4 1 6 78 7 7 98 42,6 68 9 0 8 9 1 8 8 4 0 8. 9 4 6 1 8 0 8 2 6 68 81,18 8 9 6 1 8 1 4 98 4 3 84 0 5 A.
9 8 8 B 68 0 18 8 8 1 6,1 8 9 8 8 2 1 8 8 1 8 8 18 8 8 1 8. 0 8 1 4 1 C 3 8 52 81 8 8 4 8,8 4 0 8 1 1 18 66 8 2 1 8 1 6 8 7 8 0. 8 84 7 8 1 0 8 2 8,6 0 37 1 2 2 0 90 70 1 1,6 9 77 9 2 77 3 052 0 2 797 2 05. 6 0 2 3 1 02 0 2 2 3 5 2 1, The advantages of giving clear specific content focused feedback. 8 1 1 8 2 9 1 8 8 E 8,6 0 0 6 8 8 8 8 1 8 84 0 8 8 6 6 68 2 8.
48 6 8 4 1 08 0 8 0 8 6 8 8 6 08 8,0 92 1 48 1 18 4 0 8 0 4 1 8 4 6 8 4 8. 84 B 68 6 1 0 9 08 4 2 6 81 1 1 1,8 8 2 6 8 8 1 6 8 08 F 2 4 1. E 1 9 6 68 1 6 8 8 8 8 0 92 08 1 8 0,1 8 6 2 1 1 81 6 8 08 6 68. 6 0 37 1 2 2 0 90 70 1 1,2 2 5 A 15 1 22 0 5 391 0. 4 15B CDB E 6 3B D FGHHIJD F 81 9 DG 8 8 4 1 1 4 H 1 G. I8 4J K 4 H 1 C L1 8 MNNO,Handouts for Teachers Formative Assessment H 24.
PD Module Guide Formative Assessment 13, Further Materials MAP Formative Assessment Lessons. The Mathematics Assessment Project has produced a suite of. Having Kittens Teacher Guide Alpha Version August 2011. 1 Modeling Having Kittens, Formative Assessment Lessons based on the principles discussed here 2 Mathematical goals. This lesson unit is intended to help you assess how well students are able to. Each lesson provides materials and comprehensive guidance for. 4 Interpret a situation and represent the constraints and variables mathematically. 5 Select appropriate mathematical methods to use,Make sensible estimates and assumptions. teaching a lesson on a particular topic, 7 Investigate an exponentially increasing sequence. 8 Communicate their reasoning clearly,9 Common Core State Standards.
10 This lesson involves a range of mathematical practices from the standards with emphasis on. 11 1 Make sense of problems and persevere in solving them. 12 2 Reason abstractly and quantitatively, Concept development lessons aim to strengthen students understanding 13. Construct viable arguments and critique the reasoning of others. Model with mathematics,Use appropriate tools strategically. of a specific topic and help them connect it with their other 16. This lesson also asks students to select and apply mathematical content from across the grades including the. content standards,Quantities,Linear Quadratic and Exponential Models. mathematical knowledge Problem solving lessons focus on improving 20. S IC Making inferences and Justifying Conclusions,Introduction. 22 This lesson is designed to help students develop strategies for solving a modeling problem. students ability to apply mathematical practices as they work together 23. Before the lesson students attempt the problem individually You then review their work and. formulate questions for students to answer in order to improve their solutions. 25 At the start of the lesson students individually answering your questions about the same problem. to improve their initial responses to a problem 26. Students are then grouped and engage in a collaborative discussion of the same task. In the same small groups students are given sample solutions to comment on and evaluate. In a whole class discussion students explain and compare the alternative solution strategies they have. 29 seen and used,30 Finally students review what they have learned.
31 Note that a video of this lesson is available in the professional development materials. Materials required,A typical lesson unit comprises 32. Each individual student will need a calculator and a copy of the assessment task Having Kittens and. the questionnaire How Did You Work, 35 In the main lesson each student will also need a mini whiteboard and an eraser. An assessment task for students to attempt before the main 36. Each small group of students will need copies of the Sample Responses to Discuss and a large sheet of. paper for making posters and felt tipped pens, Graph paper should be kept in reserve and used only when requested. There are also some projector resources to help you with whole class discussions. Spreadsheet software might also be helpful if available. Time needed, Teacher notes describing common issues seen in student work 42. Approximately twenty minutes before the lesson a ninety minute lesson and ten minutes in the next lesson or. for homework Timings given are only approximate Exact timings will depend on the needs of the class. 2011 MARS University of Nottingham 1, on the assessment task and suggesting formative feedback in Having Kittens Teacher Guide Alpha Version August 2011.
45 Before the lesson,the form of questions 46,Assessment task Having Kittens 20 minutes. Have the students do this task in class or for homework a day or more before the formative assessment lesson. This will give you an opportunity to assess the work and to find out the kinds of difficulties students have with. Collaborative learning activities to help students develop their. 49 it You will then be able to target your help more effectively in the follow up lesson. Having Kittens Student Materials Alpha Version,Give out the task Having Kittens Having Kittens. understanding of the mathematics contained in the task and to This is a poster made by a cats charity. encouraging people to have their cats spayed so, they can t have kittens The activity is about what. Here is a poster published by an organization that looks after stray cats. expose and challenge common misunderstandings Typical happens if you don t have your cat spayed and. whether the statement on the poster is correct,Is it realistic that one female cat would produce. Cats can t add but,they do multiply, activities include 2000 descendants in 18 months In just 18 months this female cat.
can have 2000 descendants,You are given some facts about cats and kittens. that will help you decide, o Classifying mathematical objects challenging Work out whether this number of descendants is realistic. Here are some facts that you will need,Make sure your cat cannot have kittens. definitions,o Interpreting multiple representations. o Evaluating conjectures and assertions,2011 MARS University of Nottingham S 1.
51 It is important that students are allowed to answer the questions without assistance as far as possible. 52 Students who sit together often produce similar answers and then when they come to compare their work they. o Modifying situations exploring their structure, 53 have little to discuss For this reason we suggest that when students do the task individually you ask them to. 54 move to different seats Then at the beginning of the formative assessment lesson allow them to return to their. 55 usual seats Experience has shown that this produces more profitable discussions. o Critiquing supplied examples of other students work 56. Assessing students responses, Collect students responses to the task Make some notes on what their work reveals about their current levels of. understanding and their different problem solving approaches The purpose of doing this is to forewarn you of. 59 issues that will arise during the lesson itself so that you may prepare carefully. A follow up assessment task closely related to the original 60. We suggest that you do not score students work The research shows that this will be counterproductive as it. will encourage students to compare their scores and will distract their attention from what they can do to. improve their mathematics, task in which students re engage with the original challenge 63. Instead help students to make further progress by summarizing their difficulties as a series of questions Some. suggestions for these are given on the next page These have been drawn from common difficulties observed in. trials of this lesson unit, 66 We suggest that you write a list of your own questions based on your own students work using the ideas. 67 below You may choose to write questions on each student s work If you do not have time to do this just select. 68 a few questions that will be of help to the majority of students These can be written on the board at the. Each lesson comes with a comprehensive lesson plan including whole 2011 MARS University of Nottingham 2. Having Kittens Student Materials Alpha Version August 2011. class introductions and discussions group and individual work and Sample Responses to Discuss Wayne. further suggestions for probing questions and formative feedback. The three tasks in this module appear in the lessons. Modeling Having Kittens High School,Estimating Counting Trees Middle School.
Optimizing Security Cameras Middle School, The lesson units are available2 from http map mathshell org. More about the pedagogical issues arising from these lessons can be What has Wayne done correctly. What assumptions has he made,How can Wayne s work be improved. found in PD modules 2 and 3,2011 MARS University of Nottingham S 3. 2 Having Kittens and Counting Trees are currently available to Math Development Collaborative partners but will be publicly. released in early 2012 Security Cameras is under development and will appear later in 2012.

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Join us and register now at WWW.SPLINTERCELL

Join us and register now at WWW SPLINTERCELL

As a Splinter Cell, an agent of Third Echelon, the NSA's most secret subgroup, Sam Fisher has been trained to secure his country's defence by mounting a good offence. In addition to their weapons and hand-to-hand training, Splinter Cells use the latest high technology and espionage techniques to infiltrate sensitive locations, retrieve information, and execute operations the U.S. government ...

Preparation for College - Newport News Public Schools

Preparation for College Newport News Public Schools

take the math placement test regardless of standardized test scores. These courses are generally These courses are generally offered at the Governor's School for Science and Technolog y.

Modeling of Hydraulic Turbine and Governor for Dynamic ...

Modeling of Hydraulic Turbine and Governor for Dynamic

an IEEE working group [8] and Kundur [9]. The overall block diagram of the Hydraulic Turbine with governor [13, 15], servomotor and synchronous machine is shown in Fig. 1. 2. MODELING OF A HYDRAULIC The model is comprises of single penstock and turbine without surge tank. The hydro turbine model is designed from penstock and turbine characteristic differential equations [8, 10, 11, 12]. The ...

Masturbation and Discourse on Female Sexual Practices in ...

Masturbation and Discourse on Female Sexual Practices in

Female Sexual Practices in Early Modern Japan 3 the blame for our current conflicted attitudes regarding masturbation more on the eighteenth-century Enlightenment than on Judeo-Christian medieval theology.7 The distance between self-help manuals that promote guilt-free masturbation, such as Sex for One: The Joy of Self-Loving,8 and the 1994 forced resignation of Joycelyn Elders ...

Key Components of the Pay for Success Feasibility Process

Key Components of the Pay for Success Feasibility Process

Key Components of the Pay for Success Feasibility Process In the development of a Pay for Success (PFS) Initiative and the feasibility technical assistance process, there is a series of key components related to actions that need to be completed and decisions that need to be made by the core project team charged with design and implementation in order for the PFS initiative to move forward ...

Director Sales Operations Job Description

Director Sales Operations Job Description

This report relies upon data obtained from many sources, however, and The Sales Management Association is not engaged in rendering legal, accounting, or other professional services. Its reports should not be construed as professional advice on any particular set of facts or circumstances. Members requiring such services are advised to consult an appropriate professional. Neither The Sales ...

TEST BOOKLET - Careerindia

TEST BOOKLET Careerindia

Please note that it is the candidate's responsibility to encode and fill in the Roll Number and Test Booklet Series Code A, B, C or 13 carefully and without any omission or discrepancy at the appropriate places in the OMR Answer Sheet. Any omission/discrepancy will render the Answer Sheet liable for rejection. You have to enter your Roll Number on the Test Booklet in the Box provided alongside ...