Master Materials List Opening Activity – Assessment .

Mathematics TEKS Refinement 2006 – 6-8ProceduresSlide12The Assessment PrincipleAssessment should become a routine partof the ongoing classroom activity ratherthan an interruption.NCTM’s Principles and Standards for School Mathematics (2000)Slide13TAKS Item 7th Grade 2004Terri collected data on the number of cans donated byeach homeroom in her grade for a food drive. The tablebelow shows the results of the food drive.Which number could be added to theset of data in order for the median andmode of the set to be equal?a. 54b. 63c. 80d. 88Tarleton State UniversityNotesBefore participants try to answer the guidingquestions together, look at the AssessmentPrinciple from the NCTM standards.Assessment should be a routine part, not aninterruption. How can participants do thatbetter? The next activities will giveparticipants some ideas.Here is a TAKS released item from 2004 Seventh grade.Ask participants: Which of the items that welooked at would better prepare students forthis item? Specifically - would thecomputationally more difficult questionbetter prepare students for the curve in thisquestion? Or would the more open ended,higher level thinking question better preparestudents for this question?It is not possible to predict all of the waysthat a TEKS will be assessed.Would higher level thinking questions openthe door for students to at least be thinkingin that direction?Slide14Our focusThink about current classroomassessments How can they improve? Opening Activity – Assessment PyramidAgain, focusing on classroom assessmentitems, raise the question, “How can theyimprove?”Don’t answer this yet.4-7

Mathematics TEKS Refinement 2006 – 6-8ProceduresSlide15Take one typical assessmentWhat is the purpose of the assessment?Where are the items in the pyramid? Are you satisfied with the balance? Tarleton State UniversityNotesHere Trainers could have participantschoose one of their classrooms’assessments (assignments, quizzes, tests)and answer these questions.This could be a group activity where thegroup looks at a common assessment,perhaps a textbook assessment or sharedexam.Trainers could also have each teacherindividually select a quiz he/she has givenand then share with others an example ofan item from 3 different places in thepyramid.Slide16Changing existing questionsto higher leveling reasoningto concept questions maintain balance between concept andskill questions shift focus from what students do notknow to what they do know This is a transition slide to get participantsprimed for the next activity which ischanging and improving items. Slide17Targeted Content 6(10) Probability and statistics. The student usesstatistical representations to analyze data. The studentis expected to: (A) select and use an appropriaterepresentation for presenting and displayingdifferent graphical representations of the same dataincluding line plot, line graph, bar graph, and stemand leaf plot; (B) identify mean (using concreteobjects and pictorial models) , median, mode, andrange of a set of data.Opening Activity – Assessment PyramidNote that the items and discussion will bebased on targeted content - the TEKS listedin the following slides.4-8

Mathematics TEKS Refinement 2006 – 6-8ProceduresSlide188(12) Probability and statistics. The student isexpected to: (C) select and use anappropriate representation for presentingand displaying relationships amongcollected data, including line plots, linegraphs, stem and leaf plots, circle graphs, bargraphs, box and whisker plots, histograms,and Venn diagrams, with and without the useof technology.Additional Areas to Highlight Slide217(10) Probability and Statistics. Thestudent recognizes that a physical ormathematical model can be used todescribe the experimental and theoreticalprobability of real-life events. The studentis expected to: (A) construct samplespaces for simple or compositeexperiments.Targeted Content Slide20NotesTargeted Content Slide19Tarleton State University6(4) Patterns relationships, and algebraic thinking. Thestudent uses letters as variables in mathematicalexpressions to describe how one quantity changeswhen a related quantity changes. The student isexpected to: (A) use tables and symbols to representand describe proportional and other relationships suchas those involving conversions, arithmetic sequences(with a constant rate of change) , perimeter and area.Additional Areas to Highlight 7(5) Patterns, relationships, and algebraicthinking. The student uses equations tosolve problems. The student is expectedto: (B) formulate problem situationswhen given a simple equation andformulate an equation when given aproblem situation.Opening Activity – Assessment Pyramid4-9

Mathematics TEKS Refinement 2006 – 6-8ProceduresTarleton State UniversityNotesSlide22So, let’s look at some ways toimprove Slide23Consider the following: What is the probability of rolling a 1 or a 6 on a dotcube? What is the probability of landingon blue? Create 3 different spinners so that the probability oflanding on red or blue is 3/4.Explain what each number in the ratio means if theprobability of an event is 3/4. This is the alternate set of questions - moreprobability than statistics.Resources: Romberg, Thomas A. ed., Standards-Based Assessment in MiddleSchool: Rethinking Classroom Practice. New York: Teachers CollegePress. 2004Verhage, H., & de Lange, J. (1997, April). Mathematics education andassessment. Pythagoras, 42, 14-20.Opening Activity – Assessment Pyramid4-10

Mathematics TEKS Refinement 2006 – 6-8Tarleton State UniversityActivity:What’s Your Problem?Overview:Examination, discussion, and writing of three types of assessment items:snapshot problems, un-doing problems, and error analysis problems.Materials:Handout 1-Sample Assessment Items-What’s the Difference?(pages 4-25 – 4-26)Handout 2-Three Problem Types Labels, 1 for large group(pages 4-27 – 4-29)Handout 3-What’s Your Problem? Items (pages 4-30 – 4-65)Handout 4-Three Problem Types – How to Write (page 4-66)Blank paperPowerPoint: What’s Your Problem?Copies of the PowerPoint with space for note takingGrouping:Groups of 3Time:1.5 hoursLesson:Distribute the PowerPoint copies to participants to help them focus on theimportant ideas from the PowerPoint presentation as they take notes.Show the PowerPoint presentation What’s Your Problem? Use thefollowing notes pages to elaborate on the content of each slide.ProceduresNotesSlide1What’s Your Problem?Slide2The purpose of this PowerPoint is to giveparticipants examples and experience withalternate problem types.Discuss the disclaimers:Ways to Modify QuestionsGiven limited time Focus on three categories Not the only ones Prompt other methods We only have a limited amount of time.Therefore we are going to focus on threecategories.They are certainly not the only ways to turnlower level thinking, closed questions intohigher level thinking questions – there areother ways for sure, but these are helpfulWhat’s Your Problem?4-11

Mathematics TEKS Refinement 2006 – 6-8ProceduresTarleton State UniversityNotesgeneralities to look at. They are a place tostart.This discussion will certainly prompt othermethods, and that is also one of the goals –to get participants to consider alternatives.Slide3Three Ways to Modify QuestionsUn-DoingError Analysis Snap Shot So, there are three possibilities that will bereferred to loosely as “Un-doing,” “ErrorAnalysis,” and “Snap Shot.” These are nottechnical names, just general descriptors ofbroad categories, again with the intent ofgiving participants alternatives.Slide4Examples of the Three TypesSlide5A Typical Textbook ItemCynthia surveyed the students at her schoolabout their favorite month during the schoolyear. Construct a to display the data.MonthsNumber at’s Your Problem?(Line graph, line plot,circle graph, pictograph,bar graph, histogram,stem and leaf, box andwhisker, Venn diagrams)A typical item - students are given data andasked to represent it with a particulargraph. Do students need to be able to dothis? Of course. What other kinds ofquestions could be asked so that studentswould learn more about representing data?4-12

Mathematics TEKS Refinement 2006 – 6-8ProceduresSlide6Tarleton State UniversityNotesWhat might it look like .Construct a to display the data.MonthsNumber ofStudentsOctober240December360FebruaryMay300420as an Un-Doing problem?Slide7Un-Doing ExampleFind a data set that could berepresented by the below:Have participants briefly discuss thisproblem with a partner or group.In mathematics, we often do something andthen un-do it. We multiply, we factor. Weadd, we subtract. Here, instead of givingstudents data and having them represent itwith a particular graph type, we givestudents the graph and ask them to comeup with the data needed to produce such agraph.What kind of thinking and understanding isrequired to be able to do this?Slide8Un-Doing ExampleFind a data set that could berepresented by each of the below:Here are some more examples of the kindsof graphs students could be given andasked to create the data set. (Note thateach graph does not necessarily representthe same data set.)Have participants briefly discuss. Ask themto consider how a student might thinkdifferently to solve these problems. Whatextra or additional parts about graphs mightbe embedded in this problem, beyond whatstudents had to think about to do theoriginal “make a graph” problem?Did this and the previous example seemmore open? Might this possibly allow theteacher to see a greater variety of solutionsand strategies that when discussed canbuild strength in connecting the differentapproaches? How many different answersWhat’s Your Problem?4-13

Mathematics TEKS Refinement 2006 – 6-8ProceduresTarleton State UniversityNotesare possible for each?If participants do not mention it, ask aboutthe labels on the graphs. How does leavingoff the labels open the question up evenmore?Slide9What might it look like .Construct a to display the data.MonthsNumber ofStudentsOctober240December360FebruaryMay300420as a snap shot problem?Slide10An important issue in graphing is scale.Snap Shot ExampleThese two groups graphed the same data. Whathappened? What could explain the difference inthe graphs?Tom and JerryNumber of VotesNumber of VotesAsh and ctoberDecemberSnap Shot ExampleCameron and Abby were graphing the data and spilled some ketchup ontheir homework. Help them clean it up by filling in the labels.Favorite FebruarySet the stage: In class the day before, twogroups had graphed the same data buttheir graphs looked different because ofscale. This came out in the classdiscussion.Did all students make sense of the changeof scale and its effect on the graph? Here isone way to assess.Another way to open up the discussion is totake a procedure or process and hidecarefully selected parts of it. In this waystudents have to think about someoneelse’s strategies. This is a way to see ifstudents really know what is going on, thereasons for the steps, or if they are stuck inone way of “doing” it.MayMonthWhat’s Your Problem?4-14

Mathematics TEKS Refinement 2006 – 6-8Tarleton State UniversityProceduresSlide12NotesWhat might it look like .Construct a to display the data.MonthsNumber ofStudentsOctober240December360FebruaryMay300420as a error analysis problem?Slide13A technique to help students is todetermine why others might choose anincorrect answer.Error Analysis ExampleChoose the graph to bestrepresent the data below:MonthsNumber y might one choose the other three choices?Slide14Error Analysis ExampleCreate a graph to bestrepresent the data below:Favorite Months500450400350MonthsNumber ents are asked to examine erroneoussolutions and find the error(s). Ask teachersto consider the common errors of their ownstudents. Suggest that instead of only reteaching the correct method, they mightalso consider asking students to analyzethe common errors made in their ownclassrooms.What do you say to Amelia about her graph?Here we see that Amelia put a bar at thevalue in the table for each month andextended the bar out to the month. The bardoes not represent a numerical amount.Slide15TAKS Item (6th grade 2003)Cynthia surveyed the students at her schoolabout their favorite month during the schoolyear. The table below shows the results of thesurvey.What’s Your Problem?MonthsNumber re is a released item from the 2003 6thgrade TAKS. Ask participants to considerthe various problems at which they havejust looked and how these problems mighthave prepared students for this item.Compare the original, typical question’splace on the pyramid with the locations ofthe other questions.4-15

Mathematics TEKS Refinement 2006 – 6-8ProceduresSlide16Slide17Tarleton State UniversityNotesTAKS Item (6th grade 2003)Earlier, rolling diceA more effective discussion of assessmentbegins with a common experience todiscuss. After participants have done theWhat’s the Difference? activity (pages 3-3 –3-12), they can now have a rich discussionabout how to assess it. Ask participants tobrainstorm how they might assess theWhat’s the Difference? activity.The following are several examples ofpossibilities, ranging from low level to midlevel reasoning questions. Ask participantsto generally categorize the problem as UnDo, Error Analysis, Snap Shot or other.(These examples are provided in Handout1-Sample Assessment Items-What’s theDifference?, pages 4-25 – 4-26)This problem can be considered a SnapShot with an un-doing feel - taking a snapshot of the activity and asking students toun-do, or reverse the procedures they did inWhat’s the Difference?. In the game, theyrolled and took away a counter. Here theyneed to determine what was rolled if acounter was correctly removed.What’s Your Problem?4-16

Mathematics TEKS Refinement 2006 – 6-8Tarleton State UniversityProceduresSlide18NotesSnap Shot with an un-do twist.Earlier, rolling dicePB&J played the Remove One game and they got the following line plotXXX0XXXXXXXXXXXX12453Based on their plot, did they rollSlide19Were they paying attention in class? Didthey understand the rules? Can they gofrom the graph to the roll? Why or why not?Error analysis.Earlier, rolling diceCould group 8 have gotten the following line plot? Explain why or whynot?What do the numbers on the line Earlier, rolling diceDesign a line plot so that the following experimental probabilities arerepresented for the differences of rolling 2 dice.p(0) Slide2112231, p(1) , p(2) , p(3) , p(4) , p (5 ) 1010101010In the activity, students rolled dice,removed counters and recordedexperimental probabilities. Can studentsgo backward? Do they understand whatthose experimental probabilities represent?Can they go from one representation toanother?Un-Do.Earlier, rolling diceCreate two different line plots that represent that the experimental probabilityof rolling a difference of 2 was 1/12.What’s Your Problem?This is an open ended item where studentsare asked to create two differentrepresentations, going backward from theexperimental probability to the plot. If theyunderstood where the experimentalprobabilities came from, they should beable to create the scenarios and the plots4-17

Mathematics TEKS Refinement 2006 – 6-8ProceduresSlide22Slide23Earlier, rolling dicePart 2: As A ClassEveryone should have one problem fromthe set Discuss the problems in your group. Decide where the items would best fit. Post your problem Gallery walk - do you agree? Choose one to discuss as a group Tarleton State UniversityNotesError analysis - moving betweenrepresentations.Have participants look at some more itemsto continue to get a better sense of ways toalter and adjust classroom assessment forbetter student learning.Use Handout 2 (pages 4-27 – 4-29) to labelsections of the room as Un-Do, Snap Shot,and Error Analysis.Distribute the problem items (Handout 3pages 4-30 – 4-65), one per person ifpossible. Have participants decide as agroup and post the problem items underpreviously labeled sections of the room(Un-Do, Snap Shot, and Error Analysis).After items are posted, participantsconsider if they agree as they take a gallerywalk. For items they think are postedincorrectly, participants could flag them witha red flag.The purpose here is not so much the threeproblem types, it is more to exposeparticipants to alternative ways to assess.As a whole group, discuss the groupings.Bring out the following points.Un-Doing: Much of mathematics is doingsomething and un-doing it. Many times agreat question to assess if students “got it”when doing something is to ask students toun-do it, to back up from the answer, tocome at it from a different direction orWhat’s Your Problem?4-18

Mathematics TEKS Refinement 2006 – 6-8ProceduresTarleton State UniversityNotesrepresentation.Some of the Un-Doing questions are aspecific type – a creating type. This is afine time to discuss this type that, for ourpurposes, is included in the Un-Doinggroup.Note: In the creating type of Un-Doingquestions, students are asked to create orgenerate different answers. Posingquestions where the answer becomes thequestion opens up the social “space” in theclassroom to allow all students theopportunity to participate and makes themaccountable for the content they arelearning.“Generative design centers on taking tasksthat typically converge to one outcome andturning them into tasks where students cancreate a space of responses.” Stroup,Ares, Hurford, 2005Error analysis: Taking commonmisconceptions and mistakes and puttingthem up front for students to consider andexplain.Snapshots: Taking a snapshot out of themiddle of a process or solution or activityand asking students about it.Slide24DiscussionUn-DoingError Analysis Snap Shot What’s Your Problem?Have groups share out the one or twoproblems they found most interesting orcompelling.Use the red flags, if any, to generate moreconversation about the problems. It is lessimportant if everyone agrees on the type ofitem. It is more important to discuss howthe items assess student thinking.4-19

Mathematics TEKS Refinement 2006 – 6-8ProceduresSlide25Advantages and DisadvantagesGradingConceptual understanding Memorization Tarleton State UniversityNotesIf they have not come up already, brieflydiscuss the advantages and disadvantagesof these kinds of assessment items (Un-

Opening Activity – Assessment Pyramid 4-2 Procedures Notes Slide 2 Assessment Introduce the Assessment Pyramid (adapted from de Lange's Assessment Pyramid.) Note that the pyramid is a graphic that helps identify qualities or properties or dimensions of assessment items. Point out the two primary sections: concepts mathematical skills