To assess students' learning of statistical terminology, data collection techniques and knowledge of statistical graphing using performance-based assessment

Authentic Performance Task Worksheet
Authentic Performance Task Checklist
Authentic Assessment Rubric
"Data Insights" by Sunburst (or other graphing software) and
Apple computers (or others)
Poster board, markers, protractors, compasses, rulers, index cards,
overhead sheets(if needed), video camera and tapes(if desired)

Students calculate fractions, decimals, percents at least with calculators.
Students correctly use statistical terminology (mean ,median, mode, quartiles, clusters, etc.)
Students make bar graphs, pie graphs, number line plots,
box plots and stem-and-leaf plots with uniform scales and
appropriately labeled axes.
Students can use rulers, protractors and compasses correctly.

1. Pass out Authentic Performance Task Worksheet.
2. Give students time to complete the four open-ended statements in the middle of the sheet. Be sure to encourage them to use appropriate cooperative learning manners, including no criticizing during brainstorming, taking turns speaking and so on.
3. Collect the sheets from each group to read about their ideas for improving the school. On the back of the sheet, provide feedback regarding their idea's importance, uniqueness and ability to be studied in a way that will provide quantitative data. Also comment on the groups' ideas for collecting data, including when might be the best times during the day for surveying or observation of behaviors, who might be good to interview for extra information, what questions might help prove their point, etc.
4. Send a memo to the principal, requesting his/her presence for the day the presentations are planned. This is motivational for students who really care about the topic they have chosen.

1. Pass back Authentic Performance Task Worksheet with your feedback on it. Give students time to discuss your comments and add additional thoughts of their own.
2. Pass out Authentic Performance Task Checklist and the Authentic Assessment Rubric. Read through both of them with the students so that the students understand the expectations.
3. Encourage each group to focus on at least four sets of data that they could collect that will help them create a convincing argument for their improvement idea. Remind them that data can be collected from surveys, from observing certain behaviors, interviewing, measurement, or researching information in an encyclopedia. After you have done this activity in the past, allowing students to see the research that students in previous years have done would also be a way of collecting data.
4. Help each group set up data collection charts for surveys they want to conduct. Make sure that each group member has the same kind of data collection chart. Require them to keep track of the sex and age or grade of each person they survey or interview. This provides more data to make comparisons from later. Also encourage them to find out people's reasons for the responses they give to survey or interview questions. This provides good graphing data as well.
5. Depending upon how much time you have for this whole project, you may want to discuss sources of bias they might face when surveying. Discuss possible problems they might face with the project in general.
6. Encourage students to fill in the "task and responsibility chart" at the bottom of the Authentic Performance Task Worksheet as far as they can. For students who are less self-motivated, you may want to provide specific dates in the "to be done by when?" column.
7. 0n an overhead projector or on the chalkboard, help students get started on the rough draft of their written report. Have them make a rough title page with whatever information you would normally expect to be there and have them use the format you like. Then for the introduction to their report, give them key phrases to begin each paragraph. (Even for my accelerated sixth graders, this was a tremendous help to them. For older students with more writing experience, this might not be necessary.)
   "Our school could be improved in several ways. One of the
   most important ways we thought was by..."
   
   "We think this is important because..."
   
   "We collected data by..."
   
   "The graphs on the following pages will summarize the
   data we collected."
8. Collect these rough drafts of their introductions and provide written feedback again on their revised ideas for improvement of the school and their proposed data collection methods.
9. Students should begin their data collection and should have all the data they need by Day Four.

1. Hand back the groups' introduction rough drafts. Give them time to discuss your feedback. They should also take this time to discuss any data they were able to collect and propose what data collection needs to be completed for Day Four.
2. With the data that was collected, have the students experiment with whatever graphing software you have decided to use. Time for experimentation is extremely important because only now do they start to understand what kinds of data will work for which kinds of graphs. My students needed a great deal of help determining what kinds of graphs would best show certain sets of data.
3. Students should be assigned to come to class on Day Four with all the data they need to prove their point with at least four graphs.

1. Students should go straight to the computers for more experimentation with all of their data on this day. By the end of the period, they should have rough drafts (either computer-made or hand drawn) of all of the graphs they think will help to prove their point best.
2. Have the students take the last 10 minutes of class to analyze each graph. Encourage them to include statistical terminology such as mean, median, mode, extreme values, outliers if there are any, gaps, clusters, quartiles, and ranges. Hopefully, their analyses will make their idea for improving the school seem very worthwhile, wanted and able to be done.
3. Collect the rough drafts of the graphs and the corresponding analyses. Provide written feedback as to the correct use of the terminology, incomplete analysis of any graphs or ways you think the data might be better displayed.
4. Students should be given posterboard and other materials to make hand-drawn graphs at home or to mount graphs made on home computers.

1. Hand back the rough drafts of the graphs and analyses. Give the students time to discuss your feedback, make corrections and decide who will type the final drafts of the analyses and who will prepare the final drafts of the graphs.
2. 0n overhead sheets or on the chalkboard, provide guideline phrases to help students write the conclusion to their written report.(Again, this might not be necessary for older students.)
   "The graphs on the preceding pages show that..."
   
   "Based on these findings, we think that the school could
   be improved by..."
   
   "The school could start making changes by doing...first. And then..."
   
   "We encountered the following problems in collecting our data:..."
   
   "If we were to do this research again, we would do... instead."
   
   "Research on this topic in the future might want to explore..."
3. Students should decide who is going to type the rough drafts of the introduction and conclusion for Day Six. The other students should be preparing the graphs needed for the presentation.

1. Give students 10 minutes to read each other's typewritten parts of the rough drafts and to organize them in the appropriate order with the appropriate graphs and analyses.
2. Collect the entire set of rough draft materials from each group and provide feedback wherever necessary about organization, fluency, conclusions, etc.
3. While you read the rough drafts in class, students should be organizing who will present the introduction, each graph and its corresponding analysis and the conclusion to the class on Day Seven. Give the students index cards on which to write notes for their presentation. Encourage them to quietly practice their presentation with their group members.
4. For the next day, students should decide who will prepare the final draft of the introduction, analyses and conclusion. Students should also decide who will prepare the final drafts of the graphs to be used in the written report and the presentation.
5. Hand back the rough drafts with your comments at least 10 minutes before the end of the period so that the group members can discuss your comments before leaving.
6. If you have time, it would be beneficial to coach the students on good presentation skills, such as making eye contact, facing the audience at all times, avoid swaying, avoid reading word for word, etc.

1. Videotape each groups' presentation if possible. This makes it easier to concentrate on the presentation itself instead of on grading the presentation at the same time. Later, at home, you can play back the tape and check off the appropriate behaviors on the Authentic Assessment Rubric.
2. Another option is to allow the other students to grade each groups' presentation. Simply provide each student with enough blank rubrics for each group except their own.
3. The audience should be encouraged to ask questions.

Attached: Lesson Worksheet
(Click to Zoom "Full Size")

I was extremely pleased with my first attempt to create a real authentic assessment activity. It took a great deal of thought, planning and preparation for each day, beginning with the unit I taught on probability and statistics prior to the start of the project. At first, my students seemed upset to have gotten a topic about school, but they soon realized that they were able to think of legitimate ways their schools could be improved and that others felt the same way. When I told them that I was inviting the principals to hear their presentations, they became very motivated to find convincing data to prove their points. If I had let them choose their own topics, they might not have seen the importance in their research. There may not have been as much authenticity.

I thought that the way I provided them with written and oral feedback on a continuing basis was a good idea. I also thought that giving them key phrases to help them write about their topic was a necessary step, especially with the time constraints we had. I wish that I would have placed a greater emphasis on understanding possible sources of bias in surveying and interviewing. I also wish I would have spent at least a little bit of time teaching the students some basic public speaking skills.

Time constraints caused some aspects of my project to be failures. I know that according to the ASA Quantitative Teaching Principles, statistics should not be taught as a separate unit, but with my regular curriculum, I needed to fit the statistics unit in after a certain chapter. I wish I had done more of the probability lessons earlier in the year when they fit into lessons about fractions, decimals and percents. Then I would have had more time for just statistics in February. Due to the time crunch, my students were required to create a brief written report and an oral presentation in about eight days. They did a great job, but I was a thorn in their sides prodding them through the process at lightning speed. Next year, I think I will have them prepare a written report first, grade it, and then have them present their findings to the class after they receive their reports back. This would take some of the pressure off of them and then they could enjoy the process more.

As with any teacher-made assessment tool, my rubric was not sufficient, despite the many hours I put into its creation. One does not see arubric's deficiencies until after one tries to use it. I have included the original rubric and my revised version which reflects changes in my expectations for my students. The checklist that goes along with the nxbric was useful for some students because it provided more detail that the rubric did not have room for showing. Again, I revised this checklist after assessment of the projects in response to what I learned. This revision is also included.

The survey I created to assess the students interests, attitudes and retainment of knowledge is well-done for the most part. It showed me what I needed to see. Much of the data I collected via this survey could have been used in a portfolio to assess students perceptions before and after the project.

In response to the students' comments on the survey, I need to consider allowing them to pick their own group members. Perhaps they would have enjoyed the project more. I was afraid to allow them to choose their partners for fear someone would get left out, but there was a strong response to the statement about preferring to choose their own partners on the survey (45/59).

Lastly, at the recommendation of all of the principals I work for, I need to find a way to share the students' efforts with others in the district who might have an interest in their findings. One principal suggested encouraging the students to take their ideas to student council meetings or to the school board or to food service management. If the students could be given this opportunity, it would be a great way to really make the assessment authentic.

Demonstration of Interest in the Lesson/Activity and Attitude toward Quantitative Literacy:

The following page contains the results of a survey I conducted with my students who completed the Authentic Performance Task described in my Formal Lesson/Activity Write-Up. The results are quite positive. Of 59 students surveyed, 58 strongly agreed or moderately agreed with the statement "I enjoyed the probability activities [done in class]." Fifty-one students also agreed that they enjoyed learning new ways to graph data. Specifically regarding the Authentic Performance Task, I was pleased to find that 53 out of 59 agreed that they enjoyed applying statistics to the school improvement project. The last two statements for students to consider gave some different results, however. Thirty-five students said that we should spend more time doing SEQuaL activities and 34 students said that they hoped they would learn more about probability and statistics this year. Both of these figures were surprisingly low to me even though both are greater than 50% in agreement.

When asked to make comments and suggestions, many students put that they enjoyed the activities we did and would have liked the school improvement authentic performance assessment better if they had had more time. Listed on the survey summary that follows on the next page are the students suggestions for me to improve the project in the future, not their comments regarding how well they liked the project.

Demonstration of Students' Knowledge of the Quantitative Literacy Topics:

Using a rubric I designed, I graded each of the projects for a variety of characteristics. See attached rtbric. The grade distribution included 41 A's, 16 B's and 1 C. I did not test the students in a traditional way for attainment and retention of material, primarily due to lack of time in the curriculum. Included are the actual rubrics T used to grade my students' projects.

As part of the same survey mentioned above, I had students evaluate themselves for how well they perceived their own understanding of specific concepts. Students placed a 1 next to terms that they thought they knew well enough to explain to others, a 2 next to terms they thought they knew but might have trouble explaining and a 3 next to terms of which they still have little grasp. The results did not surprise me much. Since probability concepts were the first quantitative literacy material I taught and the survey was conducted approximately a month afterward, probability concepts such as frequency and relative frequency had the highest averages at 2.08 and 2.36 respectively. I expected terms such as mean and median to have the lowest averages, but pie graphs was lowest with an average of 1.01, 0.06 below the average for mean and 0.13 below the average for median.

Again on the survey on the next page, I asked students to complete three open ended statements, two of which I had emphasized a great deal during our quantitative literacy lessons and activities and one which I wished I had emphasized more. Apparently, the students misunderstood what I wanted to know in the first question because only 51% had answers which I thought reflected understanding of the question. The second question about the size of a sample was handled quite well to my satisfaction with 80% of the students answering correctly. The last question regarding bias, which I did not address nough during our lessons and activities, was handled reasonably well by 72% of the students. All of he surveys completed by 59 out of my 61 students have been included.

After your group has collected all of its data, the following items will need prepared and your group will be evaluated on each of them. Use this checklist to help your group meet the expectations of a FANTASTIC project.

Written report- 20 points:

__ Typed, double-spaced, placed in report cover
__ Includes title page with group members' names, elementary school,
title of project
__ Defines research problem clearly and specificalty
__ States research methods (how data was collected exactly)
__ Includes collections of data in charts
__ Includes a copy of each survey used if applicable
__ Includes a list of sources from which data was collected if applicable
__ Includes computer print-outs of graphs or hand drawn graphs
used to depict data with all graphs titled, axes labeled,
and uniform scales used
__ Includes an analysis in paragraph form of each graph used
__ States general conclusions based on the findings
__ States recommendations for improvement in the school
__ Describes problems that occurred during the collection or
analysis of the data
__ States ways the research could have been improved, expanded
or done differently
__ Due Thursday, February 29, 1996

Group Presentation-15 points (no longer than 10 minutes):

__ Involves all group members
__ All group members can be heard
__ No one should read word for word, although notecards
for help are permitted
__ States research problem, its importance to the group
__ States the methods used to collect data
__ Summarizes data collected on visual aids with the
following characteristics:

__ Represent data in at least four kinds of graphs, appropriate
for the data collected
__ Each graph is titled, axes should be labeled and all scales
should be uniform
__ Clear, neat and colorful when applicable
__ Able to be seen by the entire class when held at a distance

__ Includes analysis of graphs presented
__ States conclusions and recommendations for improvement
__ Asks for audience cluestions
__ Due on Friday, March 1, 1996

** I can provide report covers, posterboard, crayons, construction paper and other supplies if you need them. I will also be happy to look at rough drafts of anything you write or draw.

Attached: Lesson Rubric
(Click to Zoom "Full Size")

Part One: Circle the number that most closely reflects your feelings.

I enjoyed taking a break from the textbook to do the SEQuaL unit.
I enjoyed the probability activities (globe, m 'n' m's, hop the pond game).
I enjoyed learning new ways to graph data (box plot, stem and leaf plot, etc).
Statistics was easier than I thought it would be.
I enjoyed applying statistics to the school improvement project.
My group worked well together.
I would have liked to work alone better than in a group.
I would have liked to choose who to work with in the group.
I enjoyed learning how to make different kinds of graphs on the computer.
The computer software we used in class ("Data Insights") was helpful.
I learned more about my computer at home because of this project.
Our blue SEQuaL packets had interesting and real-life problems in them.
The amount of homework we had in the packets was reasonable.

Part Two: Make any comments or suggestions here for ways that the project and its requirements could be improved.

Part Three: Put a 1 next to all of the following terms which you could explain to someone else easily. Put a 2 next to all of the following termis which you think you understand, but might have trouble explaining to someone else. Put a 3 next to all of the following terms which you still don't understand well.

Part Four: Complete the following open ended statements.

The use of statistics in an oral presentation or in a written report helps to...

If the sample size of a suevey is not large enough, then the results might...

Bias in research can occur when...