MATH DIAGNOSTIC PROJECT

This Math Diagnostic Project is designed to assist high schools prior to the Graduation Test: > to identify specific students who can benefit from additional support; > to identify specific math QCC objectives which need to be re-taught.

This Math Diagnostic Project also offers opportunities for the school staff: > to analyze data; > to discover gaps in the math curriculum; > to work as a professional learning community.

The following documents and materials are needed to perform this project: > QCC math objectives for the graduation test > The four math diagnostic assessments > The keys to the four assessments > Scantron Forms (four per student) > Several “Item Analysis” Scantron forms

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RATIONALE: WHY THIS MATH DIAGNOSTIC PROJECT MAY HELP Secondary schools are struggling as the math bar rises and more rigor enters the curriculum. Many high schools are only in the initial stages of implementing standards-based practices. Data-driven instructional decisions and formative assessment practices are beginning to take root, but currently some high schools are struggling especially in math with several sub-groups. Because the math problems on these diagnostic assessments shed some light down to the objective level of the QCC -rather than just to the strand level –- identification of areas in need of improvement is more specific. Used properly, these short assessments can help school staffs to target objectives which need to be re-taught and to provide interventions for students before the high school graduation test in the spring. Please read the last section of this document (Cautions and Tips) before starting this project. THE MATH DIAGNOSTIC PROJECT AT A GLANCE 1. 2. 3. 4. 5. 6. 7.

Engage a Math Learning Team to conduct the project. Administer the diagnostic assessments to current juniors. Analyze the data to select target students and target objectives. Design and implement instructional interventions. Plug the gaps in the current 6-11 math curriculum. Administer the diagnostic assessments to the current sophomores. Cautions and Tips

1. Engage a Math Project Learning Team to conduct the process. Like most significant undertakings, this project requires a team. The members of the math department, working as a professional learning team, are the best candidates. Make certain to involve any special education teachers who are teaching math. Assistance should be provided as needed from the school leadership team, as well as from the administration. Having a team member with intermediate spreadsheet skills is a must. 2. Administer the diagnostic assessments to current juniors. Decide how to administer the diagnostic assessments to the juniors. Administering them during the students’ math classes on four consecutive days and using the fifth day as a makeup day often works well. Many students will finish the short assessments in 25-35 minutes; other students may take longer. Because this is a diagnostic project, it is very important that the students be allowed to finish all of the problems. If some students do not have a math class during the semester, other arrangements should be made. Copies of the assessments need to be made for the teachers to use in their classrooms. Four Scantron forms (one for each strand assessment) will be needed for each student. Several “Item Analysis” Scantron forms will be needed to tally up the most missed items on each strand assessment. Students should clearly write their names, their math teachers’ names and current math classes on the Scantron form. Also, the students should accurately label the Scantron form for each assessment as “Numbers and Computation, “Algebra,” “Data Analysis,” “Measurement and Geometry.” All of this information will allow opportunities for valuable scanning by courses and teachers later.

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3. Analyze the data to select target students and target objectives. Before beginning the scanning process, a spreadsheet should be prepared. Often the student information for all juniors can be imported directly into the spreadsheet from most student information systems. Assistance should be solicited from the building or system SIS administrator if needed. Obviously, information such as names and sub-groups are very important to include in the spreadsheet. Also columns for each of the four strands (N&C, Alg, DA, M&G) should be inserted. A column for a “weighted average” should also be included. The formula for this weighted column is shown below. Wt. Avg. = ((H3*0.18)+(I3*0.3)+(J3*0.2)+(K3*0.32)) Tweak the formula columns and cells (H3, I3, J3, K3) as needed. Here the columns reflect that the Numbers and Computation section is weighted at 18%; the Algebra section is 30%; the Data Analysis section is 20%; and the Measurement and Geometry section is 32%. Begin the scanning process to score the assessments. The Scantron will mark the sheets with a percentage correct. Record these percentages in your spreadsheet. Use the formula above to get the weighted average. Name Perez, J. Jones, M.

Tcher Class Ethnic SWD Smith Alg I White Yes Cooper Trig Black No

ED No No

ELL Yes No

N&C 84 96

Alg 80 92

DA 70 88

M&G 58 94

Avg. 71 92

When the students’ scores (% correct) are entered for each strand and the weighted averages are calculated, begin the analysis. Obviously, a sort by “weighted average” reveals students who struggled with these particular assessments. A sorting by the “Numbers and Computation Strand” scores may reveal students who are struggling with arithmetic skills. A sorting of the “Algebra Strand” scores may also bring to light students who performed well on more advanced math skills. Never make judgments solely on the basis of one snapshot assessment. Now is the perfect time to “huddle up” with the Math Learning Team to discuss the performances of these students. This learning team should evaluate the validity of the results by using their knowledge about the students’ performances in their classes. Quality discussion and debate within this professional learning team are vital at this point. Sorting by class (such as Algebra I, Geometry, or Concepts of Algebra) and sorting by teacher are also possible when you have the data and information in this spreadsheet format. Selecting the specific objectives to target is also critically important. By running the students’ Scantron forms through, followed by an “item analysis” Scantron form, it is possible to discover the most missed items on each of the four assessments. Since the test items are keyed to the objective numbers, it is easy to determine which objectives need to be re-taught. It is possible to scan by class or teachers to get more specific objective information as needed. The Math Learning Team should again be quite engaged in the process of selecting a few objectives within each strand to target before the math graduation test. When selecting the objectives, keep in mind: > The Measurement and Geometry strand counts the highest percentage (32%). > The Numbers and Computation strand counts the least (18%).

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> Students who struggle on the Algebra section can still pass the graduation test if they do well on the other strands. > Student who struggle on the Numbers and Computation strand often struggle on all of the strands. At this point, the Math Learning Team should have developed a one-page list of the math objectives that will be targeted by the school. Also, by this time, a list of students who can benefit from being re-taught those targeted objectives should be developed. Make sure that the students to be served are all willing and well-behaved participants who will attend school on a regular basis during the reteaching of these objectives. 4. Design and Implement instructional interventions. The Math Learning Team should spend several days collaborating and planning the mini-lessons to use when the intervention process starts. All team members should participate in this design process. Participation by other members of the school staff would be excellent. Keep in mind: >The way the objectives were originally taught was not very successful. > Several sample problems will be needed during the re-teaching. > Hands-on activities often work the best. > Letting students work in pairs is a good idea. > Encouraging students to “draw” to solve the problem is a good strategy. > Listening to students explain their work out loud will be helpful for the teacher and all of the students. > It is important to raise these students’ level of concern, but it is also very important to be positive with them. > Having the students keep their work in a specific folder is a good practice. > Let the students know exactly which objectives are the most missed in the school. Explain the objectives to the students. > This important part of the process should be everyone’s job -- not just one or two teachers. > Students should use the same calculator during this intervention time that they will use on the actual graduation test. > Homework can be used to save time and monitor student effort. > Student grades should not be negatively affected by their work during this re-teaching time. The Math Learning Team, working with the administration, should determine the best time to serve the targeted students. Some schools that are on six-period schedules probably can serve their students in their current math classes. Very often the targeted students will already be in a small number of classes. Schools on block schedules may have to be creative because some of the students may not have math classes. 5. Plug the gaps in the current 6-11 math curriculum. An important part of this project is to discover where the curriculum, instruction and assessment did not work for these students. A simple first step is to take the targeted math objectives and get teachers to “map” where they were likely taught. Those objectives not addressed in the curriculum

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should be incorporated into the curriculum of the appropriate course. This step should also involve middle school math teachers. The time spent on this step will pay big dividends in the coming year. There is no need to have to fill in the same gaps next year. 6. Administer the diagnostic assessments to the current sophomores. To get ahead for next year, a school may choose to use the four assessments with the sophomore class in the spring during the same time that the juniors are taking the graduation tests. This proactive approach will allow teachers to have plenty of time to crunch the data, reflect on the results, and design even better interventions that can be used in the fall. At this point teachers would have more than enough formative data to begin to critically think about their curriculum maps, their instructional practices and their assessment techniques. 7. Cautions and Tips 1. Using these diagnostic assessments simply for practice tests will result in very little, if any, gain in student performance. 2. Scores from these diagnostic assessments should not be used to negatively influence students’ grades. 3. Make the weakest math objectives “public” knowledge at your school, but the scores for individual students should be handled with confidentiality. 4. To scale down this project, assess only a few specific eleventh grade math classes that, in previous years, have had higher percentages of students to score below 516 on the math graduation test. However, using these math assessments with all juniors does provide an opportunity to help more students score at the “pass plus” level. 5. The Algebra diagnostic math assessment does not contain items related to the graphing objectives (Algebra 41-44). See Math Objectives. 6. Don’t stop when you discover the weakest students and the weakest objectives. True professionals will act upon what they know to ensure student success. 7. Schools that have seen gains with these assessments had teachers who were relentless in attacking the weaknesses and were willing to do “whatever it takes” to support the learning of their students. 8. Use the results from this project to patch the holes in your school or system’s “learned” math curriculum. 9. Work to make good formative assessment a frequent event during instruction. It should not be an annual event; it should occur often during every unit. 10. Use this math diagnostic project as an opportunity to work to become an action-oriented professional learning team.

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