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PSSA Workshop October 25, 2003 8:30 – 12:30 Agenda • Introduction • Multiple-Choice Items • Open-Ended Items • Rubrics & Revisions • PSSA Scheduling Introduction The PSSA is a team effort Team Effort •Review the PSSA practice test to look for … •Where are basic skills tested? •What items are taught at the 8th grade level? •In which 8th grade book are these items taught? Where do all the items on the Practice Test fit?...by grade level Number of Percentage of Grade Level Items Items Elementary 7 9.6% Grade 6 31 42.5% Grade 7 16 21.9% Grade 8 40 54.8% THINK ABOUT THIS!!! Why does the “Percentage of Items” column add up to more than 100% ? Where do all the items on the 2003 PSSA fit?...by standard Standard Description Number of Items Percentage of Items 2.1 Numbers 11 12.9% 2.2 Computation and Estimation 16 18.8% without calculator 7 8.2% with calculator 9 10.6% 2.3 Measurement and Estimation 6 7.1% 2.4 Reasoning and Connections 6 7.1% 2.5 Problem Solving and Communications 3 *** 2.6 Statistics and Data 4 4.7% 2.7 Probability and Predictions 4 4.7% 2.8 Algebra and Functions 17 20% 2.9 Geometry 14 16.5% 2.10 Trigonometry 3 3.5% 2.11 Calculus 4 4.7% ***NOTE: For Standard 2.5, there are 3 open-ended question that each receive 5 points. How do the 2003 items compare to the 2002 items?...by standard Standard Description 2002 Items 2003 Items 2.1 Numbers 7 (8.2%) 11 (12.9%) 2.2 Computation and Estimation 10 (11.7%) 16 (18.8%) without calculator 7 (8.2%) 7 (8.2%) with calculator 3 (3.5%) 9 (10.6%) 2.3 Measurement and Estimation 12 (14.1%) 6 (7.1%) 2.4 Reasoning and Connections 4 (4.7%) 6 (7.1%) 2.5 Problem Solving and Communications 3 *** 3 *** 2.6 Statistics and Data 6 (7.1%) 4 (4.7%) 2.7 Probability and Predictions 9 (10.6%) 4 (4.7%) 2.8 Algebra and Functions 20 (23.5%) 17 (20%) 2.9 Geometry 9 (10.6%) 14 (16.5%) 2.10 Trigonometry 4 (4.7%) 3 (3.5%) 2.11 Calculus 4 (4.7%) 4 (4.7%) ***NOTE: For Standard 2.5, there are 3 open-ended question that each receive 5 points. Students need to be taught to be mathematical thinkers. Multiple-Choice Items Multiple-Choice Items • What is a multiple-choice item and how is it addressed on the PSSA • What topics are in the PSSA toolkit and how are they to be addressed in instruction • Learn ways to address multiple-choice items in your classroom practices • Learn ways to assign multiple-choice practice for homework • Learn strategies for answering multiple-choice items What Is a Multiple-Choice Item? • A multiple-choice math item asks students to choose the correct answer to a problem from 4 choices. PSSA • Each student has 70 multiple-choice items on the PSSA • Each multiple-choice item has a value of 1 point. Calculator Usage • Students are not permitted to use a calculator on the first 7 items. • Calculators are allowed when working on the remaining items. • Students need to be familiar with using the specific calculator before the test! PSSA Toolkit • Topics covered: – Percent of Increase and Decrease – Data Distribution – Inequalities – Geometry – Order of Operations – Transforming Coordinates – Scientific Notation Tips from Teachers • Warm Ups • Classroom Practices • Jeopardy • Homework • Strategies for Multiple Choice Items Time to Share your Tips • What other strategies do you currently implement with your students with which you have found success? Conclusion • A large portion of the PSSA consists of multiple-choice items. Drilling skills and relying on PSSA coach books is not the answer. Using these tools effectively in your classroom is a step towards the answer. Students need to be taught to be mathematical thinkers who feel confident to attack 20 different problems that could cover 20 different topics on all 11 standards. Open-Ended Items Open-Ended Items • What is an open-ended item and how is it addressed on the PSSA • Analyze past PSSA results for open- ended items • Learn tips on solving open-ended items • Learn where to find open-ended items or how to create your own • Learn ways to use open-ended items in your classroom/curriculum What Is an Open-Ended Item? • An open-ended math item asks students to solve a multi-step problem and explain WHY they chose each step. PSSA • Each student has 4 open ended items on the PSSA – 3 on the common form – 1 on the matrix form PSSA • Each open-ended item has a maximum value of 5 points. • Therefore, open-ended items account for approximately 18% of the student‟s PSSA score. • Responses to open-ended items are graded using a rubric. The PSSA Rubric • To earn all 5 points, students need to show each step of their work, and explain WHY they chose each of their steps. • They can earn at least 1 point by showing a correct step toward solving the problem. Calculator Usage • Calculators can be used for all open-ended items on the PSSA • Students need to be familiar with using the specific calculator before the test! Open-ended Results From 2000-2001 percent 0 5 10 15 20 25 30 7 5 Advanced Grade 8 4 satisf 3 almost 11 6 satis 2 partial 20 scores 1 minimal 26 0 no 26 underst 4 Blank State ave Sample 8th Grade Question • Four members of the Johnson family took a trip from Pittsburgh to Harrisburg, a distance of 221 miles. It took them 4 hours and 15 minutes to make the trip. The car required 13 gallons of gasoline at $1.25 per gallon. The turnpike toll was $6.50, and they spent $12.84 for food. What was the average cost per mile based on the total expenses of gas, food and tolls for this trip? (Standards 2.2 & 2.5) The Directions • For full credit, you must do the following: 1. Show OR describe each step of your work, even if you did it in your head (“mental math”) or used a calculator, 2. Write an explanation stating the mathematical reason(s) why you chose each of your steps. The Work 1) $1.25 X 13 gal = $16.25 2) $16.25 + $6.50 + $12.84 = $35.59 3) $35.59 221 mi $0.1610407 4) $0.16 per mile Tips for Solving from Teachers • Use SPEAK UP – S…State the objective – P…Provide background information – E…Explain your strategy without math – A…Add in the math – K…Key in on the results – U…Use the rubric as a guide – P…Provide the standards Tips for Solving from Teachers • Make 2 columns – Put “work” on the left – Put “explanation” on the right work explanation Solving Tips from Teachers • Show and number each step of the work – Even/especially if the work was done in the student‟s head or calculator. Explanation Tips • Encourage students to EXPLAIN their work - not DESCRIBE it – Description: “I multiplied $1.25 and 13 and got $16.25” – Explanation “I multiplied the price of gas per gallon and the number of gallons to get the price for the gas used.” Explanation Tips from Teachers • Make sure ALL steps are explained in words. • Encourage students not to use numbers in their explanations – this will stop them from describing their work. Explanation Tips from Teachers • Use “magic words”* in the explanation. • These are words that gear students to „explain‟ their work rather than „describe‟ it. * Article on “Magic Words” can be found in the math assessment handbook What are the Magic Words? • To find • To get • To figure out • To show • Because • Since • Therefore……. Explanation Tips from Teachers Encourage your students NOT to use the words “to find THE ANSWER” The words “the answer” do not explain what the answer represents. The Explanation 1) I multiplied the price of gas and the number of gallons TO GET the total cost of gas. 2) I added the cost of gas, food and tolls together TO FIND the total cost of the trip. 3) I divided the total cost of the trip by the number of miles and I FOUND the cost per mile. 4) SINCE I had many decimal places, I rounded to the hundredth BECAUSE I wanted money. The Final Product Work Explanation 1) $1.25 X 13 gal = $16.25 1) I multiplied the price of gas and the number of gallons TO GET the total cost of gas. 2) $16.25 + $12.84 + $6.50 2) I added the cost of gas, food and tolls = $35.59 together TO FIND the total cost of the trip. 3) $35.59 221mi 3) I divided the total cost of the trip by the number of miles and I FOUND $0.161041 the cost per mile. 4) SINCE I had many decimal places, I 4) $0.16 per mile rounded to the hundredth BECAUSE I wanted money. Where to Find Open-Ended Problems • ACE Questions from Connected Math • Mathematics assessment handbook www.pde.psu.edu/pssa/mathbook.pdf • Released Items handbook www.pde.psu.edu/pssa/mathrelitems.pdf • PSSA Practice Tests Options for Schools with Money to Spend • “Measuring Up” books 1-800-822-1080 or www.patesthelp.com • “PSSA Mathematics Coach” books 1-800-221-9372 or www.educationaldesign.com • “Continental Press PAM Prep” 1-800-233-0759 • “Exemplars” www.exemplars.com Hints to Creating Your Own Open- Ended Problems • Make sure problems address a standard at or near your grade level. • Make sure all problems require more than 1 step to solve. • Use your students‟ names, other teachers‟ names and your school‟s name to make the problems more interesting to your students. Hints to Creating Your Own Open- Ended Problems • Use the same directions that the PSSA uses at your level (show/describe AND explain) • Use a specific rubric for each of your problems that is based on the general rubric in the handbook • Have students use calculators so they can focus more on the explanation and less on the number crunching. Ways to Use Open-Ended Items in Your Classroom • Put a problem on every test or quiz • Homework • Math journal • Open-ended portfolio….. • DO NOT use only as extra credit Practice, Practice, Practice • Practice should occur the entire year • Open-ended questions should be addressed about once a week • Incorporate these types of questions into ALL grade levels • Open-ended questions are an integrated part of the math curriculum at ALL grade levels Curriculum • Your Goal: – Open-ended items should become a part of your classroom instruction! • NOT just an added activity to do if you have time at the end of the chapter or on days before vacation! Tips for Teachers • Insist that students use correct mathematical vocabulary in their explanations (when developmentally appropriate) • Refer to the “Terms to Know” in the math standards (all grade levels) • Review the formula sheet before taking the PSSA Tips for Beginners • Provide time for students to solve problems individually • Share answers/ideas with partners or in small groups • Discuss as a class Conclusion • Teaching the adopted curriculum as intended will not only help improve your PSSA scores, but will also help improve your students‟ understanding and the ability to communicate that understanding. Rubrics & Revisions Proficiency Level Handbook • Use as a tool to work towards proficiency • Give students specific details of the different expectations for the different performance levels PSSA General Rubric • How can this tool be used in your class? • How can this tool be adapted for better use in your class? • How can this tool be used as a model for the creation of other materials? Introduction to Rubrics • This introduction is a process. • Possible activities: – students can rewrite a rubric in kid-friendly terms – students can create a rubric for a problem – students can score each other‟s work Evaluation & Revision Process • Who should do the evaluation? Teacher Peers Self • What evaluation format will provide the most valuable feedback to the student? • How does the teacher manage the revision process? Rubric for “Taking the PSSA” • What is expected behavior? • Is this an observable behavior? • How will the student‟s PSSA results benefit from this behavior? PSSA Scheduling PSSA Scheduling • It is never too early to plan. • Considerations when creating your school‟s testing schedule: – How many students, teachers, rooms and calculators does your school have? – What has been done in the past? Did it work? – What are your current priorities? – How do you create a schedule that addresses your priorities? – Are your priorities worth fighting for?