Do Students Understand If They Select the Correct Response? Dr. Maria Timmerman VCTM Annual Conference Longwood UniversityMarch 10, 2012

“Rather than continue to complain about how these tests can adversely affect teaching and learning, we thought it better to turn the testing situation on its head– that is, take full advantage of all that multiple-choice testing can offer.” (p. 1) --- Wickett, M., & Hendirx-Martin, E. (2011). Beyond the bubble: How to use multiple-choice tests to improve math instruction.

Think-Pair-Share  What is assessment?  What is the purpose of assessment?

What is assessment? Assessment is the “the process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward mathematics and of making inferences from the evidence for a variety of purposes” (p. 3) ---NCTM (1995). Assessment standards for school mathematics.

Four Purposes of Assessment  Monitoring student progress… promote mathematical growth  Making instructional decisions… improve instruction  Evaluating student achievement… recognize accomplishment  Evaluating programs… modify programs ---NCTM (1995). Assessment standards for school mathematics.

“ Multiple-choice Testing… Filling in the Right Bubble “The assumption is that if a student marks a correct answer—if he or she fills in the right bubble—that student is proficient in the corresponding skill or objective. However, a correct answer can often mask fragile knowledge or misconceptions, or it may have been just a lucky guess.” (p. 1) --- Wickett, M., & Hendirx-Martin, E. (2011). Beyond the bubble: How to use multiple-choice tests to improve math instruction.

“ Multiple-choice Testing… Filling in the Wrong Bubble “If a student marks an incorrect answer—if he or she fills in the wrong bubble—that student is considered to be in need of remediation. But the student may have just misread the problem or made a mistake when selecting an answer.” (p. 1) --- Wickett, M., & Hendirx-Martin, E. (2011). Beyond the bubble: How to use multiple-choice tests to improve math instruction.

“ Improvement in Our Nation’s Schools “These schools succeed not by teaching to standardized tests, but by teaching for deeper, important learning.” (p. 45) - -- Neill, M. (2003). The dangers of testing. Educational Leadership, Volume 6, No.5. Alexandria, VA: Association for Supervision and Curriculum Development.

“ Task: Summer Weekend Travel Using at least two different strategies, show all your work and solve the following problem: Last weekend a gas station sold 2,487 gallons of gas on Saturday and 935 gallons of gas on Sunday. What was the total number of gallons of gas sold over the weekend?

Polya’s Four Phases of Problem Solving  Understand the Problem… Big Ideas  Devise a Plan… brainstorm strategies  Carry Out the Plan… your strategies and models  Look Back… Have you answered the question? Can you solve the problem using a different strategy?

Possible Student Solution Strategies  Predict and write out at least 2 different strategies (correct or incorrect) 2 nd and 3 rd grade students may use to solve the summer weekend travel problem, including the final answer for each strategy.  With a partner, discuss both correct and incorrect final answers students would find; and discuss any student misconceptions related to the solutions.

“ Task: Summer Weekend Travel and Multiple-Choice Responses  Analyze each of the possible responses for this problem. Which response is correct? Which are incorrect? If incorrect, what are the misconceptions embedded in each response? What strategies or models did a student use to arrive at this incorrect response? Did you or your partner predict any of the incorrect multiple-choice answers?  Turn to the new K-3 VA SOL (2009) for all strands, and make a list/highlight any that relate to this summer travel problem.

Moving ‘Beyond the Bubble’… Asking Follow-up Questions  For each response (both correct and incorrect), make a list of follow-up questions that may be asked of students to uncover their understanding and misconceptions.  For example, What is this problem asking you to do? Why does your solution make sense? Which answer choice makes no sense at all? (Also, see Polya questions for each phase)

“ More on the Summer Weekend Travel Problem  Compare your lists of ‘student strategies and misconceptions’ and follow-up questions (conversation starters) to the ones listed. Any surprises or new insights?  Read the student work samples of Tam, Ned, Konner, Bella, and Kara. Without reading the box of information listed below each work sample, write one follow-up question for each of the 5 students, based on their work sample.  Lastly, read and compare your ideas to what is written in the boxes below the work samples.

Construction of Knowledge “If learning is developmental, then it is an impossible goal to get all children to use the same strategy, attain the same understanding, at the same time. Genuine learning takes many paths” (p. 69). --- Fosnot & Dolk (2001). Young mathematicians at work: Constructing number sense, addition, and subtraction. Portsmouth, NH: Heinemann.

Next Steps… Assessment Informs Instructional Decisions  Consider each of these 5 students… Identify and describe different activities/lessons to meet the needs of each student.  Potential resources: New Virginia Curriculum Framework K-3 Math SOL Achievement Record Activities to Undo Math Misconceptions text Marian Small’s Differentiation text Your own classroom activities

Reassessment  Examine some of the Spring 2010 grade 3 VA released test items. Is there a similar item to the weekend travel problem that could be used for reassessment?  Why is this VA SOL test question useful? How successful were your students on this test item? What new insights do you now have related to this test item?  Create 2 reassessment tasks, including 4 multiple- choice responses, for the weekend travel problem: (a) same level of difficulty, and (b) slightly more challenging. Share and discuss with your partner.

“ Task: Analyze Released Grade 3 SOL Test Questions Using poster paper, document the following process: 1. Working with a partner, solve the selected test question; discuss and write down 2 different strategies used to solve the given problem. 2. Predict and write out 1 different incorrect student strategy. 3. Analyze the given multiple-choice responses and discuss student misconceptions; write out how they would find each response. 4. Make a list of all related K-3 SOL for this problem. (new numbers and text) 5. Identify and write out different activities to meet the needs of each student selecting different responses. Create 2 reassessment tasks.

Five Attributes of an Instructionally Useful Assessment  Significance Do my classroom assessments measure genuinely worthwhile skills and knowledge?  Teachability Will I be able to promote my students’ mastery of what’s measured in my classroom assessments?  Describability Can I describe what skills and knowledge my classroom tests measure in language sufficiently clear for my own instructional planning?

Five Attributes of an Instructionally Useful Assessment  Reportability Do my classroom assessments yield results that allow me to tell which parts of my instruction were effective or ineffective?  Nonintrusivenes Do my classroom tests take up too much time away from my instruction? ---Popham, W. James. (2003). The seductive allure of data. Educational Leadership (pp ). Alexandria, VA: ASCD.

Resources  Bamberger, H.J., Oberdorf, C., and Schultz-Ferrell, K. (2010). Math misconceptions: From misunderstanding to deep understanding. Portsmouth, NH: Heinemann.  Bamberger, H.J., and Schultz-Ferrell, K. (2010). Activities to undo math misconceptions. Portsmouth, NH: Heinemann.  Small, M. (2009). Good questions: Great ways to differentiate mathematics instruction. Reston, VA: NCTM.  Wickett, M., and Hendirx-Martin, E. (2011). Beyond the bubble: How to use multiple-choice tests to improve math instruction, grades 2-3. Stenhouse Publishers.