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Formative Feedback for Math Problem Solving Accountability ConferenceFebruary 2008 • Mike Gallagher • Math Test and Measurement Consultant • Accountability Services, NCDPI • firstname.lastname@example.org
Opening Activity • SAT Question of the Day – 2008. What thinking do SAT math questions tap? www.collegeboard.com • Achieve, Inc’s report Aligned Expectations, April 2007. SAT’s math emphasis is heavily on understanding and problem solving, beyond routine procedural. www.achieve.org
Purposes Today • Emphasize the importance of problem solving for students now and later. • Highlight the potential of formative assessment feedback for problem solving growth. • Discuss tools and strategies for professional development.
2 Books of Note • G. Polya ... How to Solve It, the book is from the 1950s, but it’s stood the test of time. • R. Stiggins … Student-Based Classroom Assessment, Very readable textbook. Stiggins has done a lot on focusing assessment feedback to the learner.
NC Curriculum (Math 2003SCS) emphasizes problem solving • “Problem solving and reasoning are stressed throughout the goals at each grade level and in every course. … Experiences in problem solving processes should permeate instruction. Problem solving should be integrated early and continuously into each student’s mathematics education.”
Web Pages • Menu Page • Good Strategies Missing • Adaptation of Polya’s Problem Solving Strategy. • Key Classroom Activities • Feedback Sheet • Problem Sources • www.ncpublicschools.org/accountability/testing/eog/math/ • Scroll down to Formative Assessments for Problem Solving
Basics – 1: Start Up • Get students acquainted with Polya’s heuristic, using the web sheet. • Set the target for students: become better math problem solvers. • Explain that they will be getting feedback on problem solving throughout the school year.
Basics – 2: Assessing • Be sure to include “juicy” items in each of your regular assessments or tests. Such items get at problem solving more than procedures. • When reviewing how students did on each assessment or test, give descriptive feedback on problem solving.
Basics – 3: Feedback X & O • Feedback when students have a plan ……… Which steps in the strategy sheet pertain? Mark with an “X” for “executing.” • Feedback when students don’t have a plan …….. Which strategy steps pertain? Mark with an “O” for a magnifying glass to hunt for how.
A Message from the President! * • “NCTM’s Assessment Principle indicates that assessment should not be done to students; rather, assessments are for students and should be used to guide and enhance their learning …” (continued) • *Francis (Skip) Fennell, President of the National Council of Mathematics Teachers (NCTM)
President’s Message (cont) • “Formative assessment involves using classroom-based assessments to collect feedback that can be used to improve teaching and learning.” • From NCTM News Bulletin (December 2006) Complete message on the web at http://www.nctm.org/ … just one page and well worth reading!
Motivation and Testing • Over-use of summative assessment can impair motivation for many students: Some students who frequently get low grades take away a lesson we don’t want to give, that they are unable to learn. • Formative assessment, with emphasis on feedback rather than grades, can help low performers connect hard work with achievement.
Beyond Basics -> Planning to teach students to MAKE A PLAN • Students need to spend some time on each Polya approach to finding a plan. (These are the “O”s on Slide 9) • For example, what are some problems for which “Make a Table” will help? Work on those problems for a week or two.
Examples of “make a table” problems • See attached sheet from Patricia Casey’s Teacher to Teacher handout. • To get Casey’s slides and handout, • Go to www.free.ed.gov/ • Type “problem solving” in the search window. • Then select “4. Teacher Workshops” • Scroll down and select: • We Can Teach Problem Solving
Feedback becomes key for higher-level learning • When it comes to learning, students are the key assessment users: “Am I succeeding? Am I improving over time? What should I do next to succeed? Does my teacher think I am capable of success? Do I think I am capable of success?” • …from Student-Involved Classroom Assessment, 3rd Edition. Richard J. Stiggins, 2001, Prentice-Hall.
Geography: Where are we in assessment land? The test/assessment landscape & Examples Examples Feedback on Criteria PSAT? Peer Assessment SAT Mid- Terms EOG
Assessment for Learning inverts the pyramid of users • Classroom Formative Assessment is Assessment for Learning • For large scale, summative assessment, the key users are often national and state, moving down to teachers. • For classroom formative assessment, the key users should start with the student.
NC math’s great progress • NAEP results from 1992 to 2005 • Compared with the U.S. average and with other states, North Carolina went from back of the pack to ahead of the pack. NC was somewhat sluggish 2003 to 2005. • For the NAEP data in the following slides, go to: • http://nces.ed.gov/nationsreportcard/mathematics/
Fourth Grade NAEP Math Achievement in North Carolina – (National Assessment of Educational Progress)
NAEP Scale Score Averages – A Decade of Great Progress Grade 8 U.S. Average North Carolina Grade 4 U.S. Average North Carolina
NC Math SAT Results • Mean Scores, North Carolina and U.S. • North Carolina • 1992 ……486 • 2006 …………….……….....…513 • United States • 1992 ……………………….508 • 2006 ………………………………518 • Source: www.dpi.state.nc.us/accountability/reporting • Scroll down to “2006 SAT Report”
Are we there yet? • Helping our students become better problem solvers is an important piece of NC making further progress. • Please check and use our web materials: “Formative Feedback for Math Problem Solving” • http://www.ncpublicschools.org/accountability/testing/eog/math/ • … Follow the link under Test Resources
NAEP Scale for Grade 4 • 282 – Advanced • 249 – Proficient • 241 – North Carolina in 2005 • 237 – United States Average in 2005 • 219 – United States Average in 1992 • 214 – Basic • 213 – North Carolina in 1992
Try it! Formative Assessment for Higher-Level Thinking • “Students who participate in the thoughtful analysis of quality work, so as to identify its critical elements or to internalize valued achievement targets, become better performers. When students learn to apply those standards so thoroughly that they can confidently and competently … more
Higher-Level (cont) • … evaluate their own and each others’ work, they are well down the road to becoming better performers in their own right (Stiggins, p. 25) • Good papers to read and other resources at Stiggins’ ATI website: • http://www.assessmentinst.com/
Going Deep • Paul Black & Dylan Wiliam, Assessment and Classroom Learning, Assessment in Education, Vol. 5, No.1, 1998, pp 7-71. • This is a literature review. The teachers in these projects saw strong, positive effects, both in achievement and motivation, especially for students starting at lower levels.
Conclusion • Balance Assessment of Learning with Assessment for Learning. • Balance emphasis on algorithms with emphasis on heuristics.
Next Steps • Use and share the Problem Solving Strategy sheet and the Key Classroom Activities sheet. • Encourage formative assessment with feedback that transfers to problem solving strategies. • At home: Students discuss & explain math problems and puzzles.