Problem Solving and SES

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This is a narrated slide presentation that reports on Dr. Lubienski's study of 7th-graders' experiences with a problem-centered curriculum, analyzing dependency on Socio-Economic Status (SES).
Summary of Results:
(1) “Higher SES students tended to display confidence and solve problems with an eye toward the intended mathematical ideas”
(2) “Lower SES students preferred more external direction and sometimes approached problems in a way that caused them to miss the intended mathematical points”

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Problem Solving and SES

  1. 1. RESEARCH REPORT: “PROBLEM SOLVING AS A MEANS TOWARD MATHEMATICS FOR ALL: AN EXPLORATORY LOOK THROUGH A CLASS LENS” DEC 7, 2010 Alan Mitchell, Urban Teacher Resident CUNY-Hunter College, School of Education MATH 635, Problem Solving - Prof. Sandra Clarkson
  2. 2. AGENDA <ul><li>Overview </li></ul><ul><li>Study Background </li></ul><ul><li>Example Results </li></ul><ul><li>Summary of Results </li></ul><ul><li>Epilogue: Researcher’s Caveats </li></ul>
  3. 3. OVERVIEW <ul><li>Dr. Lubienski studied 7th-graders' experiences with a problem-centered curriculum, analyzing dependency on Socio-Economic Status (SES) </li></ul><ul><li>Abstract - Summary of Results </li></ul><ul><ul><li>“ Higher SES students tended to display confidence and solve problems with an eye toward the intended mathematical ideas” </li></ul></ul><ul><ul><li>“ Lower SES students preferred more external direction and sometimes approached problems in a way that caused them to miss the intended mathematical points” </li></ul></ul>Ref. Sarah Theule Lubienski, “Problem Solving as a Means Toward Mathematics for All: An Exploratory Look Through a Class Lens”, National Council of Teachers of Mathematics (NCTM), www.nctm.org , Journal for Research in Mathematics Education (JRME), July 2000, Volume 31, Issue 4, Pages 454 - 482
  4. 4. STUDY’S BACKGROUND: THE CONNECTED MATH PROJECT (CMP) <ul><li>NCTM argued that problem solving should become the focus of math in school </li></ul><ul><li>NSF funded CMP, a middle school curriculum development to create problem-centered materials aligned with NCTM “reform” standards </li></ul><ul><li>CMP emphasizes problem solving as a means to learn math content and processes, not as an end in itself </li></ul><ul><li>Key: </li></ul><ul><li>NCTM – National Council of Teachers of Mathematics </li></ul><ul><li>NSF – National Science Foundation </li></ul>
  5. 5. STUDY’S BACKGROUND: THE RESEARCHER <ul><li>From working class family – believes math can help break lower SES cycle of poverty </li></ul><ul><li>Held masters in math and secondary math teaching certificate </li></ul><ul><li>Was completing doctoral program, studying the theories underlying the NCTM reform </li></ul><ul><li>In third year with CMP, functioning in dual role for a year as CMP pilot teacher and researcher </li></ul>
  6. 6. STUDY’S BACKGROUND: THE SCHOOL AND CLASS <ul><li>School </li></ul><ul><ul><li>socio-economically diverse school in declining neighborhood of medium sized Midwestern city </li></ul></ul><ul><ul><li>84% Caucasian, 11% African-American, 3% Hispanic American, 2% Asian American </li></ul></ul><ul><li>Class </li></ul><ul><ul><li>30 7 th -graders, dedicated to math </li></ul></ul><ul><ul><li>studied 18: equally male:female and lower:higher SES </li></ul></ul><ul><ul><li>most closely followed a targeted subgroup of eight: a low and high achieving male and female from each SES level </li></ul></ul>
  7. 7. STUDY’S BACKGROUND: THE CURRICULUM AND RESEARCH <ul><li>Curriculum </li></ul><ul><ul><li>eight units, each containing several “Investigations” </li></ul></ul><ul><ul><li>1-4 problems per Investigation </li></ul></ul><ul><ul><li>Investigations followed by homework and assessments </li></ul></ul><ul><ul><li>“ Launch, Explore, Summarize” instructional model </li></ul></ul><ul><li>Research </li></ul><ul><ul><li>studied dependency on SES of students’ experience with two aspects of problem-centric curriculum: </li></ul></ul><ul><ul><ul><li>openness (problems having no obvious solution, taking hours to weeks for groups to solve) </li></ul></ul></ul><ul><ul><ul><li>context (problems arising from a motivational situation, often based on the real world) </li></ul></ul></ul><ul><ul><li>three sets of interviews, various surveys, student work, teaching journal entries, and daily audio recordings over one school year </li></ul></ul>
  8. 8. EXAMPLE RESULTS: PIZZA PROBLEM <ul><li>Even high-achieving lower-SES failed to discover or employ unit ratio principles </li></ul><ul><ul><li>e.g., “tables offer same opportunity because if pizzas are cut into fourths then all but four people get seconds at either table” </li></ul></ul>
  9. 9. EXAMPLE RESULT: HOMEWORK-ASSESSMENT CORRELATIONS <ul><li>Assessment averages correlate with homework completion, except for lower-SES females </li></ul><ul><li>lower-SES and higher-SES females equally diligent on homework, but assessment results quite different </li></ul><ul><li>lower-SES and higher-SES females more diligent than males on homework </li></ul>
  10. 10. EXAMPLE RESULT: STUDENTS’ ASSESSMENT OF TOP-3 <ul><li>No lower-SES ranked themselves among top-3, even two females who were ranked by others </li></ul><ul><li>Every higher-SES mentioned by others also ranked themselves </li></ul><ul><li>Two higher-SES (one male, one female) were only ranked by themselves </li></ul>
  11. 11. SUMMARY OF RESULTS: OPENNESS <ul><li>4 consistently preferred CMP, all were higher-SES </li></ul><ul><li>6 consistently preferred Traditional, 4 were lower-SES </li></ul><ul><li>sample of lower-SES experiences </li></ul><ul><ul><li>8 of 9 often complained problems were confusing or too hard </li></ul></ul><ul><ul><li>none said CMP was easier than Traditional </li></ul></ul><ul><ul><li>difficulty often attributed to vocabulary, sentence structure </li></ul></ul><ul><ul><li>prefer specific teacher direction (especially girls) - would quit when stuck </li></ul></ul><ul><li>sample of higher-SES experiences </li></ul><ul><ul><li>often offered suggestions (e.g., provide a glossary) </li></ul></ul><ul><ul><li>several said CMP was easier than Traditional </li></ul></ul><ul><ul><li>often would think harder, persevere when stuck </li></ul></ul><ul><ul><li>four who really liked to figure-out problems were higher-SES </li></ul></ul>
  12. 12. SUMMARY OF RESULTS: CONTEXTUALIZATION <ul><li>lower-SES </li></ul><ul><ul><li>categorically known to be more contextualized in orientation, so CMP seemingly would be a match </li></ul></ul><ul><ul><li>study found them less likely to deduce a general pattern or proof, so CMP as means to learn math content and processes often failed </li></ul></ul><ul><li>higher-SES </li></ul><ul><ul><li>categorically known to be less contextualized in orientation </li></ul></ul><ul><ul><li>study found them able and inclined to pull back from context and analyze intended mathematical ideas </li></ul></ul>
  13. 13. EPILOGUE RESEARCHER’S CAVEATS <ul><li>Data and literature on lower-SES suggest they have the most to gain from problem-solving instruction </li></ul><ul><li>Study raises questions about problem-solving as a means for lower-SES to learn other mathematical concepts and skills </li></ul><ul><ul><li>improved both lower-SES and higher-SES understanding of math, but increased the gap in performance </li></ul></ul><ul><ul><li>direct, algorithmic mode of instruction might provide a relatively level playing field </li></ul></ul>
  14. 14. ADDENDUM
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