Download - Problem Solving and SES
RESEARCH REPORT:RESEARCH REPORT:
“PROBLEM SOLVING AS A “PROBLEM SOLVING AS A MEANS TOWARD MATHEMATICS MEANS TOWARD MATHEMATICS FOR ALL: FOR ALL: AN EXPLORATORY LOOK THROUGH A AN EXPLORATORY LOOK THROUGH A CLASS LENS”CLASS LENS”
DEC 7, 2010DEC 7, 2010
Alan Mitchell, Urban Teacher ResidentCUNY-Hunter College, School of Education
MATH 635, Problem Solving - Prof. Sandra Clarkson
AGENDA
Overview Study Background Example Results Summary of Results Epilogue: Researcher’s Caveats
OVERVIEW Dr. Lubienski studied 7th-graders' experiences with a
problem-centered curriculum, analyzing dependency on Socio-Economic Status (SES)
Abstract - Summary of Results“Higher SES students tended to display confidence and solve
problems with an eye toward the intended mathematical ideas”
“Lower SES students preferred more external direction and sometimes approached problems in a way that caused them to miss the intended mathematical points”
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
STUDY’S BACKGROUND:THE CONNECTED MATH PROJECT (CMP)
NCTM argued that problem solving should become the focus of math in school
NSF funded CMP, a middle school curriculum development to create problem-centered materials aligned with NCTM “reform” standards
CMP emphasizes problem solving as a means to learn math content and processes, not as an end in itself
Key:•NCTM – National Council of Teachers of Mathematics•NSF – National Science Foundation
STUDY’S BACKGROUND:THE RESEARCHER
From working class family – believes math can help break lower SES cycle of poverty
Held masters in math and secondary math teaching certificate
Was completing doctoral program, studying the theories underlying the NCTM reform
In third year with CMP, functioning in dual role for a year as CMP pilot teacher and researcher
STUDY’S BACKGROUND:THE SCHOOL AND CLASS
Schoolsocio-economically diverse school in declining
neighborhood of medium sized Midwestern city84% Caucasian, 11% African-American, 3% Hispanic
American, 2% Asian American Class
30 7th-graders, dedicated to mathstudied 18: equally male:female and lower:higher SESmost closely followed a targeted subgroup of eight: a low
and high achieving male and female from each SES level
STUDY’S BACKGROUND:THE CURRICULUM AND RESEARCH
Curriculum eight units, each containing several “Investigations” 1-4 problems per Investigation Investigations followed by homework and assessments “Launch, Explore, Summarize” instructional model
Research studied dependency on SES of students’ experience with two aspects
of problem-centric curriculum: openness (problems having no obvious solution, taking hours to weeks for
groups to solve) context (problems arising from a motivational situation, often based on
the real world) three sets of interviews, various surveys, student work, teaching
journal entries, and daily audio recordings over one school year
EXAMPLE RESULTS: PIZZA PROBLEM
Even high-achieving lower-SES failed to discover or employ unit ratio principles• e.g., “tables offer same opportunity because if pizzas
are cut into fourths then all but four people get seconds at either table”
EXAMPLE RESULT:HOMEWORK-ASSESSMENT CORRELATIONS
• Assessment averages correlate with homework completion, except for lower-SES females
• lower-SES and higher-SES females equally diligent on homework, but assessment results quite different
• lower-SES and higher-SES females more diligent than males on homework
EXAMPLE RESULT:STUDENTS’ ASSESSMENT OF TOP-3
• No lower-SES ranked themselves among top-3, even two females who were ranked by others
• Every higher-SES mentioned by others also ranked themselves• Two higher-SES (one male, one female) were only ranked by themselves
SUMMARY OF RESULTS:OPENNESS
4 consistently preferred CMP, all were higher-SES 6 consistently preferred Traditional, 4 were lower-SES sample of lower-SES experiences
8 of 9 often complained problems were confusing or too hard none said CMP was easier than Traditional difficulty often attributed to vocabulary, sentence structure prefer specific teacher direction (especially girls) - would quit when stuck
sample of higher-SES experiences often offered suggestions (e.g., provide a glossary) several said CMP was easier than Traditional often would think harder, persevere when stuck four who really liked to figure-out problems were higher-SES
SUMMARY OF RESULTS:CONTEXTUALIZATION
lower-SES categorically known to be more contextualized in orientation, so CMP
seemingly would be a match study found them less likely to deduce a general pattern or proof, so
CMP as means to learn math content and processes often failed higher-SES
categorically known to be less contextualized in orientation study found them able and inclined to pull back from context and
analyze intended mathematical ideas
EPILOGUERESEARCHER’S CAVEATS
Data and literature on lower-SES suggest they have the most to gain from problem-solving instruction
Study raises questions about problem-solving as a means for lower-SES to learn other mathematical concepts and skills improved both lower-SES and higher-SES understanding of math, but
increased the gap in performance direct, algorithmic mode of instruction might provide a relatively level
playing field