Slide 2 Research in Mathematics Education: New Directions for
Two-Year Colleges April Strom, Scottsdale Community College (AZ)
Ann Sitomer, Portland Community College (OR) Mark Yannotta,
Clackamas Community College (OR) Amy Volpe, Glendale Community
College (AZ) Slide 3 RMETYCRMETYC esearch in athematics ducation in
wo- ear olleges Purpose: To encourage and support quality research
in mathematics education in two-year colleges, conducted by
two-year college faculty. New AMATYC Committee Slide 4 Guiding
Questions Why conduct research in mathematics education at
community colleges? Theory without practice is empty; practice
without theory is blind (Kwame Nkrumah, 1966). Schoenfeld (2000)
says Research in mathematics education has two main purposes, one
pure and one applied: Pure (Basic Science): To understand the
nature of mathematical thinking, teaching, and learning; Applied
(Engineering): To use such understandings to improve mathematics
instruction. What are some examples of research studies and
findings conducted by two-year college faculty? Slide 5 Current
Trends in Math Education Cognitive Research: Focus on student
reasoning Quantitative and Proportional Reasoning (Thompson, 1994;
Smith III & Thompson, 2008) Covariational Reasoning (Carlson et
al., 2002) Advanced Mathematical Thinking (Rasmussen & Zandieh,
2005); Realistic Mathematics Education (Freudenthal, 1991)
Research-based curricula: Rational Reasoning Group (Arizona State);
Abstract Algebra Group (Portland State) Slide 6 Presentations Talk
1: Experience as a researcher (Ann Sitomer) Talk 2: Experience as a
subject (Mark Yannotta) Talk 3: Experience with research design
(April Strom) Talk 4: Experience with data snooping (Amy Volpe)
Slide 7 Exploring the Mathematical Knowledge Embedded in Adults
Life Experiences Ann Sitomer Portland State University Portland
Community College Slide 8 Exploring the Mathematical Knowledge
Embedded in Adults Life Experiences Adult returning students in
developmental mathematics courses Placement tests measure what
adult returning students recall or do not recall about school
mathematics. Students who have been away from school often place
into the most elementary mathematics classes offered by mathematics
departments at community colleges. But to what extent do adult
students return to school with mathematical competencies not
measured by placement tests? Slide 9 Exploring the Mathematical
Knowledge Embedded in Adults Life Experiences To what extent do
adult students return to school with mathematical competencies not
measured by placement tests? Contexts for the question Teaching
Research The study Setting Proportional reasoning Data collection
Sample of student work on The Wage Problem Refining the research
questions and the design of the study An exploratory study Slide 10
Exploring the Mathematical Knowledge Embedded in Adults Life
Experiences Contexts for the question To what extent do adult
students return to school with mathematical competencies not
measured by placement tests? Practice My work as a teacher Research
Adults learning mathematics Research Out-of-school mathematical
practices Slide 11 Exploring the Mathematical Knowledge Embedded in
Adults Life Experiences Contexts for the question: Research
Out-of-school mathematical practices Over the last 30 years,
researchers have studied both adults and childrens mathematics in
contexts outside of school: Liberian tailors (Lave, 1977) Dairy
workers (Scribner, 1984) Young street vendors in Brazil (Carraher,
Carraher, & Schliemann, 1985) Female shoppers in the US (Capon
& Kuhn, 1979; Lave, 1988) Odds makers at the horse track (Ceci
& Liker, 1986) Bookies for an unofficial lottery game
(Schliemann & Acioly, 1989) Carpet layers (Masingila,
Davidenko, & Prus-Wisniowska, 1996) Apprentice iron workers
(Martin, LaCroix, & Fownes, 2006; Martin & Towers, 2007)
Structural engineers (Gainsburg, 2007) Slide 12 Exploring the
Mathematical Knowledge Embedded in Adults Life Experiences Contexts
for the question: Research Out-of-school mathematical practices
Over the last 30 years, researchers have studied both adults and
childrens mathematics in contexts outside of school: Liberian
tailors (Lave, 1977) Dairy workers (Scribner, 1984) Young street
vendors in Brazil (Carraher, Carraher, & Schliemann, 1985)
Female shoppers in the US (Capon & Kuhn, 1979; Lave, 1988) Odds
makers at the horse track (Ceci & Liker, 1986) Bookies for an
unofficial lottery game (Schliemann & Acioly, 1989) Carpet
layers (Masingila, Davidenko, & Prus-Wisniowska, 1996)
Apprentice iron workers (Martin, LaCroix, & Fownes, 2006;
Martin & Towers, 2007) Structural engineers (Gainsburg, 2007) A
partial catalog of mathematical competencies developed outside of
school Slide 13 Exploring the Mathematical Knowledge Embedded in
Adults Life Experiences Contexts for the question: Research Adults
learning mathematics The role of affect (Evans, 2000; Wedege &
Evans, 2006) Translation between worlds (Benn, 1997; Martin et al.,
2006) Slide 14 Exploring the Mathematical Knowledge Embedded in
Adults Life Experiences To what extent do adult students return to
school with mathematical competencies not measured by placement
tests? Contexts for the question Teaching Research The study
Setting Proportional reasoning Data collection Sample of student
work on The Wage Problem Refining the research questions and the
design of the study An exploratory study Slide 15 Exploring the
Mathematical Knowledge Embedded in Adults Life Experiences The
study: Setting The students participating in the study are enrolled
in Basic Mathematics at a community college in an urban setting.
Participating students were enrolled in four of the 12 sections of
this course offered on campus Fall 2009. The participation rate in
each section varied from about 20% to 75% of the students enrolled
in a section. Basic Math, along with a developmental reading and a
developmental writing course, are standard prerequisites for most
lower division collegiate courses offered at the college. Slide 16
Exploring the Mathematical Knowledge Embedded in Adults Life
Experiences The study: Setting Basic Mathematics Use fractions,
decimals, percents, integer arithmetic, measurements, and geometric
properties to write, manipulate, interpret and solve application
and formula problems. Introduce concepts of basic statistics,
charts and graphs. What are the core ideas of the course? Problem
solving Proportional reasoning Slide 17 Exploring the Mathematical
Knowledge Embedded in Adults Life Experiences The Study:
Proportional reasoning What is meant by proportional reasoning? I
propose that proportional reasoning means supplying reasons in
support of claims made about the structural relationships among
four quantities (say, a, b, c, d) in a context simultaneously
involving covariance of quantities and invariance of ratios or
products; this would consist of the ability to discern a
multiplicative relationship between two quantities as well as the
ability to extend the same relationship to other pairs of
quantities (Lamon, 2007, p. 638, emphasis added). Slide 18
Exploring the Mathematical Knowledge Embedded in Adults Life
Experiences The Study: Proportional reasoning Why examine
proportional reasoning for this study? If people with little or no
schooling really understand proportional relations in these
contexts, or if highly schooled individuals who have difficulty
understanding proportionality in school-type settings fail to
exhibit such difficulty in informal learning contexts, then there
is something important to be understood (Schliemann & Carraher,
1993, p. 49). Slide 19 Exploring the Mathematical Knowledge
Embedded in Adults Life Experiences The study: Data collection
Three types of data are being collected: Participating students
responses to a brief biographical surveybiographical survey
Participating students work done on a problem solved
collaboratively during the second class meeting of the term, as
well as field notes taken while students collaborated on a solution
to this problem.problem Selected participating students responses
to interview questions about their work on The Wage Problem, about
the mathematics they have used outside of school, and on a selected
tasks from the research literature on proportional
reasoning.interview questions Slide 20 Exploring the Mathematical
Knowledge Embedded in Adults Life Experiences To what extent do
adult students return to school with mathematical competencies not
measured by placement tests? Contexts for the question Teaching
Research The study Setting Proportional reasoning Data collection
Sample of student work on The Wage Problem Refining the research
questions and the design of the study An exploratory study Slide 21
Exploring the Mathematical Knowledge Embedded in Adults Life
Experiences Students written work on The Wage Problem Two things to
consider What mathematics do the students know before they return
to school? Are there strategies or concepts that students are
bringing to bear on The Wage Problem that suggest that a student is
building on her/his out-of-school experiences? A guiding principle
These researchers [ethnographers] have consistently tried to
understand mathematical problem solving in the same way as their
subjects (Eisenhart, 1988, p. 110). Slide 22 Exploring the
Mathematical Knowledge Embedded in Adults Life Experiences Students
written work on The Wage Problem Page 8 of the submitted work with
computational support on pages 9 and 10. Slide 23 Exploring the
Mathematical Knowledge Embedded in Adults Life Experiences
Observations Slide 24 Refinements Goals of data analysis from pilot
study Is there evidence of mathematical competencies with which
adult students are returning to school? If so, how might these
competencies be categorized and further studied? If not, what
another type of experimental design might uncover these
competencies? What themes emerge from the data? How might these
themes refine future research questions aimed at uncovering the
mathematical knowledge embedded in adults life experiences? Do the
emerging themes suggest questions that might help us understand how
adults students mathematical knowledge interacts with the
mathematics they are learning in their mathematics classes? Slide
25 Exploring the Mathematical Knowledge Embedded in Adults Life
Experiences Thank you Questions? Slide 26 Math 299: A Bridge to
University Mathematics Mark Yannotta Portland State University
Clackamas Community College Slide 27 Overview Background on bridge
courses and Math 299 The Math 299 Class of 2009 Some preliminary
results from the data Participant activity Slide 28 My dissertation
area: What are the challenges and opportunities associated with
developing and sustaining a mathematics bridge course in a
community college setting? Slide 29 What do we know about
mathematics bridge courses? About 40% of colleges and universities
in the US offer a dedicated course No consensus on content
(although many people argue that proof should be integral) Research
supports that bridging does not occur in a single course Community
colleges might provide some new direction for these courses Slide
30 PORTLAND STATE UNIVERSITY DEPARTMENT OF MATHEMATICS AND
STATISTICS BA/BS DEGREE REQUIREMENTS Mth 251, 252, 253, 254:
Calculus I-IV (16) Mth 256 or Mth 421: Differential Equations (4/3)
Mth 261: Introduction to Linear Algebra (4) Mth 311, 312: Advanced
Calculus (8) Mth 344: Group Theory (4) Additional 21 - 28 credits
of elective courses A GAP IN THE CURRICULUM Slide 31 The Evolution
of Math 299 YearStudentsInstructor(s)Curriculum 2005103 proof,
topology & group theory 200761 group theory, proof & math
history 200862 group theory (g.r.) & topology 200991 group
theory (g.r.) 2010??1 group theory (g.r.) Slide 32 How did I get
involved with this abstract algebra curriculum? 2006: I took a
topics course with Sean Larsen. I started thinking about ways to
incorporate more research-based ideas into Math 299 when I taught
it again. 2007: Sean contacted me about being Co-Pi on a
collaborative NSF grant. 2008: The grant was funded and I began
incorporating some of the materials into the class. 2009: In
conjunction with the grant, we used a modified version of the group
theory curriculum in Math 299 and collected data at CCC. Slide 33
Benefits of guided reinvention Freudenthal (1991) argues that,
knowledge and ability, when acquired by ones own activity, stick
better and are more readily available than when imposed by others
(p. 47). The students actively participate in developing symbols,
notation systems, definitions, and theorems. Freudenthal, H.
(1991). Revisiting mathematics education: China lectures. Norwell,
MA: Kluwer Academic Publishers. Slide 34 The students in my 2009
class: Consisted of 9 community college students aged 17 - 35 years
(6 in the 18 - 24 age category) 4 males, 5 females* 4 math majors,
2 engineering majors, 1 music major, 2 undecided Various math
backgrounds and experience 4 completed differential equations (2
had taken a different version of the transition course in 2008) 1
completed calculus III 3 completed calculus II 1 completed college
algebra Slide 35 The classroom environment: Low risk An elective
course Little homework was required Inexpensive (
