Transcript Randall E. Groth Salisbury University   Generate: “To launch a research program, mathematics educators need to generate some ideas about the phenomena of interest.

Randall E. Groth
Salisbury University
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Generate: “To launch a research program,
mathematics educators need to generate some
ideas about the phenomena of interest so that
they can begin to explore them. Those ideas
might emerge from theoretical considerations,
previous research, or observations of practice” (p.
5).
Frame: “A frame is seen as involving
clarification of the goals of the research
program and definition of the constructs it
entails, formulation of tools and procedures for
the measurement of those constructs, and
consideration of the logistics needed to put the
ideas into practice and study their feasibility”
(p. 5).
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Examine: “to understand the phenomena
better and to get indicators of what might
work under which conditions” (p. 6).
Generalize: “generalization can address
questions of scale (studying different
populations or sites, using more
comprehensive measures, examining
different implementation conditions), or it
can be used to refine the theory or reframe
the entire research program” (p. 6).
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Extend: “A body of research that has yielded
some generalizable outcomes can be extended in
a variety of ways. Multiple studies can be
synthesized; long-term effects can be examined;
policies can be developed for effective
implementation” (p. 7).
Cycling: Each component “has the possibility and
potential to cycle back to any earlier component,
and such cycling should be a conscious effort of
the researchers. Progress in research is generally
more of circular process than a linear one” (p. 7).
Generate
Goals &
Constructs
Logistics &
Feasibility
Measurement
Examine
Generalize
Extend
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Curriculum recommendations in school
statistics (e.g., GAISE - Franklin et al., 2007;
NCTM, 2000) and teachers’ need for content
knowledge to implement them.
Conceptual and procedural knowledge
(Hiebert & Lefevre, 1986) as an important
distinction for teachers to understand.
Profound understanding of fundamental
mathematics (Ma, 1999) marking out a
specialized domain of teachers’ mathematical
knowledge for teaching.
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SOLO Taxonomy (Biggs & Collis, 1982) – preservice teachers’ conceptual knowledge of mean,
median, & mode (Groth & Bergner, 2006).
Spontaneous metaphors as an indicator of
content knowledge and pedagogical content
knowledge (Groth & Bergner, 2005).
Partially correct constructs (Ron, Dreyfus, &
Hershkowitz, 2010) for SKT related to elementary
categorical data analysis
Participation in item-writing camps for LMT
project – production of quantitative scales.
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Analysis and discussion of practitioneroriented journal articles on NAEP results
(Groth, 2009)
◦ Teachers’ personal frameworks, formed in practice,
can differ markedly from those of researchers (e.g.,
debate on whether students should learn an
algorithm for calculating the arithmetic mean
without understanding its meaning) and be
resistant to change.
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Analysis and discussion of written cases of
teaching (Groth & Shihong, in press)
◦ Common knowledge of content need not be
developed in isolation from other components of
the knowledge base for teaching (e.g., prospective
teachers developed knowledge of randomness,
sampling, and independence while discussing
students’ conceptions of the likelihood of making a
long string of basketball shots (Merseth, 2000)).
◦ Conjecture for further research: It would be
profitable to develop courses that do not
compartmentalize the development of common
knowledge of statistics from other components of
SKT.
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On average, participants (n = 80) improved
their scores on an LMT-designed CKT-M
instrument on content knowledge for
teaching statistics by 0.87 standard
deviations.
The mean difference between pre- and posttest scores was statistically significant (M =
0.87, SD = 0.53), t (79) = 14.71, p < .0001,
CI.95 = .75, .99.
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Assess implementation of the SKT course at
different sites (e.g., local community
colleges).
Experimental design to compare performance
of prospective teachers in SKT course and
conventional introductory statistics.
Refinement of the LMT measure and
development of equated forms.
Cycling back: Continued refinement of theory
of SKT by gathering data on PreK-8 student
learning outcomes of SKT course completers
and other teachers.
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Retention studies – re-administration of SKT
test and gathering of qualitative classroom
observation data once completers of the SKT
course begin teaching.
Observation of difficulties encountered as
teachers in many different institutions begin
to implement the SKT course, and
development of interventions to address
them.
Randall Groth
Department of Education Specialties
Salisbury University
[email protected]
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Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content
knowledge for teaching: What makes it special? Journal of
Teacher Education, 59, 389-407.
Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of
learning: The SOLO taxonomy. New York: Academic.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R.,
Perry, M., & Scheaffer, R. (2007). Guidelines for
assessment and instruction in statistics education (GAISE)
report. Alexandria, VA: American Statistical Association.
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Groth, R.E. (2007). Toward a conceptualization of
statistical knowledge for teaching. Journal for Research in
Mathematics Education, 38, 427-437.
Groth, R.E. (2009). Characteristics of teachers'
conversations about teaching mean, median, and mode.
Teaching and Teacher Education, 25, 707-716.
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Groth, R.E., & Bergner, J.A. (2005). Preservice elementary
school teachers' metaphors for the concept of statistical
sample. Statistics Education Research Journal, 4 (2), 2742.
Groth, R.E. & Bergner, J.A. (2006). Preservice elementary
teachers' conceptual and procedural knowledge of mean,
median, and mode. Mathematical Thinking and Learning,
8, 37-63.
Groth, R.E., & Shihong, X. (in press). Preparing teachers
through case analyses. In C. Batanero & G. Burrill (Eds.),
Teaching statistics in school mathematics - Challenges for
teaching and teacher education: A joint ICMI-IASE study.
Dordrecht, The Netherlands: Springer.
Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural
knowledge in mathematics: An introductory analysis. In J.
Hiebert (Ed.), Conceptual and procedural knowledge: The
case of mathematics (pp. 1–28). Hillsdale, NJ: Lawrence
Erlbaum Associates, Inc.
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Hill, H.C., Schilling, S.G., & Ball, D.L. (2004). Developing
measures of teachers’ mathematical knowledge for
teaching. Elementary School Journal, 105, 11-30.
Ma, L. (1999). Knowing and teaching elementary
mathematics. Mahwah, NJ: Lawrence Erlbaum Associates,
Inc.
Merseth, K.K. (2003). Windows on teaching math: Cases of
middle and secondary classrooms. New York: Teachers
College Press.
Ron, G., Dreyfus, T., & Hershkowitz, R. (2010). Partially
correct constructs illuminate students’ inconsistent
answers. Educational Studies in Mathematics, 75, 65-87.
Scheaffer, R., & Smith, W. B. (2007). Using statistics
effectively in mathematics education research: A report
from a series of workshops organized by the American
Statistical Association with funding from the National
Science Foundation. Alexandria, VA: American Statistical
Association. [Online:
http://www.amstat.org/research_grants/pdfs/SMERReport
.pdf]