ICOTS8 (2010) Invited Paper Madden
In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society. Proceedings of the
Eighth International Conference on Teaching Statistics (ICOTS8, July, 2010), Ljubljana, Slovenia. Voorburg, The
Netherlands: International Statistical Institute. www.stat.auckland.ac.nz/~iase/publications.php [© 2010 ISI/IASE]
OVERCOMING OBSTACLES TO SUPPORTING SECONDARY TEACHERS’
STATISTICAL CONTENT KNOWLEDGE FOR TEACHING
Sandra Madden
University of Massachusetts Amherst, United States of America
smadden@educ.umass.edu
Supporting teachers’ statistical content knowledge for teaching poses a number of challenges.
Many grades 6-12 mathematics teachers’ prior experiences with statistics insufficiently prepared
them to support students grappling with big ideas of statistics. Teachers’ view of statistics tends to
be procedural and cookbook-oriented. Many mathematics teachers feel that statistics has little
place in their instruction, thus professional development is unnecessary. Finally, many teachers
have not experienced learning statistics in an environment in which student-centered discourse,
learner-centered technology, and worthwhile statistical tasks has been the norm. Research from
two professional development projects in which significant changes in teachers’ understanding of
statistical big ideas occurred is presented. Potential solutions to obstacles, tasks with potential for
engaging and challenging teachers, and lessons learned are discussed.
INTRODUCTION
The National Council of Teachers of Mathematics (NCTM) Principles and Standards for
School Mathematics (PSSM) recommends that data analysis ands probability be part of the
curriculum experience for all students across grades preK-12. The Guidelines for Assessment and
Instruction in Statistics Education (GAISE) (Franklin, et al., 2007) augment the NCTM’s
recommendations by specifically addressing statistical ideas developmentally and especially with a
focus on the nature of variability and its relationship to statistics. Both the NCTM’s
recommendations and those detailed in GAISE, suggest the importance of the use of technology for
supporting student learning of mathematical and statistical ideas as they explore the generation of
statistical questions, collect and analyze data, and interpret and communicate results and
conclusions. For this vision to be enacted in classrooms, critical to the mission is that teachers are
equipped with personal understanding of statistical concepts and connections, and facility with
tools for supporting the exploration of such concepts and connections by students.
Teaching mathematics requires both common mathematical knowledge and specialized
content knowledge in order to support students’ mathematical learning (Hill & Ball, 2004).
Common mathematical knowledge may be considered as the type of knowledge developed in a
mathematics class (e.g., know how to solve problems, computing correctly, using logical
arguments), whereas specialized mathematical knowledge includes knowledge that teachers need
to attend to the teaching of mathematics (e.g., multiple solution methods, constructing worthwhile
mathematical tasks, recognizing and supporting student mathematical reasoning). Groth (2007)
extended this work by proposing a framework for thinking about aspects of statistical knowledge
for teaching. He differentiated between common and specialized statistical knowledge and within
both, he accounted for mathematical and nonmathematical knowledge needed by teachers. While
teaching statistics in a mathematics classroom context, teachers’ specialized content knowledge
must allow them to connect statistical big ideas within the domain of mathematics while being
sensitive to the stochastic versus deterministic differences of the disciplines, all the while
understanding issues of student learning, curriculum, technology, equity, and assessment.
Teachers’ professional preparation to support the advancement of students’ learning of
data analysis and probability is likely inadequate (College Board of Mathematical Sciences, 2001;
Madden, 2008). Though statistics has made its way into national curricular recommendations (e.g.,
NCTM, GAISE) and state level curriculum framework documents, a cursory examination of
textbooks used in many schools reveals a strong disconnect between what visionary documents
intend and the actual opportunities students have to learn statistics. When teachers hold procedural
views of statistics, even when they read curricular recommendations, they may fail to fully
appreciate what is really being asked of them. When their instructional resources further exacerbate
this issue, teachers may believe that the familiar procedural approach to supporting students’
statistical understanding is appropriate.