IMPACT in MATH: April 2009

Thursday, April 30, 2009

What are the core elements of effective instruction? critical features of professional development

We need shared explicit notion of best practice.

Critical features of professional development
Desimone, Laura (2009). Improving Impact studies of Teachers' professional development: toward better conceptualizations and measures.

No quality control

Tuesday, April 28, 2009

What is math understanding?

Understanding a mathematics topic consists of having the
ability to operate successfully in three cognitive domains. The first
domain, knowing, covers the facts, procedures, and concepts students
need to know, while the second, applying, focuses on the ability of
students to make use of this knowledge to select or create models and
solve problems. The third domain, reasoning, goes beyond the solution
of routine problems to encompass the ability to use analytical
skills, generalize, and apply mathematics to unfamiliar or complex
contexts.
Knowing
Facility in using mathematics or reasoning about mathematical situations
depends on mathematical knowledge and familiarity with
mathematical concepts. The more relevant knowledge a student is able
to recall and the wider the range of concepts he or she has understood,the greater the potential for engaging in a wide range of problemsolving
situations and for developing mathematical understanding.
Without access to a knowledge base that enables easy recall of
the language and basic facts and conventions of number, symbolic
representation, and spatial relations, students would find purposeful
mathematical thinking impossible. Facts encompass the factual
knowledge that provides the basic language of mathematics, and the
essential mathematical facts and properties that form the foundation
for mathematical thought.
Procedures form a bridge between more basic knowledge and the
use of mathematics for solving routine problems, especially those
encountered by many people in their daily lives. In essence, a fluent
use of procedures entails recall of sets of actions and how to carry
them out. Students need to be efficient and accurate in using a variety
of computational procedures and tools. They need to see that particular
procedures can be used to solve entire classes of problems, not just
individual problems.
Knowledge of concepts enables students to make connections
between elements of knowledge that, at best, would otherwise be
retained as isolated facts. It allows them to make extensions beyond
their existing knowledge, judge the validity of mathematical statements
and methods, and create mathematical representations.

Behaviors Included in the Knowing Domain
1 Recall Recall definitions, terminology, notation,
mathematical conventions, number
properties, geometric properties.
2 Recognize Recognize entities that are
mathematically equivalent (e.g., different
representations of the same function or
relation).
3 Compute Carry out algorithmic procedures (e.g.,
determining derivatives of polynomial
functions, solving a simple equation).
4 Retrieve Retrieve information from graphs, tables,
or other sources.
Applying
Problem solving is a central goal, and often a means, of teaching mathematics,
and hence this and supporting skills (e.g., select, represent,
model) feature prominently in the domain of applying knowledge. In
items aligned with this domain, students need to apply knowledge of
mathematical facts, skills, procedures, and concepts to create representations
and solve problems. Representation of ideas forms the core of
mathematical thinking and communication, and the ability to create
equivalent representations is fundamental to success in the subject.
Problem settings for items in the applying domain are more
routine than those aligned with the reasoning domain and will typically
have been standard in classroom exercises designed to provide
practice in particular methods or techniques. Some of these problems
will have been expressed in words that set the problem situation in
a quasi-real context. Though they range in difficulty, each of these
types of “textbook” problems is expected to be sufficiently familiar
to students that they will essentially involve selecting and applying
learned procedures.

Problems may be set in real-life situations or may be concerned
with purely mathematical questions involving, for example, numeric
or algebraic expressions, functions, equations, geometric figures, or
statistical data sets. Therefore, problem solving is included not only in
the applying domain, with emphasis on the more familiar and routine
tasks, but also in the reasoning domain.
Behaviors Included in the Applying Domain
1 Select Select an efficient/appropriate method
or strategy for solving a problem where
there is a commonly used method of
solution.
2 Represent Generate alternative equivalent
representations for a given mathematical
entity, relationship, or set of information.
3 Model Generate an appropriate model such as
an equation or diagram for solving a
routine problem.
4 Solve Routine Problems
Solve routine problems, (i.e., problems
similar to those students are likely to
have encountered in class). For example,
differentiate a polynomial function, use
geometric properties to solve problems.

Reasoning
Reasoning mathematically involves the capacity for logical, systematic
thinking. It includes intuitive and inductive reasoning based on
patterns and regularities that can be used to arrive at solutions to nonroutine
problems. Non-routine problems are problems that are very
likely to be unfamiliar to students. They make cognitive demands over
and above those needed for solution of routine problems, even when
the knowledge and skills required for their solution have been learned.
Non-routine problems may be purely mathematical or may have reallife
settings. Both types of items involve transfer of knowledge and
skills to new situations, and interactions among reasoning skills are
usually a feature. Problems requiring reasoning may do so in different
ways. Reasoning may be involved because of the novelty of the
context or the complexity of the situation, or because any solution to
the problem must involve several steps, perhaps drawing on knowledge
and understanding from different areas of mathematics.
Even though many of the behaviors listed within the reasoning
domain are those that may be drawn on in thinking about and
solving novel or complex problems, each by itself represents a valuable
outcome of mathematics education, with the potential to influence
learners’ thinking more generally. For example, reasoning involves
the ability to observe and make conjectures. It also involves making
logical deductions based on specific assumptions and rules, and justifying
results.

Behaviors Included in the Reasoning Domain
1 Analyze Investigate given information, and select
the mathematical facts necessary to solve
a particular problem. Determine and
describe or use relationships between
variables or objects in mathematical
situations. Make valid inferences from
given information.
2 Generalize Extend the domain to which the result
of mathematical thinking and problem
solving is applicable by restating results
in more general and more widely
applicable terms.
3 Synthesize/
Integrate
Combine (various) mathematical
procedures to establish results, and
combine results to produce a further
result. Make connections between
different elements of knowledge and
related representations, and make
linkages between related mathematical
ideas.
4 Justify Provide a justification for the truth or
falsity of a statement by reference to
mathematical results or properties.
5 Solve
Non-routine
Problems
Solve problems set in mathematical
or real-life contexts where students
are unlikely to have encountered
similar items, and apply mathematical
procedures in unfamiliar or complex
contexts.
2

Thursday, April 23, 2009

Let's talk math! Books on math discourse

Books and Articles Relating to Discourse in the Classroom
 Chapin, Suzanne, Catherine O’Connor, and Nancy Anderson; Classroom Discussions Using Math Talk to Help Students Learn
 Allen, Janet; Words, Words, Words: Teaching Vocabulary in Grades 4-12
 Johnston, Peter; Choice Words: How Our Language Affects Children’s Learning
 Allen, Janet; Inside Words: Tools for Teaching Academic Vocabulary Grades 4-12
 Denton, Paula; The Power of Our Words: Teacher Language That Helps Children Learn
 Hill, Jane and Kathleen Flynn; Classroom Instruction That Works with English Language Learners
 Hyde, Arthur; Comprehending Math Adapting Reading Strategies to Teach Mathematics, K-6
 Sullivan Peter and Pat Lilburn; Good questions for Math Teaching Why Ask Then and What to Ask K-6
 Developing Mathematical Thinking with Effective Questions; PBS TeacherLine
 Beck, Isabel, Margaret McKeown and Linda Kuean; Bringing Words to Life
 Zwiers, Jeff and Marie Crawford; “How to Start Academic Conversations” Educational Leadership; p.70; April 2009.
 “Analyzing Classroom Discourse to Advance Teaching and Learning”; education update; volume 50; number 2; February 2008.

Tuesday, April 21, 2009

call for manuscript for AMTE

Background
The Association of Mathematics Teacher Educators (AMTE) is an organization designed to
bring together individuals interested in mathematics teacher education in order to promote and
improve the education of preservice and inservice teachers of mathematics. Two of its goals are
to facilitate communication and to promote collaboration among mathematics teacher educators,
including those in Colleges of Education, in Departments of Mathematics, and outside higher
education settings. In an effort to support these goals, AMTE published its first monograph in
2004. The 2010 monograph, Mathematics Teaching: Putting Research into Practice at All
Levels, will be the seventh volume in the series designed to be a forum for mathematics teacher
educators to exchange ideas about their work with preservice and inservice teachers and about
their collaborative efforts with others who play significant roles in mathematics teacher
education (e.g., content faculty, clinical faculty responsible for mentoring student teachers).
Anticipated Audience
The anticipated audience for this monograph includes individuals responsible for the
professional development of mathematics teachers, such as college or university faculty,
community college faculty, or professional development specialists. Hence, the focus of the
monograph is on issues related to the development of mathematics teachers, practices in postsecondary
classrooms (content or pedagogy) for mathematics teachers, or practices that help
individuals responsible for the preparation of mathematics teachers gain knowledge they need to
be more effective in their work.
Possible Topics
The 2010 monograph aims to include manuscripts addressing aspects of the practices of
mathematics teacher educators. In particular, we welcome research studies, as well descriptions
of mathematics teaching practice informed by research. Topics may include but are not limited to
the following broad categories:
• The mathematics needed for pre-service and in-service teacher education;
• Preparation/professional development of mathematics teacher educators and teacher
leaders (content or pedagogy);
• Innovative delivery methods for content and programs, including alternative routes to
certification in mathematics;
• Innovative materials developed for K-16 mathematics teacher education; and
• Collaboration among various mathematics teacher educators, e. g., mathematics/science
partnerships or professional learning communities.
**Authors are encouraged to consider what other mathematics teacher educators can learn from
the manuscript to inform personal practice with pre-service and/or in-service teachers.
Preparation of Manuscripts
Any questions about possible topics for inclusion may be directed to one of the co-editors of the
monograph. Editorial decisions will be made by the co-editors and members of the Editorial
Panel:
Co-editors Jennifer Luebeck, Montana State University, luebeck@math.montana.edu
Johnny W. Lott, University of Mississippi, jlott@olemiss.edu
Series editor Marilyn Strutchens, Auburn University
Panel members Carol Malloy, University of North Carolina
Melfried Olson, University of Hawaii
Trena Wilkerson, Baylor University, Texas
Laura Spielman, Radford University, Virginia
Eric Milou, Rowan University
Dorothy White, University of Georgia
Jane Keiser, Miami University of Ohio
Amy Hillen, Kennesaw State University, Georgia
Sheri Stockero, Michigan Technological University
AMTE board
liaison
Marilyn Strutchens, Auburn University
Manuscripts should be completed in APA style, double-spaced in 12 point font using 1 inch
margins, and should not exceed 15 pages in length, including references, tables, and figures.
Submission of manuscripts will be accepted electronically, as instructed below. Authors submit
two electronic versions of their manuscript; one copy should include a cover page with all
appropriate author information (name, address, phone, fax, and email); the other copy should
allow for blind review. Please name your WORD document files as follows:
Identifiable copy: LASTNAME.doc
Blind copy: LASTNAMEblind.doc
Send both electronic files to: Johnny W. Lott
Email: jlott@olemiss.edu
*AMTE is planning for an online submission system. Please check www.amte.net for
details. If the system is ready, manuscripts will be accepted either by email or through the
online system.
Submission Due Date: June 1, 2009
Anticipated Publication Date: 2010

SD Themes for 2009-2010
NSDC now prefers electronic submissions. For guidelines on submitting articles to the JSD, visit the complete writer's guidelines. Fall 2008: Using evidence
Manuscript deadline: Nov. 15, 2007
This issue will examine how professional development leaders work with teachers to examine and use evidence about student learning to guide decisions about instruction. For this issue, JSD editors will consider articles that address these questions:
How are teachers developing and learning to use assessment data to improve their daily instruction?
How are districts and schools effectively sorting through the data they collect to use it in a way that deepens teachers' knowledge?
What are strong examples of schools or districts that have regularly evaluated and used data in a way that has transformed teachers' practices?
How are districts using data to guide their discussion and planning of professional development that will improve student achievement?
How are professional development leaders, particularly principals, involved in supporting teachers' use of data and in communicating the importance of data in changing instruction?
Where are there examples of districts or schools that have effectively assessed their professional learning programs?
-->Winter 2009: What works in professional development
Manuscript deadline: Feb. 15, 2008
This issue will examine what is known about professional development that leads to improved student learning. For this issue, JSD editors will consider articles that address these questions:
What empirical research can we examine to answer the question of what works in professional development?
What strategies are believed to be most effective and why?
What do staff developers need to know in order to be successful in having teachers and leaders transfer knowledge from formal learning to practice?
What do we still need to do / learn in order to answer this question?
What examples are there of schools or districts that believe their professional development has led to changes in student learning?
-->Summer 2009: High-quality teaching
Manuscript deadline: Aug. 15, 2008
This issue will examine how leaders can work to ensure that every child is taught by an effective, professional learning leader. For this issue, JSD editors will consider articles that address these questions:
How do we define and objectively measure quality teaching?
What have schools and districts done to improve the quality of teaching and what measures show their success in doing so?
Where are examples of high-quality teaching, and what professional learning has contributed to the effectiveness of those teachers?
What schools and districts are demonstrating the effect on student achievement of improvements in the quality of teachers' learning?
-->Winter 2010: Professional learning 101
Manuscript deadline: Feb. 15, 2009
This issue will focus on fundamental aspects of professional learning in schools. For this issue, JSD editors will consider articles that address these questions:
What are key elements of high-quality professional learning? How can NSDC’s Standards for Staff Development assist schools and districts in establishing effective professional learning?
What first steps can a school or district take in examining and improving professional learning practices? How can they begin school improvement planning?
What facilitation practices encourage effective school-based learning and collaboration?
What organizational structures and elements of school culture support effective professional development?
What is the research base for high-quality professional learning?
-->
Summer 2010: Using technology for professional learning
Manuscript deadline: Aug. 15, 2009This issue will explore how technology, in a variety of forms, can be used for professional learning. For this issue, JSD editors will consider articles that address these questions:
How are schools, districts, or technical assistance providers effectively using technology for professional development?
When and where can particular technology-based learning models be useful?
What conditions and support make this type of learning successful?
How can technology support aspects of professional learning known to be critical to effective school improvement: ongoing and job-embedded, data-driven decision making, leadership, collaboration, reflection, content-based knowledge growth, etc.?
How are schools and districts ensuring that technology-supported learning meets standards for high-quality professional development and improves student learning?
Fall 2010: The new central office
Manuscript deadline: Nov. 15, 2009This issue will examine how school systems can best support high-quality professional learning in an era when school-based learning is being emphasized. For this issue, JSD editors will consider articles that address these questions:
How are central offices organized to ensure effective professional learning at the school level?
How do central office staff developers strike a balance between supporting successful district initiatives and meeting school-based learning needs?
How have the roles of central office personnel changed as new school-based leadership roles, including coaches, have developed?
What relationships and interactions between district- and school-level staff best support effective professional learning?
Where are there models of central offices that support effective professional learning for all schools in the system?
Winter 2011: Content-specific professional learning
Manuscript deadline: Feb. 15, 2010This issue will explore effective content-specific professional learning models. For this issue, JSD editors will consider articles that address these questions:
Why is content-specific professional learning important?
How is content-specific professional learning integrated with a school or district improvement plan?
What are the particular professional learning needs for different content areas? How are those best supported?
Where are there examples of schools and districts using content-specific professional learning effectively?
Spring 2011: Working with external partners
Manuscript deadline: May 15, 2010This issue will focus on the important role of external partners, including universities, state departments of education, vendors and consultants, and other technical assistance providers, in effective professional learning. For this issue, JSD editors will consider articles that address these questions:
How do schools and districts identify appropriate external partners? How do they decide when they need a partner?
What are important elements to establishing an effective partnership for professional learning? What are the benefits and challenges of working with partners?
How can external partners support aspects of professional learning known to be critical to effective school improvement: ongoing and job-embedded, data-driven decision-making, leadership, collaboration, reflection, content-based knowledge growth, etc.?
How do schools and districts sustain and leverage the work of an external partner once the formal partnership has ended?
Where are there examples of schools and districts in successful partnership with outside entities for the purpose of high-quality professional learning?
Copyright © 2009 National Staff Development Council. Call 800-727-7288. E-mail NSDCoffice@nsdc.org