Developed at

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A Research-Based Communication Model

• Developed at
• Clemson University
• College of Engineering and Science
• www.mathoutofthebox.org

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Communication Reflection

• What do you know about the research-base for
  communication in the classroom?
• How does verbal and written communication impact
  you as a learner?

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Essential Components

• A model for verbal and written communication
• Development of a community of learners
• Balanced assessment practices
• Explicit connections that make mathematics
  meaningful
• A variety of problem solving experiences
• A diversity of materials, manipulatives, and
  models

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Development of a community of learners

• Explicit representation and sharing of ideas with
  others increases the likelihood that students
  will connect what they have learned with what
  they already know and retain their learning.
  (Pellegrino, Chudowsky, and Glaser, 2001).

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Balanced assessment practices
Numerous studies support the practice of
formative assessment as a way to increase student
success, particularly with low-achieving students
(Fuchs and Fuchs, 1986 Wiliam and Black, 1996).
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Explicit connections that make mathematics
meaningful

• The ability to recognize relationships among
  mathematical ideas and to apply those ideas
  beyond the mathematics classroom has long been
  recognized as a hallmark of mathematical
  understanding (Brownell, 1954 Skemp, 1978
  Grouws Cebulla 2000).

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A variety of problem solving experiences

• Research indicates that opportunities to explore
  new ideas balanced with opportunities to practice
  skills results in successful problem solving
  (Grouws and Cebulla, 2000).

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A diversity of materials, manipulatives, and
models

• Researchers advocate an environment of hands-on
  experiences in mathematics classrooms. In
  addition to manipulatives, materials needed for
  this rich environment include charts, graphs,
  writing models, diagrams, technology, and any
  tool that aids students in sense-making and
  problem solving (Sowell, 1989 Hiebert et al.,
  1997 Kilpatrick, Swafford, and Findell, 2001
  Van de Walle, 2004).

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Learning Cycle Engage Students pose questions,
define problems, brainstorm ideas, and discuss
solutions. Investigate Research,
experimentation, observation, building models,
and redefining questions are all part of
investigation. Reflect Students communicate and
represent their findings by sharing in many ways
with others. It is in this phase that students
take ownership of new knowledge. Apply Students
make connections to past learning, new knowledge,
and real-world experiences.
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A model for verbal and written communication

• Communication in the mathematics classroom
  permits learning to build on the students
  informal knowledge, gives students practice in
  explaining their mathematical thinking to others,
  and provides students and teachers with evidence
  that learning has occurred. (Yackel , Cobb, Wood,
  and Merkel, 1990 Malloy, 1997 Moody, 2004).

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Communication as a Way of Learning
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Big Idea Patterns are in the world around us.
Sub-concept Patterns can be described.
Lesson 4 Analyzing and Describing
Patterns Students analyze and extend patterns and
share their ideas about patterns orally and in
writing.
Lesson 1 Exploring Collections Students
brainstorm a list of collections and describe
personal collections orally and in
writing. Pre-assessment
Lesson 3 Representing a Pattern Students
represent patterns with collections, letters,
movements, and sounds.
Lesson 2 Exploring Patterns Students recognize
existing patterns in the classroom, on a walk,
and at home, and then create their own
pattern. Pre-assessment
Sub-concept Predictions can be made and verified.
Lesson 7 Number Patterns With the
Calculator Students explore the operation of a
calculator and use calculators to generate and
verify number patterns.
Lesson 5 Verifying Predictions Students predict
positions on a number line and verify their
predictions.
Lesson 6 Positions on a Number Line Students
investigate common counting patterns and use a
rule to extend the pattern on a number line.
Sub-concept Patterns can be extended.
Lesson 8 Making Number Charts Students explore a
variety of number patterns by using a pattern
rule to create, extend, and analyze patterns to
100.
Lesson 9 Hundreds Charts Students use pattern
rules to explore a variety of number patterns on
number charts including numbers to 500.
Lesson 10 Solving Pattern Problems Students solve
pattern problems as well as create and analyze a
pattern made with stickers. Post-assessment
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Teacher Reflection

• This communication model has had an impact on my
  students because it has created a true sense of
  community among them. The learning environment in
  my classroom is stronger because the students are
  collaborating about their learning. They are
  communicating with one another mathematically and
  they are having fun!

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• Experiences in my classroom involving written and
  verbal communication have been extremely
  positive. Students that (in the past) have felt
  intimidated and uncertain about their own
  mathematical skills and knowledge have blossomed.
  The group discussion in the beginning allows
  for a free contribution to the story we are
  attempting to tell and students very often will
  build on the ideas that their peers are offering.
  Students learn to have confidence and trust their
  own ideas with group support, and then they
  confidently can transition to individual work.
  This process has worked throughout all the
  concepts taught, and my students have become
  excellent problem solvers in cooperative groups,
  in pairs, and individually.

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Trends
At low-performing Title I schools, a trend
towards positive immediate impact on mathematics
achievement on statewide standardized tests for
sub-groups of students has been noted. The
subgroups of subsidized lunch students and
African American students show movement from
below basic to meeting standard at levels that
reflect a closing of the achievement gap.
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Trends
When individual teachers changed the components
of the lessons, the student achievement on
mathematics assessments did not show the gains of
students in classrooms where the teachers
followed the design of the lessons. Analysis of
classroom observations of teachers and teacher
reflections show a change in teaching strategies
after experiencing our professional development
and implementing the lessons. Preliminary
analysis of teacher reflections and interviews
indicate that teachers using our model become
practitioners of formative assessment techniques.

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Fulfilling the mathematical promise that exists
in every child
www.mathoutofthebox.org
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• Sources
• Brownell, W. (1987, April, originally 1956,
  October). Meaning and Skill Maintaining the
  Balance. The Arithmetic Teacher, 18-25.
• Fuchs, L.S. and D. Fuchs. (1986). Effects of
  Systematic Formative Evaluation A Meta-Analysis.
  Exceptional Children. 53 199-208.
• Grouws, D. and Cebulla, K. (2000). Improving
  Student Achievement in Mathematics. Brussels
  International Academy of Education. Retrieved
  February 14, 2005,from http//www.ibe.unesco.org/I
  nternational/Publications/EducationalPractices/Edu
  cationalPracticesSeriesPdf/prac04e.pdf.
• Hiebert, J., T.P. Carpenter, E. Fennema, K.C.
  Fuson, D. Wearne, H. Murray, A. Olivier, and P.
  Human. (1997). Making Sense Teaching and
  Learning Mathemaics with Understanding.
  Heinemann Portsmouth, NH.
• Johnson, D.W., R.T. Johnson, and M.B. Stanne.
  (2000). Cooperative Learning Methods A
  Meta-Analysis. Minneapolis, MN University of
  Minnesota.
• Karplus, R., and H. D. Their. (1967). A New Look
  at Elementary School Science. Chicago, IL Rand
  McNally.
• Kilpatrick, J., J. Swafford, and B. Findell, eds.
  (2001). Adding It Up Helping Children Learn
  Mathematics. Washington, DC National Academy
  Press.
• Lawson, A. E., M.R. Abraham, and J. W. Renner.
  (1989). A Theory of Instruction Using the
  Learning Cycle to Teach Science Concepts and
  Thinking Skills. National Association of Research
  in Science Teaching (NARST) Monograph, Number
  One.

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• Sources (continued)
• Malloy, C.E., ed. (1997). Challenges in the
  Mathematics Education of African American
  Children. Proceedings of the Benjamin Banneker
  Association Leadership Conference. Reston, VA
  National Council of Teachers of Mathematics.
• Marek, E.A., and A. M.L. Cavello. (1997). The
  Learning Cycle Elementary School Science and
  Beyond. Portsmouth, NH Heinemann.
• Pellegrino, J. W., N. Chudowsky, and R. Glaser,
  eds. (2001). Knowing What Students Know The
  Science and Design of Educational Assessment.
  Washington, DC National Academy Press.
• Skemp, R.R. (1978). Relational Understanding and
  Instrumental Understanding. The Arithmetic
  Teacher. 3, 9-15.
• Sowell, E.J. (1989). Effects of Manipulative
  Materials in Mathematics Instruction. Journal for
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• Van de Walle, J. A. (2004). Elementary and Middle
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  Inc.
• Wiliam, D. and P. Black. (1996). Meanings and
  Consequences A Basis for Distinguishing
  Formative and Summative Functions of Assessment.
  British Educational Research Journal. 22 537-48.