Professional Development that Supports and Follows Mathematics Teachers in Teaching with Spreadsheets

1
Professional Development that Supports and
Follows Mathematics Teachers in Teaching with
Spreadsheets
11th Annual AMTE Conference Irvine,
California January 26, 2007

• Maggie Niess
• Oregon State University
• http//oregonstate.edu/niessm
• niessm_at_onid.orst.edu
• 541-737-1818

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Satellite Movies or DVD Movies?

• The Smith family is trying to decide between
  installing a satellite dish and receiving and
  movies through the satellite or purchasing a DVD
  and signing up for DVD rentals per month. The
  Smiths need to compare the cost of each option
  over several months in order to make an
  appropriate decision.
• Satellite
• One time installation of 29 and 49 per month
  for the service that allows them to unlimited
  access to their choice of movies with the
  stipulation that they must maintain this system
  for at least one year.
• DVD
• Purchase a DVD player for 250 and unlimited
  rental of DVDs for 30 per month.
• Help them make a decision

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Possible Approaches

• Symbolic approach
• Satellite 29 49 ( of months)
• DVD 250 30 ( of months)
• So
• 250 20( of months) 29 49( of months)
• of months 11.63
• Tabular approach
• Spreadsheet approach
• Dynamic_Function_Machine.xls

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Question?

• What do students learn
• Using prepared spreadsheets to solve mathematics
  problems?
• Designing and using spreadsheets for solving
  mathematics problems?

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Mathematics ContentLife is too short for long
division!

• Understanding patterns, relations, and functions
• Represent, analyze, and generalize a variety of
  patterns with tables, graphs, words, and when
  possible, symbolic rules
• Relate and compare different forms of
  representation for a relationship
• Identify functions as linear or nonlinear and
  contrast their properties from tables, graphs, or
  equations
• NCTM, 2000, Algebra Standard for Grades 6-8
• Analyze change in various contexts
• Use graphs to analyze the nature of changes in
  quantities in linear relationships
• NCTM, 2000, Algebra Standard for Grades 6-8
• Understand how mathematical ideas interconnect
  and build on one another to produce a coherent
  whole
• NCTM, 2000, Connection Standard for Grades 6-8
• Select, apply, and translate among mathematical
  representations to solve problems
• NCTM, 2000, Representation Standard for Grades 6-8

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TechnologyI think there is a world market for
maybe five computers. Watson, 1943

• Technology is essential in teaching and learning
  mathematics it influences the mathematics that
  is taught and enhances students learning The
  study of algebra need not be limited to simple
  situations in which symbolic manipulation is
  relatively straightforward. Using technological
  tools, students can reason about more general
  issues, such as parameter changes, and they can
  model and solve complex problem that were
  heretofore inaccessible to them Spreadsheets
  offer a useful tool for posing worthwhile
  problems When technological tools are available
  students can focus on decision making,
  reflection, reasoning, and problem solving.
• NCTM, 2000, The Technology Principle
• The computational and graphical capabilities of
  current technologies enables users to efficiently
  generate and manipulate a variety of
  representations of mathematics ideas and
  processes. Activities that engage students in
  connecting multiple representations (e.g.,
  graphical, numerical, algebraic, and verbal), and
  those that invite students to analyze or create
  images, visualizations, and simulations provide
  wide-ranging opportunities for mathematical
  exploration and sense-making.
• AMTE, 2006, Technology Position Statement
  Preparing Teacher to Use Technology to Enhance
  the Learning of Mathematics
• Promoting technology-literate students using
  technology as an integral component or tool for
  learning within the context of the subject use
  spreadsheets as productivity tools, research
  tools and problem-solving and decision making
  tools.
• National Educational Technology Standards for
  Students, 2000

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PedagogyHope is not a strategyThomas
McInerney

• Effective mathematics teaching requires
  understanding what students know and need to
  learn and then challenging and supporting them to
  learn it well. It requires
• reflection and continual efforts to seek
  improvement
• serious commitment to the development of
  students understanding of mathematics
• challenging and supportive classroom environment
• observing students, listening carefully to their
  idea and explanations, having mathematical goals,
  and using the information to make instructional
  decision
• NCTM, 2000, The Teaching Principle
• The kinds of experiences teachers provide clearly
  play a major role in determining the extent and
  quality of students learning. Students
  understanding of mathematical ideas can be built
  throughout their school years if they actively
  engage in tasks and experiences design to deepen
  and connect their knowledge.
• NCTM, 2000, The Learning Principle
• The effective use of technology in the
  mathematics classroom depends on the teacher
• NCTM, 2000, The Technology Principle
• Teachers need to have a strong pedagogical
  knowledge base related to the effective use of
  technology to improve mathematics teaching and
  learning.
• AMTE, 2006, Technology Position Statement
  Preparing Teacher to Use Technology to Enhance
  the Learning of Mathematics
• Teachers need to incorporate new strategies,
  analyzing the potential benefits of technology
  Student-centered instruction, collaborative work,
  active inquiry-based learning, critical thinking
  and informed decision-making.
• National Educational Technology Standards for
  Students, 2000
• Teacher need to apply technology to develop
  students higher-order skills and creativity.
• National Educational Technology Standards for
  Teachers, 2002

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Key Questions!!
If we teach today as we taught yesterday, then we
rob our children of tomorrow. John Dewey

• What knowledge and skills do mathematics teachers
  need to teach with technologies such as
  spreadsheets?
• How do they gain this if they are already
  teaching?

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Technology Pedagogical Content Knowledge (TPCK)
Technology
TPCK
Content
Pedagogy
PCK
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Central Components of TPCK (Adapted from
Grossmans (1989, 1990) components of PCK,
revised for TPCK by Niess, 2005)

• Teacher demonstrates knowledge and beliefs
  consistent with
• an overarching conception about the purposes for
  incorporating technology in teaching mathematics
• What the teacher knows and believes about the
  nature of mathematics, what is important for
  students to learn, and how technology supports
  learning mathematics are keys to the teachers
  knowledge and beliefs about teaching mathematics
  with technology in ways that serve as a basis for
  decisions about classroom instruction (objective,
  strategies, assignments, curriculum ad text, and
  evaluation of student learning)
• knowledge of students understandings, thinking,
  and learning in mathematics with technology
• Teacher relies on and operates from knowledge
  about how students learn mathematics with
  technologies and believes that technologies are
  useful in learning appropriate mathematics
• knowledge of curriculum and curricular materials
  that integrate technology in learning and
  teaching mathematics
• Teacher discusses and implements various
  technologies available for teaching particular
  topics and how the topics and ideas in a
  technology-enhanced environment with concern for
  how the activities are organized, scaffolded,
  structured, and assessed throughout the
  curriculum and
• knowledge of instructional strategies and
  representations for teaching and learning
  mathematics with technologies
• Teacher adapts mathematical representations with
  technologies in multiple ways to meet specific
  instructional goals and the needs of the breadth
  of learners in the class.

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Model of TPCK Professional DevelopmentTPCK
Professional Development
Classroom Teaching (Academic School Year)
Summer Program
-Learning about spreadsheets ? design
dynamic spreadsheets -Scaffolding lessons to
teach about and with spreadsheets
? Gathering resources ? Designing lessons
? Project - design multiple units -Practice
? Peer Teaching ? Teaching actual
students -Reflection ? Daily Journal ?
Observation ? Project
-Revising and Adapting Project -Practice ?
Own Students -Scaffolding/building student
Math and Spreadsheet skills ? Duplicate
what have experienced ? Generate new ideas in
curriculum and instruction -Reflection
? Interview ? Lesson Plan ? Project
TPCK
TPCK
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Levels of Development of TPCK(developed through
Niess professional development research)

• Recognizing
• Accepting
• Adapting
• Exploring
• Advancing

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What was their progress?
During Summer Program
Classroom Teaching
TH - Exploring MB - Exploring SG - Exploring FC -
Exploring AS - Adapting DH - Adapting CT -
Adapting MJ - Accepting JH - Accepting MM -
Recognizing
Highly motivated, previous exper w/ss Searching
for apps to math class
TH - Advancing MB - Accepting SG - Exploring FC -
Adapting AS - Exploring DH - Adapting CT -
Adapting MJ - Advancing JH - Recognizing MM -
Recognizing
Beliefs about learning math
Limitations of time/crowded curr.
Difficult students
School support, enthusiasm for tech
Personal knowledge with technology
Personal knowledge, new curriculum
Highly motivated, school support, work w/
multiple technologies
Substitute teaching, low motivation
Unwilling to change instruction
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Questions for Discussion

• What are the affordances and constraints with
  professional development framed by specific
  content (spreadsheet, math, etc.)?
• What operations and concepts support spreadsheets
  as dynamic and dependable tools for learning
  mathematics?
• What are the affordances and constraints of
  particular activities included in the
  professional development (planning, practice,
  reflection)?
• Where are math problems that can guide learning
  about spreadsheets with math in the PD?
• What strategies can be used to encourage and
  support teachers when teaching as they attempt to
  implement ideas from the professional
  development?
• What are barriers that affect their efforts at
  implementation?

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Question for Discussion

• What are the affordances and constraints with
  professional development framed by
• Spreadsheet operations and concepts - developed
  through multiple mathematics topics such as
• Dynamic and dependable spreadsheets?
• Creating formulas and charting?
• Planning and designing learning environments and
  experiences
• with key mathematics topics - variables,
  visualization and representations?
• with one mathematics unit - such as linear
  functions?
• scaffolding learning about spreadsheets while
  concurrently learning mathematics concepts?
• Teaching, learning and the mathematics curriculum
  
• focused on managing student learning activities
  in a spreadsheet-enhanced environment?
• Focused on applying spreadsheets to develop
  students higher order skills and creativity?
• Assessment and evaluation of mathematics learning
• focused on a variety of assessments techniques
  for applying spreadsheets in assessing student
  learning?

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Question for Discussion

• What operations and concepts support spreadsheets
  as dynamic and dependable tools for learning
  mathematics?
• Avoid numeric values in formulas (sum(B2B10)/8)
• Refer to values by cell referencing
  (sum(B2B10)/B1)
• Use built in formulas (average(B2B10))
• Be careful with cell referencing (absolute vs.
  relative) (B3B5C3)
• Linking table information to charting

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Question for Discussion

• What are the affordances and constraints of
  activities during the professional development
• planning toward scaffolding integration of
  learning with and about spreadsheets with
  learning mathematics ideas
• individual lessons?
• a unit?
• yearly scope and sequence?

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Question for Discussion

• What are the affordances and constraints of
  activities during the professional development
• planning toward scaffolding integration of
  learning with and about spreadsheets with
  learning mathematics ideas
• individual lessons?
• a unit?
• yearly scope and sequence?
• practice teaching mathematics with spreadsheets
• with peers?
• with school-aged students in mathematics with
  spreadsheets?

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Question for Discussion

• What are the affordances and constraints of
  activities during the professional development
• planning toward scaffolding integration of
  learning with and about spreadsheets with
  learning mathematics ideas
• individual lessons?
• a unit?
• yearly scope and sequence?
• practice teaching mathematics with spreadsheets
• with peers?
• with school-aged students in mathematics with
  spreadsheets?
• reflecting on
• planning lessons?
• practice teaching?

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Question for Discussion

• Problems to guide learning about spreadsheets
  with math in the PD?
• Create own to match?
• Search for sources?
• http//eusesconsortium.org/edu/problems.php
• Others I have found

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http//eusesconsortium.org/edu/problems.php
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Just some sources

• http//www.microsoft.com/Education/default.mspx
• http//edweb.sdsu.edu/wip/
• http//www.teacherlink.org/content/math/activities
  /excel.html
• http//www.stfx.ca/special/mathproblems/welcome.ht
  ml
• http//mathforum.org/pow/
• http//sln.fi.edu/school/math2/
• http//www.algebra.com/algebra/homework/word
• http//www.teach-nology.com/teachers/lesson_plans/
  
• http//www.lttechno.com/links/spreadsheets.html
• http//members.aol.com/mind2ls/spreadsheet.htm
• http//www.hawaii.edu/suremath/intro_algebra.html

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Question for Discussion

• What strategies can be used to encourage and
  support teachers in implementing ideas from the
  professional development?
• Credit course
• School subject matter teams in prof. dev.
• Teachers administrators in prof. dev.

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Question for Discussion

• What are barriers that affect implementation?
• Difficulty with handling student with access to
  hands-on use of technology
• Lack of school support
• Lack of access to technology
• Technical requirements when incorporating
  technology
• Lack of preparation
• New mathematics curricula