professional development that supports and follows mathematics teachers in teaching with...
TRANSCRIPT
Professional Development that Supports and Follows Mathematics Teachers in Teaching
with Spreadsheets
Maggie Niess
Oregon State University
http://oregonstate.edu/~niessm
541-737-1818
11th Annual AMTE ConferenceIrvine, CaliforniaJanuary 26, 2007
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.
– SatelliteSatellite: • One time installation of $29$29 and $49$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.
– DVDDVD: • Purchase a DVD player for $250$250 and unlimited
rental of DVDs for $30$30 per month.
Help them make a decision
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 approachDynamic_Function_Machine.xls
Question?
What do students learn– Using prepared
spreadsheets to solve mathematics problems?
– Designing and using spreadsheets for solving mathematics problems?
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
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
PedagogyHope is not a strategy
~Thomas 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
Key Questions!!
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?
If we teach today as we taught yesterday, then we rob our children of
tomorrow. ~John Dewey
Technology Pedagogical Content Knowledge (TPCK)
Content
Technology
Pedagogy
PCK
TPCK
Central Components of TPCK (Adapted from Grossman’s (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 teacher’s 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.
Model of TPCK Professional DevelopmentTPCK Professional Development
Summer ProgramClassroom Teaching
(Academic School Year)-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
Levels of Development of TPCK(developed through Niess professional development research)
Recognizing
Accepting
Adapting
Exploring
Advancing
What was their progress?
TH - Exploring
MB - Exploring
SG - Exploring
FC - Exploring
AS - Adapting
DH - Adapting
CT - Adapting
MJ - Accepting
JH - Accepting
MM - Recognizing
During Summer Program Classroom Teaching
TH - Advancing
MB - Accepting
SG - Exploring
FC - Adapting
AS - Exploring
DH - Adapting
CT - Adapting
MJ - Advancing
JH - Recognizing
MM - Recognizing
Personal knowledge, new curriculum
Difficult students
Unwilling to change instruction
School support, enthusiasm for tech
Personal knowledge with technology
Highly motivated, school support, work w/ multiple technologies
Highly motivated, previous exper w/ssSearching for apps to math classBeliefs about learning math
Limitations of time/crowded curr.
Substitute teaching, low motivation
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?
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?
Question for Discussion
What operations and concepts support spreadsheets as dynamic and dependable tools for learning mathematics?– Avoid numeric values in formulas (=sum(B2:B10)/8)– Refer to values by cell referencing (=sum(B2:B10)/B1)– Use built in formulas (=average(B2:B10))– Be careful with cell referencing (absolute vs. relative)
(=$B$3*B5+$C$3)– Linking table information to charting
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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are needed to see this picture.
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?
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
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?
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
http://eusesconsortium.org/edu/problems.php
Just some sources…
http://www.microsoft.com/Education/default.mspxhttp://edweb.sdsu.edu/wip/http://www.teacherlink.org/content/math/activities/excel.htmlhttp://www.stfx.ca/special/mathproblems/welcome.htmlhttp://mathforum.org/pow/http://sln.fi.edu/school/math2/http://www.algebra.com/algebra/homework/wordhttp://www.teach-nology.com/teachers/lesson_plans/http://www.lttechno.com/links/spreadsheets.htmlhttp://members.aol.com/mind2ls/spreadsheet.htmhttp://www.hawaii.edu/suremath/intro_algebra.html
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.
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