Professional Development that Supports and Follows Mathematics Teachers in Teaching

with Spreadsheets

Maggie Niess

Oregon State University

http://oregonstate.edu/~niessm

niessm@onid.orst.edu

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