1. 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 Conference Irvine, California January 26, 2007

2. 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 –Satellite: $29$49One 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 –DVD: $250 $30Purchase a DVD player for $250 and unlimited rental of DVDs for $30 per month. Help them make a decision

3. 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

4. Question? What do students learn –Using prepared spreadsheets to solve mathematics problems? –Designing and using spreadsheets for solving mathematics problems?

5. Mathematics Content Life 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

6. Technology I 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

7. Pedagogy Hope 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

8. 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

9. Technology Pedagogical Content Knowledge (TPCK) Content Technology Pedagogy PCK TPCK

10. 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.

11. Model of TPCK Professional Development TPCK Professional Development Summer Program Classroom 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

12. Levels of Development of TPCK (developed through Niess professional development research) Recognizing Accepting Adapting Exploring Advancing

13. 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 ProgramClassroom 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/ss Searching for apps to math class Beliefs about learning math Limitations of time/crowded curr. Substitute teaching, low motivation

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

15. 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?

16. 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

17. 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?

18. 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?

19. 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?

20. 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

21. http://eusesconsortium.org/edu/problems.php

22. 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.html 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

23. 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.

24. 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