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Exploring the Possibilities: Teaching and Learning Mathematics with Technology

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Title: Exploring the Possibilities: Teaching and Learning Mathematics with Technology


1
Exploring the Possibilities Teaching and
Learning Mathematics with Technology
  • Carly Hall
  • CEP 805
  • Fall 2004

2
NCTM Principles
  • Equity High expectations and support for all
    students
  • Curriculum Activities that are coherent,
    focused on important content, and articulated
    across grade levels
  • Teaching - Requires understanding of student
    knowledge, what needs to be learned, and when to
    challenge and provide support

3
NCTM Principles (continued)
  • Learning Students learn and understand by
    actively building new knowledge through
    experience and prior knowledge.
  • Assessment Supports learning and provides
    useful information
  • Technology Essential in influencing and
    enhancing learning

4
NCTM Strands Explored
  • Number Operation
  • Algebra
  • Geometry
  • Data Analysis Probability
  • Problem Solving

5
Affordances of Technology
  • Providing Access to information
  • Automating, simplifying, and transforming tasks
  • Representing knowledge and thinking
  • Communicating and collaborating with peers and
    experts

6
Number Operations Standard Grade 3-5 and 6-8
  • Understand numbers, ways of representing numbers,
    relationships among numbers, and number systems
  • Understand meaning of operations and how they
    relate to one another
  • Compute fluently and make reasonable estimate

7
What This Looks like in a Grades 3-5 Classroom
  • Students continue to develop number sense
    with an emphasis on multiplication and division.
    They work with larger number, fractions, and
    decimals using models and other strategies. They
    look at the relationship between multiplication
    and division and the types of problems that can
    be solved with these operations. Students compute
    whole numbers, develop algorithms, often using
    estimation, and selecting the appropriate
    computational tool.

8
What This Looks Like in a Grades 6-8 Classroom
  • Students build on prior number sense knowledge
    to broaden their understanding with more complex
    numbers and operations They divide fractions and
    decimals, use place value to extend their
    understanding of whole number addition and
    subtraction to decimals by examining and using
    properties of operations. Students examine
    whether an exact answer or an estimate is
    appropriate, determine the reasonableness of
    their answers, and choose methods in which to
    solve the problem.

9
Examples of Technology
  • Tools for Understanding Website
  • Using spreadsheets to explore Number and
    Operation concepts
  • - Lowest Common Multiple Activity
  • - Prime, Composite, and Square Number Activity

10
Algebra Standard for Grades 3-5 and 6-8
  • Understand patterns, relations, and functions
  • Represent and analyze mathematical situations and
    structures using algebraic symbols
  • Use mathematical models to represent and
    understand quantitative relationships
  • Analyze change in various contexts

11
What This Looks Like in a Grade 3-5 Classroom
  • Students begin to develop emerging algebraic
    ideas that serve as a precursor to grades 6-8.
    They build numerical and geometric patterns, look
    for and apply relationships between quantities,
    make generalizations, use graphs to describe
    patterns or make predictions, explore number
    properties, and use invented notation, symbols
    and variables to express a situation.

12
What This Looks Like in a Grade 6-8 Classroom
  • Students make more use of algebraic symbols,
    represent patterns related to linear functions,
    use tables, graphs words and expressions to
    examine and represent patterns of change, such as
    comparing and contrasting sets of data to two
    different representations of the same data. They
    also use formulas, and analyze change in
    graphical representations. All of this serves as
    a precursor to calculus. Student use of graphing
    calculators and computer software is also more
    prevalent in this grade span.

13
Examples of Technology
  • SimCalc
  • Magic Squares Lesson
  • Mangoes Problem Lesson
  • - From NCTMs Illuminations website
    (http//illuminations.nctm.org)

14
Geometry Standard Grades 3-5 and 6-8
  • Analyze characteristics and properties of two-
    and three-dimensional geometric shapes and
    develop mathematical arguments about geometric
    relationships
  • Specify locations and describe spatial
    relationships using coordinate geometry and other
    representational systems

15
Geometry Standard Grades 3-5 and 6-8 (continued)
  • Apply transformations and use symmetry to analyze
    mathematical situations
  • Use visualization, spatial reasoning, and
    geometric modeling to solve problems

16
What This Looks Like in a Grade 3-5 Classroom
  • Students describe and classify geometric
    objects and sort, build, draw, trace, measure,
    and construct geometric relationships. They
    construct mathematical arguments and expand
    vocabulary. Students learn about location,
    direction and distance on the coordinate plane.
    They explore transformations and reason about
    spatial relationships.

17
What This Looks Like in a Grade 6-8 Classroom
  • Students build on their knowledge of two-and
    three-dimensional shapes, visualizing figures
    from their experience with interacting with these
    objects in their daily lives. They explore a
    variety of geometric shapes and examine their
    characteristics using different types of
    manipulatives or geometry software. Students
    investigate congruence and similarity, draw
    representations of figures on the coordinate
    plane, and interpret shapes through
    transformations, They visualize spatial
    relationships by analyzing views of solid figures
    and using models to represent relationships.

18
Examples of Technology
  • Geometers Sketchpad
  • Symmetry and Pattern The Art of Oriental Carpets
    (http//mathforum.org/geometry/rugs/symmetry)
  • Getting It Right- The Pythagorean Theorem
    (http//cnets.iste.org/students/pf/pf_get_it_right
    .html)

19
Data Analysis Probability Standard Grades 3-5
and 6-8
  • Formulate questions that can be addressed with
    data and collect, organize and display relevant
    data to answer them
  • Select and use appropriate statistical methods to
    analyze data
  • Develop and evaluate inferences and predictions
    that are based on data
  • Understand and apply basic concepts of probability

20
What This Looks Like in a Grade 3-5 Classroom
  • Students build on their experiences with data
    to seeing a set of data as a whole, describing
    its shape, and using statistical characteristics
    to compare sets of data. They should pose
    questions relevant to themselves and their
    environment, become familiar with representations
    of data and construct graphs. Students use data
    to make inferences and predictions. They learn
    that probability is is a measurement of the
    likelihood of events and explore experiences to
    determine outcomes.

21
What This Looks Like in a Grade 6-8 Classroom
  • Students formulate questions, design surveys,
    and compare data to build upon their knowledge of
    collecting, organizing, and representing data.
    They use and interpret measures of central
    tendency and explore more complex graphical
    representations such as histograms, stem-and-leaf
    plots, and scatterplots. Questions are answered
    based on data representations and comparisons
    made between data sets. Students also use the
    idea of chance and number theory to examine and
    describe events.

22
Examples of Technology
  • Tools for Understanding Website
  • (Using spreadsheets to explore Data Analysis)
  • - Soda Survey Activity

23
Problem Solving Standard for Grades 3-5 and 6-8
  • Build new mathematical knowledge through problem
    solving
  • Solve problems that arise in mathematics and in
    other contexts
  • Apply and adapt a variety of appropriate
    strategies to solve problems
  • Monitor and reflect on the process of
    mathematical problem solving
  • At each grade span, students should have
    experiences with problems that interest,
    challenge, and engage their thinking.

24
Examples of Technology
  • Jasper Software that allows students to solve
    problems given a real-life scenario while using
    various skills found in each content area of
    mathematics.
  • (http//peabody.vanderbilt.edu/projects/funded/ja
    sper/)

25
Summary
  • Using the NCTM standards and the affordances
    of technology as the basis for planning
    instruction, teachers have a wide variety of
    technology resources to explore for engaging
    students in meaningful, relevant, and interactive
    learning. The possibilities are endless!
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