# Exploring the Possibilities: Teaching and Learning Mathematics with Technology - PowerPoint PPT Presentation

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

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### 1. Exploring the Possibilities: Teaching and Learning Mathematics with Technology ... Solve problems that arise in mathematics and in other contexts ... – PowerPoint PPT presentation

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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
• 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
• 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

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
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
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
• 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
• 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!