Transcript The Mathematics of Movement: O&M and Math Education

The Mathematics in Movement:
Teaching Mathematics Content
Through Orientation and Mobility
Presented by
Derrick W. Smith, Ed.D., COMS
University of Alabama in Huntsville
Recommendations Based on Research
• Students can learn both concepts and skills by solving
problems.
• Giving students both an opportunity to discover and
invent new knowledge and an opportunity to PRACTICE
what they have learned improves student achievement.
• Teaching mathematics with a focus on number sense
encourages students to become problem solvers in a
wide variety of situations and to view mathematics as a
discipline in which thinking is important.
• Long-term use of concrete materials is positively related
to increases in student mathematics achievement and
improved attitudes toward mathematics.
– Grouws & Cebulla (2002)
Learning Mathematics
• "When students can connect mathematical
ideas, their understanding is deeper and more
lasting." (NCTM, 2000, p. 63).
• NCTM encourages students to EXPERIENCE
mathematics in MULTIPLE CONTEXTS.
• Common Core places great emphasis on
application, generalization, and problemsolving (i.e. “critical thinking skills”)
So what does this mean?
For students to develop a grounded
understanding of the importance and
application of mathematics, they have to be
provided opportunities to not only learn the
basic concepts but EXPERIENCE the concepts
and MAKE applications!
Who's Job Is It Anyway?
• Direct instruction should come from general
educators.
• TVIs have a unique role as collaborators.
• O&M specialists are considered related
service providers.
• All are part of the multidisciplinary team (as
required by law) but hopefully moving toward
become more interdisciplinary!
Numbers and Operations
• Defined:
– understanding numbers (including systems);
– understanding meanings of operations and how they are
related to one another;
– compute fluently and make reasonable estimations.
• Common Core Connections: Counting & Cardinality;
Operations & Algebraic Thinking; Number &
Operations in Base Ten/Fractions; The Number System
• Concepts:
– numeracy, counting and cardinality, sets (odds, evens,
multiples, integers), addition, subtraction, multiplication,
division, fractions, estimations
Number and Operations Connections
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Counting (doors, driveways, steps, etc.)
One-to-One correspondence
Even and Odds (address systems)
Basic fractional concepts
Numerals (print and Nemeth)
Integers (2 steps forward, 3 steps back)
Estimations (distance, length, etc.)
Operations (take every opportunity)
Algebraic Thinking
• Defined:
– 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.
• Common Core Connections: Operations & Algebraic
Thinking; Expressions & Equations; Functions
• Concepts:
– equations, inequalities, relationships, problem solving
Algebra Connections
• Number patterns (even, odds, blocks, etc.)
• Basic functions (How many steps would it take
to get and back? 2x? How many steps would
it take to get and back and there and back?
4x?)
• Shopping exercises (If 1 can costs $0.59, how
much would 4 cans cost? Oh yeah, that's
algebra!)
Geometry
• Defined:
– analyze characteristics and properties of two- and threedimensional geometric shapes and develop mathematical
arguments about geometric relationships;
– specify locations and describe spatial relationships using
coordinate geometry and other representational systems;
– apply transformations and use symmetry to analyze
mathematical situations;
– use visualization, spatial reasoning, and geometric
modeling to solve problems.
• Common Core Connections: Geometry
• Concepts:
– Geometry means to "measure the earth". The
connections are limited only by our imagination.
Geometry Connections
• Spatial Concepts
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positional terms (up, down, below, above, etc.)
directional terms (right, left, compass, etc.)
geometric terms (point, line, line segment, ray)
reasoning (If the east wing of the building is shaped
like this, what will the west wing look like?)
Angles (degree turns)
Parallel and Perpendicular (duh!)
Polygons (blocks, roundabouts, etc.)
Perimeter and Area
Maps (location on a grid, transformations)
Measurement
• Defined:
– understand measurable attributes of objects and the
units, systems, and processes of measurement;
– apply appropriate techniques, tools, and formulas to
determine measurements.
• Common Core Connections: Measurement
• Concepts:
– Units of measurement (length, height, weight, time,
currency, capacity)
– Use of appropriate tools
Measurement Connections
• Develop understanding of length
measurement in nonstandard and standard
terms (both English and metric systems).
• Development of small time increments
(seconds, minutes)
• Distance formula (d = rt) (How long will it take
you get from point A to point B if you are
walking 50 yards/minute and point B is 300
yards away?)
• Appropriate clothes to wear.
Measurement Connections, Part 2
• Consumer mathematics:
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The value of currency;
Folding systems;
Addition, Subtraction
Estimation (Do you have enough money to buy these
items?)
• Weight
– Differentiate between nonstandard weights
• Capacity
– Measurement of volume (liquids and solids)
Measurement Connections, Part 3
• Tools
– Do you provide your students opportunities to
measure as they travel?
– Nonstandard units such as steps compared to
standard units.
– GPS systems?
Data Analysis and Probability
• Defined:
– 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.
• Common Core Connections: Statistics &
Probability
Data Analysis and Probability
Connections
• Data Analysis
– Sales price (alternative methods of
computing)
– Weather forecast (everybody laugh)
• Probability
– What are the odds...
Process Standards
• While the previous sections were content
focused, math instruction also focuses on
processes.
• They include:
– Problem solving
– Reasoning and proof
– Communication
– Connections
– Representations
Process Standards, Part 2
• Problem Solving: Provide your students with
the opportunity to problem solve when
applicable (reading maps, "drop-off" lessons,
addresses, distance determination, "Can you
afford" exercises).
• Reasoning and Proof: When your students are
discussing mathematical principles in
application, make sure their logic is clear and
correct.
Process Standards, Part 3
• Communication: Can the student discuss their
application of math? This is relevant in all
areas, but especially in geometric terms and
consumer math.
• Connections: In essence, this is what we are
doing! FIND WAYS TO CONNECT!!
• Representation: Tactile maps using geometric
figures and measurement tools.
Collaborate
• Attempt to collaborate with the general
education teacher to reinforce math content
being taught in the classroom.
• Ask questions of the general education
teacher if you are unclear of the content
(especially in high school).
• The Expanded Core Curriculum utilizes the
Core!
• Find opportunities and USE THEM!
MAKE MATH MEANINGFUL
THROUGH ORIENTATION AND
MOBILITY!
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