Transcript The Mathematics of Movement: O&M and Math Education
The Mathematics of Movement: O&M and Math Education
Presented by Derrick W. Smith, Ed.D., COMS®
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.
Correlated to constructivist concepts of learning, especially those of Richard Skemp and the development of schema.
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!
Vision Professionals
• • Keep in mind the unique barriers that our students/clients encounter and how vision professionals can help circumvent these.
– TVIs serve a unique role in providing access to information and co-teaching concepts.
– – O&M specialists focus on independent travel.
Both focus on providing meaningful experiences.
My contention is that in the midst of providing these "experiences" that we can provide student opportunities to apply the concepts learned in the classroom!
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.
Concepts: – numeracy, sets (odds, evens, multiples, integers), addition, subtraction, multiplication, division, fractions, estimations
Number and Operation Connections
• • • • • • • Counting (doors, driveways, steps, etc.) One-to-one correspondence Even and Odds (address systems) Basic fractional concepts Numerals (print and Nemeth) Estimations (distance, length, etc.) Operations (take every opportunity)
Algebra
• • 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.
Concepts: – 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 three dimensional 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. Concepts: – Geometry means to "measure the earth". The connections are limited only by our imagination.
Geometry Connections
• • • • • • Spatial Concepts – 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. 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?)
Measurement Connections, Part 2
• • • Consumer mathematics: – – 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.
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 standards were content focused, the final five are considered "process standards".
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: Honestly, I cannot find a good way to connect this to O&M!
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!