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Arithmetic and Mathematics

Arithmetic and Mathematics. Stephanie Brown & Mattie Ball. What is Arithmetic and Mathematics?. -- Arithmetic is to math like spelling is to writing --.

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Arithmetic and Mathematics

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  1. Arithmetic and Mathematics Stephanie Brown & Mattie Ball

  2. What is Arithmetic and Mathematics? -- Arithmetic is to math like spelling is to writing -- Arithmetic: (1) the branch of mathematics that deals with addition, subtraction, multiplication, and division; (2) the use of numbers in calculation Mathematics: (1) the study of the relationships among numbers, shapes, and quantities; (2) it uses signs, symbols, and proofs and includes arithmetic, algebra, calculus, geometry, and trigonometry

  3. Review of Research Trends in International Mathematics and Science Study (TIMSS), Programme for International Student Achievement (PISA), and U.S. National Assessment of Educational Progress (NAEP) all found in similar studies that the USA, compared to other nations: Ranked high in mathematics in 4th grade Below average when students entered 9th grade Among the poorest achievement when students reached 12th grade

  4. The National Council of Supervisors of Mathematics • Created in 1977 due to the low mathematics scores • Identified ten basic skill areas that needed to be included in the curriculum • Problem solving • Applying mathematics to everyday situations • Alertness to the responsibleness of results • Estimation and approximation • Appropriate computational skills • Geometry • Measurement • Reading, interpreting, and constructing tables, charts, and graphs • Using mathematics to predict • Computer literacy

  5. The Outcome • The Curriculum and Evaluation Standards for School Mathematics in 1989 was created, later revised and better known as Standards 2000 • Included six principles that have undertones for working with and accommodating the needs of students with disabilities • Equity - strong support for all students • Curriculum - focused on important skills • Teaching - understanding what the children need • Learning - using experiences • Assessment - increased time and modifications • Technology - enhances student learning

  6. The Purpose Raise student achievement so that all students have access to the competitive society with changing job requirements and advances in technology To eliminate the achievement gaps among students of diverse populations No Child Left Behind - 2002

  7. What is Functional Arithmetic and Mathematics? • Skills needed in order to reach goals such as everyday living at home and/or working in the community • Money management, time, estimation and geometry • Teachers must reflect on the purpose of mathematics instruction and a student’s present level of functioning • Programs must include content that is based on the type of mathematics that will be needed for each individual student because what constitutions functional, varies from student to student

  8. Conceptual Skills • Concept of numbers, money, and time • Social Skills • Leisure activities • Practical Skills • Self-help, daily living, health care, transportation, and schedules Connecting Mathematics to Adaptive Behaviors

  9. Problem Solving Abstract Thought Poor Short-Term Memory Identifying Patterns Developing Strategies Poor Generalization Distractible Areas of Difficulties for Students with IDD

  10. Possible Mathematical Difficulties Recognizing and writing numbers as well as mathematical symbols Counting without the use of their fingers Ordering numbers Recalling or remembering number facts as well as being able to count quickly Performing operations Accomplishing multidigit calculations Switching from one operation to another Using estimation and approximation skills Selecting and implementing effective mathematical strategies Problem solving

  11. Assessment • Consider strengths and weaknesses when trying to obtain information • Assessment in mathematics should utilize all techniques listed below and should never be limited solely to a single demonstration • Observation of student behavior • Interview • Checklists • Rating scales • Student classroom work

  12. Types of Assessment • Standardized Measures of General Achievement • Wide Range Achievement Test - 4 • Diagnostic Achievement Battery - 3 • Test of Early Mathematics Ability - 3 • Standardized Diagnostic Measures • KeyMath 3 Diagnostic Assessment (K-8) • Stanford Diagnostic Mathematics Test 4 - Screening Test (1.5-13) • Test of Mathematical Abilities (3-12) • BRIGANCE • Curriculum Based Measures • Most instructionally useful • Asses a specific skill • Enough problems to ensure knowledge/mastery • Similar problems can be constructed • Student-specific data can guide meaningful instruction • Informal Diagnostic Techniques • Subdividing and expanding the concepts/skills • Pinpoints the difficulties students are having through error patterns and task analysis

  13. BRIGANCE

  14. Brigance Life Skills • Basic Telephone Skills (10) • 1. Answers telephone and gets person requested • 4. Selects requested number from a small personal list or directory • 5,6,7. Selects numbers from a list….etc • 9. Knows how to call 911 • Money and Finance Skills • Values of coins & bills • Values of groups of coins • Convert coins • Price signs • Makes change • Computes totals • Computes and understands savings on purchases (sale, more than, less than) • Uses charts and tables to compute expenses • Applications for credit card, understands deposit slips, writes checks, and computes balance.

  15. Norm-referenced Intended to identify the level of mathematical ability for children 3-8. Strengths and weaknesses in mathematics and learning arithmetic. Test of Early Mathematics Ability (TEMA-3)

  16. Method for Creating Lessons • Determine what is functional math for your students • Plan instruction based on prerequisite skills, standards, and goals • Have necessary materials ready • Teach to mastery • Ensure maintenance and generalization Important to keep Paraprofessionals in the loop and help them to teach their own groups consistently/effectively.

  17. Strategy

  18. Scope and sequence reflecting a realistic examination of their future environment Teach students to understand mathematical concepts, do not force them to memorize rote responses for basic facts Connect to everyday situations to promote motivation through relevance Ensure fluency and mastery Direct Instruction Instructional Implications

  19. Solve mathematical problems and then apply what they have learned to hands-on-activities Cooperative Learning - grouping students fosters positive social skills and individual accountability Teach learning strategies and/or mnemonics Use math manipulatives, if strong material control Peer tutoring Instructional Implications Continued...

  20. Video Self-Modeling on an iPad to Teach Functional Math Skills to Adolescents with ASD and ID - Burton, C., et al. • Video-Based Interventions • Video Self-Modeling (VSM) - the student observes themselves accurately and independently performing the target behavior. Created by the teacher creating a script of the steps of the task analysis and prompting each student as necessary in reading the steps and solving the math problems • Researchers concluded that students who viewed themselves successfully completing math problems performed at higher levels than students who did not watch the VSM • Fading procedures occurred to reduce the number of video models provided to the student over time

  21. The Use of Peer Tutoring for the Acquisition of Functional Math Skills among Students with Moderate Retardation (sic) - Schloss, P. J., et al. • Same-age, peer tutoring (one-way or reciprocal) was effective in teaching functional math skills • Be sure to teach appropriate behaviors and provide reinforcement • All students mastered the next dollar strategy • Students we able to generalize the skill to make actual purchases in consumer settings

  22. Teaching Tips and Tricks

  23. Teaching Tips and Tricks Continued...

  24. Teaching Tips and Tricks Continued...

  25. TouchMath

  26. Vmath

  27. Materials - Kits - Programs OFF TO THE CURRICULUM LAB! Questions?!

  28. References Burton, C. E., Anderson, D. H., Prater, M. A., & Dyches, T. T. (2013). Video self-modeling on an iPad to teach functional math skills to adolescents with autism and intellectual disability. Focus On Autism And Other Developmental Disabilities, 28(2), 67-77. FitzSimons, G. E. (2008). A comparison of mathematics, numeracy, and functional mathematics: What do they mean for adult numeracy practitioners?. Adult Learning, 19(3-4), 8-11. Polloway, E. A., Patton, J. R., & Serna, L. (2008). Chapter 8: Mathematics instruction. Strategies for teaching learners with special needs. Upper Saddle River, N.J: Pearson Merrill Prentice Hall. Schloss, P. J., Kobza, S. A., & Alper, S. (1997). The use of peer tutoring for the acquisition of functional math skills among students with moderate retardation. Education And Treatment Of Children, 20(2), 189-208.

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