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Technology Solutions for Mathematic Instruction

Technology Solutions for Mathematic Instruction. Sean J. Smith, Ph.D. University of Kansas seanj@ku.edu. UDL Context to Mathematics What we Know!.

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Technology Solutions for Mathematic Instruction

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  1. Technology Solutions for Mathematic Instruction Sean J. Smith, Ph.D. University of Kansas seanj@ku.edu

  2. UDL Context to MathematicsWhat we Know! • Provide rationale or develop relevance through an activity prior to a lesson. If student sees the real need for the skill, their attention will be engaged and effort will be increased.

  3. UDL Context to MathematicsWhat we Know! • Develop lessons that focus on mathematics in daily living skills, functional tasks, or consumer skills (NCTM data analysis, statistics, and probability – collect data on weather by recording rainy, cloudy, or sunny days). • Integrate mathematics across the curriculum.

  4. UDL Context to MathematicsWhat we Know! • Integrate values and cultures of students in the classroom into mathematic examples and problem-solving activities to provide a meaningful context (bakery to solve word problems with fractions…Navajo Bread, Greek baklava, German strudel, etc.) • Dance Simulation • http://www.ccd.rpi.edu/Eglash/csdt/subcult/brdance/software/dancer.html

  5. NCTM Standards • Does ALL mean ALL? • Instructional/Assistive Technology can result in Meaningful Access.

  6. Math + LD = Challenges

  7. Characteristics - Math Challenges • Passive Learners • They often do not make connections - connecting prior knowledge to present circumstances is limited. • For example, students may learn that 8 x 4 = 32, but when presented with 8 x 5 = ___, they do not actively connect the process of multiplication to that of repeated addition.

  8. Characteristics - Math Challenges • Memory Challenges • Complicates learning math facts • Challenges multi-step problem completion • Attention Problems • Difficulty staying on task • Difficulty building on previous knowledge • Math Anxiety

  9. Characteristics - Math Challenges • Difficulty processing • Visual information • Auditory Information • Processing challenges present time limitations • Often never have enough time or opportunity to master the foundational concepts/skills that make learning higher level mathematics possible. • http://www.teachers.ash.org.au/jeather/maths/dictionary.html

  10. Mathematics - What We Know • MathVids • http://coe.jmu.edu/mathvids2/ • Research based effective math instructional strategies • Detailed lesson plans with video based instructional models

  11. Mathematical Knowledge and Learning NCTI Mathematics Matrix • Building computational fluency; • Converting symbols, notations, and text; • Building conceptual understanding; • Making calculations and creating mathematical representations; • Organizing ideas; and • Building problem solving and reasoning

  12. FASTT Math -Fluency

  13. Mathematics and the web • The web offers a variety of tools that support math instruction, completion of mathematic equations, and the ability to illustrate mathematics.

  14. Google Math Tricks Google as a Calculator • Go to google.com • Type a math problem in the search window. • Click the Google search button. • The answer will appear in the next screen

  15. Google as a conversion tool! • In the search window type something you want to convert (Be sure to use the word “in”). 2 feet in inches 1 mile in meters 100 dollars in cents 72 c in f • Click the Google Search Button • The answer will appear in the next screen.

  16. Popular Math Illustrations • BrainPop - www.brainpop.com • Nutshell Math- www.nutshellmath.com • AAA Math - www.aaamath.com • Cool Math www.coolmath.com

  17. Number Sense • Identifying - Naming • Sequencing - Order • Memory - Remembering

  18. Numbers & Operations • Rote Counting– involves saying number names in sequence from memory. • Rational counting– involves coordinating rote counting with each object in a particular group. • Ordinal counting– involves saying the numbers relative to their position in time or space (e.g., first, second, third, fourth).

  19. In developing Number Sense students must develop the ability to: • Read and Write Number Symbols and Words • Identify relationship among Whole Numbers • Symbol-Quantity Match • One-to-One Correspondence between Groups • Quantity Comparison • Place Value • Column Alignment • Place Value Recognition • Base Ten Identification

  20. Number Sense - Tech Ideas • Shodor Activities www.shodor.org/interactivate/activities/#num • Concentration http://illuminations.nctm.org/ActivityDetail.aspx?ID=73 • Five Frame http://illuminations.nctm.org/ActivityDetail.aspx?ID=74 • National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/topic_t_1.html • Colour It http://www.mathsyear2000.org/magnet/minus/colour/index.html

  21. Number Sense - Tech Ideas • Math Magician http://oswego.org/ocsd-web/games/mathmagician/cathymath.html • Dog Bone http://www.oswego.org/ocsd-web/games/DogBone/gamebone.html • Sum to 10 http://www.mathsyear2000.org/magnet/minus3/sumtox/index.html • Guess the Number (All) http://www.funbrain.com/guess/index.html

  22. Understanding Numbers • Organizing Information • Categories • Organize • Connect • Number Sentences • Breaking concepts down • Sorting or Classifying • Analyzing and Comparing Numbers

  23. Number Sense - Calculators • Calculators will promote student laziness; • Students will not be stimulated/challenged if they use calculators; • Using calculators impedes the development of basic mathematical skills; and • The use of calculators will create a dependency on technology.

  24. Number Sense - Calculators • Promote achievement; • Improve problem-solving skills; and • Increase understanding of mathematical ideas. • Math Cats Age Calculator (3-8) http://www.mathcats.com/explore/age/calculator.html

  25. Rational Numbers • Equivalent Fractions http://illuminations.nctm.org/ActivityDetail.aspx?ID=80 • Fresh Baked Fractions (3-6) http://www.funbrain.com/cgi-bin/fob.cgi?A1=s&A2=0 • Fraction Flags (2-6) http://www.oswego.org/ocsd-web/games/fractionflags/fractionflags.html

  26. Measurement • Attribute Comparison (e.g., what is length) • Comparison of 2 or more objects or pictures • Measuring with Nonstandard Units • The desk is 15 new crayons long • The fish bowl holds 20 paper cups of water

  27. Measurement • Understanding Standard Customary Units • Identify specified unit when presented a pictorial, concrete, or descriptive examples • Identify the appropriate tool for measurement • Read/write the unit term and abbreviation/symbol • Measuring with Standard Units • They understand and are now ready to measure.

  28. Geometry • Instruction must include and target conceptual understanding (i.e., what concepts such as congruence means), declarative knowledge (i.e., factual memory of names of shapes), procedural development (i.e., step-by-step construction of a figure), and problem-solving ability (i.e., applications).

  29. Teaching Algebraic Thinking • teach within authentic and meaningful contexts • use multisensory methods to discriminate between and among concepts • incorporate language experiences • teach procedural knowledge and strategic thinking

  30. Ways to Create Authentic Contexts • Video/Digital Photography • Depict contexts of mathematics concepts • www.unitedstreaming.com • Skits/Plays/Drama • acting out real-life situations • Literature • Newspapers descriptions of sporting events • Art • Explore relationships and patterns

  31. Problem Solving • Rationale for enhancing problem-solving abilities • Mathematical Problem Solving in the Workplace • Mathematical Problem Solving in Daily Living • Mathematical Problem Solving in Leisure Activities

  32. Building Conceptual Knowledge and Understanding • Teaching isolated math skills = inert knowledge - restricted set of contexts • Our students must understand the real-world contexts - organized to spark a trigger. • Anchored instruction - anchoring or situating mathematical knowledge in meaningful, real-world applications.

  33. Building Conceptual Knowledge and Understanding • Microsoft’s Movie Maker • Allows user to develop engaging movies - Windows operating system. • Apple’s iMovieneed to add direct links • Allows user to develop engaging movies - Apple operating system. • Teaching Enhanced Anchored Mathematics • Visual representation of math concepts

  34. Building Conceptual Knowledge and Understanding

  35. Building Problem Solving • reading the problem, • thinking about the problem, • deciding the operation, • writing the numerical sentence, • calculating the math operation, • labeling the answer, and • checking the work

  36. Building Problem Solving • Schema-Based Instruction • Using diagrams to represent word problems • Put-Together • Change-Get-More • Change-Get-Less • Compare • Breaks down the problem for student context. • Context allows for student to complete the word problem.

  37. Building Problem Solving

  38. Next Steps • Review Wiki • Review Tracks • Thank you for your time! Sean J. Smith seanj@ku.edu

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