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Multi sensoryaccess2mathri17final
- 1. Multisensory Access to Math Slidesare posted here: Madalaine Pugliese madalaine@comcast.net
- 2. Multisensory Access to Math MadalainePugliese Assistive Learning Technologies, LLC (Karen Janowski) EdTech Solutions, LLC
- 3. Presentation Overview • Definitions:UDL and Differentiated Instruction, multisensory learning • Overview of math challenges • Brief overview math intervention • NCTM listserv comments = real world implementation • Stages Math: Number Sense - features • Stages Math Intervention Kit • Stages Math: Number Sense – demo • Hands-on Stations
- 4. Definition - UDL •Multiple means of representation, to give learners various ways of acquiring information and knowledge • Multiple means of expression, to provide learners alternatives for demonstrating what they know • Multiple means of engagement, to tap into learners' interests, offer appropriate challenges, and increase motivation
- 5. Definition - UDL •Based on creating flexible goals, methods, materials, and assessments that consider diversity. • Centers the need for multiple approaches to meet the needs of diverse learners • Mirrors the universal design movement in architecture (curb cuts, and close-captioned television—all universally designed to accommodate a wide variety of users) • Features that support challenges benefit everyone. • Uses technology's power and flexibility to make education more inclusive and effective for all
- 6. Definition Differentiated Instruction • Strategiesthat enable all students to participate and make progress in the general curriculum • Educators provide additional support to students who need it during regular instruction • Facilitates being able to individualize instruction for a diverse group
- 7. Definition Differentiated Instruction • Canbe enhanced with the use of technology scaffolds • Technology scaffolds increase teacher capacity to individualize instruction • Especially useful in support of learners with math, reading or writing difficulties
- 8. Definition Multisensory Learning • Usemany sensory areas to activate brain • grow student engagement • build student interest (fun) • activate prior knowledge while building new concepts • create associations between new learning and memory
- 9. Definition Multisensory Learning • connectlearning to language hearing own or the teacher's/parent’s voice (auditory) • facilitates development of new meaning through multiple representations, associate new concepts with memory (visual) • build meaning and memory as hands manipulate objects to build understanding in numeracy, place value, basic operations, fractions (tactile)
- 10. Make Your OwnMath for Multisensory Learning • Use cardboard, markers and scissors to make your own Cuisenaire rods or pattern blocks • Food for fractions (pizza, corn chips...) • Egg cartons for sorting, counting and place value Sources “Math Toolbox in Every Home” http://mathcats.org/ Printable instructions for making and using manipulatives “15 Homemade Math Manipulatives” http://theendinmind.net/15-homemade-math-manipulatives-2/
- 11. Math Challenges • Learningchallenges in mathematics are complex. • There is no single mathematics challenge.
- 12. Math Challenges • Studentsmay be strong in some areas of math and weak in others. • From 6–7% of all students exhibit challenges in one or more areas of math.
- 13. Math Challenges • Somemathematics challenges are independent of reading disability and some are not. • Research about math challenges has progressed more slowly than research about reading challenges.
- 14. Signs of aMath Challenge • Has difficulty keeping track of numerical information while counting. • Forgets arithmetic facts or doesn’t remember as many. • May use immature problem solving procedures.
- 15. Signs of aMath Challenge • Has difficulty with the abstract concepts of time and direction. • When writing, reading and recalling numbers: adds, substitutes, transposes, omits, and reverses numbers. • Demonstrates poor mental math ability.
- 16. Signs of aMath Challenge • Has difficulty keeping score during games; loses track of whose turn it is. • Unable to grasp and remember math concepts, rules, formulas, sequence (order of operations), and basic math facts. • Gets lost or disoriented easily; may have a poor sense of direction.
- 17. Signs of aMath Challenge • Children with a math challenge can have one or both of two memory problems: 1. Getting basic facts into long term memory and accessing memorized facts. 2. Sifting through all the recalled memorized facts for the relevant information; e.g., 2 + 3 might evoke answers of 4, 5, or 6
- 18. Despite the signsof a math challenge, a learner may: • Show normal or accelerated language acquisition: verbal, reading, writing. • Have good visual memory for the printed word. • Excel in other areas. • Catch up; it may be a developmental delay and not a more fundamental deficit.
- 19. Assessing Math Abilities •Conduct a one-to-one mathematics interview. • Note how the child does mathematics. • Search for strategies that work or don’t work, strengths and weaknesses.
- 20. Assessing Math Abilities •Assess the full range of areas: computation, pattern prediction, sorting, measuring, organizing space with flexibility. • Observe and note any verbalization, drawings, asking for repeat of directions/question. • Ask child to estimate answer before computing.
- 21. From the NCTMlistserv… "Strategically" indicates that students will select an appropriate tool based on the task. For example, given 10 x 5 x 2, a student might pick up a pencil, calculator or calculate the product mentally. Providing opportunities for students to reflect on their choices in terms of efficiency and effectiveness deepens their understanding of their strategic choices. As teachers, we can use students' tool selection to provide diagnostic information and help us prepare other learning opportunities.
- 22. How to helpstudents with math challenges: • Work to define the student’s strengths. • Encourage students to estimate their answers before they begin to work out the problem. • Have students work together in small groups to solve problems. • Allow the use of calculators and manipulative materials.
- 23. Use of calculators Researchhas shown that using calculators does not: • promote laziness • impede development of basic math skills • create a dependency on technology Instead it does: • promote achievement • improve problem solving skills • increase understanding of mathematical ideas Students retain more information and gain a better attitude toward math.
- 24. To be successful… Studentsshould work toward: • number sense mastery • good problem solving strategies • automaticity (recall of facts) this allows more brainpower to go toward problem solving (not spent on computing)
- 25. Students with numbersense can: • Count rationally past 100. • Understand that the sequence of counting doesn’t change. • Count objects in any order. • Know that last number named is total number. • Count past difficult numbers (19, 29, 100). • Count backwards, starting with any number. • Skip count by 2s, 5s, and 10s. • Relate basic addition and subtraction facts. • Explain operation of multiplication. • Explain place values through the hundreds.
- 26. A Letter toMy Math Teacher: • “I need instant answers and a chance to do the problem over once if I get it wrong the first time.” • “Problems written too closely together on the page cause me mental confusion and distress.” • “Please allow me more than the standard time to complete problems and please check to see that I am free of panic (tears in my eyes, mind frozen).” • “If possible, please allow me to take the exam on a one-to-one basis in your presence.” • “I am not lazy, and I feel really smart in everything but math. That is what frustrates me the most! Everything is easy for me to learn, but Math makes me feel stupid! Please, do be patient with me, and please do not give up on me!” (source at end)
- 27. 10 Tips forSoftware Selection for Math Instruction by Beatrice C. Babbitt 1. The less clutter on the screen, the better. 2. Procedures should match those being taught in school. 3. Choose modifiable software. Software should allow for customized speed, number of problems and instructional levels. 4. Choose software with small increments between levels.
- 28. 10 Tips forSoftware Selection for Math Instruction 5. Choose software with helpful feedback. Provide clues to the correct answer. 6. Choose software that limits the number of wrong answers for a single problem. Limit the number of attempts, give clues to the correct answer, provide the correct answer, reintroduce that same item at a later time. 7. Choose software with good record keeping capabilities.
- 29. 10 Tips forSoftware Selection for Math Instruction 8. Choose software with built in instructional aids; e.g., counters, number lines, base ten blocks, hundreds charts, or fraction strips. 9. Select software that simulates real-life solutions; e.g., multiple roads to a problem solution. 10. Remember that software is a learning tool – not the total solution!
- 30. Highlights of StagesMath: Number Sense iPad app or computer software 28 main activities within 9 key content areas of number sense
- 31. Stages Math Options Optionsto manage users
- 32. Stages Math Settings Generalsettings for mode, Rewards, Number line, Animations …
- 33. Stages Math Settings Selectcontent area, then activity, then specific skill. Then save settings for each student.
- 34. Stages Math Settings Accessibilitysettings are saved separately for each student.
- 35. Highlights of StagesMath: Number Sense • Universal and Accessible design for both iPad and computer mouse, keyboard, switch, touch screen; auditory scanning, text-to-speech, pointer with dwell on computer • Feedback for incorrect answers that builds learner understanding • Scaffolding to support learner success turn on or off prompting, graphical support, help buttons, etc.; talk boards for classroom inclusion • Adjustable settings you can save for each learner • Record keeping and certificates
- 36. Karen’s Case Study Thirdgrade Student • Cognitive Disabilities • Dependent on prompts and adults • Significant fine motor challenges Stages Math was recommended and implemented following an AT Assessment and school-based team meeting
- 37. Karen’s Case Study DanielleD. Special educator reflections: • Preparation • Implementation • Observations • Next Steps
- 38. “When I giveHannah (not her real name) choices, she chooses to use Stages Math!” ”It has given me data that guides my instruction. I can see she needs to better understand Math symbols and Math language.” “I need to use it for all my students!” Mia - "I love that app! It's very fun! It's just the right level for me! I think I want to play this every time I get to do math games!"
- 40. Highlights of StagesMath Intervention Kit Look at Math Introductory Kit covers a wide range of concepts with a 120-lesson Instructor’s Guide, a heavily illustrated Student Book, and a PDF for printouts.
- 41. From the NCTMlistserv… "I need help as it relates to the cognitive and physical tools being used strategically." This really got me thinking... I did a little "Googling" and found this: Three Ways to Use Appropriate Tools Strategically (Mathematical P . (Sandler mentions number bonds as a cognitive "tool.”)
- 42. Highlights of StagesMath Intervention Kit Look at Math Introductory Kit covers a wide range of concepts with a 120-lesson Instructor’s Guide, a heavily illustrated Student Book, and a PDF for printouts. Place Value Packaging is a hands-on activity, requiring students to use number pegs to solve place value and addition problems.
- 43. From the NCTMlistserv… I am trying to wrap my head around the word "Strategically". I need help as it relates to the cognitive and physical tools being used strategically. Please help!! I use place value blocks and an assortment of tools to illustrate fractions. Many times the students play with the materials, such as building towers. However, as we begin to learn about the numbers with the tools, the towers disappear and the tools are being used strategically to illustrate the concept, such as division of fractions, regrouping, etc.
- 44. Explore YouTube… Lots ofexpert/teacher/parent made exploration activities. Place Value Introduction Number Rock Place Value Song
- 45. Highlights of StagesMath Intervention Kit Look at Math Introductory Kit covers a wide range of concepts with a 120-lesson Instructor’s Guide, a heavily illustrated Student Book, and a PDF for printouts. Place Value Packaging is a hands-on activity, requiring students to use number pegs to solve place value and addition problems. Talking Calculator gives students auditory feedback when solving computations.
- 46. Highlights of StagesMath Intervention Kit Look at Math Introductory Kit covers a wide range of concepts with a 120-lesson Instructor’s Guide, a heavily illustrated Student Book, and a PDF for printouts. Place Value Packaging is a hands-on activity, requiring students to use number pegs to solve place value and addition problems. Talking Calculator gives students auditory feedback when solving computations. Six laminated Day Planner Books simplify daytime schedules.
- 47. Highlights of StagesMath Intervention Kit Look at Math Introductory Kit covers a wide range of concepts with a 120-lesson Instructor’s Guide, a heavily illustrated Student Book, and a PDF for printouts. Place Value Packaging is a hands-on activity, requiring students to use number pegs to solve place value and addition problems. Talking Calculator gives students auditory feedback when solving computations. Six laminated Day Planner Books simplify daytime schedules. Hands-On Money provides an organized collection of realistic bills and coins and 3 coin cubes.
- 48. From the NCTMlistserv… The problem with using manipulatives to teach numbers is that the manipulatives do not have numbers on them. The teacher is banking on the students understanding and remembering what is said; but some students do not hear a lot of what is said. I made a YouTube video that shows how to make and use "manipulatives on paper" to effectively address this problem. (Jeff Sandler, Mastery Learning Systems) Learning to Count to 10 Using 10 Blocks Number Line Learning to Count to 20 with Place Value Hands On Money
- 49. Highlights of StagesMath Intervention Kit Look at Math Introductory Kit covers a wide range of concepts with a 120-lesson Instructor’s Guide, a heavily illustrated Student Book, and PDF for printouts. Place Value Packaging is a hands-on activity, requiring students to use number pegs to solve place value and addition problems. Talking Calculator gives students auditory feedback when solving computations. Six laminated Day Planner Books simplify daytime schedules. Hands-On Money provides an organized collection of realistic bills, coins and coin cubes. TimeWheel™ a realistic clock to help learn to tell time
- 50. Stages Math InterventionKit = multisensory access to math • Universal Design – multiple means of representation, engagement and expression • Differentiate Instruction – variety of scaffolds • Multisensory – manipulative materials • Access –content accessible through digital interactions
- 51. Research References “A Letterto My Math Teacher”, compiled by Renée M. Newman http://www.dyscalculia.org/teacher.html “Learning Disabilities in Mathematics”, by C. Christina Wright http://www.ldonline.org/article/5947 “Mathematical Disabilities: What We Know and Don't Know”, by David C. Geary, http://www.ldonline.org/article/5881 “Math Intervention: What Strategies Work for Struggling Learners” articles collected by Education Northwest http://educationnorthwest.org/resources/mathematics-interventions-what-strategies-work-struggling- learners-or-students-learning “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities”, by Russell Gersten and David J. Chard http://www.ldonline.org/article/5838 “Strategies for Teaching Math: What are the Facts?” by Carol H. Geller http://www.ldworldwide.org/pdf/journal/2000/11-00_arithmetic.pdf “Technology-Supported Math Instruction for Students with Disabilities” by Hasselbring, Lott, and Zydney http://209.61.229.180/library/resourcedocs/Tech-SupportedMathInstruction-FinalPaper_early.pdf http://www.citeducation.org/mathmatrix/ “10 Tips for Software Selection for Math Instruction”, by Beatrice C. Babbitt http://www.ldonline.org/article/6243
- 52. URLs Demonstrated Videos “Three Waysto Use Appropriate Tools Strategically” blog by Jeff Sadlier • https://www.sadlier.com/school/sadlier-math-blog/three-ways-to-use-appropriate-tools-strategically-math- practice-5 “Place Value Introduction” • https://www.youtube.com/watch?v=fshyCNqHIbw “Number Rock Place Value Song” • https://www.youtube.com/watch?v=a4FXl4zb3E4 “Learning to Count to 10 Using 10 Blocks Number Line” • https://www.youtube.com/watch?v=ji-jsPbovv0&index=5&list=PLm4gYQg22haYidp4sISJMX_h4xC7gXKQ_ “Learning to Count to 20 with Place Value Hands On Money” • https://www.youtube.com/watch?v=45yeM- At9F4&index=4&list=PLm4gYQg22haYidp4sISJMX_h4xC7gXKQ_ Sources of Home Made Manipulatives “Math Toolbox in Every Home” • http://mathcats.org/ Printable instructions for making and using manipulatives “15 Homemade Math Manipulatives” • http://theendinmind.net/15-homemade-math-manipulatives-2/
- 53. Hands-On Stations Station 1:iPads for Stages Math app – demo first Station 2: Hands-on “Money” Place Value Packaging Talking Calculator Hands-On Money with Coin Cubes Station 3: Hands-on “Time” TimeWheels Day Planners Look At Math (Teachers Guide and Students Workbook)
- 54. Thanks for coming! Let’ssee the software/app in action!
Editor's Notes
- #2 Use this slide if your audience needs to have the slides as handouts. Post them to Slideshare so that they can be used but not copied.
- #4 NCTM identified 5 skill areas: Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability. Our Stages Math addresses skills in the first area, Number and Operations.
- #5 Classic definition
- #6 Fine tuning ideas to incorporate
- #7 Teaching considerations are planned ahead placing a wide range of materials strategically within the environment. (Stages Math Intervention Kit)
- #8 Stages Math Intervention Kit
- #11 Give audience a “make your own” option right away to diffuse the tone of a “sales pitch”
- #12 refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons.
- #13 an increasingly heated controversy about how to teach mathematics but no disagreement that strategic instruction is key
- #14 concept of number sense is as important to mathematics learning as phonemic awareness has been to the reading research field
- #15 Needs to work on ability to represent the same number in multiple ways depending on the context and purpose of this representation.
- #16 Needs to understand that 1 + 12 = 12 + 1
- #17 Counting, 1 to 1 correspondence, quantifying
- #18 #2 means that if learners see the numbers 2 and 3, they may not pay attention or understand what they should do with those numbers, and so may come up with 4 (the next number in the sequence), 5 (their sum), or 6 (their product (multiplication)).
- #19 Reading the problem. Students are taught how to read mathematical problems, including using reading strategies to understand the problem (e.g., focusing on important information), developing mathematical vocabulary, and recognizing when they do not understand relationships among mathematical terms and quantitative concepts expressed in a problem. Paraphrasing. Students are taught how to put the problem into their own words and convey meaning. Visualizing. Students are taught to draw a representation or to make a mental image of the problem. Hypothesizing about problem solutions. Students are taught how to decide the number of operations that are needed to solve the problem, select and order the operations, and then to transform the information into correct equations and algorithms. Estimating the answer. Students are taught how to stay focused on the type of outcome (e.g., number of yards rather than feet), and then how to predict the answer by using the information in the problem and their projected solution path. Computing. Students are taught how to recall the correct procedures for working through the algorithms and the necessary math facts for accuracy. Checking the problem. Students are taught how to check the mathematical problem solving process to ensure that they have understood the problem, accurately represented the problem, selected an appropriate solution path, and solved the problem correctly.
- #20 In the interview one focuses as intently on how the child does mathematics as on what or how correct they do it. It is essential to keep in mind that you are searching for what does work at the same time as you are probing to find out what doesn't work.
- #21 include the use of manipulatives, i.e. coins, base ten blocks, geoboards, cuisenaire rods, and tangrams. A calculator is an important tool and can be used to uncover the difference between comprehension and computation difficulties.
- #22 NCTM advocates and supports the integration of manipulative materials
- #24 Wouldn’t a multisensory calculator help lots of kids? Yes!
- #25 Researchers explored the devastating effects of the lack of automaticity in several ways. Essentially, they argued that the human mind has a limited capacity to process information, and if too much energy goes into figuring out what 9 plus 8 equals, little is left over to understand the concepts underlying multi-digit subtraction, long division, or complex multiplication.
- #27 http://www.dyscalculia.org/teacher.html
- #28 Stages Math, which you will see shortly, demonstrates all these key features.
- #29 Students who use appropriate technology persist longer, enjoy learning more, and make gains in math performance.
- #30 With software based on principles of Universal Design, students are able to access course materials in ways that are flexible and customizable. A central feature of UDL is its ability to adapt to students with different perceptual and cognitive needs.
- #36 Various forms of scaffolding is one of the primary ways software can be customized and aligned with a UDL approach
- #37 The student was a member of an substantially separate program for students with cognitive disabilities. She was included at the beginning of the school day and during specials. The student had a difficult time during periods of instruction and sometimes had meltdowns. She was dependent upon adults for most of her work. Stages math was recommended as part of an AT Assessment to promote independence during math work and the team agreed. She struggled with all aspects of Number Sense and other online resources were too visually distracting and could not be customized. Danielle, the special education teacher reported Hannahloved using Stages Math. She used it in the inclusion third grade classroom during math and Hannah was able to work on the iPad independently.
- #38 Danielle received Stages Math over the summer and was so excited to use it, she taught herself and then implemented it right at the start of the new school year. Two weeks later, I met with the entire team, including Hannah’s mom, and showed them how they could review the data. Danieele had discovered many of the features on her own. She observed that Hannah was engaged by Stages Math and was able to use it independently. Next steps – she was so excited with Stages Math, Danielle couldn’t wait to try it with other students. In addition, two other special education teachers wanted to get the app to use with their students! They saw the potential!
- #39 Mads, this is a note to you – the black ink shows a quote from a different student – the next steps were that two other teachers implemented it with their students (because of the gift codes). A different teacher, Shoshana, gave me the bottom quote that I just added. It came from Mia, a second grade student. (I tired to add another slide but the background doesn’’t copy for some reason).
- #40 This data shows one sitting. Data captured over time is pending.
- #41 Multiple means of engagement in the same skills aligned with a UDL approach
- #42 Key is to be strategic with how manipulative materials are used. There is lots of support for this online. Several examples are included in this presentation.
- #43 Multiple means of engagement in the same skills aligned with a UDL approach
- #44 Place Value tools start as toys but progress toward helping to formulate math concepts
- #45 Show a little bit of each to get the general idea
- #46 Multiple means of engagement in the same skills aligned with a UDL approach
- #47 Multiple means of engagement in the same skills aligned with a UDL approach
- #48 Multiple means of engagement in the same skills aligned with a UDL approach
- #49 Video: Learning to Count to 10 – Show 3:20 – 5:00 as an example of a way to incorporate tools in establishing 1 to 1 correspondence, numeral recognition and counting Video: Learning to Count to 20 – Show 1:58 – up to 4:00 as am example of using play money
- #50 Multiple means of engagement in the same skills aligned with a UDL approach
- #51 Multiple means of engagement in the same skills aligned with definitions cited earlier in presentation