Explicit Instruction in the Math Classroom for Students Receiving Special Education Services

Transcription

1 Explicit Instruction in the Math Classroom for Students Receiving Special Education Services Kimberly Baumgardner, M.Ed. Educational Specialist, ESC-20 National Board Certified Teacher Special Education Services = Specially Designed Instruction 34 CFR (a)(1) Specially Designed Instruction: adapting, as appropriate to the needs of an eligible child, the content, methodology or delivery of instruction to address the unique needs of the child that result from the child s disability; and to Ensure access of the child to the general curriculum so that the child can meet the educational standards within the jurisdiction of the public agency that apply to all children. (34 CFR (b)(3)) 1

2 Differentiated Instruction vs. Specially Designed Instruction DI Heterogeneous Grouping Movement Manipulatives Cues, questions, and advance organizers Nonlinguistic representations Cooperative learning Graphic Organizers (Instructional Strategies) Technology- Speech-to-text software Student Choice on Assessment Options/Homework Assignments/Text Selection Small Group Instruction Pre-Teach Opportunities V e r s u s SDI Extraneous information is removed Simplified numbers Three answer choice options on MC tests Instruction is direct,small group or individualized, and intensive, meaning emphasized over time Simplified graphics Simplified vocabulary Complex tasks are broken down into component parts and each part is completed before trying to combine the components Important tasks require frequent repetitions Assignments are shortened and/or divided into parts Accommodations that allow access to general ed curriculum;i.e., calculator, graphic organizer, oral administration, speech-to-text software NCTM acknowledges that, The need to understand and be able to use mathematics in everyday life, and in the workplace has never been greater and will continue to increase. Therefore instruction needs to be carefully planned and executed to emphasize conceptual understanding. 2

3 Conceptual Understanding 78% of adults cannot explain how to compute the interest paid on a loan; 71% cannot calculate miles per gallon on a trip; 58% cannot calculate a 10% tip for a lunch bill; U.S. Department of Education 2008 Students with learning disabilities Have more retention difficulties than students without disabilities Acquire skills in a broken sequence and have lower retention rates than their nondisabled peers these retention problems increase as the concepts become more difficult Demonstrate problems when they first encounter algebraic concepts because of the symbolic or abstract reasoning involved Research from Brad Witzel, How can I help students with learning disabilities in algebra? Intervention in School & Clinic, November

4 Five Evidence Based Guidelines for Implementing Mathematics Instruction Miller and Hudson. (2006). Helping students with disabilities understand what mathematics means. Teaching Exceptional Children, Sept/Oct. ARTICLE Guideline #5 Explicit Instruction 4

5 One of the most important methods of ensuring access to the general education curriculum for students with disabilities is through use of empirically validated instructional approaches. Explicit Instruction is a recommended teaching sequence endorsed by the U.S. Department of Education and the National Council of Teachers of Mathematics. 5

6 Gradual Release of Responsibility Explicit Instruction The ultimate goal of mathematics instruction is to teach students to solve problems independently. The flexible nature of these components encourages the gradual release of responsibility. Laney Sammons 6

7 How Does This Instructional Strategy Positively Impact Students Who Have Learning Problems? Teacher as model makes the concept/skill clear and learnable. High level of teacher support and direction enables student to make meaningful cognitive connections. Provides students who have attention problems, processing problems, memory retrieval problems, & metacognitive difficulties an accessible "learning map". Links between sub skills are directly made, making confusion and misunderstanding less likely. Multi-sensory cueing provides students multiple modes to process and thereby learn information. 7

8 Explicit Instruction Sequence Graphic Organizer Independent Practice Demonstration This sequence provides a gradual shift of responsibility from the teacher s demonstration to the student s independent performance. Guided Practice Graphic organizers are powerful tools for instruction since they enable students to organize data into segments or chunks that they can comprehend and manage. Graphic Organizers Graphic organizers can be used to bridge the connections between a student s prior knowledge, what the student is currently learning, and what the student can apply and transfer to mathematical problem solving in the future. 8

9 Why use Graphic Organizers? The use of graphic organizers can help students: See how ideas are organized or organize their own ideas Use a concrete representation to understand abstract ideas Arrange information so it is easier to recall Understand the hierarchy of ideas (from larger to smaller) Understand the interrelationship of complex ideas Why use Graphic Organizers? Graphic organizers are powerful tools for instruction since they enable students to organize data into segments or chunks that they can comprehend and manage. Graphic organizers can be used to bridge the connections between a student s prior knowledge, what the student is currently learning, and what the student can apply and transfer to mathematical problem solving in the future. 9

10 Graphic Organizers KWL Venn Diagram Bubble Map Consists of a review of previous knowledge, stating the purpose or objective of the lesson, and a rationale for learning the new content. Venn Diagram 10

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12 dryeraseboard.com dryeraseonline.com 12

13 Allowable Accommodation for STAAR & STAAR Modified All Subjects: Blank Graphic Organizers Blank graphic organizers may be used. Blank graphic organizers NEVER contain titles, words, labels, pictures, acronyms, mnemonics, numbers, symbols, or variables. Group 1 1 & 2 Group 2 13

14 All subjects: Blank Graphic Organizers Blank graphic organizers NEVER contain titles, words, labels, pictures, acronyms, mnemonics, numbers, symbols, or variables. Tertiary Consumer Secondary Consumer Primary Consumer Primary Producer All Subjects: Blank Graphic Organizers Blank graphic organizers NEVER contain titles, words, labels, pictures, acronyms, mnemonics, numbers, symbols, or variables. G 14

15 Math Graphic Organizers I Do Demonstration 15

16 I Do Demonstration Teacher models the concept and solves the problem Keep student engagement through participation Talk/Think aloud Asking questions Choral responses Allows teacher to gauge student understanding to determine how much modeling is needed Think Aloud To model for students the thought processes that take place when difficult material is read. When using think alouds, teachers verbalize their thoughts while they are reading orally. Students will understand comprehension strategies better because they can see how the mind can respond to thinking through trouble spots and constructing meaning from text. 16

17 Think Aloud Examples on-plan/math-think-alouds easoningprobsolvingthinkalouds69.ht m/ Pete s PowerPoint Station 17

18 Technology is an essential tool for teaching and learning mathematics effectively; it extends the mathematics that can be taught and enhances students' learning. 18

19 Conceptua Math Free Fractions Guided Lessons /studyjams/jams/math/index.htm 19

20 Teach Me How to Factor Exponents 20

21 Educreations Interactive Whiteboard Educreations turns your ipad into a recordable whiteboard. Creating a great video tutorial is as simple as touching, tapping and talking. Explain a math formula create an animated lesson add commentary to your photos.diagram Teach what you know: Help students with homework by working through an example problem. Put your lessons on the web so students can watch them before and after class. Tutor someone from afar. Showcase your video tutorials on educreations.com and share your knowledge with the world. Add your commentary Screen Chomp Share a great idea... Explain a tricky concept... Help kids with their homework... A simple doodling board, markers, and oneclick sharing tools make spreading your ideas and know-how easy and fun! Just - Record It. Sketch It. Share It. - to create a sharable, replay-able video that tells your story clearly. 1. Touch RECORD to capture your touch interactions and audio instructions on a plain background, or an image from your ipad camera roll. 2. SKETCH out your ideas and talk the viewer through the "how" and "why" of it all. 3. Stop and SHARE your video snack to ScreenChomp.com to generate a simple web link you can paste anywhere. 21

22 Audio Note- $4.99 Reviews: This is the BEST note-taking app in the App Store. Must have app for business. Perfect for school and lectures. Features: Synchronized note taking and audio recording Text or handwritten notes Seek directly within audio by tapping text or drawings Highlighted notes during playback and share note and audio files We Do Guided Practice 22

23 We Do Guided Practice Begins with a high level of teacher support (step-by-step prompts), then moves to a medium level of support (multiple steps performed with fewer prompts), and then moves to a low level of support (reduces prompts so students take on more responsibility) and then ends with no prompts. HOW? Have students come to the chalkboard, dry erase board, overhead, or SMART Board and work problems that can serve as a visual for the remainder of the class. Have them explain the steps in solving the problem so that students have an auditory link to the visual problem. 23

24 We Do Guided Practice Specific information about why a student did not complete a task correctly is important to convey to students with learning disabilities. 24

25 Math Manipulatives Why use Manipulatives? The best teaching techniques for fostering intelligence unite mind and body (Wilson, 1999). Kinesthetic learners are at their best when engaged in physical movement or when completing meaningful reallife learning activities (Gregory & Chapman, 2002). 25

26 Manipulatives in Math Conceptua Math Free Online Fraction Tools 26

27 Virtual Manipulatives Wikki Stixs 27

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29 Allowable Accommodation for STAAR & STAAR Modified 29

30 Allowable Manipulatives for STAAR & STAAR Modified real or play money (both heads and tails) clocks (with or without numbers shown on clock face) base-ten blocks various types of counters (e.g., two-sided chips, blocks, beans) algebra tiles; the tiles should NEVER contain words, labels, pictures, acronyms, mnemonics, numbers, symbols, or variables fraction pieces (e.g., fraction bars, fraction circles); the fraction pieces may be labeled to show each individual fraction, but they should NEVER show equivalencies (e.g., 1/2 = 2/4 = 0.5 = 50%) or the cumulative sequence (e.g., 1/4, 2/4, 3/4, 4/4) geometric figures that are grade- or course-appropriate; the figures may be provided in either three-dimensional form or twodimensional form (net), but NOT in both forms; the figures should NEVER contain words, labels, colors used as labels, pictures, acronyms, mnemonics, numbers, symbols, or variables Translucent (tracing) paper Math Supplemental Aids 30

31 Mathematics: Addition Charts Addition charts may be used. The addition chart must be a grid used to find the sum, not a list of addition facts. Each axis may be numbered up to 9, but no higher than 9. Indicating special numbers (e.g., highlighting or circling even numbers within the body of the chart) is NEVER allowed = = = = = = = = = = 20 Mathematics: Multiplication Charts Multiplication charts may be used. The multiplication chart must be a grid used to find the product, not a list of multiplication facts. Each axis may be numbered up to 12, but no higher than 12. Indicating special numbers (e.g., highlighting or circling perfect squares) in the body of the chart is NEVER allowed. 1 x 0 = 0 2 x 0 = 0 1 x 1 = 1 2 x 1 = 2 1 x 2 = 2 2 x 2 = 4 1 x 3 = 3 2 x 3 = 6 1 x 4 = 4 2 x 4 = 8 1 x 5 = 5 2 x 5 = 10 1 x 6 = 6 2 x 6 = 12 1 x 7 = 7 2 x 7 = 14 1 x 8 = 8 2 x 8 = 16 1 x 9 = 9 2 x 9 = 18 31

32 Mathematics: 100 Chart A 100 chart may be used. Indicating special numbers (e.g., highlighting or circling prime numbers within the body of the chart) is NEVER allowed. Mathematics: Place Value Chart A place value chart may be used. Words for place value labels and a decimal point are allowed only if they are grade-appropriate. Including numbers as specific examples is NEVER allowed

33 Mathematics: Pictorial Models Pictorial models of fraction bars or fraction circles may be used. The models may be labeled to show each individual fraction, but they should NEVER show equivalencies or a cumulative sequence. Mathematics: Pictorial Models Pictorial models of one-,two-, and three-dimensional figures may be used. The figures may NEVER contain titles, words, labels, acronyms, mnemonics, numbers, symbols, or variables. TRIANGLE vertex 33

34 Mathematics: Nets A pictorial model of a geometric figure may be provided in either three-dimensional form or two-dimensional form (net), but NOT in both forms. NOT 3-D and 2-D on the same aid You Do Independent Practice 34

35 You Do Independent Practice Demonstrate mastery without teacher assistance Manipulative aids used in instruction should continue to be available for students to use during independent practice as well as on TAKS (for students with disabilities) Excel Quiz with/without feedback HOW? Provide students with a written model solution (examples that you have worked out) to refer to when they are solving problems on their own. These model solutions can serve as visuals to guide the thinking of your students and assist them when confusion exists. 35

36 Guided Math Assistance Idea: Homework 36

37 MathBoard More than just standard drills, MathBoard encourages students to actually solve problems, and not just guess at answers. This is done by providing multiple answer styles, as well as a scratchboard area where problems can be worked out by hand. Students can also turn to MathBoard's Problem Solver for further help. This powerful teaching feature walks students through the steps required to solve addition, subtraction, multiplication, and division equations. Additionally, the included quick reference tables serve as a valuable learning tool. GAMES Play speeds up the brain s maturation process since it involves the built in processes of challenge, novelty, feedback, coherence, and time. ~Jenson,

38 Brain-Based Research Strategies Games when your brain gets to play a game it gets excited! Allowing learners to redesign any game that they already know, such as Wheel of Fortune, Are you Smarter than a 5 th Grader, Jeopardy, Who Wants to be a Millionaire, Ball Toss provides the brain connections necessary for better understanding of the content (Jensen). Real World Connection Games Problem Solving Games 38

39 Explicit Instruction IN REVIEW Review previously taught skill of finding the least common multiple (venn diagram) Review vocabulary (denominator, numerator, multiple) Teaching PowerPoint Teacher: Model process & talk aloud Teacher/Students go through process together (students use whiteboards) teacher talk through, ask questions, walk around & observe Give students more opportunity to work through process without teacher assistance Teacher give feedback, re-teach as needed Move to independent practice Review and offer more practice using Excel Quiz Would I do all of this on one day? 39

40 Explicit Instruction Classroom Lesson, 6:40 Teaching Matters Explicit Instruction, 4:54 Math Instructional Videos: Explicit Instruction tments/sped/mathvids/strategies/em. html 40

41 Kimberly Baumgardner (210)