1. Vocabulary CRA Fluency Problem Solving MATH METHODS

2.  To teach math vocabulary, teachers can provide additional time on task, use flash cards and peer tutors, and monitor progress toward mastery. Learning of vocabulary concepts can also be promoted by direct verbal elaboration including mnemonic strategies (Mastropieri & Scruggs, 2010).  Mnemonic strategy instruction produced significant gains for students with a learning disabilities in math (Maccini et al., 2007).  Use mnemonics like "Please Excuse My Dear Aunt Sally" (order of operations) to remember sequenced steps. MATH VOCABULARY/MNEMONICS

3.  Using the concrete-representational abstract (CRA) teaching sequence integrates the use of manipulative devices and pictorial representations into explicit instruction designed to teach important concepts (Miller & Hudson, 2007).  1) Students first represent the problem with concrete objects (manipulatives).  2) Then move to the representational (pictures) phase and draw or use pictorial representations of the quantities.  3) Finally the abstract phase involves numeric representations, instead of pictures. CONCRETE, REPRESENTATIONAL, ABSTRACT (CRA)

4.  Using materials/manipulatives you can help students learn a numerous MATH concepts: addition and subtraction; operations with integers; fraction equivalents; counting money; telling time, measurement, place value, etc.  A helpful intermediate step between counting actual numbers and operating with numbers is the use of a number line that has lines with marks to represent quantity.  Providing modeling, prompting, and evaluation to ensure students are independent at calculator use is a training not to be overlooked. (Mastropieri & Scruggs, 2010) MANIPULATIVES

5. Teachers should model and encourage calculator use when:  The focus of instruction is problem solving.  Anxiety about computation might hinder problem-solving.  Student motivation and confidence can be enhanced through calculator use. CALCULATOR USE

6.  Students who are taught math skills until they achieve fluency tend to maintain their skills (Axtell et al., 2009).  FASTT Math is an intervention program that provides systematic adaptive instruction and practice to help students close fluency gaps.  There are 390 BASIC arithmetic facts  100 addition- deal with only whole numbers  100 subtraction- with difference only 1 digit  100 multiplication- single digits  90 division- single digit  3 types of activities for teaching basic facts  understanding – CONCRETE DEMONSTRATIONS  relationships- FACT FAMILIES  mastery- MEMORIZATION MATH FLUENCY

7. TouchMath: Used to promote computation, materials represent quantities by dots on the numbers 1-9.  The numeral 1 is touched at the top while counting, “One”  The 2 is touched at the beginning and the end of the numeral while counting, “One, two.”  6 is touched and counted from top to bottom, “One-two, three- four, five-six.  It’s important that the correct dot/circle (circle is introduced for numbers 6+) arrangement is used; does not matter whether the dot or circle is counted first. http://www.youtube.com/watch?v=-H_fdf-odsc http://www.youtube.com/watch?v=baaFE3j660U&feature=related MULTISENSORY MATH TOOL: TOUCH MATH

8.  Some students have difficulty understanding how words are used in word problems, and what specific operations are applied by these problems (Mastropieri & Scruggs, 2010).  There are many problem solving strategies available to incorporate self-monitoring of steps completed (metacognition).  S.O.L.V.E method: Study the problem Organize the facts Line up a plan Verify your plan with action Evaluate your answer PROBLEM SOLVING

9.  Use graphic organizers to indicate which step is to be done. Gradually reduce cues.  Color-code math steps next to math problems.  Provide an example of the first problem, with steps on the paper as an example.  Have steps in solving math problems readily available on graphic organizer, chalkboard, bulletin board, on student’s desk, etc.  Have the student check answers to math problems on a calculator.  Have student equate math problems to real-life situations in order that he/she will better understand the steps involved in solving the problem.  Have student verbalize the problem solving steps to self or teacher. DIFFICULTY FOLLOWING STEPS IN MATH PROBLEMS

10.  Computer-assisted instruction (CAI) refers to instruction or remediation presented on a computer. http://www.k8accesscenter.org/training_resources/computeraided_m ath.asp  It improves instruction for students with disabilities because students receive immediate feedback and do not continue to practice the wrong skills.  Students may also progress at their own pace and work individually or problem solve in a group.  Textbooks have websites with tutorials or self-check quizzes for students to practice skills independently. http://www.glencoe.com/sec/math/msmath/mac04/course2/index.p hp/na COMPUTER ASSISTED INSTRUCTION (CAI)

11.  Steps to solve equations: 1) Isolate the variable. 2) Perform the opposite operation on both sides. 3) Remember operation order is opposite of PEMDAS, add or subtract first to get rid of whole #, then multiply or divide. 4) Substitute your answer for variable to check accuracy. eg. 4x + 6 = 26 4x + 6 – 6 = 26 – 6 4x = 20 4 x = ? ALGEBRAIC CONCEPTS

12. Students should move through six levels of mastery to learn and retain mathematical concepts:  Level 1: Connects new knowledge to existing knowledge and experience  Level 2: Searches for concrete materials to construct a model or show a demonstration of the concept  Level 3: Illustrates the concept by drawing a diagram to connect the concrete example to a symbolic picture or representation  Level 4: Translates the concept into mathematical notation using number symbols, operational signs, formulas, and equations  Level 5: Applies the concept correctly to real-world situations, projects, and story problems  Level 6: Can teach the concept successfully to others or can communicate it on a test 6 LEVELS OF MASTERY

13.  Number line  Multiplication chart, arithmetic table, number chart  Graphic organizers highlighting steps or new math word  Templates for recording information  Calculator  Color cubes, color tiles, attribute blocks, numeral cards, number cubes, pattern blocks, tangrams, dominoes, color tiles  Larger or partially filled-in templates  Compasses, protractors, rulers  Geoboards, tangrams, geometric solids ACCOMMODATIONS FOR MATHEMATICS

14.  Axtell, P. K., McCallum, R. S., Bell, S. M., & Poncy, B. (2009). Developing math automaticity using a classwide fluency building procedure for middle school students: A preliminary study. Psychology in the Schools, 46, 526- 538. doi: 10.1002/pits.20395  Mastropieri, M. A. & Scruggs, T.E. (2010). The inclusive classroom: Strategies for effective differentiated instruction, 4 th edition. Upper Saddle River, NJ: Merrill.  Miller, S. P., & Hudson, P. J. (2007). Using evidence-based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research and Practice, 22, 47-57. doi: 10.1111/j.1540-5826.2007.00230.x REFERENCES