Vocabulary

CRA

Fluency

Problem Solving

MATH METHODS

To teach math vocabulary, teachers can provide additional time on task, use fl ash 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 signifi cant

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

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)

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

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

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 fl uency 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

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

Some students have diffi culty understanding how words are used in word problems, and what specifi c 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 problemOrganize the factsL ine up a planVerify your plan with actionEvaluate your answer

PROBLEM SOLVING

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 fi rst 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

Computer-assisted instruction (CAI) refers to instruction or remediation presented on a computer.

http://www.k8accesscenter.org/training_resources/computeraided_math.asp

It improves instruction for students with disabilities because students receive immediate feedback and do not continue to practice the wrong skil ls.

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 skil ls independently.

http://www.glencoe.com/sec/math/msmath/mac04/course2/index.php/na

COMPUTER ASSISTED INSTRUCTION (CAI)

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 fi rst to get rid of whole #, then multiply or divide.

4) Substitute your answer for variable to check accuracy.

eg. 4x + 6 = 264x + 6 – 6 = 26 – 64x = 204x = 204 4x = ?

ALGEBRAIC CONCEPTS

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

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 fi lled-in templates Compasses, protractors, rulers Geoboards, tangrams, geometric solids

ACCOMMODATIONS FOR MATHEMATICS

Axtell, P. K., McCallum, R. S., Bell, S. M., & Poncy, B. (2009). Developing math automaticity using a classwide fl uency 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 diff erentiated instruction, 4 t h 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