Vo c a bula r y
MATH METHODS
CRA
Fl ue n c y
P ro bl e m So l ving
MATH VOCABULARY/MNEMONICS
 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.
CONCRETE, REPRESENTATIONAL,
ABSTRACT (CRA)
 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.
MANIPULATIVES
 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 )
CALCULATOR USE
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.
MATH FLUENCY
 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
MULTISENSORY MATH TOOL:
TOUCH MATH
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, threefour, 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
PROBLEM SOLVING
 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
DIFFICULT Y FOLLOWING STEPS IN MATH
PROBLEMS
 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.
COMPUTER ASSISTED INSTRUCTION (CAI)
 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
ALGEBRAIC CONCEPTS
 Steps to solve equations:
1) Isolate the variable.
2) Per form the opposite operation on both sides.
3) Remember operation order is opposite of PEMDAS, add or
subtract fir st 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
4x = 20
4
4
x = ?
6 LEVELS OF MASTERY
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
ACCOMMODATIONS FOR MATHEMATICS
 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
REFERENCES
 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 , 526538. 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