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17 Cards in this Set

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TYPES OF REPRESENTATIONS
THE MIDDLE SCHOOL TEACHER NEEDS TO BE ABLE TO USE THE FOLLOWING: COORDIANTE, ALGEBRAIC, GEOMETRIC
LOOK AT FIRST EXAMPLE: tHE CIRCLE BELOW
HAS BEEN REPRESENTED ON A COORDINATE PLANE, ASN AN ALGEBRAIC EQUATION AS A GEMOETRIC FIGHRE
ALGEBRA FIGURE
(X+4)^2 + (Y-2)^2
GEMOTERIC CIRCILE
WITH A RAIDUS OF 5 MM
KEYS OF THE COMMUNICATION OF MATH IDEAS
TEACHERS MUST RECOGNIZE AND LOOK FOR WAYS TO HELP STUDETNS DEVELOP AND UNDERSTAND MATH IDEAS. COMMUNICATION OF MATH IDEAS IS NOT ABOUT TELLING BUT ABOUT TEACHING. sO YOU NEED TO HAVE A VARIETY OF COMMUNICATION PRESENTATIONS FOR DEVELOPING MATH IDEAS
KNOW THE FOLLOWING FORMS OF MATHMAICAL COMMUNICATION AND WHAT GRADE USES IT
CONCRETE
VERBAL
PICTORIAL
SYMPOLIC
GRAPHICAL
SYMBOLIC NUMVERIC
EXAMPLE: DEVELOP TEH PROCESS FOR MULTIPLYING FRACTIONS:
CONCRETE: ues transparent unit grids marked in fractional parts and have students laay them on top of each other to determine the products. When the grid with 3/43 marked is alaid on top of the grid wiht 1/2 marked, there are now 8 equal areas marked and 3 of the 8 equal are shaded both directions
EXAMPLE: DEVELOP TEH PROCESS FOR MULTIPLYING FRACTIONS:
Pictorial version: have the students draw a box and seperate it into 4 equal areas horizontally and two equal areas vertically. Have them color thre of the foru horizontal strips in o ne color and one of the two veritcal strips in another color. This allows them to determine that 3/4's of 1/2 is 3/8
EXAMPLE: DEVELOP TEH PROCESS FOR MULTIPLYING FRACTIONS:
verbal: multiply the numerators and multiply the denominators
Communication of math information
although this appears to be very much like communicating math ideas, this about ways to communicate data relationships.
Table, Diagrams, Graphs
COMMUNICATION OF MATH PROPERIES AND CONCEPTS
COMMUNICATE MATHEMATICAL IDEAS USING A VARIETY OF REPRESENTATIONS. aPPROPRIATLEY USE THE VISUAL MEDIA TO COMMUNICATE MATHMATICAL INFORMATION
EXAMPLE 1: oUT OF 960 STUDENTS IN MS, 55% OF THEM ARE INVOLVED INSOME TYPE OF MUSIC PROGRAM AND AN ADDITIONAL 1/3 OF THE STUDENTS ARE INVOLVED IN SOME TYPE OF ATHLETICS PROGRAM. hOW MANY STUDEENTS ARE NOT INVOLVED IN EITHER OF THESE TWO PROGRAMS?
SOLUTION D
.55(960)=528 AND 1/3(960)=320
848 STUDENTS=TOTAL NUMBER INVOLVED IN MUSIC OR ATHLETICS, BUT NOT BOTH
EXAMPLE 2: PAGE 105 A SIXTH GRADE CLASS (CONCRETE ) WAS ABOUT TO STUDY OF THE VARIOUS PARALLELOGRAMS. THE STUDENS HAVE JUST COMPLETED A PAPERER FOLDING ACTIVITY WHERE THEY INVESTIGATED THE RELATIONSHIPS OF ONE SIDE LENGTHS AND ANGLE MEASURES WHICH OF THE FOLLOWING WOULD BE A GOOD NEXT STEPS, DEVELPMETNALLY?
gIVEN A SET OF PARALLELOGRAM, HAVE THE STUDETNS MARK THE CONGRUNET ANGLES IN THE SAME COLOR FOR EACH OF THE PARALLELOGRAMS. STUDETNS SHOULD DO THE ACTIVITY IN (B) SO THAT THEY CAN VISUALL AND PHYSICALLY BE ABLE TO IDENTIFY OPPOSITE SIDES AND ANGLES AND USE THE RELATIONSHIPS DISCOVERED IN THE PAPER FOLDING ACTIVITY
Concrete Operational Students (Third Grade - Fifth Grade)
Concrete Operational Students (Third Grade - Fifth Grade)
ABSTRACT THINKING
6-8TH
TYPES OF CONCRETE LEAARNING
A concrete learner is the child who has difficulty making the shift from the hands-on learning of early childhood to the symbolic world of formal education; the child who finds not only letters and printed words inadequate but sometimes spoken words as well; the child who always continues to need hands-on experiences. All young children are by their nature concrete learners.

Concrete learners like a hands-on approach. They don't want just to read about an experiment; they want to do it. Concrete learners advertise their nature to observant parents and teachers as they touch everything. Children with ADD usually learn better by concrete methods.

Effect on learning: The concrete learner will remember best what has been made real to her through hands-on instruction.

Strategies: Any time you need to make materials, such as flash cards, have the child help you. She'll understand the materials better and work harder with them just because she's helped make them.

Example: If you're making flash cards for math facts, guide the child as she makes them instead of making them yourself. Don't tell her the answer to the facts; give her a calculator and let her find the answer.
WHAT IS ABSTRACT LEARNING
Abstract reasoning
Abstract learners make the leap from the real to the symbolic world easily, and soon work comfortably with printed language. Abstract reasoning skills can be stronger or weaker either verbally or non-verbally.

Children weak in abstract reasoning will be concrete learners, children who learn best with hands-on activities.

Verbal strengths in abstract reasoning allow the child to understand idioms ("raining cats and dogs," "up a tree"). He may get the point of jokes at an early age. Weak verbal reasoning skills will lead to more difficulty than he should have with idiomatic language. He may have trouble arguing his point in disagreements and thus resort to name-calling or fighting.

Strong non-verbal reasoning skills are shown when a child excels at activities like puzzles, Legos (tm) and Erector Sets(tm). Often such a child will be interested in tools at an early age. Some will take household items apart, like the two-year-old boy who removed all the lower kitchen cabinet doors from their hinges. (After that, he took his crib apart.) Sometimes these junior mechanics can put the dismantled items back together as well, but don't count on it! Children who show a weakness in non-verbal reasoning may have difficulty with some hands-on learning activities