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17 Cards in this Set
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 Back
 3rd side (hint)
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 + (Y2)^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

68TH



TYPES OF CONCRETE LEAARNING

A concrete learner is the child who has difficulty making the shift from the handson 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 handson experiences. All young children are by their nature concrete learners.
Concrete learners like a handson 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 handson 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 nonverbally. Children weak in abstract reasoning will be concrete learners, children who learn best with handson 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 namecalling or fighting. Strong nonverbal 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 twoyearold 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 nonverbal reasoning may have difficulty with some handson learning activities 
