[PDF] THINKING IN PATTERNS TO SOLVE MULTIPLICATION DIVISION

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xefpiiewiehhmxmsrQi THINKING IN PATTERNS TO SOLVE MULTIPLICATION, DIVISION, AND FRACTION PROBLEMS IN SECOND GRADE4 "%&/)BK / 10 ;.4 /20 two-;.4

1 one 11

;.4 -one 21 two ;.4 -one

2 two 12/

;.4 -two 22 two- ;.4 -two

3 three 13

;.4 -three

4 four 14

;.4 -four 30 three- ;.4

5 five 15/

;.4 -five 31 three- ;.4 -one

6 six 1/6

;.4 -six

7 seven 17

;.4 -seven 40 four- ;.4

8 eight 18

;.4 -eight 41 four-;.4-one

9 nine 19

;.4 -nine

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3. Teaching multiplication, division, and fractions as

interconnected patterns, replaced teaching the three separately.

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Participants in the study, students who had been taught with P&$1P, |POWNCFTUPD'-&, L during kindergarten, first, and second grade, were in three different second grade classes at a suburban public school. Classes were sorted by gender (to balance the number of girls and boys) and not by ability. The school adhered to the Core Curriculum State Standards (2011) in mathematics. The new mate rials r eplaced materials from the district cur- riculum F|&d!+!'&NBVIGcovering numbers and numeric relations. The district curriculum was used for topics (e.g., graphs, measurements) outside the scope of the new curriculum. Daily mathematics lessons lasted for an hour. Teachers were required to use P&$1P, |POWNCFTU D'-&, LP for a minimum of fifteen minutes.

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There were 8 female and 16 male student

s. Of these, 8 we re Hispanic, 8 were White, 3 were African-American,

3 were multi-racial, and 2 were Asian. Nine students

qualified for free or reduced fee lunch. All were profi-

cient in English and 6 were bi-lingual, speaking a lan-guage other than English at home. Mean age at the time

of post-testing was 8 years, 2 months (98 months); range was 7 years, 8 months (92 months) to 8 years, 7 months (103 m onths). Sc

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Two classes had the same teachers for the entire school year. One teacher had four years" experience teaching second grade; the other had nine years" experience teach- ing both second and third grades. The third class had two teachers. The first, who went on leave at the end of December, taught for 23 years. She had experience with kindergarten, first, second and fifth grade classes. The s econd was a substitute who taught at the school for t hree years. She was the only teacher with prior experi- ence using the intervention (in kindergarten and first grade). Professional development was provided by the researcher.

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The chart is shown in Figure 3. There are several things to notice about the format. First, the upper left cell con- tains symbols for multiplication and division. Second, each column begins with the square of its number. For example, the twos column begins with 4 (2 x 2 = 4). This is because 2 (1 x 2 = 2) is included in the ones column.

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