What Young Children Need to Learn
About Numbers-Differences in learning style and response to error correction
in pre-kindergarten and kindergarten students using adaptive iPad based
William M. Jenkins and Logan De Ley
Scientific Learning Corporation
While children have a general number sense, some things that are obvious to adults are not so obvious to children. For example, to adults, it is obvious that you should give more objects to someone who asks for six than to someone who asks for four. Many preschoolers, however, do not find this obvious at all – even preschoolers who can count from one to ten flawlessly (Le Corre & Carey, 2007; 2008). Likewise, adults see it as obvious that seven must be larger than five, because seven comes after five when counting from one to ten. Yet many children who can count from one to ten have no idea which of any two numbers in that range is larger (Okamoto & Case, 1996; Ramani & Siegler, 2008).
To overcome these limitations on their number knowledge, children must learn to connect groups of objects or events to symbolically expressed numbers. For instance, a child must learn to connect 12 dots with the spoken number name “twelve” and to connect seven tolls of a bell with the written numeral “7.” Making these connections is one of the most important mathematical competencies children are asked to acquire during the preschool and early elementary school years. One of the most common learning tasks given young children is to determine the number of objects in a set, either by visual recognition (subitizing) or by counting (Gelman & Gallistel, 1978; Trick & Pylyshyn, 2003). Other important challenges during the early school years include acquiring skills relevant to cardinality, such as recognizing and generating the number symbols that accompany sets of a particular size, and skills relevant to ordinality, such as identifying the larger of two numbers.
Beyond learning number names and counting routines, research has shown that verbal representations of numbers are linked to spatial representations, and that this linkage plays an important role in numerical understanding (Ansari, 2008; Hubbard, Piazza, Pinel, & Dehaene, 2005; Siegler & Ramani, 2009). At the neural level, a circuit connecting the prefrontal cortex and an area in the parietal lobe known as the horizontal intraparietal sulcus (HIPS) area has been found to be crucial for these linked representations (Nieder & Dehaene, 2009; Dehaene, Molko, Cohen, & Wilson, 2004; Hubbard & McCandliss, 2011). At the behavioral level, how precisely the verbal and spatial representations of number are linked is related to both preschool and elementary school children‘s arithmetic skills, and to elementary school children‘s overall math achievement test scores (Booth & Siegler, 2006; 2008; Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007).
We developed an adaptive iPad-based game for preschool children that works on basic numeracy skills in conjunction with working memory skills. The game begins with simple counting of sets of objects and matching sets to numerals. At first, the learner is presented with a set of objects arranged like the dots on a domino, and asked to select the matching numeral (numbers 1-6). Next, the learner is presented with several sets of
objects arranged in a 10-frame, and asked to select the correct set associated with a given numeral (numbers 3-10). In the next higher levels of the game, the learner is presented with an array of numerals and sets. The sets are represented as spots on a ladybug (numbers 1-6, domino pattern) or on a caterpillar (numbers 1-10, 10-frame pattern). The learners is asked to match all the numerals to the appropriate sets when both numerals and sets are visible until matched. In the highest levels of the game the bugs and numerals are hidden under leaves and can only be exposed one at a time. In this condition accurate matching of numerals to number counts requires working memory recall of the visual-spatial locations of the matching items, as well as counting and numeral identification.
At two public schools, 65 students (48 pre-kindergarten students and 17 kindergarten students) worked with our iPad-based number game for an average of 15 days, spending roughly 10 minutes each day on the number game. For pre-kindergarten students the average total number of trials was 805, while for kindergarten students the average number of trials was 1484. Feedback was provided on each error in the form of both verbal and visual information indicating when an error was made. In some cases, the student was given a second try with additional verbal supports.
Major performance differences were seen between pre-kindergarten students and kindergarten students, with a much larger percentage of the kindergarten students advancing to higher completion levels. Data was collected for each learning trial, and our analysis of the data suggests that providing additional supports immediately after the first error may not be the best strategy to support learning in younger students. Other differences were seen among those students (17 pre-kindergarten students and 14 kindergarten students) who were able to master the game. On average, the pre-kindergarten students required 738 learning trials to pass the highest stage, whereas the kindergarten students required only 563 learning trials.