Martha W. Alibali

Developing conceptual understanding and procedural skill in mathematics: An iterative process

The authors propose that conceptual and procedural knowledge develop in an iterative fashion and that improved problem representation is 1 mechanism underlying the relations between them. Two experiments were conducted with 5th- and 6th-grade students learning about decimal fractions. In Experiment 1, childrens initial conceptual knowledge predicted gains in procedural knowledge, and gains in procedural knowledge predicted improvements in conceptual knowledge. Correct problem representations mediated the relation between initial conceptual knowledge and improved procedural knowledge. In Experiment 2, amount of support for correct problem representation was experimentally manipulated, and the manipulations led to gains in procedural knowledge. Thus, conceptual and procedural knowledge develop iteratively, and improved problem representation is 1 mechanism in this process.

Visible embodiment: Gestures as simulated action

Spontaneous gestures that accompany speech are related to both verbal and spatial processes. We argue that gestures emerge from perceptual and motor simulations that underlie embodied language and mental imagery. We first review current thinking about embodied cognition, embodied language, and embodied mental imagery. We then provide evidence that gestures stem from spatial representations and mental images. We then propose the gestures-as-simulated-action framework to explain how gestures might arise from an embodied cognitive system. Finally, we compare this framework with other current models of gesture production, and we briefly outline predictions that derive from the framework.

Conceptual and procedural knowledge of mathematics : Does one lead to the other?

This study examined relations between childrens conceptual understanding of mathematical equivalence and their procedures for solving equivalence problems (e.g., 3 + 4 + 5 = 3 + ). Students in 4th and 5th grades completed assessments of their conceptual and procedural knowledge of equivalence, both before and after a brief lesson. The instruction focused either on the concept of equivalence or on a correct procedure for solving equivalence problems. Conceptual instruction led to increased conceptual understanding and to generation and transfer of a correct procedure. Procedural instruction led to increased conceptual understanding and to adoption, but only limited transfer, of the instructed procedure. These findings highlight the causal relations between conceptual and procedural knowledge and suggest that conceptual knowledge may have a greater influence on procedural knowledge than the reverse.

Transitions in Concept Acquisition: Using the Hand to Read the Mind

Thoughts conveyed through gesture often differ from thoughts conveyed through speech. In this article, a model of the sources and consequences of such gesture-speech mismatches and their role during transitional periods in the acquisition of concepts is proposed. The model makes 2 major claims: (a) The transitional state is the source of gesture-speech mismatch. In gesture-speech mismatch, 2 beliefs are simultaneously expressed on the same problem--one in gesture and another in speech. This simultaneous activation of multiple beliefs characterizes the transitional knowledge state and creates gesture-speech mismatch. (b) Gesture-speech mismatch signals to the social world that a child is in a transitional state and is ready to learn. The childs spontaneous gestures index the zone of proximal development, thus providing a mechanism by which adults can calibrate their input to that childs level of understanding.

Can Infants Map Meaning to Newly Segmented Words? Statistical Segmentation and Word Learning

The present experiments investigated how the process of statistically segmenting words from fluent speech is linked to the process of mapping meanings to words. Seventeen-month-old infants first participated in a statistical word segmentation task, which was immediately followed by an object-label-learning task. Infants presented with labels that were words in the fluent speech used in the segmentation task were able to learn the object labels. However, infants presented with labels consisting of novel syllable sequences (nonwords; Experiment 1) or familiar sequences with low internal probabilities (part-words; Experiment 2) did not learn the labels. Thus, prior segmentation opportunities, but not mere frequency of exposure, facilitated infants∗ learning of object labels. This work provides the first demonstration that exposure to word forms in a statistical word segmentation task facilitates subsequent word learning.

The function of gesture in learning to count: more than keeping track *

Preschoolers count objects most accurately when they gesture as they count. This study tests two possible explanations for this effect. One is that gesture helps children keep track of counted items. Another is that gesture helps children coordinate saying the number words and tagging the items. Twenty preschoolers counted chips under three types of conditions: with gesture prohibited, with active gesture, and with a puppet gesturing as children counted aloud. The puppet conditions were intended to distinguish the benefits of keeping track with gesture from the benefits of active gesture. Children counted more accurately when they or the puppet gestured than when gesture was prohibited. However, childrens errors differed when they and the puppet gestured. When children gestured themselves, they made errors keeping track, but when the puppet gestured, they made errors coordinating number words and items. Thus, active gesture helps children both to keep track and to coordinate tagging the items and saying the number words. In these ways, active gesture helps children implement their knowledge of one-to-one correspondence.

Teachers’ gestures facilitate students’ learning: A lesson in symmetry

This study investigated whether teachers gestures influence students comprehension of instructional discourse, and thereby influence students learning. Pointing and tracing gestures ‘‘ground’’ teachers speech by linking abstract, verbal utterances to the concrete, physical environment. We hypothesize that such grounding should facilitate students comprehension, and therefore their learning, of instructional material. Preschool children viewed one of two videotaped lessons about the concept of symmetry. In the verbal-plus-gesture lesson, the teacher produced pointing and tracing gestures as she explained the concept. In the verbal-only lesson, the teacher did not produce any gestures. On the posttest, children were asked to judge six items as symmetrical or asymmetrical, and to explain their judgments. Children who saw the verbal-plus-gesture lesson scored higher on the posttest than children who saw the verbal-only lesson. Thus, teachers gestures can indeed facilitate student learning. The results suggest that gestures may play an important role in instructional communication.

How children change their minds : Strategy change can be gradual or abrupt

This study investigated patterns of change in childrens strategies for solving mathematical equivalence problems. The strategies children expressed in speech and in gesture were assessed both before and after an instructional intervention. In the intervention, children received either no input, accuracy feedback, or feedback plus instruction about a principle, an analogy, or a procedure. From pretest to posttest, many children changed both the variability of their strategy use and the content of their strategy repertoires. Patterns of change depended on type of instruction and on childrens initial level of variability. Children who received instruction were especially likely to generate new strategies, and children with high variability were especially likely to abandon prior strategies. Gradual change was most common; however, many children modified their repertoires abruptly. Abrupt strategy change was especially prevalent among children who received procedure-based instruction and among children with low initial variability.

THE ROLE OF GESTURE IN CHILDREN'S COMPREHENSION OF SPOKEN LANGUAGE: NOW THEY NEED IT, NOW THEY DON'T

Two experiments investigated gesture as a form of external support for spoken language comprehension. In both experiments, children selected blocks according to a set of videotaped instructions. Across trials, the instructions were given using no gesture, gestures that reinforced speech, and gestures that conflicted with speech. Experiment 1 used spoken messages that were complex for preschool children but not for kindergarten children. Reinforcing gestures facilitated speech comprehension for preschool children but not for kindergarten children, and conflicting gestures hindered comprehension for kindergarten children but not for preschool children. Experiment 2 tested preschool children with simpler spoken messages. Unlike Experiment 1, preschool childrens comprehension was not facilitated by reinforcing gestures. However, childrens comprehension also was not hindered by conflicting gestures. Thus, the effects of gesture on speech comprehension depend both on the relation of gesture to speech, and on the complexity of the spoken message.

I see it in my hands’ eye: Representational gestures reflect conceptual demands

The Information Packaging Hypothesis (Kita, 2000) holds that gestures play a role in conceptualising information for speaking. According to this view, speakers will gesture more when describing difficult-to-conceptualise information than when describing easy-to-conceptualise information. In the present study, 24 participants described ambiguous dot patterns under two conditions. In the dots-plus-shapes condition, geometric shapes connected the dots, and participants described the patterns in terms of those shapes. In the dots-only condition, no shapes were present, and participants generated their own geometric conceptualisations and described the patterns. Participants gestured at a higher rate in the dots-only condition than in the dots-plus-shapes condition. The results support the Information Packaging Hypothesis and suggest that gestures occur when information is difficult to conceptualise.