Ilyse Resnick

Breaking new ground in the mind: an initial study of mental brittle transformation and mental rigid rotation in science experts

The current study examines the spatial skills employed in different spatial reasoning tasks, by asking how science experts who are practiced in different types of visualizations perform on different spatial tasks. Specifically, the current study examines the varieties of mental transformations. We hypothesize that there may be two broad classes of mental transformations: rigid body mental transformations and non-rigid mental transformations. We focus on the disciplines of geology and organic chemistry because different types of transformations are central to the two disciplines: While geologists and organic chemists may both confront rotation in the practice of their profession, only geologists confront brittle transformations. A new instrument was developed to measure mental brittle transformation (visualizing breaking). Geologists and organic chemists performed similarly on a measure of mental rotation, while geologists outperformed organic chemists on the mental brittle transformation test. The differential pattern of skill on the two tests for the two groups of experts suggests that mental brittle transformation and mental rotation are different spatial skills. The roles of domain general cognitive resources (attentional control, spatial working memory, and perceptual filling in) and strategy in completing mental brittle transformation are discussed. The current study illustrates how ecological and interdisciplinary approaches complement traditional cognitive science to offer a comprehensive approach to understanding the nature of spatial thinking.

Delaware Longitudinal Study of Fraction Learning: Implications for Helping Children with Mathematics Difficulties.

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children (N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and that some showed only a basic grasp of the meaning of a fraction even after several years of instruction. Children with low growth in fraction knowledge during the intermediate grades were much more likely to fail to meet state standards on a broad mathematics measure at the end of Grade 6. Although a range of general and mathematics-specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a uniquely important marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to whole number magnitude representations that are complicated by the introduction of fractions into the curriculum. Implications for helping students with mathematics difficulties are discussed.

Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade.

Development of fraction number line estimation was assessed longitudinally over 5 time points between 4th and 6th grades. Although students showed positive linear growth overall, latent class growth analyses revealed 3 distinct growth trajectory classes: Students who were highly accurate from the start and became even more accurate (n = 154); students who started inaccurate but showed steep growth (n = 121); and students who started inaccurate and showed minimal growth (n = 197). Younger and minimal growth students typically estimated both proper and improper fractions as being less than 1, failing to base estimates on the relation between the numerator and denominator. Class membership was highly predictive of performance on a statewide-standardized mathematics test as well as on a general fraction knowledge measure at the end of 6th grade, even after controlling for mathematic-specific abilities, domain-general cognitive abilities, and demographic variables. Multiplication fluency, classroom attention, and whole number line estimation acuity at the start of the study predicted class membership. The findings reveal that fraction magnitude understanding is central to mathematical development. (PsycINFO Database Record

Dealing with Big Numbers: Representation and Understanding of Magnitudes Outside of Human Experience.

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed.

Chapter 2: Training Spatial Skills in Geosciences: A Review of Tests and Tools

Abstract Characterizing spatial thinking and the development of spatial expertise is essential to understanding how to train geoscientists to succeed in both academia and industry. The Spatial Intelligence and Learning Center has supported an eight-year-long collaborative research program, which brings together disciplinary expertise in cognitive science and geology to characterize and develop spatial thinking in the geological sciences. To facilitate our understanding of science education and practice, we have characterized the spatial skills of geoscience discipline experts and the spatial thinking impediments experienced by students studying the geological sciences. In this chapter we review recent research on measuring and improving spatial thinking skills in the geosciences and on characterizing individual differences in spatial thinking, including the role of gender and age. We conclude with a discussion of important unanswered questions and some directions for future research. The research discussed here may help guide the development of best practices for spatial thinking training in both academic and industry settings.

How students reason about visualizations from large professionally collected data sets: A study of students approaching the threshold of data proficiency

ABSTRACT This study identifies a population of students who have an intermediate amount of relevant content knowledge and skill for working with data, and characterizes their approach to interpreting a challenging data-based visualization. Thirty-three undergraduate students enrolled in an introductory environmental science course reasoned about salinity data as shown in map and vertical profiles from the Mediterranean while thinking aloud and being eye-tracked. Students reasoned about 2D and 3D interpretations in the context of two hypothesis arrays (a suite of potential interpretations about a set of data). Findings suggest the students have some effective strategies in reading data: They look at cartographic elements, correctly identify the image as a salinity map, and draw inferences from the data. Common looking strategies include scanning along the salinity gradient, comparing areas of interest, and aligning the color bar with the map. Individual differences emerge in the interpretation of the data, with no interpretations being fully aligned with the scientifically normative explanation. Post hoc analyses identify reasoning tasks and spontaneous behaviors related to a construct we refer to as “data expertise,” which is intended to capture the degree of conceptual sophistication and resourcefulness in reasoning about data. A data expertise scale was developed, with scores ranging from zero (weak) to six (strong) that were normally distributed. Our findings suggest that appropriately coordinating data with a model, comparing and contrasting across data representations from different times or places, and extracting 3D structure from 2D representations are associated with data expertise.

Children’s reasoning about decimals and its relation to fraction learning and mathematics achievement.

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a decimal comparison task in 4th grade, before systematic decimals instruction. Three classes of response patterns were identified, indicating empirically distinct levels of decimal magnitude understanding. Class 1 students consistently gave correct responses, suggesting that they understood decimal properties even before systematic decimal instruction. Class 2 students were accurate when a 0 immediately followed the decimal, but were inaccurate when a zero was added to the end of the decimal string, suggesting a partial understanding of place value; their performance was also negatively influenced by a whole number bias. Class 3 students showed misunderstanding of both place value and a whole number bias. Class membership accurately predicted 6th grade mathematics achievement, after controlling for whole number and fraction magnitude understanding as well as demographic and cognitive factors. Taken together, the findings suggest students may benefit from instruction that emphasizes decimal properties earlier in school.

Using analogy to learn about phenomena at scales outside human perception

Understanding and reasoning about phenomena at scales outside human perception (for example, geologic time) is critical across science, technology, engineering, and mathematics. Thus, devising strong methods to support acquisition of reasoning at such scales is an important goal in science, technology, engineering, and mathematics education. In two experiments, we examine the use of analogical principles in learning about geologic time. Across both experiments we find that using a spatial analogy (for example, a time line) to make multiple alignments, and keeping all unrelated components of the analogy held constant (for example, keep the time line the same length), leads to better understanding of the magnitude of geologic time. Effective approaches also include hierarchically and progressively aligning scale information (Experiment 1) and active prediction in making alignments paired with immediate feedback (Experiments 1 and 2).

Fraction Development in Children: Importance of Building Numerical Magnitude Understanding

This chapter situates fraction learning within the integrated theory of numerical development. We argue that the understanding of numerical magnitudes for whole numbers as well as for fractions is critical to fraction learning in particular and mathematics achievement more generally. Results from the Delaware Longitudinal Study, which examined domain-general and domain-specific predictors of fraction development between third and sixth grade, are highlighted. The findings support an approach to teaching fractions that centers on a number line. Implications for helping struggling learners are discussed.