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Showcase April 2016: Learning to Measure through Action and Gesture

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Learning to Measure through Action and Gesture

Eliza L. Congdon and Susan C. Levine (Co-PI)

University of Chicago

Background

Learning through physical action is an effective way to help children acquire new ideas and concepts. Gesture is a type of physical action, but it differs from other kinds of actions in that it does not require interacting directly with external objects. As such, gesture provides an interesting comparison to action-on-objects, and allows us to identify the circumstances under which physical interaction with objects (and it’s associated effects on the external world) may be either beneficial or harmful to learning. In the current study, we ask whether individual differences in first grade children’s prior knowledge about a foundational mathematical concept – their understanding of linear units of measure -- might interact with their ability to glean insight from action- and gesture-based instruction.

Measurement is an important early mathematical concept that young children consistently struggle with, making it an important focus of research on math learning. In fact, measurement remains the only domain of mathematics in which elementary school children in the US consistently perform lower than the international average (TIMSS, 2011). Furthermore, we know that children consistently and robustly make one of two interesting errors on shifted-object linear measurement problems (see Figure 1 for sample shifted problem).

Figure 1
Figure 1. A sample “shifted problem” test item. Children make mistakes on problems like these throughout elementary school.

In a hatch-mark counting error, children count the hatch mark lines on the part of the ruler that is aligned with the object being measured instead of the intervals of space that fall between an object’s left-most and right-most edges. In a read-off error, children simply read off the number on the ruler that aligns with the rightmost edge of the object no matter where the object’s left most edge starts on the ruler. Notably, both errors provide the correct answer on typical measurement problems where the object-to-be-measured is aligned with the zero point of the ruler (e.g. Blume, Galindo, & Walcott, 2007; Kamii, 1997; Lehrer, Jenkins, & Osana, 1998; Solomon, Vasilyeva, Huttenlocher, & Levine, 2015).

Pretest

One hundred and twenty-two first grade children answered 10, “shifted object” multiple-choice questions at the beginning of the session so that we could determine their dominant measurement strategy (N = 59 used a hatch mark counting; N = 36 used a read off strategy; N = 27 were correct and were excluded from further analysis).

Training

During the training session, an experimenter showed children how to measure colorful wooden sticks with a 9-unit paper ruler and either 1) discrete plastic unit chips or a thumb and forefinger gesture and 2) shifted objects or unshifted objects (see Figure 2 for photos).

Figure 2
Figure 2. A photograph (in gray scale) of each of the four training conditions. A – Unshifted unit chip training condition; B – Shifted unit chip training; C – Unshifted gesture training; D – Shifted gesture training

Results

Immediately after training (Posttest) and one week later (Follow-up), all children answered 10 more “shifted object” multiple-choice measurement questions. For children in the hatch-mark counting group, performance improved after training with shifted objects, irrespective of the type of movement: both actions and gestures were beneficial for learning (Figure 3). However, for children in the read-off strategy group, only the shifted unit chip training condition was effective.

Figure 3
Figure 3. Average performance by starting strategy and training condition across the three sessions. Bars represent +/- 1 standard error of the mean when the data are aggregated by participant.

Implications

First, this study underscores the importance of providing children with instruction involving shifted-object problem types (also see: Showcase August 2009: Improving Children’s Understanding of Units of Measure: A Training Study). These types of problems can not only reveal children’s misconceptions about measurement in a way that unshifted problems do not, but they also seem to encourage the development of a more flexible and conceptually rich understanding of measurement.

Furthermore, the current study offers revealing new evidence about when and how children can best learn new ideas through hand movements. We argue that far from being a cure-all solution, gesture appears to be a double-edged sword. Though there is good, compelling research showing that gesture can promote learning, generalization, and retention (e.g., Cook, Mitchell & Goldin-Meadow, 2008; Novack, Congdon, Hemani-Lopez & Goldin-Meadow, 2014; Goldin-Meadow, 2014), the current findings emphasize the need to consider the learner’s current level of conceptual understanding, as well as the nature of the target concept, before using gesture-based instruction. The very same properties of gesture that differentiate it from action and facilitate long-lasting and flexible conceptual change may in fact make it inaccessible to some learners or inappropriate for some types of problem-solving contexts.

References

  • ♦ Blume, G. W., Galindo, E., & Walcott, C. (2007). Performance in Measurement and Geometry From the Viewpoint of Principles and Standards for School Mathematics. In P. Kloosterman & F. K. Lester (Eds.), Results and Interpretation of the 2003 Math Assessment of the National Assessment of Educational Progress (NAEP), chapter 5 (pp. 95-138). Reston, VA: National Council of Teachers of Mathematics.
  • ♦ Cook, S. W., Mitchell, Z., & Goldin-Meadow, S. (2008). Gesturing makes learning last. Cognition, 106, 1047–1058.
  • ♦ Foy, P., Arora, A. & Stanco, G. M. (Eds.). (2013). TIMSS 2011 User Guide for the International Database. Lynch School of Education, Boston College: TIMSS and PIRLS International Study Center.
  • ♦ Goldin-Meadow, S (2014). How gesture works to change our minds. Trends in Neuroscience and Education, 30, 23.
  • ♦ Kamii, C., & Clark, F. (1997). Measurement of length: The need for a better approach to teaching. School Science and Mathematics, 97, 116-121.
  • ♦ Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children’s reasoning about space and geometry. Designing learning environments for developing understanding of geometry and space, 1, 137-167.
  • ♦ Novack, M. A., Congdon, E. L., Hemani-Lopez, N., & Goldin-Meadow, S. (2014). From Action to Abstraction: Using the Hands to Learn Math. Psychological Science, 25, 903-910.
  • ♦ Solomon, T. L., Vasilyeva, M., Huttenlocher, J., & Levine, S. C. (2015). Minding the gap: Children’s difficulty conceptualizing spatial intervals as linear measurement units. Developmental Psychology, 51(11), 1564-73.
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