Vol. 10 #1 Gesture and Learning Mathematics
Gesture and Learning Mathematics
Barbara Allen-Lyall, Ph.D.
Manhattanville College, Purchase, NY
Learning something new is a complex process. It is complex because learning occurs both consciously and unconsciously and takes many forms in day-to-day life. Whether one is young or older, encountering and responding to unique situations requires integration of sensory stimuli and a mental or physical response of some sort, one that helps to internalize new learning.
To facilitate teaching and learning mathematics, educational researchers seek ongoing understanding of what helps children to comprehend essential mathematical concepts. The more we know about how individuals learn, the more we can influence the instructional process and expand access to new ideas while nurturing fluid responses when asking children to demonstrate what they know. A research area exhibiting promising results involves gesture on the part of both teachers and learners. While we may think of gesture as random physical expression by those who intend to relay information, intentional gesture during both learning input and output may influence how ideas are processed and recalled.
Spontaneous gesture is common and communicates a range of ideas, for example, intent (a hand outstretched with palm facing away, “No!”); appreciation (hands clapping in response to a good suggestion); and position (fingers undulating to coax someone to move forward). However, gesture in tandem with speech in the classroom bolsters communication of important learning ideas (Hostetter, 2011).
Gesture With Verbalization
Research suggests that gesture-accompanying speech reveals much about what children comprehend relative to what teachers hope to convey (Valenzeno, Alibali, & Klatzky, 2003). If a child wishes to “gesture show” a shape in the air (a square), she may adjust measurements as she creates a square with her fingers, saying “like this” to approximate equal side lengths. Conceptualizing a square is somehow easier when using gesture to organize and consolidate smaller bits of information to eventually create an intended whole. This protracted physical action helps a child to strengthen learning while providing the teacher with a sense of what his student understands about a square’s attributes.
Teachers gesture a great deal, perhaps when they hope to explain ideas with which students have little experience (Hotsetter, 2011). A teacher may also gesture when reminding students about prior engagement with a task or concept, using fingers to form circles while verbally describing the intersecting regions of a Venn diagram. The intent here would be to encourage student recall of an image displayed earlier on the white board. However, what happens when both teachers and students gesture with practiced intent in the teaching/learning process? What if teachers rehearse gesture to communicate concepts, prompting students to gesture with specificity at various stages of mathematics learning? Would this matter? Can gesture impact learning and eventual achievement? Studies suggest that recall is positively affected by teacher and student gesture rehearsal in the learning process (Jaroslawska, Gathercole, Allen, & Holmes, 2016; Novak, Congdon, Hemani-Lopez, & Goldin-Meadow, 2014). Gesture is also especially important for learning mathematics, a subject that often involves recalling concrete or representational models prior to and during computation (Goldin-Meadow, 2015).
How Does Gesture Actually Help?
Gesture Guides Language. Communication requires language formulation using specific, relatively linear cognitive pathways that draw upon a cache of words accumulated via individual experience. When a teacher or a student attempts to explain ideas, they rely upon their personal word collection that may or may not precisely convey their ideas to others. In contrast, gesture utilizes non-linear brain processes and often expresses information absent in speech. Effective gesture is not reliant upon language, however, it supplements speech and assists explanations by connecting brain pathways that allow elusive words to spring to the fore. In the example above, when the child gestures to exemplify the notion that squares have equal side-lengths and four right angles, future use of this gesture may serve to elicit correct descriptive language. In this way, gesture helps to mentally connect ideas that may then stimulate usage of more precise language. Research shows that gesture assists in the construction of ideas, as well as in their retention (Goldin-Meadow, 2015).
Teacher Gesture is Impactful. In mathematics learning, teacher gesture indicating an effective strategy for finding a missing addend in an equivalence problem (e.g., 2 + 3 + 7 = ___ + 7) results in improved student response (Goldin-Meadow, 2015). For example, the 2 + 3 is gesture-selected on the left with two fingers and swooped over to the right side of the equal sign to imply combining values into the unknown value place. This gesture directs attention to a particular strategy involving partial addition. Offering explicit methodologies can be important for learners who benefit from accumulating strategies that are both conceptual and effective. While research directs attention to this process for all students, it is especially true for students with mathematics learning disabilities (MLD) (Schneider, Rittle-Johnson, & Star, 2011).
A study by Goldin-Meadow, Cook, and Mitchell (2009) demonstrated the effect of researchers teaching students to correctly gesture and verbalize strategies for solving problems before instruction by their own teacher. Learners who did so retained new ideas longer, especially if they somehow incorporated gestured strategies into spoken communication after learning. In other groups within the study, students who gestured during learning improved even if gestures were partially incorrect. The principle element was that gesture assisted personal meaning making and the construction of new ideas.
Gesture Connects Concrete Models to Abstract Procedures. An important precursor to the gesture-laden procedural strategy above would be to use concrete manipulatives to model 2 + 3 + 7 as equivalent to (2 + 3) + 7. The use of manipulatives has been shown to improve learning and retention for students with MLD (for example, Cass, Cates, Smith, & Jackson, 2003). A next step would be to align conceptual steps to the procedural phase in conjunction with explicit gesture. Teachers can gesture during directives and students can gesture to show what transpired in the process of using the concrete materials. This is important to do given that students with MLD develop proficiency via integration of both conceptual and procedural undertakings (Schneider, Riddle-Johnson, & Star, 2011). Careful attention to this progression while incorporating gesture experiences helps to foster meaningful, lingering cognitive connections (Broaders, Cook, Mitchell, & Goldin-Meadow, 2007). Additionally, gesture as communication is likely important so that students feel connected in non-verbal fashion to what they understand.
Gesture Before Instruction Affects Retention. Broaders et al., (2007) elaborate on this notion of communicating understanding via gesture and promoting learning within the individual. These researchers posit that asking children to represent a strategy element using gesture before actual instruction produces a higher incidence of correct solutions. An example would be to ask children to swoop first with the left hand toward the center and then with the right hand before instruction related to equivalence problems, such as the one mentioned earlier. The concept here is that the value on one side of the equal sign must be equivalent to the value on the other. Gesture with verbalization before instruction may allow learning to be more sensitive to procedures due to embodied meaning that resonates at the level of each individual. In addition, learning is more readily retained (Goldin-Meadow, 2015).
Incorporating Gesture for Children With Mathematics Disabilities
While there is a growing body of research related to teaching and learning for children with MLD (for example, Fuchs et al., 2009; Geary, Hoard, & Bailey, 2012; Tolar et al., 2016), studies related to employing explicit gesture during instruction are increasingly noteworthy (Alibali et al., 2013; Hord et al., 2016). If students are encouraged to verbally connect ideas to their gestures, they can make mental connections that bolster overall understanding. Importantly, learners may retain new ideas longer, especially if they find ways to incorporate gestured strategies with verbalizations after learning (Goldin-Meadow, Cook, & Mitchell (2009).
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Barbara Allen-Lyall, Ph.D., is an Assistant Professor in the Department of Curriculum and Instruction at Manhattanville College located in Purchase, New York. Dr. Allen-Lyall teaches courses in elementary mathematics methods; teacher research; and classroom management, curriculum development and assessment. She speaks at national conferences on topics related to mathematics education research and cognition. She also presents on topics related to the brain and learning as part of the Gural Mind Matters series in New York City. Dr. Allen-Lyall can be reached at Barbara.AllenLyall@mville.edu.