Using the index finger to trace over advanced and multi-step maths problems can help students with problem solving, new research shows.
Tracing can assist learning not only for spatial topics such as triangles and angle relationships, but also for non-spatial tasks such as learning the order of tasks in arithmetic problems.
For instance, students who traced over the addition, subtraction, multiplication, division and brackets symbols in problems such as 7 x (31 – 20) + 56 ÷ (5 – 3) = ? solved more problems correctly on a subsequent test.
We also found that students who traced over key elements of maths problems (eg, the arithmetic symbols +, -, ÷, x, and brackets used in order of operations problems) were able to solve other questions that extended the initial maths problem further. Superior performance on such “transfer” problems indicates students who traced weren’t simply memorising solutions to problems. Instead, tracing was helping them develop a deeper, more flexible understanding of the problem-solving methods.
Why tracing against a surface may enhance learning
The index finger plays a vital role in early learning. The specific gesture of pointing with the index finger is common across all cultures as a means of guiding attention.
As young as nine months of age, babies learn to manage their conversations with caregivers by pointing to things in the environment. When the caregiver names the object, this helps build the child’s vocabulary.
Hand movements (including tracing and pointing gestures) may also help us form and organise spatial images in our conscious mind.
We have evolved to pay close attention to things that our eyes can easily see. This means that objects near our hands are more quickly recognised and receive prolonged scrutiny. So, when using an index finger to physically touch while tracing visual stimuli, the stimuli receive processing priority.
Gestures, including tracing, may play an important role in helping learners combine or “chunk” different sources of information (eg, text and diagrams) into an integrated, coherent understanding of a problem (Ping & Goldin-Meadow, 2010). Chunking acts to reduce the load on working memory, and can support more effective learning (Sweller, 1994).
Finger-tracing has been used by teachers for more than a century.
In the early 1900s, Italian educator, Maria Montessori – who developed an educational method that builds on the way children naturally learn – got young children to trace over letters of the alphabet made from sandpaper with their index fingers.
This technique was based on the intuition that a multi-sensory approach (i.e., visual, auditory, tactile, and kinaesthetic) would benefit young children.
Subsequent studies over the past 40 years have confirmed Montessori’s intuitions for topics relevant to early childhood education, including letter recognition (Bara et al., 2004) and geometrical shape recognition (Kalenine et al., 2011).
Our research shows the benefits of tracing extend well beyond early childhood, to complex topics in primary and secondary maths.
This simple, no-cost teaching strategy can enhance the effectiveness of maths instruction.
At the classroom level, teachers can assist students to learn new mathematical content by incorporating instructions to “trace over” the important elements of maths problems that already appear in mathematics textbooks or worksheets.
Tracing may also be useful in computer-based maths tutorials where students can then trace out animated maths lessons.