Children Learn When Their Teacher’s Gestures and Speech Differ 

By

Melissa A. Singer and Susan Goldin-Meadow

The study by Singer and Goldin-Meadow (2005) discusses the role of gestures in mathematics instruction, specifically how mismatched gestures (gestures that convey a different strategy than speech) influence students' learning of mathematics. The authors argue that gestures are not just a supplement to verbal instruction but can actively contribute to cognitive development. 

The study explores questions:

(a) Does teaching children more than one strategy for solving a problem facilitate their mastery of the problem? 

(b) Does it matter whether those strategies are presented in speech, in gesture, or in both speech and gesture?

 The researchers worked with 160 third- and fourth-grade students from Chicago schools, excluding those who solved problems correctly in a pretest. Students were randomly assigned to six questions that varied in the number of strategies (like 5+7+6=.....+6)taught in speech and the use of gestures (no gesture, matching gesture, or mismatching gesture). During instruction, students were taught problem-solving strategies using four math problems, with each problem explained twice. In the no-gesture condition, the teacher only used speech; in the matching gesture condition, the teacher’s gestures reinforced the spoken strategy; and in the mismatching gesture condition, the teacher’s gestures conveyed a different strategy from speech. After instruction, students took a posttest similar to the pretest to measure learning outcomes. 

The study found that gestures helped students learn better, but only when they showed a different strategy from what was said. Students understood more when the teacher used gestures to introduce a second way to solve the problem, instead of just repeating the spoken explanation. When gestures matched speech, they didn’t add much benefit. The best results came when one strategy was explained in speech and another through gestures, making it easier for students to understand without feeling overloaded.

Stop 1

"children profit from gesture when it conveys information that differs from the information conveyed in speech"(p.88)

As a math teacher, when I first read this, I thought it was wrong. I always believed that clear, consistent explanations were the best way to help students understand math concepts. It seemed logical that gestures should match speech to reinforce learning rather than introduce a different strategy. However, after thinking more about it, I realized that providing multiple ways to solve a problem—one through speech and another through gestures—might actually help students process information in a deeper way.

An example is when teaching multiplication as repeated addition. I might say, "3 × 4 means adding 3 four times (3 + 3 + 3 + 3)." At the same time, instead of just repeating this idea with gestures, I could hold up three fingers on one hand and show four groups by tapping four times with my other hand, helping students visualize multiplication as grouping. This gesture introduces a different way of understanding multiplication rather than just reinforcing my words. So gestures can be more than just reinforcements; they can introduce alternative ways of thinking, which is especially helpful for diverse learners. 

Stop 2

"when children are at a transitional point in acquiring a concept, they often find it easier to produce ideas relevant to that concept in gesture than in speech"(p.88)

We all know that children often use gestures before they can fully explain their thoughts in words. Gestures help them organize ideas and understand concepts more easily. In math, children might use their hands to show size, quantity, or movement before they can describe them clearly. For example, a child learning addition might hold up fingers to show numbers before saying the answer, or a student solving an equation may use hand movements to show balancing before explaining the steps. Sometimes, children even show correct ideas in gestures before they can put them into words, which means they might understand more than they can express. Gestures also make learning more engaging and interactive, helping students remember concepts better. As teachers, we can observe these gestures to understand students' thinking, encourage them to use hand movements while solving problems, and guide them toward clearer explanations.

 Question

How can we use gestures effectively in the classroom to help students express and understand mathematical concepts better?

 A Linguistic and Narrative View of Word Problems in Mathematics Education

 By

SUSAN GEROFSKY

Summary

This article explores the way mathematical word problems are structured and understood. For many students, word problems are like nightmares and they face difficulties when they  transfer it into arithmetic or algebra. The author wants to analyze mathematical word problems as a a linguistic genre rather than just math exercises. She plans to examine how these problems are structured in terms of pragmatics (how language is used in real-life communication) and discourse features .

By comparing word problems to other types of writing—such as stories or spoken conversations,she aims to uncover the hidden assumptions behind why and how word problems are used in teaching. Essentially, she wants to make us think about word problems differently, questioning whether they are truly effective as a teaching tool or if they serve more as a rigid tradition in math education.

Word problems and their three component structure

1)A "set-up" component, establishing the characters and location of the putative story. (This component is often not essential to the solution of the problem itself)

2) An "information" component, which gives the information needed to solve the problem (and sometimes extraneous information as a decoy for the unwary)

3) A question

Many students have found that these word problems are really difficult and it is not even related to their daily lives. For those students who have difficulty in word problem solving, Johnson(1992)advises the following steps:

• Identify the Question: Look for the question at the end of the problem.
• Break the Problem into Two Parts: set up the unknowns (define what you don’t know) and provide the necessary equation information (give numbers and relationships)
• Translate Words into Symbols: Convert the problem step by step into mathematical expressions.
• Solve the Equation

The author analyzes word problems in mathematics using J.L. Austin's speech act theory, which looks at how language functions in communication. She explains that word problems have three aspects: locutionary force (the literal meaning of the words), illocutionary force (the intention behind the problem, such as solving for X), and perlocutionary force (the effect on students, such as motivation or confusion). She argues that while word problems appear to be small stories, they do not actually describe real-life situations. They lack true storytelling elements like characters, emotions, or meaningful plots, making them more about decoding math hidden in words than about solving real-world problems. Gerofsky explains that students learn to solve word problems mechanically by ignoring the story, finding numbers, and following a set process to get one correct answer. She argues that since teachers and textbooks rarely encourage students to question the real-world meaning of these problems, educators should rethink their approach to teaching math and focus on real problem-solving skills.

She explains the truth value of problems: that word problems are not real-life situations but made-up scenarios for students to solve. She says they do not follow the rule that statements must be either true or false because their stories are fictional and can be changed without affecting the math. She also looks at how tense is used in word problems and finds that it is often inconsistent or unrealistic, proving that these problems are not about real events. Since word problems do not follow real-world logic, students and teachers understand that the goal is not to think about the story but to find the math and solve the problem.

She also explores the idea of word problems as parables but finds the comparison weak. Unlike parables, which offer open-ended lessons, word problems focus on a single correct answer and lack deeper meaning. While some word problems have lasted for centuries, she suggests this may be due to the conservatism of mathematical tradition rather than their educational value. She encourages educators to rethink their use of word problems and explore new ways to teach problem-solving that are more meaningful for students.

stop 1

A water tank has two taps, A and B Line A on the graph shows how the tank drains if only tap A is open line B shows how the tank drains if only tap B is open

a) How long does it take to drain if only tap A is open?

b) How long does it take to drain if only tap B is open?

c) Use the graph to find out how long it would take to drain

the tank if both taps were open [Kelly et al , 1987, 213]

Pinder writes of the father of one of her students who complained that his child wasn't being taught problems like the one above (which he had studied in school)(p.41)

Pinder’s reflection raises important concerns about the relevance of certain word problems in math education. The problem highlights a disconnect between mathematical exercises and practical situations, prompting the question of whether such problems are truly useful for students. But, parents always give importance to these kinds of problems because they think it is "real math". As educators, it’s crucial to focus on problems that are grounded in real-life scenarios, as this not only helps students see the value of math but also encourages critical thinking and problem-solving skills. Rather than simply manipulating symbols, students should engage with problems that allow them to apply math meaningfully, such as understanding water management or responding to emergencies like climate problems, floods or displacement of people, which offers more tangible learning experiences for them.

stop 2

"You can't go out and use them in daily life, or in electronics, or in nursing. But they teach you basic procedures which you will be able to use elsewhere."(p.38)

In India, where rote learning and memorization were often prioritized, many students including myself were taught to solve equations or word problems by following set procedures without truly understanding the underlying concepts or knowing how to use them in practical situations. For instance, we would memorize formulas for calculating speed, distance, and time, but we didn’t always get to explore situations where these calculations would be practically useful, like planning travel time for a family trip or determining the best route between two places.

As a teacher now, I want to ensure that students not only learn the procedural steps but also understand when and why these steps are useful. For example, in the context of nursing, knowing how to calculate medication dosages and understanding rates of change is vital. Similarly, in everyday life, knowing how to budget, plan for a trip, or manage time efficiently all require mathematical thinking.

Question

As educators, have you ever used math problems in scenarios that are related to students' real lives?