Summary

Children Learn When Their Teacher’s Gestures and Speech Differ Melissa A. Singer and Susan Goldin-Meadow

The authors of this article carried out this study on the effect of gestures by instructors on children's learning of mathematics, specifically on mathematical equivalence problem-solving. The researchers, in their study, asked whether gestures illustrating a different solution to the teacher's speech — gesture-speech mismatch — would facilitate the learning process or not. The researchers tested 160 third and fourth-grade students, who were divided into six groups. Different groups learned either one speech strategy or two. Students also learned under different conditions of gestures: no gesture, gestures that reflected the speech, or gestures that disclosed a different strategy from that disclosed in the verbal explanation.

It was discovered that children learned best when gestures were reflective of a different strategy from the one explained through speech. This mismatch between speech and gesture allowed students to learn two strategies without being overwhelmed with too much verbal information. Children who were taught two strategies only in speech did not perform as well, as expected, which means too much spoken information can mislead students. However, when the first strategy was explained through speech and the second strategy was presented only by gestures, students performed much better. This finding identifies that gestures have the potential to provide a valuable second channel of learning, complementing key concepts in a more palatable way.

The authors concluded that mismatching gestures can enhance learning by offering students an alternative way of learning the material. Gestures appear to contribute a little extra information in a soft, but effective, manner and make it easier for students to connect ideas. This study suggests that teachers intentionally supplement instruction with gestures — not as a rewording of what is being said, but as offering complementary methods for enhancing students' understanding of mathematics concepts.

Stop 1

Even teachers routinely produce gestures as they instruct children in both individualized tutorials (Goldin-Meadow, Kim, & Singer, 1999) and the classroom (Crowder & Newman, 1993; Flevares & Perry, 2001; Neill, 1991; Roth & Welzel, 2001; Zukow-Goldring, Romo, & Duncan, 1994). And children pay attention to those gestures, often gleaning substantive information from gesture that cannot be found anywhere in the teacher’s speech (Goldin-Meadow et al., 1999).(p.g.85)

I stopped at this quote there because it reminded me of my own teaching experience. During my teaching career, I used gestures many times without ever consciously thinking about them — they simply seemed to be a natural addition to what I was saying. Whether I was demonstrating addition by spreading out my hands to show grouping or spreading out a finger to gesture towards different spots in an equation to show key points, gestures were an essential aspect of my classroom. I realize now that gestures played a significant role in helping students to understand certain concepts. After reading this quote, how effective are the spontaneous hand movements and being mindful of my gestures can make my explanations more clear and more effective for students.

Stop 2

Gesture-speech mismatch occurs when gesture conveys information that is different from (although not necessarily contradictory to) the information conveyed in the speech it accompanies.(p.g.85)

I stopped at this quote because it helped me realize that gestures can be more effective than simply repeating what we say. Sometimes, a teacher's gestures express another solution to an issue or highlight an important idea that was not addressed verbally. This doesn’t mean the gesture is contradicting the verbal message; it is simply adding information that can help students think about the concept in a different way. As mentioned in the article, mismatched gestures can offer a second problem-solving strategy. However, in my opinion, this can’t happen all the time, especially when teaching younger students. If we mismatch gestures, it can confuse them and make it harder for them to understand the concepts clearly.

Do you have experience using gestures to enhance your teaching, and how do you balance them with verbal explanations to ensure clarity?

A Linguistic and Narrative View of Word Problems in Mathematics Education

By

SUSAN GEROFSKY

Susan Gerofsky's paper analyzes mathematical word problems from the perspective of linguistics and discourse analysis. Author highlights that while word problems appear to tell stories, they actually follow a pattern based on arithmetic and algebraic formulas rather than real-world stories. Susan first describes the three general components of a word problem which include:

1. A 'set up' component typically viewed as a narrative and generally non-essential

2. An 'information' component providing information to solve the problem

3. The question

Though some believe narratives are engaging, students tends to disregard them, focusing only on analysing them.

Susan takes into account the language features of word problems, their absence of empirical relevance in the world, and so they are indeterminate in the sense of locutionary force (i.e., what they literally mean). She outlines how there is a requirement for students to do some kind of "pretend" reading, reading fictionalized hypotheticals as if they were real, but completely fabricated. The study also discusses verb tense inconsistencies, showing how math word problems mix up grammatical tenses in ways not found in ordinary speech or storytelling.

Susan concludes the paper by explaining David Pimm's idea that word problems can be considered parables. Although they share some things in common, she wonders if this is an accurate comparison. Her general thesis is that we must critically examine the role of word problems within mathematics education and re-look at why they continue to be used so prevalently.

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"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

From my childhood experience I learned word problems following specific steps, without showing how the steps worked to solve problems related to real life. It led me to question whether the students were simply being taught to memorize steps to solve problems rather than to think.

While learning processes is important, I felt like not relating them to real applications made math seem less applicable. Students can possibly do math problems, but maybe not understand how they can utilize those skills in their future occupations or daily life.

If mathematical problems were related to the real world, students would be able to recognize how mathematics functions in their world. For example, understanding mathematics in nursing or electronics would allow students to visualize the relevance of their studies in real-life situations. The realization would allow students to be critical and understand the application of mathematics in life.

Stop 2

That delineating the boundaries of the word problem genre can allow us to play with those boundaries in interesting ways(p.g.43)

I stopped at this quote because in my opinion we can identify new ways to use the word problems by delineating the boundaries. We can use open-ended questions and by creating word problems more interesting to the students can help them to explore math beyond just applying formulas. Moreover, by connecting word problems to real life, we can encourage students to think critically rather than treating it as simple exercises. As a result, students recognize that math is relevant and useful.

One of the experiences that remain in my memory is when I witnessed how my students solved a division word problem. I knew that traditional word problems have the effect of making students think about calculations and not so much about thinking. But when I altered the problem a bit—by asking questions, allowing different answers, and making it real-life related—the students started thinking more deeply. This opened my eyes to the fact that as teachers, we can make word problems more than just exercises. We can use them to help students explore and understand math on a deeper level.