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Can moving their hands help children learn math? This is the question investigated by the authors of the paper "Gesturing Gives Children New Ideas about Math" (Psychological Science [2009]: 267-272). An experiment was conducted to compare two different methods for teaching children how to solve math problems of the form \(3+2+8=\underline{ }+8\). One method involved having students point to the \(3+2\) on the left side of the equal sign with one hand and then point to the blank on the right side of the equal sign before filling in the blank to complete the equation. The other method did not involve using these hand gestures. The paper states that the study used children ages 9 and 10 who were given a pretest containing six problems of the type described. Only children who answered all six questions incorrectly became subjects in the experiment. There were a total of 128 subjects. To compare the two methods, the 128 children were assigned at random to the two experimental conditions. Children in one group were taught a method that used hand gestures, and children in the other group were taught a similar strategy that did not involve hand gestures. Each child then took a test with six problems and received a score based on the number correct. From the resulting data, the researchers concluded that the average score for children who used hand gestures was significantly higher than the average score for children who did not use hand gestures. a. Answer the following seven questions for the experiment described above. (Hint: Reviewing Examples 1.6 and 1.7 might be helpful.) 1\. What question is the experiment trying to answer? 2\. What are the experimental conditions (treatments) for this experiment? 3\. What is the response variable? 4\. What are the experimental units and how were they selected? 5\. Does the design incorporate random assignment of experimental units to the different experimental conditions? If not, are there potentially confounding variables that would make it difficult to draw conclusions based on data from the experiment? 6\. Does the experiment incorporate a control group and/ or a placebo group? If not, would the experiment be improved by including them? 7\. Does the experiment involve blinding? If not, would the experiment be improved by making it single-or double-blind? b. Based on the study design, do you think that the conclusions are reasonable?

Step by step solution

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1. Experiment's question

The experiment is trying to answer the question: Can moving their hands (gesturing) help children learn math better than without gesturing?

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2. Experimental conditions (treatments)

The two experimental conditions (treatments) for this experiment are: 1. Teaching children a method that used hand gestures. 2. Teaching children a method that did not use hand gestures.

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3. Response variable

The response variable in this experiment is the score each child received based on the number of correct answers out of the six problems on the test.

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4. Experimental units and selection

The experimental units in this study are the children ages 9 and 10 who answered all six pretest questions incorrectly. A total of 128 subjects were selected for the experiment.

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5. Random assignment and confounding variables

Yes, the design incorporates random assignment of experimental units as the 128 children were assigned at random to the two experimental conditions. This random assignment helps to minimize the effects of potentially confounding variables.

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6. Control group and/or placebo group

The experiment does not include a separate control group or placebo group, but the group taught mathematics by a method that did not use hand gestures could be considered as the control group since it represents the traditional method of teaching without gestures. Adding a separate placebo group would not improve the experiment in this case.

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7. Blinding in the experiment

The experiment does not seem to involve blinding as it is not mentioned in the provided information. Single or double-blinding could potentially improve the experiment by eliminating potential biases from the researchers and/or the participants. b.

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Conclusions' reasonableness

Based on the study design, the conclusions drawn seem to be reasonable. The random assignment helps to minimize potential confounding variables, and there is a consideration for a control group (the non-gesture group). However, the experiment could have been improved by incorporating blinding to eliminate potential biases.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Educational Experiment Design

In the context of discovering whether hand gestures can improve math learning in children, researchers employed an educational experiment design. This design is pivotal as it ensures that the findings are substantiated by evidence. The criteria for a well-designed experiment include clear definition of the experimental conditions, random assignment to these conditions, consideration of a response variable, and inclusion of control groups when appropriate.

An experiment designed with these elements can effectively assess the effectiveness of the teaching methods employed. Good design also accounts for potential confounding variables and utilizes methods like blinding to minimize bias. The design in the given study comparing gesture-based teaching to traditional methods embodies many of these principles, using random assignments and defining clear experimental conditions.

Response Variable in Experiments

The central component of an experiment that assesses outcomes based on different conditions is the response variable. In educational experiments like the one presented, the response variable is a quantifiable measure of student performance – in this instance, the scores obtained from the test following the teaching intervention.

This response variable allows researchers to evaluate the impact of hand gestures in math learning. Through analysis of the scores, the effectiveness of the teaching methods can be measured. The response variable is crucial for drawing conclusions from the data, as it reflects the direct effect of the experimental conditions on the subjects.

Random Assignment

One of the most critical processes in conducting educational experiments is random assignment. This technique involves randomly placing participants into different experimental conditions to ensure that each group is statistically equivalent at the start of the experiment. The goal is to eliminate biases or systematic differences between groups that could affect the outcome.

In the gesture-based teaching study, random assignment was used to allocate the children into groups that used hand gestures and those that did not. This is an essential aspect of the experimental design that helps to ensure that the results are attributable to the teaching method rather than pre-existing differences among the children.

Control Groups in Experimental Studies

A control group serves as a benchmark in experimental studies, allowing researchers to compare the effects of the experimental condition against a standard or traditional practice. In our example, the group taught without hand gestures acts as a control group to the experimental hand gesture group. The existence of a control group helps to highlight the differences attributable to the experimental intervention.

Without a control group, attributing improvements in the response variable to the treatment becomes challenging. Therefore, a control group in this study is essential for assessing the relative effectiveness of gesture-based learning.

Effectiveness of Teaching Methods

Evaluating the effectiveness of teaching methods is a significant motive behind such educational experiments. In our discussed experiment, the method involving hand gestures was compared with a traditional non-gesturing method. The difference in scores provides insight into which method might be superior.

Effectiveness in educational studies is often gauged through performance metrics like test scores, providing a quantitative assessment. Such experiments can inform educational practices, potentially leading to improved learning strategies if the results indicate a significant benefit of one method over another.

Experimental Units in Education Research

In education research, experimental units are the individuals or groups upon which an experiment is conducted. Here, the experimental units were children who initially did not perform well on a pretest. These units were carefully selected based on specific criteria to ensure the research targets the appropriate population.

The concept of experimental units is critical because the validity of an experiment hinges on how accurately these units represent the larger population of interest. Careful selection and handling of experimental units in educational research are foundational to obtaining generalizable and meaningful results.

Blinding in Educational Experiments

The concept of blinding refers to concealing the details of the experiment from participants, researchers, or both to prevent bias. Blinding can be single or double, with the latter being the more rigorous option as both subjects and experimenters are unaware of which group the subjects belong to.

Although not employed in the hand gesture experiment, incorporating blinding could potentially improve its credibility by ensuring that the expectations of the researchers or the behavior of the subjects do not influence the results. Blinding is an advanced methodological tool that enhances the integrity of research in educational settings.