Using analogies to overcome student teachers' probability misconceptions

Fast, Gerald R.

doi:10.1016/s0732-3123(97)90011-0

Cited by 21 publications

(26 citation statements)

References 12 publications

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“…Kahneman and Tversky (1972) stated that for a family with 6 children, it's believed that the order of genders will more likely be MFF-MFM (M: Male; F: Female) instead of MMMMMM or MMM-FFF. It's possible to find similar results in the studies by Fast (1997) and . However, it can be suggested that these mistakes disappeared considerably in the posttest.…”

Section: Levelsupporting

confidence: 73%

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The Effects of Teaching Mathematics Performed with the Help of CSCM on Conceptual Learning

Gürbüz¹,

Erdem²,

rat³

2012

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This paper explores the effect of teaching mathematics performed with the help of Computer-Supported Concept Maps (CSCM) on the conceptual learning. To achieve this end, CSCM were developed and used in the process of teaching probability subject. Within the true-experimental research method, a pre-and post-test control groups study was conducted with 39 seventh graders-20 in experimental group, and 19 in the control group. Each group was taught three times/week, 40 min/session, for 2 weeks. A 12-item instrument was used to collect data. After the teaching intervention, the same instrument was re-administered to both groups as post-test. The results suggested that students in the experimental group performed significantly better than those in the control group, in terms of conceptual learning.

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Section: Levelsupporting

confidence: 73%

“…Some of the questions were developed by the researchers, and some were developed with the help of related literature (Fast, 1997;Pratt, 2000;Baker & Chick, 2007;Nilsson, 2007Nilsson, , 2009Gürbüz, 2006b;.…”

Section: Instrumentmentioning

confidence: 99%

The Effects of Teaching Mathematics Performed with the Help of CSCM on Conceptual Learning

Gürbüz¹,

Erdem²,

rat³

2012

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“…He also showed how coupling those tangible environments with computer simulations allow students to develop more complex theories about chance [1]. His approach is related to Fast's [11] attempt at using analogies to make concepts in probability more intuitive. By providing familiar or anchoring situations, Fast's findings suggest that analogies can prevent the activation of some misconceptions.…”

Section: Teaching Probability In a Constructivist Waymentioning

confidence: 99%

Flipping the Flipped Classroom: A Study of the Effectiveness of Video Lectures Versus Constructivist Exploration Using Tangible User Interfaces

Schneider

Blikstein

2016

IEEE Trans. Learning Technol.

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In this paper, we show results suggesting that Tangible User Interfaces (TUIs) can be used to prepare students for future learning. In a previous study, we found that students who used an interactive tabletop first and then studied a text significantly outperformed participants who read a text first and then used the tabletop. This finding shows that discoverylearning approaches are more suited to TUIs than traditional "tell-and-practice" approaches. In this paper, we generalize this effect to a different population, a different learning material and a different topic. The tangible interface, Combinatorix (Fig. 1) enables small groups of students to collaboratively discover concepts in probability. Our system supports students' exploration of principles in combinatorics (i.e., permutations and combinations) that serve as foundations for learning about probability. We describe the design of Combinatorix, as well as an experiment that examined the interaction between focused lectures and free exploration. We found that students who first explored the topic on a tangible interface and then watched a video lecture significantly outperformed students who watched a lecture first and then completed a hands-on activity. We discuss how the "functional fixedness" induced by the video lecture limited students' learning of probability, and conclude with guidelines for implementing interactive tabletops in classrooms.

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“…Clement was the originator of using anchoring example analogies to successfully overcome misconceptions in physics where other methods had limited success. One of the authors of this research adopted the use of anchoring examples in successfully overcoming misconceptions in the area of probability (Fast, 1997, 1999, 2001, 2007) with both high school students and preservice teachers in various educational settings including Canada, the United States, and Zimbabwe. The belief that this approach might also be successful with preservice elementary school teachers in better understanding both elementary mathematics content and pedagogy was well grounded in previous successes.…”

mentioning

confidence: 99%

“…The essence of success in using an anchoring example in making a connection between that which is not well understood, the target situation, and that which is well known, the anchoring example, is that the anchoring example must be well understood by the student for it to be an anchor. In previous studies conducted by the one of the authors, it was shown that for the analogical approach to be effective, the student having the misconception must be confident that the anchoring example is mathematically correct and that the anchoring example is clearly analogous to the target example (Fast, 1997, 1999, 2001, 2007). Therefore, it is paramount in making a convincing case for anchoring example‐based constructivism as a best practice approach to teaching mathematics that the anchoring examples themselves are well understood and are already a part of the students' constructed knowledge.…”

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confidence: 99%

Intentional Integration of Mathematics Content Instruction with Constructivist Pedagogy in Elementary Mathematics Education

Fast

Hankes

2010

School Science and Mathematics

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The purpose of the research was to improve the effectiveness of instruction in constructivist pedagogy in a college elementary mathematics education course through intentional integration of instruction in mathematics content. Instructors of this course previously used examples involving mathematics content on an ad hoc basis in an attempt to illuminate desirable constructivist pedagogy but discovered that they were ineffective because students experienced difficulty with the mathematics content itself. An instrument was created to assess students' mathematics content knowledge required to understand these examples. Based on the outcome of the assessment, intentional instruction of mathematics content using anchoring examples was integrated with pedagogical instruction. Results showed significant improvement in mathematics content knowledge and confidence in that knowledge with a better understanding of constructivist pedagogy.s sm_43 330..340 330Volume 110 (7) Intentional Integration

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Using analogies to overcome student teachers' probability misconceptions

Cited by 21 publications

References 12 publications

The Effects of Teaching Mathematics Performed with the Help of CSCM on Conceptual Learning

The Effects of Teaching Mathematics Performed with the Help of CSCM on Conceptual Learning

Flipping the Flipped Classroom: A Study of the Effectiveness of Video Lectures Versus Constructivist Exploration Using Tangible User Interfaces

Intentional Integration of Mathematics Content Instruction with Constructivist Pedagogy in Elementary Mathematics Education

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