Analogical reconstruction of the probability knowledge of Zimbabwean female secondary school students

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

“…As in previous studies (Fast, 1997, 1999, 2001, 2007), the selection of effective anchoring examples is a key to the success of this approach. Elementary mathematics teachers need time and practice discerning and creating these anchors.…”

“…Any change in the positive direction is desirable even if the change is from highly negative to less negative. The directional knowledge confidence score was developed and utilized by one of the authors of this study in previous research (Fast, 1997, 1999, 2001, 2007) to provide additional relevant evidence of change that would not be evident from a confidence score change in itself.…”

“…For example, in addition to knowing how to compute, a teacher might need to know how and why specific mathematics procedures work, how best to define a term for children at a particular grade level, or how to interpret, remediate, or prevent students' errors. Furthermore, students' errors may be indicative of misconceptions that the students have developed or are in the process of developing (Fast, 2007). Misconceptions are generally highly resistant to change once they have been fully developed (Smith, 1992), and it is thus desirable to prevent misconceptions or curtail their development at the earliest opportunity (Fast).…”

“…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.…”

“…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.…”