Problem solving, problem posing, multicultural literature, and computer scaffolding

Author(s):  
Jacqueline Leonard
ZDM ◽  
2021 ◽  
Author(s):  
Haim Elgrably ◽  
Roza Leikin

AbstractThis study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.


2020 ◽  
Vol 105 (3) ◽  
pp. 303-324 ◽  
Author(s):  
Maike Schindler ◽  
Arthur Bakker

AbstractEducators in mathematics have long been concerned about students’ motivation, anxiety, and other affective characteristics. Typically, research into affect focuses on one theoretical construct (e.g., emotion, motivation, beliefs, or interest). However, we introduce the term affective field to account for a person’s various affective factors (emotions, attitudes, etc.) in their intraplay. In a case study, we use data from an extracurricular, inquiry-oriented collaborative problem posing and problem solving (PP&PS) program, which took place as a 1-year project with four upper secondary school students in Sweden (aged 16–18). We investigated the affective field of one student, Anna, in its social and dynamic nature. The question addressed in this context is: In what ways does an affective field of a student engaging in PP&PS evolve, and what may be explanations for this evolvement? Anna’s affective field was dynamic over the course of the program. Her initial anxiety during the PP&PS program was rooted in her prior affective field about mathematics activities, but group collaboration, the feeling of safety and appreciation, together with an increased interest in within-solution PP and openness for trying new things went hand in hand with positive dynamics in her affective field.


2015 ◽  
pp. 333-354 ◽  
Author(s):  
Roslinda Rosli ◽  
Mary Margaret Capraro ◽  
Dianne Goldsby ◽  
Elsa Gonzalez y Gonzalez ◽  
Anthony J. Onwuegbuzie ◽  
...  

1990 ◽  
Vol 37 (5) ◽  
pp. 30-33
Author(s):  
Alan Zollman

The National Council of Teachers of Mathematics recommends that … mathematics programs take full advantage of the power of calculators and computers at all grade levels” (NCTM 1980, 8). Somehow, without meaning to, the calculator has taken a subsidiary role to the computer in the implementation of NCTM's An Anemia for Action recommendation. High technology is getting the majority of education's emphasis, while low technology, namely the calculator, is not having the impact that it could in the elementary school. This situation prevails despite the fact that 98 percent of this country's population uses calculators in everyday mathematics applications (Saunders 1980). It is time to reaffirm the viable role of the calculator in mathematics education (NCTM 1987). This article presents an interesting aspect of the geometrical array of the keys on a calculator that can be turned into a problem-solving, problem-posing situation for the upper elementary or middle school classroom. Read this article with a calculator in hand.


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