Background and Analysis of Falk's Research

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Key point: Falk's research provide a framework to understand how to achieve a deeper level of understanding and awareness and learning
Background and Analysis
Falk evaluates discourse on learning infinity and what differentiates those who grasp the concept of infinity from those who do not. The infinity of integers implies that there is a never-ending possibility of numbers, but young learners are firsts exposed to finite numbers. Beliefs and surroundings influence behavior and behavior in turn affects perceptions including conceptualization of infinity in mathematics and the sciences. Some of these learners may still face challenges trying to understand infinite sets. Asking learners about their understanding and representation of concepts can provide insights about their interpretations, even as there are divergent perceptions about certain concepts. Inconsistencies in understanding concepts make it difficult to evaluate the learners’ understanding when they attach multiple meanings to concepts.
The interview approach is useful to understand students’ understating of concepts, but the interpreter may misunderstand the responses. As such care should be exercised when evaluating responses so that there is a clear understanding of the learners' intention.Different learning and intellectual practice do not have the same effect on learners’ understanding of concepts. Having interviewed the respondents so they can give detailed explanations and reasons can provide insights about their learning (Falk 8). Acquisition of concepts is partly dependent on age, but without a clear understanding of how this occurs interviewing students is necessary to uncover how understanding can vary depending on the context and age.
Assessing ideas on concepts and student understanding
Sfard (210) points out that to understand research studies, it is necessary to evaluate the use of keywords, getting meaning from context, and her own understanding and interpretation of the text. Falk does not explicitly describe the meaning of concepts or include keywords. Still, there is an explanation of how the research was carried out to evaluate students’ understanding of the concept of infinity (Sfard 212). There is a need to distinguish concepts where readers can then evaluate the different meanings and concepts in various contexts. Falk (6) also addressed how children of different ages understand the infinity of numbers. This approach helps understand how the meaning of concepts changes over time and where the teaching and learning processes influence a deeper understanding. 
Evaluating students’ conceptions can indicate how teaching and learning influences their understanding. A greater understanding of concepts, but few studies have focused on the potential barriers to understanding certain concept. Motivating and meaningful tasks are useful to determine a child’s best learning ability and their understanding of certain concepts (Falk 5)
Thinking and learning are intertwined and students' assumptions can affect how they learn, and interviews are one way to uncover the learners’ experience in their own words. In any case, interviewing allows the res...