Background and Analysis of Falk's Research
Step 3. Draft essay with framework-questions
The essay should argue for one, and only one, assertion. The draft essay must satisfy all the “Specific
Requirements” listed below. Suggested approximate length for the draft essay: 1,300 words. At the
beginning of each paragraph put in brackets [ ] and ALL CAPS the question/questions from the
Pearlman-Carillo framework that that paragraph addresses.
Specific Requirements
The draft essay and final essay must satisfy/include the following:
12 point font; double-spacing; 1 inch margins all around; PDF format
a separate title page with the title of your essay, your name, and the date
an introduction and a conclusion
a bibliography at the end of the essay listing, in proper MLA bibliographic format, the two sources you
used. YOU MAY NOT USE MORE THAN TWO SOURCES.
proper in-text citations, as appropriate, in MLA format
descriptive section headings (note: you may NOT use the terms “Analyze”, “Question”, “Evaluate”,
“Complicate” as section headings, since they are not adequately descriptive)
an argument for one, and only one, assertion.
utilization, at least implicitly, of the Pearlman-Carillo framework.
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Draft Essay
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 researchers to pose new question when there is a need to get clarity. There is increased knowledge for both the interviewer and the interviewees about how students conceptualize and how this relates to the learning process.
Evaluating the researchers’ ideas and concepts
Sometimes there are difficult concepts for students to understand where they can evaluate and compare new concepts with what they already know. Investigations about an understanding of concepts that consider the learners’ experiences are helpful to identify gaps in teaching and learning. Falk (7) conducted experiments to investigate children’s understanding of potential infinity, actual infinity, and the infinite gap. Since the findings were based on the learner’s responses and performances, Falk’s approach helps uncover the students’ reasoning and learning at different ages. Falk’s demonstrated that children are more comfortable performing tasks but are not necessarily well placed to explain how and why they choose ce...