Imagine you are sitting in your office when a little child comes bouncing in to the room, filled with curiosity. They look around the room and begin to question everything they see before their eyes fall on a large bookshelf against the wall. The little child looks at the shelf in awe, and exclaims “There must be a million books there!” Most of us who have spent time with a little kid at some point have probably heard them over exaggerate when it comes to guessing the amount of something, but not all of us have considered why this might be. It is interesting that as a person looks at an item presented before them, they also have a concept of the amount in front of them, and this develops more and more with age. It is not innate.
In the article by Ashcraft and Moore, the authors investigate the development of an individual’s numerical concept. The two authors have written a few articles together, and Ashcraft is currently the chair of the Department of Psychology at the University of Nevada, Las Vegas, and has written approximately 12 research based articles. Ashcraft’s area of focus lies in investigating issues in mathematical cognition and many of his articles, such as the one referenced here, explore this area of cognition. This article has been referenced in at least 15 other articles as well, and seems to prove a reliable source on the topic.
In the original article I have chosen to replicate, the authors tested elementary age children and a small group of college students. In the study a number line was presented on a computer monitor with the appropriate endpoints shown below the line, 0 was placed on the left and a number, either 100 or 1000, was presented at the right. They would show a hash mark on the screen f...
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...al jar, I did not account for the students counting the candies and trying to mathematically attempting to figure out the amount in the jar. In the second reduplication of the study I believe if I had given the students a larger sample, it would have given more clear results rather than the amount I had given. I also had no way to tell if students were indeed guessing, or counting the amount on the page.
I believe that I understand the original study much more after my attempt to reduplicate it and form it to a college setting. If I was to do this again, I would do what I could to limit variables, such as allowing students to count. The experiment could also benefit much from a sample with larger age differences.
Works Cited
Ashcraft, M. &. (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology , 246-267.
While this study did not produce the result we wanted, we believe that we could use the information learned from this study and develop a study that would be more effective.
However, there was counteracting evidence that supported the idea of children developing subitizing later, as a shortcut to counting. It is still debatable which of these skills develops first in children, but the understanding of the two types of subitizing may account for both models. There is a very basic form of subitizing that is referred to as perceptual subitizing. This is the ability to recognize a number of items without any mathematical understanding.
Siegler, R., & Alibali, M. (2005). Children’s Thinking Fourth Edition. Prentice Hall Inc. Upper Saddle River NJ.
Anytime these children saw three times five, they would instantly know the answer is fifteen without missing a beat. Once memorized, the teacher will move onto other concepts, and the children continue learning. While this may sound like a solid method for teaching, there remains one underlying problem that most children will never learn through this method: why? Why is three times five fifteen?... ...
One of my largest concerns for the study overall was the fact that there was a significant difference in the number of male and female participants (67 males to 48 females). Along with the fact that these participants were allowed to select their own groups under no constraints. Which for me, knowing that all these student participants were from the same area of study, business, I feel many of these students may have already been well acquainted or even good friends with some of their classmates. Especially being in an upper level business course. In theory researchers had the right idea in not controlling the group selection process, but I feel in some ways other factors have now come into play, which may have altered the overall results of the study. Also, another questionable factor was the size and makeup of the groups. Some groups had five members, some had six, some had four or even seven; and then some groups had up to two women, and one had none at all (Kent, Moss 1339). For me, there just seemed to be too many variables in the makeup for group selection that possibly could have influenced the outcome for the overall study. And again, is something researchers may want to look into correcting in future
In order to become a fluent reader, a person must memorize the sounds that letters make and the sounds that those letters make when combined with other letters. Knowing math facts, combinations of numbers, is just as critical to becoming fluent in math. Numbers facts are to math as the alphabet is to reading, without them a person cannot fully succeed. (Yermish, 2011 and Marquez, 2010). A “known” fact is one that is “answered automatically and correctly without counting” (Greenwald, 2011).
In order to test this hypothesis 60 students will be randomly recruited. In order to get my 60 participants, I will pick students who id begins with the numbers 08. A total of 30 females and 30 males will be chosen, all psychology undergraduate students from Texas A&M International University, largely in the age range 20-25 years. No payment, other than receive 5 points of extra credit, will be offered for participation.
According to Piaget in the “preoperational stage, which goes through 2 to 7 years of age a child should have the ability to use symbols to represent objects in the world and thinking remains egocentric and centered” (Slavin ,2015) For example, I lined up two sets of quarters on a table in front of Ahmad. Each set of quarters had four in a row, I asked Ahmad which set of quarters had the most he told me that they all had the same amount. For the second part I lined the quarters up differently, but they still had the same amount the second row of quarters I spaced them out. I then proceeded to ask Ahmad the same question which row of quarters had the most he replied the second row. I asked Ahmad why did he think the second row had the most, he replied because it is larger. This method would be conforming to Piaget’s principle of conservation, “one manifestation of a general trend from a perceptual-intuitive to an orientation, which characterizes the development of conceptual thinking” (operational Zimiles
Tubbs, Robert. What is a Number? Mathematical Concepts and Their Origins. Baltimore, Md: The Johns Hopkins
...ett, S. (2008) . Young children’s access to powerful mathematical ideas, in English, Lyn D (ed), Handbook of international research in mathematics education, 2nd edn, New York, NY: Routledge, pp. 75-108.
This representation is called preverbal number knowledge, which occurs during infancy. Preverbal number knowledge occurs when children begin representing numbers without instruction. For instance, children may be familiar with one or two object groupings, but as they learn strategies, such as counting they can work with even larger numbers. As stated in Socioeconomic Variation, Number Competence, and Mathematics Learning Difficulties in Young Children “Thus only when children learn the count list and the cardinal meanings of the count words, are they able to represent numbers larger than four” (Jordan & Levine 2009, pp.61). Typical development occurs along a continuum where children develop numerical sense, represent numbers and then begin to understand the value of the numbers. These components are required when differentiating numbers and
Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.
The chair of the UK Government had a test made to see the ability to think in “divergent or non-linear ways” between the ages 3- 25. Out of 1,600 children aged three to five showed that 98% of them can think divergent. Out of the same number of kids age’s eight to ten, 32% could think divergently. When the same test was applied to 13-15 year olds, 10% could think divergently. Then when the test was us...
The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...
Allowing children to learn mathematics through all facets of development – physical, intellectual, emotional and social - will maximize their exposure to mathematical concepts and problem solving. Additionally, mathematics needs to be integrated into the entire curriculum in a coherent manner that takes into account the relationships and sequences of major mathematical ideas. The curriculum should be developmentally appropriate to the