Psychology

Child development is a process that every child has to undergo while growing up and it involves mastering as well as learning different skills in life for instance walking, sitting, tying shoes and talking (Uttal, ODoherty, Newland, Hand  DeLoache, 2009).

A developmental milestone is a skill acquired by a child within a specified period, for instance learning how to walk (Uttal, et al., 2009).  Developmental milestone occurs in sequences in that one skill has to be fully developed before another one can be learned.

COURSEWORK
Theoretical Advance
It has been observed that children tend to learn mathematical knowledge in a number of ways (Uttal, et al., 2009).  However, theory has it that it is not enough to use manipulation of concrete objects as a way of giving children the ability to understand symbolic representations of mathematical ideas or abstract (Uttal, et al., 2009).

Theoretical challenge for Future Developmentalists
Developmentalists have discovered that even though learning algebra can prove quite helpful in creating a gateway for future science and mathematics achievement in child development, there is a challenge involving understanding the figurative nature of algebraic representations (Uttal, et al., 2009).

Research Methods Advance
The concept of dual representation can prove as an advance in understanding the symbolic nature of representations (Uttal, et al., 2009).

Research Methods Challenge for Future Developmentalists
Unlike in the case of adults, dual representation is a developmental challenge to children since they are required to pay more attention to what exactly is represented by a symbolic object and not its inherent properties (Uttal, et al., 2009).

Advance in Understanding Milestones
Prevention of interaction with the model as an object by children actually enhances their use of it as a symbolic representation (Uttal, et al., 2009).  In the process, a strong support for challenges experienced in the course of dual representation is provided.

Milestones that Need Greater Specification
Research on dual representation has been observed to highlight the importance as well as difficulty of being able to link a symbolic object to what its representation (Uttal, et al., 2009).  Even though it might appear simple to an adult, it can prove difficult for children under the age of 3 years.

Advance in Understanding Mechanisms
By learning a mathematical concept from either generic symbols or perceptually rich and concrete symbols described as written language, children are able to understand the mathematical symbols (Uttal, et al., 2009).  On the other hand, those learning from the concrete instantiations are less able to use what they have learned to the more generic symbols.  However, those learning from abstract symbols are in a better position to transfer their knowledge to new concepts (Uttal, et al., 2009).

Mechanisms that need Greater Specifications
Manipulatives that are computer-based being used on children need to consider use and design of concrete manipulatives (Uttal, et al., 2009). This is because it reduces the demands for the dual representation and in the end enables children to pay less attention to on-screen objects and more on the relationship between mathematical representations and the manipulatives (Uttal, et al., 2009).

Advance in Developing Applications
Simple manipulatives that facilitate abstraction as well as reflection enable children to focus and reflect on their actions, leading to more learning (Uttal, et al., 2009).  Therefore, as it has been observed, manipulation is best applied when children use them as tools for learning as compared to focusing on the objects properties (Uttal, et al., 2009).

Applications that need Further Effort
Majority of teachers assume that interesting or highly attractive manipulatives will further facilitate learning and transfer of knowledge in children (Uttal, et al., 2009).  However, it has been observed that children may not be able to link symbolic representations with what they learn from concrete objects (Uttal, et al., 2009).  Therefore, a balanced approach considering how interesting and attractive concrete objects hinder and assist learning should be considered.