# Assessing Mathematical Capabilities in Children

ASSESSING MATHEMATICAL CAPABILITIES IN CHILDREN 1

Children undergo different stages of development from birth that havedifferent characteristics based on their physical, mental andcognitive capabilities. The rationale for the inquiry on thechildren’s mathematical capability is to challenge the conventionknowledge that preschool children are incapable of completing simplemathematical tasks. It will also uphold the various researchesconducted in the various settings in Australia for favorableintroducing children to mathematics at a tender age. This informationis availed to educators introduce mathematical concepts to childrenin early childhood. The information is important to educators sinceit will help them identify the gaps that exists in their mathematicalinstructional methods. It will also acquaint them with the findingsof the current research on mathematical abilities in children andthey can, therefore, engage their learners with the most productiveage appropriate activities. The final presentation will be in powerpoint form. The rationale for this is that with their level ofknowledge, educators can engage in a collaborative learning sessionof listening and contemplating on the highlighted points. The methodalso facilitates referring back to points that may require emphasis.

Clements et al. (2008) are of the opinion that children can gothrough the Piagetian experiments successful if the contexts in whichthey learn becomes meaningful to them. However, the rationaleinclines on maximizing the level of knowledge in the differentdevelopmental stages. Also, this paper will identify the ageappropriate skills in children to avoid misusing the anxiety oflearning found in children by putting them in difficult tasks. Uninformed approaches may create a feeling of failure and loss ofconfidence that can lead to a lack of interest in learning (Clementset al., 2008).

As children develop, they show desirable results if they getassistance from others in their environment. It explains the reasontheir learning is more of group oriented than individual studyingClements et al. (2008). In learning mathematic, children perform wellthrough telling, modeling and illustrations, listening to theinstructor talking as well as performing tasks together (Fleer &Raban, 2005). An integrated method of learning putting the differentapproaches together leads to desirable learning outcomes. Earlychildhood learning inclines on the developmental characteristics.When curriculum developers design subjects, they put intoconsideration the chances of desirable outcomes.

According to Fleer & Raban (2005) the main goal is to introducechildren to tasks that they can complete comfortably without muchstrain. Children employ their senses to learn about the environment.They understand concepts about the language exposed to them beforelearning how to speak (Fleer & Raban, 2005).They also developmathematical concepts before they can conceive the idea ofsubtraction and addition. In assessing the mathematical capabilities in children, it is imperative to understand the basic concepts thatare inherent in them as they develop.

A research conducted in the mathematical Thinking of Pre-schoolChildren in Rural and regional Australia project found out thatchildren begin to exhibit mathematical thinking skills in the firstthree years of life. Therefore, pre-scholars should not be thought asincapable of completing small tasks consistent with their cognitiveskills (Fleer & Raban, 2005).

As Fleer & Raban (2005) puts it, children become aware of thedifference in size of the elements in their surroundings. They candifferentiate between a big and a small object even before they canunderstand why the difference exists. They also relate the causes andeffects of different items in their environment. For example, theyknow that if they hit a can, it can produce a particular noise. Theycan also classify various objects on the basis of observablecharacteristics. For example, they can put balls with similar colorstogether.

As they continue developing, children’s learning skills develop andthe continue polishing their understanding of various mathematicalconcepts. At the age of 4 years, children area capable of memorizingnumbers in their correct sequence (Hunting & Mousley, 2009). They can count numbers in an ascending pattern. Sometimes, they canskip some numbers or repeat some of them. A continuous practice isinstrumental in reducing the number of times they skip or makemistakes. Hunting & Mousley (2009) agree that at this age,children do not understand what the numbers mean, but it acts as afoundation for acquainting themselves with their existence. A laterunderstanding of the numbers becomes as easy task.

At this age, meaningful counting follows as children understand theuse of numbers through their continuous exploration. They understandthat the numbers can be associated with different objects. Forexample, counting the number snacks in a box by giving each of thesnacks a particular value. Assigning a number to an item is a primarymilestone for one-to-one correspondence (Van den Heuvel-Panhuizenv etal., 2009). They can also understand the difference occurring in thenumber of items is given set. For example, they can derive anobservable difference by counting the number of snacks in twodifferent boxes. After assigning numbers to the snacks, they can tellwhich box has more snacks tan the other. Recognizing the writtennumbers becomes important at this point. Apart from mentioningnumbers and putting them into their right places in a sequence,children recognize them when written against an item.

According to Van den Heuvel-Panhuizen et al. (2009) children developthe ability to recognize the basic shapes like circles, squares,triangle, and oval among others. They can associate them with theirplay items like balls, crackers among others. Identifying thedifferent appearances of objects comes with their spatialrecognition. Pre-scholars understand the relationship between itemsin their surrounding and the position they occupy regarding otherobjects in the same environment. For example, they can tell if a ballis behind or under a chair.

Other mathematical capabilities that occur from zero to four yearsinclude serialization and ordering. Serialization involves puttingitems in a sequence. The concept develops from the mathematicalability to place numbers in a given sequence. Serialization of itemscan involve sizes or pattern. When given a guide of a progressivepattern, children can predict the next item that fall on a paper leftblank. Serialization tests are instrumental in judging children’sordering skills as per their level of cognitive capabilities. Forexample, in a pattern involving black and white objects, children atthe age of three years are capable of stacking them in the correctorder up to three items. At four years, children can also matchobjects with similar appearances together. For example, they can putcups and plates on a separate rack.

As they continue growing, the can place a bigger number of items dintheir correct order. After they match objects using the mostobservable characteristics, they can identify any variation withitems in the same category. They can further sort them according toany other features (Papic et al., 2009). For example, after sortingcups and plates, they can further sort plates according to theirdifferent color. A good example is putting blues and red plates inseparate racks.

To be able to complete these tasks, educators have to use tools thatreflect the children’s interests. The Australian Association ofMathematics Teachers (2006) is of the opinion that children are veryactive during their pre-school years, and most of their activitiesrevolve around playing. The nature of their behavior acts as a goodsource of information on the best approaches to use when teachingthem mathematics. Their explorative behavior is also informative onthe tool to be used in learning. As The Australian Association ofMathematics Teachers and Early Childhood Australia (2006) put it,mathematical probes are easy to solve if appropriate tools are put inplace. The choice of tools depended on the interrelationship thatusers have with them. For example, children under the age of fouryears, children have a lot of interest in eye capturing items thathave beautiful colors. Therefore, using the items in counting and formatching tasks builds up their interest in learning. Tymms et al.(2009) term mathematical activities as semiotic since they reflectsigns, meanings and interrelationship between different concepts.Educator should, therefore, use this as a basis to develop the rightenvironment for mathematical learning in children (Tymms et al.,2009).

The Australian Association of Mathematics Studies proposes variouspedagogical practices that are consistent with the learningcapabilities of children. The rationale for the uniform set ofpractices is that all children in early childhood years can accesspowerful mathematical ideas (AAMTECA, 2006). They propose engagingthe natural curiosity in children to assist them learn mathematicalconcepts by exploring their environment.

Secondly, educators should use acceptable age approaches in earlychildhood like plays and child initiated curriculum. They should alsorecognize, celebrate and build on the skills exhibited in children.It helps to encourage children to continue making milestones in theirlearning (Gifford, 2005). Educator should provide the appropriatematerials, enough time and a conducive environment to facilitateacquiring the relevant skills. There is the possibility of havingchildren with slow learning abilities, and they cannot keep pace withthe rest. Educators should not generalize the capabilities withoutidentifying the children who require special attention (AAMTECA,2006). The use of the correct vocabulary and other customizedstrategies can help achieving the required skills exhibited by theirfast learning colleagues.

In conclusion, mathematics learning in children is delicate since,mathematics learning in children is delicate Educators shouldunderstand the age appropriate capabilities in children and exposethem to the tasks that are consistent with their cognitivedevelopment. They should maximize on the anxiety to learn through theexplorative skills inherent in children by aligning learning to them.The use of appropriate tools serves an important factor to instigatelearning while making it enjoyable at the same time. Research asproved that all children in the early childhood can conceivemathematical concepts and polish them as they advance in age.

References

Clements, D. H.,Sarama, J. H., & Liu, X. H. (2008). Development of a measure ofearly mathematics achievement using the Rasch model: theResearch‐Based Early MathsAssessment. *Educational Psychology*, *28*(4), 457-482.

Fleer, M., &Raban, B. (2005). *Literacy and Numeracy that Counts from Birth toFive Years: A Review of the Literature. *New York N.Y.: Springer.

Gifford, S. (2005).*Teaching Mathematics 3-5: Developing Learning In The FoundationStage: Developing learning in the Foundation Stage*. UnitedKingdom U.K.: McGraw-Hill Education (UK).

Hunting, R. P., &Mousley, J. (2009). When do children begin to learn mathematics?Views of preschool practitioners in regional and rural Australia.*Australian Research in Early Childhood Cducation*, *16*(2),27-38.

Papic, M., Mulligan,J., & Bobis, J. (2009). *Developing Mathematical Concepts inAustralian Pre-school Settings: Children`s Mathematical Thinking.*Australia: Happer Collins.

The AustralianAssociation of Mathematics Teachers and Early Childhood Australia.(2006). *Position Paper on Early Childhood Mathematics*.Adelaide: Early Childhood Australia Inc.

Tymms, P., Jones,P., Albone, S., & Henderson, B. (2009). The first seven years atschool. *Educational Assessment, Evaluation and Accountability(formerly: Journal of Personnel Evaluation in Education)*, *21*(1),67-80.

Van DenHeuvel-Panhuizen, M., Van Den Boogaard, S., & Doig, B. (2009).Picture Books Stimulate the Learning of Mathematics. *AustralianJournal of Early Childhood*, *34*(3), 30-39.