Comparing Preschool Teachers Knowledge Of Early Mathematical Development

Mathematicss is one topic that unleashes deep-rooted memories for many people. Most of these memories include the acquisition of mathematical constructs and accomplishments. Such acquisition may either be carry throughing or thwarting for scholars, as Math covers a broad assortment of grades of trouble. That is why an effectual Math instructor can hold so much influence over pupils in acquisition and even loving the topic. An effectual Math instructor should be able to pattern to her pupils her enthusiasm for the subject that she takes learning it earnestly while harmonizing due regard to her scholars who may non exhibit the same degree of competences for the topic.

Preschool is a clip when kids may foremost meet mathematical lessons, nevertheless, much recent research has indicated that preschool kids have the ability to understand a assortment of mathematical constructs even prior to come ining kindergarten ( Klein, Stakey, Clements, Sarama, & A ; Lyer, 2008 ; Clement & A ; Sarama, 2007 ) . That is why early childhood plans are progressively required to implement mathematics direction in schoolrooms because of immature kids ‘s early mathematical cognition. Development of early math accomplishments provides the foundation for subsequently larning ( Clements & A ; Sarama, 2008 ; NAEYC & A ; NCTM, 2008 ; Lee & A ; Ginsburg, 2008 ) .

Harmonizing to the National Council of Teachers of Mathematics, the quality of mathematical instruction in early childhood plays an of import portion in the kid ‘s apprehension of perchance hard math constructs ( Loop, 2009 ) . Although there had been many surveies refering to forms of mathematical instruction in preschool, there is a deficiency of research on how instructors of Math perceive how immature kids learn Math and even what to learn in conformity to the developmental degree of their scholars.

This current survey draws much inspiration and thought from the work of Platas ( 2008 ) entitled “ Measuring Teachers ‘ Knowledge of Early Mathematical Development and their Beliefs about Mathematicss Teaching and Learning in the Preschool Classroom ” . Platas was able to mensurate the cognition of early mathematical development and beliefs about mathematics learning and larning in the preschool schoolroom of preschool instructors utilizing developed and validated study instruments and statistical analysis ( 2008 ) . There was a important fluctuation in the cognition and beliefs of early childhood instructors on age-appropriateness of math direction, schoolroom venue of coevals of mathematical cognition, math versus socio-emotional development and the comfort degree in supplying the direction. The instrument used in the research has been found to be helpful for the readying of prospective Math instructors every bit good as for the professional development of current Math pedagogues.

Platas ‘ work has raised many issues and beliefs sing the developmental cognition of kindergartners. Such issues include age-appropriateness of mathematical direction used by instructors in preschools, the extent of larning of such mathematical constructs taught, the intent of learning math constructs in preschool and the comfort degree of instructors when they introduce such math constructs to preschool kids ( Clement & A ; Sarama, 2007 ; Ginsburg & A ; Golbeck, 2004 ; Platas, 2008 ) .


Belief – “ covers all the affairs of which we have no certain cognition and yet

which we are sufficiently confident of to move upon and besides the affairs that we

now accept as surely true, as cognition, but which however may be

questioned in the hereafter ” ( Dewey, 1933, p. 6 ) .

early mathematical development – “ the progressively complex mathematical buildings and ends that immature kids develop and prosecute in their activities ”

( Platas, 2008, p.3 ) .

In-service preschool instructors – instructors who are presently learning in the

preschool degree of instruction.

Pre-service preschool instructors – draw a bead oning instructors of early childhood instruction

who are qualified to learn but have non yet gained any teaching experience.


Many national and province organisations have provided instructors with guidelines to assist better mathematics direction for immature kids. Forty-six provinces have comprehensive acquisition criterions for preschool kids ( Barett et al. , 2008 ) . Furthermore, national organisations such as the National Association for the Education of Young Children ( NAEYC ) and National Council of Teachers of Mathematics ( NCTM ) have developed specific recommendations related to high quality mathematics direction in the early childhood schoolroom ( NAEYC & A ; NCTM, 2006 ) . As the NCTM and NAEYC proclaimed, importance in the acquisition and development of mathematical accomplishments and cognition is of import in constructing the foundation of mathematical development of preschool kids. However, some early acquisition plans do non concentrate on high quality mathematics instruction despite research back uping early mathematics experiences act uponing mathematical results subsequently in school and advancing school preparedness accomplishments in mathematics ( Lopez, Gallimore, Garnier, & A ; Reese, 2007 ; Slaby, Loucks, & A ; Stelwagon, 2005 ) .

Other singular surveies showed that there are many activities involved in learning mathematics to immature kids and this would affect cognition about the capable affair, pedagogical content cognition, lecture, debut of symbolism, and linking mundane experience to abstract thoughts ( Ginsburg & A ; Amit, 2008 ) . This would connote the demand to efficaciously develop instructors of early mathematics.

There are many important surveies in line with early childhood instruction but small information is revealed about the instruction of early mathematics ( Ginsburg & A ; Amit, 2008 ) . This spread in research in mathematics instruction calls for the demand to be filled particularly in the country of instructors ‘ cognition development and beliefs in learning math in preschool.

The lone singular research in the country of instructors ‘ cognition on preschool mathematical development is that of Platas ( 2008 ) . Platas suggested in her recommendations, farther survey is still needed in the country taking into consideration a larger sample size and other necessary accommodations ( 2008 ) .

The demand for preschool kids to be provided with high quality early childhood plans calls for competent pedagogues in general. Specific to this survey, competent math instructors concerned with the development of mathematical ability of kindergartners are the makings demanded.

It is in this respect that early childhood pedagogues in mathematics should make the basic foundation required in the instruction system. This can significantly make meaningful understanding on how pre-service instructors and in-service instructors in early childhood instruction for mathematics should manage and measure their instruction abilities and methods. However, it remains unsure whether pre-service instructors and in-service instructors in early childhood instruction for mathematics have significantly the same cognition of mathematical development and belief. Therefore, it is of import to measure their cognition of development and belief about it so as to come up with a clear justification if there is a demand to aline their degree of accomplishments, cognition and beliefs if necessary.

Even though Platas ( 2008 ) was able to compare early childhood instructors based on their cognition of early mathematical development and beliefs about mathematics learning and larning in the preschool schoolroom, there was no comparing done between pre-service and in-service preschool instructors in this respect. The research worker believes that this research spread needs to be filled since future and current instructors ‘ cognition and beliefs will necessarily make an impact in immature kids ‘s mathematical cognition development. It would be interesting to find if experience in instruction of in-service instructors have affected their cognition and beliefs on mathematical cognition development and beliefs or if they remain the same as their pre-service opposite numbers. Hence this survey will analyse and reexamine in-service instructors ‘ and pre-service preschool instructors ‘ understanding on mathematical cognition development and beliefs


The intent of this survey is to analyze and compare the mathematical development and beliefs in preschool acquisition between in-service preschool instructors and pre-service preschool instructors. The comparing will estimate the demand to heighten the instructors ‘ cognition of mathematical development and beliefs in early childhood instruction. Further development of these instructors ‘ adroitness in mathematical cognition every bit good as all right tuning their beliefs will be done in the background of the literature in preschool math development.


The research worker will compare and measure in-service instructors and pre-service preschool instructors ‘ cognition and beliefs of mathematical development and instruction. In order to happen important consequences for this, the research worker will seek to reply the chief research inquiry at of the survey:

To what extent, if any, is at that place a difference between In-service instructors and pre- service preschool instructors with respect to their cognition and beliefs of how to learn mathematics to preschool kids?

Specifically, the following sub-questions will be answered at the terminal of the survey:

What do the instructors think are the necessary constructs and accomplishments kindergartners

demand to larn in the country of math?

What learning methods do the instructors think are effectual in learning these mathematical constructs and accomplishments?

What are their beliefs sing learning math?


It is hypothesized that there are important differences between the beliefs of in-service and pre-service preschool instructors on the footing of experience. Those who have experiences in the instruction mathematics will hold a different position establishing from their ain experiences compared to those who have limited or no experience in learning mathematics to preschool kids.

It is besides hypothesized that there are important differences in the cognition of mathematical development between in-service and pre-service preschool instructors.


What Preschool Math Entails

The survey of Math incorporates the procedures of oppugning, reflecting, concluding and cogent evidence. It is a powerful tool for work outing familiar and unfamiliar jobs both within and beyond mathematics. As such, it is built-in to scientific and technological progresss in many Fieldss of enterprise ( Brewer, 2001 ) . The inclusion of Mathematicss in the course of study is aimed at developing pupils ‘ mathematical thought, apprehension, competency and assurance in the application of mathematics, their ain creativeness, enjoyment and grasp of the topic and their battle in womb-to-tomb acquisition ( Board of Studies New South Wales, 2002 )

Apart from the accomplishments developed from the survey of Math, values and attitudes are similarly emphasized. Students get to appreciate mathematics as an indispensable and relevant portion of life. They show involvement and enjoyment in enquiry and the chase of mathematical cognition, accomplishments and apprehension. Children demonstrate assurance in using mathematical cognition, accomplishments and understanding to mundane state of affairss and the solution of mundane jobs. Math besides aims to develop and show doggedness in set abouting mathematical challenges. Students recognise that mathematics has been developed in many civilizations in response to human demands ( Board of Studies New South Wales, 2002 ) .

The National Council of Teachers of Mathematics ( 2000 ) identified high quality mathematics plans for early childhood as holding the undermentioned features: ( Brewer, 2001, pp. 319-320 )

“ They build upon and widen kids ‘s intuitive and informal mathematics cognition ”

“ They are grounded in cognition of kid development ”

“ They provide environments that encourage kids to be active scholars, tidal bore for new challenges

“ They develop a strong conceptual model that provides the foundation for accomplishments acquisition ”

They nurture and develop kids ‘s disposition to work out jobs. ”

Math Teaching Strategies in Preschool

Children learn much on their ain. However, the inquiry of whether certain math constructs should be intentionally taught by the instructor or merely be freely learned by kids through drama is another issue in math acquisition ( Clement & A ; Sarama, 2007 ; Ginsburg & A ; Golbeck, 2004 ; Platas, 2008 ) .

Shaftel, Pass and Schnabel ( 2005 ) agree that kids are more motivated to larn even hard lessons in Math or other topics through instructional games and simulations instead than traditional schoolroom direction. Games have been found to ensue in improved content keeping over clip, perchance because of the chance for more engagement. Math games improved on-task behaviour and accomplishment even for pupils with mild rational disablements ( Beattie & A ; Algozzine, 1982 ) .

What motivates kids with math games is that it allows them many chances to reenforce current cognition and to seek out other schemes or techniques without fright of acquiring the incorrect reply. Trial and mistake is ever encouraged, doing them more confident in taking hazards ( Shaftel, Pass and Schnabel, 2005 ) . Math games provide pupils with an environment for sing wrong replies non as errors but as necessary stairss towards linking pieces of cognition together ( Holton et al, 2001 ; Quinn et Al, 1992 ) . Practical games such as those affecting cognition about money should be tied to real-life experiences if mathematical acquisition is to be optimized. Simulations develop metacognitive accomplishments for analysing and forming informations, look intoing responses, warranting solutions to jobs and using mathematical cognition to day-to-day activities ( Hopkins and Dorsey, 1992 ) .

Issues of Teachers Teaching Math in Preschool

This survey is besides concerned about the committedness of instructors in learning math to immature kids ( O’Connor, 2010 ) .. It is indispensable to look into if they know the value of learning math constructs to kindergartners at a really immature age, which math constructs to learn and if it is deserving learning such constructs. It would besides be interesting to cognize how comfy these instructors are in learning Mathematicss and what are their attitudes and penetrations towards it.

Teachers derive their behaviours, attitudes and moralss from their ain personal and professional doctrines on learning. Gore ( 1997 ) analyzes how such a doctrine leads to one ‘s development of a pedagogical attack. A school holding its ain doctrine should hold their instructors who hold the same beliefs. Alliance of their doctrine is indispensable for harmoniousness. Gore ( 1997 ) claims that systematic and disciplined observations of teaching method are necessary in order to clear up and possibly compromise on the doctrine everyone must believe in and unrecorded by. This implies that a instructor ‘s perceptual experience of learning a peculiar topic such as Math reflects her ain and the school ‘s doctrine sing the topic.

Many research workers have been intensively analyzing immature kids ‘s mathematical development and have come to understand the developmental patterned advance of kids ‘s

mathematical apprehension ( Baroody, A. J. , Lai, M.-L. , & A ; Mix, K.S, 2006 ; Clement & A ; Sarama 2007 ; Seo & A ; Ginsburg, 2004 ) . In order to back up early mathematical development in immature kids, research workers recommend that instructors ( a ) develop a deep apprehension of the mathematical content and constructs ( Baroody, et al. , 2006 ) ; ( B ) develop an apprehension of immature kids ‘s mathematical development, including the ability to take into consideration the anterior cognition of the kid ( Baroody et al. , 2006 ; Clement, 2001 & A ; Clement & A ; Sarama 2007 ) ; and ( degree Celsius ) be fluent in the schoolroom teaching method that supports and Fosters such development including a cognition of utile representations and schemes and common misconceptions and mistakes ( Baroody, et al. , 2006 ; Seo & A ; Ginsburg, 2004 ) .

By increasing instructor ‘s cognition and apprehension of mathematical cognition development, it is expected that kids will besides larn better and a more productive schoolroom ambiance is will be created. Therefore, it is of import for instructors to cognize how to back up kids ‘s mathematical development in the preschool schoolroom in order to develop effectual and appropriate schoolroom direction. Teachers besides need to understand how kids learn mathematical cognition every bit good as measuring their apprehension, and supervising their advancement.

Apart from the information yielded by Platas ‘ ( 2008 ) work, the literature point out that preschool instructors need to hold a specific degree of competence in their instruction which can be measured through their cognition and beliefs. It was found that kindergarten instructors ‘ different preparation experiences and school contexts have important impacts on kids ‘s preparedness for school ( Lin, Lawrence, & A ; Gorrell, 2008 ) . This implies that the degree of cognition and beliefs of preschool instructors have been significantly influenced by their preparation experiences and degree of instruction received. Preschool instructors have different positions on early childhood instruction with some of them believing the plans in their schools may either be excessively advanced or excessively basic.

Teachers ‘ readying for cultural diverseness in preschool is of import anterior to making a welcoming acquisition environment ( Hughes, & A ; Kwok, 2007 ) . Skills and cognition of instructors are of import considerations particularly on the basic instruction degree. Teachers ‘ gestures and vocalizations were found to hold a important function in kids ‘s acquisition ( Klerfelt, 2007, Valenzeno, Alibali, & A ; Klatzky, 2003 ) . In preschool instruction, high quality teacher-child relationships are expected. Knowing how to set up such good relationships with immature kids implies that the preschool instructor must hold significant cognition on relationship edifice in early childhood instruction plans ( O’Connor, 2010 ) . This besides suggests that the instructor is effectual and knows how to inculcate merriment in acquisition.

Preschool instructors must hold equal cognition and strong beliefs in a peculiar capable country they are tasked to learn. They should hold cognition of utile representations and schemes and common misconception mistakes when it comes to mathematical development in immature kids in peculiar ( Broody et al. , 2006 ) . A Development theoretical account that coincides with theory and research is needed to make the edifice blocks for early childhood mathematics ( Sarama, & A ; Clements, 2004 ) . On the other manus, a instructor ‘s belief is difficult to mensurate but it proves a dependable step of instructor ‘s experiences and actions ( Muis, Bendixen, & A ; Haerle, 2006 ) . For illustration, a instructor may believe that immature kids are capable of understanding measures because she herself has been successful in learning a kindergartner the construct of measures, of which set has more objects and which set has less. Therefore, cognition and beliefs of instructors are demands for mathematical development in early childhood instruction.

Education and specialised preparation of preschool instructors are associated with immature kids ‘s acquisition and development ( Barnett, 2004 ) . Evaluation of the impact

of Early Childhood Education teacher readying plans and professional development conclude that benefits of high-quality preschool instruction can merely be achieved if instructors are professionally prepared and well-compensated ( Barnett, 2004 ) . Research shows that a well-prepared early childhood instruction instructor brings a warm, safe and contributing environment for larning ( NAEYC, 2006 ) . Percepts of instructor on student-teacher quality and of kids ‘s academic abilities proved to act upon academic competency among pupils ( Hughes, Gleason, & A ; Zhang, 2005 ) . In add-on, it is of import to concentrate on quality of room patterns, kid features, instructors ‘ perceptual experiences of school-related climes and instructors ‘ perceptual experiences of work load emphasis ( Mantzicopoulos, 2005 ) . It was found that the sum of instructor ‘s math-related instruction was extremely associated to kids ‘s mathematical cognition ( Klibanoff, Levine, Huttenlocher, Vasilyeva, & A ; Hedges, 2006 ) . The attitudes of preschool instructors on early mathematics do non alter as they acquired cognition of preschool instructors ( Alinsinanoglu, Guven, & A ; Kesicioglu, 2009 ) . Teachers ‘ simple instruction certificates, old ages of instruction and old ages of experience have complex impact to kids ‘s acquisition ( Connor, Son, Hundman, & A ; Morrison, 2005 ) . All of these issues can basically be addressed by analyzing farther within the context, cognition and ability of early pedagogues for early childhood instruction.

Significance OF THE STUDY

This survey takes on Platas ‘ suggestion that more research should be done in footings of look intoing preschool instructors ‘ cognition and beliefs sing the developmental mathematical cognition of preschool kids. In conformity with the criterions of NCTM for high quality math plans, rating of instructors ‘ competences should be done to guarantee the quality of learning in early childhood plans.

This survey ‘s significance lies in guaranting that instructors are adequately skilled and emotionally ready to learn mathematical constructs in the preschool degree. In add-on, this survey is a part to the turning organic structure of cognition of early childhood instruction. Furthermore, new information may be derived from concerned participants in this research such as fresh thoughts coming from the position of in-service and pre-service instructors that could be helpful in bettering one ‘s public presentation in their occupations.

Therefore, the importance of prosecuting this tendency of believing will extremely profit instructors in early childhood instruction. In peculiar, there is a demand to print surveies such this in order to supply support and sweetening of accomplishments to new instructors in the field. It is of import to analyze perceptual experiences of early childhood pedagogues because they play a important function in immature kids ‘s acquisition and development of cognition and accomplishments ( Chien, & A ; Hui, 2010 ) .

This survey will assist non merely teachers to better understand the acquisition procedure involved in order to maximise mathematical cognition development of immature kids. It is besides helpful in constructing a better mathematical foundation for immature kids.


Instruments to be used for this survey are the instruments developed by Platas ( 2008 ) viz. the Knowledge of Mathematical Development ( KMD ) Survey and the Beliefs study. A demographic questionnaire assemblage information about the respondents will besides be distributed.

The Knowledge of Mathematical Development Survey ( Platas ) is a set of 20 multiple-choice inquiries that tests instructors ‘ cognition and development in the country of verbal numeration sequence, numeration, ordinal figure of words, addition/subtraction, divisions of sets, written figure symbols and words. In each figure, the teacher-respondents are to take which of two math accomplishments kids are likely to larn foremost. If the respondents think that both picks are easy learned by a kid, so the pick of “ same ” may be picked. However if the respondent does non cognize which accomplishment is easier for a kid to larn, he or she can take the option “ do non cognize ” .

The Beliefs Survey is a set of 40 beliefs about Math instruction and acquisition. It has a 5-pt. Likert graduated table with responses that range from Strongly Agree to Strongly Disagree. The belief study will measure the instructor ‘s position about 4 countries: ( 1 ) age rightness of mathematics direction in the early childhood schoolroom, ( 2 ) venue of Generation of Mathematical Knowledge, ( 3 ) Social and Emotional V. Mathematical Development as Primary Goal of Preschool and ( 4 ) Teacher comfort in mathematics direction.

The participants involved in the survey will be comprised of 200 in-service instructors and 100 pre-service instructors that will be chosen in random. Consequences will be analyzed utilizing ANOVA every bit good as correlativity analysis.


This survey will be limited to researching the cognition development and beliefs of pre-service and in-service preschool instructors sing math. It will non measure on any other capable country. It is of import to observe that in footings of experience, the pre-service instructors will hold no learning experience whereas with the in-service instructors ‘ experience may run from a few months to about 20 old ages, depending on the sample gathered. Besides, the figure of in-service participants is much higher than the pre-service participants. These factors may impact the consequences due to this imbalance and must be taken into history when information is analyzed.

Summary of Chapter 1

Mathematical acquisition now comes at an earlier age. Preschoolers surprisingly manifest basic mathematical cognition even before they start school. This realisation that immature kids can already “ make ” Math has encouraged professional organisations such as NAEYC and NCTM have come up with guidelines that Math instructors should confer with and follow to in their instruction of mathematical constructs and accomplishments.

Teachers of immature kids have the power to act upon their preschool pupils. Teachers should fundamentally possess equal cognition and accomplishments every bit good as appropriate beliefs if quality instruction is to be expected. The work of Platas ( 2008 ) entitled “ ” Measuring Teachers ‘ Knowledge of Early Mathematical Development and their Beliefs about Mathematicss Teaching and Learning in the Preschool Classroom ” has been a monumental inspiration for this current survey. However, this survey goes beyond researching instructors ‘ cognition development and beliefs about Math by comparing cognition development and beliefs of in-service preschool instructors and pre-service preschool instructors. It is presumed that the component of experience will play a important function in either beef uping or modifying instructors ‘ cognition and beliefs about Math in early childhood instruction.