Impact of Technology on Supporting First Grade Students’ Creative Thinking in Mathematics
Abstract:
This research provides an in-depth examination of the impact of technology in supporting the acquisition of mathematical creative thinking skills among first-grade student. It examines how technology can be properly integrated with mathematics to promote math’s performance without declining creative thinking skills in mathematics among the elementary students.
Social constructivism theory as the method of learning in first-grade mathematics students is advocated; it defines the developmental stages of a child and relates to his or her learning and problem-solving ability. Its requirements can properly be integrated to Computer-aided learning processes.
The value and importance of common core math’s standard has being discussed and different displays of child’s creativity and ability to solving mathematic problems in relation to their varied reactions to challenges.
Conclusively, combining technology into mathematics enhances first graders creative skills in solving problems in mathematics. This work contains a qualitative study that includes a review of the literature, interviews, observations, and a post-intervention survey that shows how integrating technology with mathematics improves student attitudes and math performance to some degree.
Introduction:
Technology has a huge impact on many aspects of human life, including education. The No Child Left Behind Act (NCLB) of 2001 suggests quite clearly that technology is extremely vital in enhancing the students' learning processes (Gerard et al., 2011). Therefore, technology has been utilized as an effective teaching assistant that allows for the achievement of multiple educational purposes (Straub, 2009). These purposes include training and simulation, which help educators to provide new types of experiences that involve various pedagogical innovations (e.g., new methods of training, practice and individual tutoring, creativity, problem-solving, simulations, and educational games) (Slavin & Lake, 2008).
The National Mathematics Advisory Panel’s final report, which has emphasized the problem of poor performance in math by primary students, has caused researchers to propose various means for improving math performance. Educators everywhere have been moved to consider new ways to apply technology in order to support the acquisition of mathematical skills in elementary school (U.S. Department of Education, 2008). Also, while extant research has provided extensive documentation of the usefulness of technology in mathematics, it has not explained the way to promote creative thinking skills for children in mathematics. According to Slavin and Lake (2008), most research that has been conducted on the impact of technology focused on its effects on academic achievements and the ways in which the use of technology impacts mathematical skills among students. However, Peterson (1993) has indicated that schools should focus on the importance of creative thinking because they are responsible for providing new experiences and practices for students. Unfortunately, Kim’s work (2011) noted a significant decline in creativity scores since 1990, especially in the fields of mathematics and science. From this study, it was shown that numerous young children in the United States, most of them between kindergarten and sixth grade, have experienced the most serious decline (Kim, 2011). The ineffective methods that are employed by schools to improve and develop students’ creative thinking skills are one of the reasons why this decline has occurred (Wheeler et al., 2002). In addition, educators have been faced with questions such as; is technology’s impact on education positive or negative? Might technology lower the IQ levels in children due to over dependency? And will technology take a different turn in the future? Among others (Hoyles et al., 2004). There are concerns about the effect of technology on the development of creativity in mathematics when applied to young children, such as those in the first grade (Erdner et al., 1998; Hyun, 2005). As it stands, technology is clearly under-utilized as a means of math pedagogy. By developing more innovations, the status of math and the gap in teaching methodologies have the potential for great improvements and an elevation of current standards. This is especially important at the elementary level because it represents the beginning of mathematical knowledge for students and has a considerable influence upon future learning.
This literature review should make a significant contribution to the available pool of knowledge concerning the development of creative thinking skills in young children through the use of technology. The specific focus is on mathematics instruction for first-grade students. Moreover, this review highlights the imperative of devising instructional approaches that employ technology for enhancing creative thinking among elementary students.
Theoretical Framework
Constructivism is a scientific theory that explains people’s learning processes. The theory focuses on a human being’s ability to learn, and it is rooted in observation and technological progress (Darling, 2010). The main notion in the theory is that knowledge in an individual is built upon an individual’s previous learning. The other notion within constructivism is that knowledge is based on the passive dissemination of information from one individual to another. The view in this concept is that reception, as opposed to construction, is vital. Constructivism also holds that knowledge is built over a period of time which is essential in aiding students’ reflection. In the context of social constructivism, the teacher ensures that learning is compelling and incorporates activities that facilitate the student’s learning. The teacher also plays an extensive role in encouraging students to learn (Larson, 2012). These findings can closely be linked to framework, as indicated in Figure 1:
Figure 1: Conceptual framework that explains the learning process (Ryszard, 1991).
In a borrowed concept, the conceptual framework that explains the learning process in the above figure demonstrates the process of inducing creativity to impart knowledge. At the input stage, students are exposed to learning where knowledge is repeatedly linked to background information that is acquired with the environment; a concept that is closely linked to social constructivism. The social constructivism approach advocates for use of cognitive tools in the learning process. This is where the students must utilize discipline-based cognitive tools. The theory is typically used in explaining social contexts such as the learning processes that pupils undergo in schools. It postulates that the ability of young students to learn from their environments determines and develops their critical thinking skills (Klein, Hamilton, McCaffrey, & Stecher, 2000). It also states that the ability of students to find solutions to problems is connected to their abilities to interact and share ideas in order to understand problems and their subsequent solutions (Darling, 2010).
In this context, elementary school learning processes in mathematics can easily be interpreted by using the social philosophy that teachers and pupils develop, this involves the study of social behaviors and interactions between the teacher and his or her pupils. The two main elements considered in this philosophy are the individuals and the society surrounding them. The responsibility of duties initiated in a child’s cycle would enhance the learning process (Munn, 2006). In his proposition of the social constructivism theory, Lev Vygotsky defined an individual as one who is framed with a social culture that mandates a continual learning process. He noted that educational institutions assist in meeting this objective as students and their instructors cooperate to advance the practice of perpetual learning. The theory inherently suggests that students connect to their instructors and their peers through social constructivism. This approach determines how students learn to solve problems and the efficiency with which they apply critical thinking. The thesis also states that the tools used for research, especially those that are computer–based, should be applied in conjunction with another control system that would ease the understanding of computer applications that guides the children on how to use the trajectories or rather, paths brought in place while employing computer skills with reference to learning formalities (Larson, 2012). Emphasis is given to social constructivism because it defines the developmental stages of a child and relates to his or her learning and problem-solving ability. It incorporates elements such as a child’s initiative and memorizing ability.
In elementary mathematics education, computer-supported collaborative learning (CSCL) is a teaching strategy that usually employs the social constructivism concepts. CSCL allows students to learn through interactive, computer-aided learning processes that aid them in problem solving and in developing creative thinking abilities. It is, therefore, true that social constructivism teaches students how to participate in collaborative activities and how to eventually use the learned concepts. This observation justifies the applicability of the social constructivism theory to first-grade mathematics learning, as it requires students to be interactive, problem-solving oriented, communicative, and able to relate concepts through creative thinking abilities (National Association for the Education of Young Children & National Association of Early of Education, 2010).
Literature Review
In this study, the analysis shows that the educational technology is defined as a variety of electronic tools and applications that help deliver learning materials and support learning processes in 1st graders classrooms to improve academic learning goals. Examples include computers-assisted instruction, integrated learning systems, video, and interactive whiteboards. Therefore this study has mainly focused on examining how Technology is important in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning. Given the importance of educational technology, it is the intent of this review to study and show the impact of various types of educational technology applications for enhancing mathematics performance in 1st grade classrooms.
Development Aspects of First Grade Mathematics:
Mathematical skills among first graders have received attention in recent years, especially during the last decade (Sarama & Clements, 2002). In the earlier periods, mathematical skills were mainly developed and given keen emphasis among the upper grades with the notion that the upper classes were in a better position to handle such skills (Koshy, Ernest, & Casey, 2009). Recent studies have, however, revealed that the math skills that a student gains during his or her early years enhance future mathematical performance (Boulder & Tempe, 2010). This section focuses on the development aspects of first-grade mathematics with a special emphasis on cognitive research related to the subject area. It also evaluates the common core math standards in the United States, specifically in the state of Ohio. This section also evaluates the various standards for the instruction of first graders; it is pertinent for teachers to have some guiding principles as they refine their skills.
a) Cognitive Research Related to Math:
Sarama and Clements (2002) conducted research in which software micro-worlds were used as a programs for building blocks used to interpret mathematical representations. For instance, when one multiplies five by two, the result is ten. Such data in the micro-world software would be represented by two rows of building blocks and five columns of building blocks. This would still total up to ten building blocks. They were among the first to study mathematical skills among young students. The focus of their study was to evaluate school principles and standards that are used in teaching mathematics. The software that was used in this study was geared toward second-grade students, and the materials used in the research were mainly intended to help mathematize the activities in which children engage on a daily basis. The findings indicated that education could not improve unless there is a system-wide commitment to curriculum and mathematical software development. Sarama and Clements (2002) also indicated that “mathematical micro-worlds” software which are developed with a collection of mathematical examples to serve as teaching aids, have not been used appropriately in mathematical development skills. The study suggests that more emphasis should be placed on this technology in order to improve mathematical performance in schools.
Nir-Gal & Klein (2004) also conducted a study to evaluate the effect of adult mediation on the use of computers among five- and six-year-old students. The findings indicated that the teacher’s role in education should change to that of an instructor, partner, and organizer, especially in a computer-learning environment. The study also described the cognitive domain to be one in which teachers aim to nurture and encourage the students’ thinking. Teachers also focus on adjusting the process to the needs of the child, which includes giving attention to details and restraining impulsive reactions, as well as problem-solving skills and abilities. The study states that it is essential to identify activities that expose the child to activities that are cognitively engaging. Their study indicated that adults should mediate children’s computer-based activities in order to foster higher scores in cognitive activities, such as abstract thinking and visual motor coordination. The study indicates that computers should be used in the early childhood years to improve and enhance young learners’ intellectual abilities and learning strategies. However, computers should not be used as a replacement for human instruction.
Iiyoshi, Hannafin, and Wang (2005) later conducted a study that indicated that a student’s knowledge is developed through his interaction with the social world. They clearly indicated that there should be a strategy to help students understand how to use their learning environments. The study indicates that lack of a good strategy leads to frustrations, doubt, and confusion among students. It also suggests that there should be tools that can help students seek significant information. In their study Iiyoshi et al. (2005) indicated that cognitive tools include computational and mental devices. The study states that the nature and context in which a tool is used determines whether or not the tool augments cognitive purposes. Cognitive tools support five functions in students’ learning environments. These functions are information seeking, knowledge organization, information presentation, knowledge integration, and knowledge generation.
Ramos, Schleser, & Varn (2008) conducted a study on math skills among first- and second-grade students. Their study mainly focused on the relationship that exists between cognitive ability and mathematic fluency in children. Their work indicated that cognitive abilities play a crucial role in mathematical skills that are possessed by children. The study also clearly stated that arithmetic competency is a vital goal that must be achieved in the early stages of schooling. Further, this skill helps in the transitional stages that students undergo in their early years of schooling. Ramoss et al. (2008) also stated that some children experience difficulties in mathematics due to a failure to acquire the basic skills in their earlier years. They also indicate that when students acquire mathematic fluency (i.e., speed and accuracy), they maintain the skills longer into their lives. The students in that category also resist distractions. This research also indicated that children’s development of mathematical skills enabled them to be better performers in terms of accurate computation, deriving formulas, interpreting mathematical data as well as giving a good analysis on a given study. The thesis stated that it is crucial to examine children’s arithmetic knowledge. This trend is employed to help children in their later development in mathematical skills. Another important finding in the thesis is that pre-operational(this are less vibrant) children show less fluency in arithmetic versus operational(this are vibrant in terms of learning skills and employing them) children. It suggests that these children should be given more time to complete their tasks in order to grasp the concepts that are needed to perform the operations.
Shayer & Adhami (2008) conducted a study that focused on the improvement of cognitive ability among children by assisting the school’s teachers in achieving their mathematical aims. The study was meant to reach students between the ages of five to seven in their first two years of study. In this study, Shayer and Adhami (2008) concluded that relative intelligence in a child can be increased, and it is not fixed. They also suggested that children can be led into the process of collaborative thinking with other students. This is cited to benefit the children’s thinking capacity with each other. The study also cited the existence of a theory-based methodology for teachers to improve their teaching. It stated that the insights derived from Vygotsky’s and Piaget’s work form a direct contribution to mathematics education. The results of the study also revealed that there is a great need to invest in a collaborative style of professional development among teachers. This professional development will help teachers to construct new insights into mathematics and the appropriate teaching skills that are needed to produce better learning.
Koshy, Ernest, and Casey (2009) also conducted a study in which policy development in mathematic giftedness was emphasized. This study of extant literature focused on students who were between the ages of five and 10. Their thesis highlighted that there is a continued need for the special needs of students who are mathematically gifted to be recognized. Their main argument mainly dwelled on the fact that there should be early identification of the special talents in pupils. Paying close attention to these students is likely to lead to the emergence of future mathematicians and people who specialize in science and technology. Koshy et al. (2009) drew from Vygotskian framework, which states that the students who are mathematically gifted require cognitive challenges and experiences that enhance their emotions and motivation. Koshy et al. (2009) also cited the launch of ‘Gifted and Talented’ by the UK government as the beginning of recognition and development of students who are mathematically gifted. They call on the local educational institutions and authorities to establish programs that identify mathematically gifted students. After the identification process, the institutions should provide distinct teaching programs. Emphasis should be given to primary-grade mathematics students and early learners to create an appreciation of mathematics and its importance in their lives. They also indicate that teachers need professional development to understand mathematically gifted students.
Carr, Taasoobshirazi, Stroud, and Royer (2011) conducted a study on a group of second-grade students from Georgia and Massachusetts in order to evaluate factors that influence mathematic fluency and achievement among the students. The students were asked to complete mathematics skills fluency tests. This process was done randomly, and it indicated that boys benefited more than girls from this intervention program. The study indicates that the main area of testing was fluency, mathematic achievement, and the cognitive strategy employed. The strategies may differ with the level of the child in terms of brain development. Nonetheless, skills such as rehearsal, self-questioning and note taking would be the best in this case. Carr et al. (2011) indicated that computer programs are used in schools and are beneficial to children with mathematic disabilities. The use of audiotape technology is also cited to be an intervention to help students improve their mathematical skills. The study indicates that students improve their mathematical fluency after a week of practicing with computer-based programs such as CSCL. It also revealed that gender differences affect performance in early elementary schools. Boys in this stage use retrieval and cognitive strategies while girls rely on cognitive strategy. The study reveals that the strategy used by girls in during their early elementary school years quickly decomposes putting them at a disadvantage over the boys. The study is a clear indication that intervention programs indeed improve performance in the later years of the student’s lives.
The findings of these studies, such as the work conducted by Sarama and Clement (2002) indicate that children, especially first- and second-graders, should have their activities linked to mathematical concepts when they are in the first grade (i.e., employ the use of mathematical software). It is clear that technology plays a vital role in the development of students’ mathematics skills; when students use computer-aided programs, their performance improves dramatically within a month. This process should, however, be mediated by adults, based on the fact that when students use computers with adults’ assistance, they are able to draw a great deal of information from the experience. In turn, as indicated by Nir-Gal and Klein (2004), these students become more knowledgeable.
It is also crucial for cognitive mathematics skills to be developed and sharpened early in the student’s lives. It is recognized that students who attain mathematics fluency early in life retain this skill at later stages in life. First-grade teachers ought to introduce mathematics learning software and be present to aid the students as they develop their mathematical skills. In this stage, teachers should ensure that they serve as organizers, partners, and instructors to the first-graders in their mathematical skills development.
The other notable observation is that systems should be put into place to ensure that first-grade teachers are have reliable sources to turn to while teaching. Students who excel in math merit extra attention since nurturing their talents might foster the development of future mathematicians and experts in science and technology (Reys & Lappan, 2007). Another form of technology that can be used for first graders is audiotape technology. An audio tape is a device that can carry audio recordings by encrypting the information on a tape. The recorded information can be listened to from time to time without bias. In a way, it serves as a rehearsal tack tick.
The use of cognitive tools is proficient for the first graders mathematics performance since it makes abstract ideas to be concrete, it helps in retention of memory, develops manipulative skills in the child, promotes creativity and innovation. These cognitive tools can properly be integrated in computational and mental devices and therefore First-grade teachers ought to introduce mathematics-learning software and be present to aid the students as they develop their mathematical skills. This will enhance child’s performance since the device is interactive both in words and in audio, can be conveniently accessed in school and even at home, and the tools can be developed in different forms depending on the learning capability of a child and the environment surrounding their background.
b) Common Core Math Standards:
Bayer (2003) states that the core structure of knowledge, is a detailed outline of all subjects for all public K-8 school curriculums in the United States. Bayer’s study also reveals that, according to standardized test results (Reys & Lappan 2007), students who attend Core Knowledge Schools perform better than students who are in non-Core Knowledge Schools. The study also states that resources such as the introduction of computer related skills of learning, should be provided to overcome challenges such as complexity in presenting an analysis as well as grasping commonly applied skills that the students face at various levels. According to Bayer, critics of the Core Knowledge sequence claim that it diminishes creative thinking among students, yet his work revealed that students under the core standard curriculum are more creative thinkers in comparison to their counterparts from other schools.
The Ohio Department of Education (2010) stipulates that the common core mathematical standards include the use of operations as well as algebraic thinking. First-grade teachers’ primary role is to teach them how to perform addition and subtraction. This skill is passed to students and is normally done within twenty days for a bright kid. The students are also exposed to the wider topic of measurement and data; they are taught how to iterate length units and how to measure lengths. The curriculum, at this point, teaches the students that the length of an object is directly proportional to same-size units corresponding to its length without any overlays or spaces.
The Ohio Department of Education (2010) also states that the other domain is the numbers and operations in base ten. At this stage, the students are taught how to extend the counting sequence: Teachers require the students to count up to fifty. In other instances, this process involves reading numerals while writing them down. It may also involve representation of objects by using written numerals. First-grade students are also taught the concept of place value (i.e., ones and tens), and they learn how to add numbers up to 100. Teachers in this stage use drawings as an enhancement to their teaching. The last domain that students learn in first grade is geometry; instructors provide an introduction to shapes and their attributes. In this stage, the students are taught how to differentiate between shapes according to their defining features, and they are also asked to construct shapes.
Various core methods and standards such as formulas and constant theories are used to help students to achieve their objectives. The derived curricula indicate that students should possess certain proficiencies and processes that are deemed as critical. These include the National Council of Teachers of Mathematics (NCTM) standard that relates to reasoning and proof, representations, problem solving, and communications. The other relevant areas are strands of math proficiencies; they include adaptive reasoning, procedural fluency and conceptual understanding among others, which are contained within the Ohio Department of Education strategy, which defines the areas that need to be improved in first graders (i.e., conceptual understanding and procedural fluency).
The initial core math standard learnt from lower grade levels, help learners to make sense of mathematical operations and solve problems. Proficient students start by attempting to explain what a particular mathematical problem means before solving it. This solution path is preferable to jumping straight to offering the solution. In this stage, first-grade students normally use pictures or concrete objects to easily conceptualize the problem.
Secondly, core mathematical standard helps first graders to reason abstractly and quantitatively; it enables them to contextualize and de-contextualize. Contextualizing is the process in which first-grade students pause in the process of solving a problem (National Association for the Education of Young Children, 2009), which gives them time to reflect on the shapes or symbols. Technological tools can, in this stage, play a vital role in quantities reasoning. De-contextualizing, on the other hand, is the process in which the students use symbols to understand abstract mathematical problems.
Thirdly, the standards ensure that students develop practical arguments. The process also encourages them to critique their peer’s arguments by using critical skills. This standard aims to ensure that students can easily make use of the stipulated assumptions and definitions with regard to one’s level. In this stage, students are able to reason and arrive at an argument that is viable (Mathis, 2010). Generally, the standards teach us how mathematical models drawn from an assumption that, first-graders’ can apply mathematics to their everyday problems. The first graders who attain this skill are able to make assumptions and approximations (Bryant, 2011).
The third standard helps students to strategically use mathematical tools. It assumes that first-graders are able to learn proficiently and apply available tools, such as geometry software, tabulation software and an analysis software to solve problems. In this stage, first-grade students should be taught that technology could easily aid their visual results, which can further help them while exploring their actions and in making comparisons and data prediction. The sixth standard concerns precision; first graders who are proficient in mathematics can communicate precisely with other people by clearly pointing out and explaining the meaning of mathematics symbols. They are also acutely proficient and precise with measurements.
Porter, McMaken, Hwang, and Yang (2011) also conducted a study that compared the common core standards that were released in 2010 with the current 2012 state standards. They also compared these standards to reports from other country’s common core standards and testimonials from a sample of teachers who described their own practices. The report indicated that the common core standards were focused on mathematics instead of English, language arts, and reading (ELAR). The research also revealed that the established standards differed from those of countries that that reported higher academic achievement. The countries that performed better placed more emphasis on performing procedures which runs differently to the emphasized need of the US cognitive demand. The standards in other countries also significantly differed from those being employed by U.S. teachers. The report indicated the need for immense change at all grade levels in order to adhere to the standards
with reference to a given state.
Dessof (2012) also lays down new common core state assessments in K-12 math that shall be effective in the 2014-2015 academic year. The main focus of this thesis is to explain what is expected in new common core standards. The standards laid down in the thesis include the fact that students will describe how they get answers to a question. This is especially true with respect to mathematical and algebraic solutions. The common core assessments probe into what and how students learn.
Fricke (2012), on the other hand, conducted research that focused on the way in which the global community uses common standards. He claimed that implementation of the standards should occur with caution so as not to overlook the investment that is required for the professional development of teachers. The study stated that the core requirements for first graders include more preparation for all early childhood teachers. The teachers should also continually develop their professional skills in order to attain greater proficiency. It also clearly states these standards are geared towards obtaining more practical goals in curriculum development such as a better understanding of mathematical principle.
The results of Fricke’s work indicate that core standards are established to serve as guidelines in the implementation of teaching mathematics to the first graders as indicated by Ohio Department of Education (2010). These standards ensure that the teachers employ common benchmarks when teaching skills to students. The standards also advocate for the provision of appropriate resources, such as cognitive tools, to aid in student learning and in removing barriers that students face as they study. The inclusion of these requirements in first-grade mathematics instruction will improve the mathematic fluency among the students.
The binding requirements in this case include the six core standards that are put into place by the Ohio Department of Education, including teaching students how to use arithmetic and algebra. It is pertinent for measurement and data to be inculcated in the early stages f a student’s development in order to form a basis for his or her mathematical foundation. The standards also stipulate that teachers must ensure that students can study quantitative and abstract data. The other core standard is that students should be able to use mathematical tools strategically and precisely.
The common core standards in Ohio, as well as the work of Reys and Lappan (2007), emphasize the use of cognitive tools in mathematics. It is also evident that the standards do not place such emphasis so much on ELAR, as indicated by Porter, McMaken, Hwang, and Yang, (2011). It is notable that creativity and the use of technology are core qualities that are emphasized in the standards. These two attributes enhance the student’s understanding in first and all subsequent grades. It is also pertinent to note that, under core standards, students tend to possess higher creativity depending with one’s exposure (Porter, McMaken, Hwang, & Yang, 2011). This is the more reason why core standards should be implemented and used compulsorily in schools, especially within mathematical skills acquisition among first graders. The results f work conducted by Bayer (2003) also reveal that common core standards improve the students’ performance.
The core standards it shows that first graders’ can apply mathematics to their everyday problems and the first graders who attain this skill are able to make assumptions and approximations. Therefore the First grade teachers should help their students to evaluate information presented in different media and formats, according to the core standards. Children should learn skills through technology and multimedia on how to use cognitive tools in helping them to perform different tasks, according to the standards. Those tools may include pencil and paper, concrete models, rulers, protractors, calculators, spreadsheets, computer algebra systems, statistical packages, and dynamic geometry software.
