Mathematical Games in the Development of Numeracy and Computational Skills - Literature review Example

Mathematical Games In the Development of Numeracy and Computational Skills in Middle Primary School Aged Students Student’s Name Institution Affiliation 1.0 Introduction This literature review seeks to explore literature relating to the importance of mathematical games in developing numeracy and computational skills in middle primary school aged students. It will start with the used search strategy, stating the way the literature examined was reviewed. This will be followed by a discussion of emerging themes related to mathematic games with the research being critically assessed. The journal articles, books, and websites were accessed electronically. Several keywords as well as combinations were used to search the literature related to the study subjects. The keywords and combinations were ‘mathematical games’ ‘mathematical games and numeracy’, ‘mathematical games and computational skills’. They were typed in Eric, Informit, and other websites. such as EBSCOhost and Springer, which generated varied amount of literature of the study subject, however only evidence-based literature was used. 2.0 Review of Literature Definition of Terms Mathematical Games: this refers to activities, which have specific mathematical cognitive aims; involve a challenge, mostly against a single or multiple opponents; with a distinct finishing point and which have a clear underlying structure and governed by a set of rules. Numeracy: A good basic knowledge of mathematics or the ability to understand and work with numbers Computational: the skills of calculation or working with numbers Benefits of Mathematical Games Mathematics games offer exceptional opportunities for learners at every level to be engaged in posing new problems, asking new questions, formulating hypotheses, and constructing strategies. They are predominantly well suited to engage and motivate learners in mathematic activities. Bragg (2012) study results indicated that the application of games to address the mathematical content being taught in a class is an important approach for increasing engagement and in turn their learning potential. Playing mathematical games is fun for the students and enables them to learn more effectively through participation and activities instead on passive instruction, as they are usually more active and better motivated to reach their goals. The games offer a visual representation of problems through manipulative operations in a social situation. They boost a learners’ knowledge and positively influence their social and cognitive development (Schiro, 2009). They also play a major role in developing learners’ numeracy and computational skills. Mathematical games assist in developing number sense (Liedtke, 2010). They motivate students as well as engage them in thinking about as well as applying skills and concepts. They also offer students an opportunity for communicating their ideas and justifying their thinking. In using games, the teachers usually play a critical function in encouraging students to explain their thinking as well as keeping them focused on mathematic ideas (Ashman & Elkins, 2009). They contribute to knowledge development through have a positive impact on the classroom setting which in turn lead to a better mental attitude towards mathematics in the students. They offer a unique opportunity to integrate the social, affective, and cognitive learning aspects (Ashman & Elkins, 2009). Generally, games create meaningful situation for applying mathematical skills. Mathematical Problems in the Australian Context According to the Chairman of the Review Panel, Australian students perform poorly in mathematics because the subject is “not generally perceived as popular subject among young person’s” (p. 1). It is also not acknowledged as an undemanding subject to teach or learn. The “Commonwealth of Australia” (2008) noted that much emphasis has been on increasing the literacy levels of primary aged learners; however, the schools have to some extent neglected numeracy. Furthermore, Garcia, Jiminez and Hess (2006) pointed that it is hard to identify learners with mathematical problems as struggling with mathematics is regarded as normal and hence the problems are more socially accepted than literacy difficulties. Integrating mathematical games can help in developing numeracy and computational skills in middle-aged students. Ashman and Elkins (2009) noted that game based technologies usually offer the students an opportunity for engaging with the content through diverse modalities, which is a critical measure in making sure that every student is engaged in the learning experience. Mathematical games are thus particularly important in the Australian context where mathematics is at a critical juncture according to the “Review Panel of the National Numeracy Review Report” (“Commonwealth of Australia”, 2008). The panel noted that numerous students in Australia are not learning the mathematics basics and they are not being well prepared for further studies or future work roles. They are also not doing well compared to other countries; they have not been performing well in international exams and they display parts of pockets of low achievement, which mirror racial/ethnic, cultural, geographical, and socio-economic factors. Mathematical Games and Computational Skills Several literatures focus on the relation between mathematics games and student computation skills. Asplin, Frid and Sparrow (2006) research indicated that constant playing of a number-based game scaffolded by teacher crafted learning structures support learner engagement in experimenting with number combinations, using a wide variety of mental approaches, verbalization of computational steps, and students’ engagement in mental recall. Leicha (2012) noted than mathematical games increase student engagement as also boost their potential for learning. The study results showed that games usually serve to increased the time-on task of students in mathematics classes. Leicha (2012) compared students on-task behaviors during non-game playing lesson compared with non-digital game-playing lessons using 6 randomly selected grade 6 and 5 students (nine to twelve year olds) who were observed during 10 mathematic lessons. The researcher recorded 2,100 observations through an observation schedule and made an analysis through comparing the percentage of the behaviors that children exhibited. The results of the study revealed that children spent 93% of their classroom time showing on-task engagement while playing mathematical games relative to 72% during the lessons when they were not playing games. This research sought to investigate the use of games in development of mental computation in a Year 6 class. The research findings also indicated that the game playing structure used in class enabled the learners not to be disheartened by the variety and number of wildcards used in the research. The structure supported the learners’ engagement in mental computation and this was evident in the enthusiastic nature of the learners’ participation in game playing as well as the varied mental strategies, mental recall, and experimentation with number combinations that they displayed. Yen-Hua, Chee-Kit and Chiu-Pin et al. (2012) also discovered a positive relation between mathematical games and computation ability. They used a “collaborative cross-number puzzle game” in developing the computation capacity of subtraction as well as addition in two Grade 4 classes consisting of 52 students. The game promoted the flexible application of subtraction and addition skills and improved the ability of the children to develop their skills progressively. In, addition, the study showed the importance of student collaboration while using the games. The authors noted, “the low-ability students in the collaborative class were found to have made the most significant progress in arithmetic skills through playing this game.” There are various types of mathematics games, which can be individual, multi-player groups or conducted in groups. Cooperative games offer a social setting for the learners. Ryan and Patrick (2001) used a longitudinal study to investigate the link between a learning environment and development in relation to changes in engagement and motivation of learners in a mathematics class. The study results pointed to an increase in engagement and motivation in social classroom setting. Ke and Grabowski (2007) also noted that “cooperative game playing was the most effective for promoting positive math’s attitudes regardless of students’ individual differences” (p. 249). Miller, Stringfellow, and Kaffar et al. (2011) argued that a balanced instructional approach in a mathematics class that include evidence-based practices related to the development of declarative, procedural, and conceptual knowledge boosts the probability of the learners to comprehend the meaning of computational operations and also demonstrates the capacity to solve problems with fluency and accuracy. Yeh, Cheng, and Chen (2010) sought to develop a PDA-based learning game to support the mental computation of students. They implemented the game on PDA and designed a unique material for studying digits, which sum to ten and applied the game in assisting students practice mental computation and mathematics addition. The evaluation of the game revealed that it motivated the students and increased their mental arithmetic computing speed. Nonetheless, the authors noted that there was no consensus conclusion and the study was a short-term experiment. To improve the reliability of the results, the authors noted that there was need for a long term and more rigorous experimental design for evaluating the system. Main and O’Rourke (2011) also showed that mathematical games enhance computational skills of middle primary school aged children. They used a pilot study to conduct a comparison between traditional teaching approaches and a “commercial off-the-shelf (COTS) handheld game consoles (HGCs)” in order to develop mathematical self-concept and calculations automaticity for year four students in two urban institutions. One class undertook every day sessions applying HGCs as well as training software for improving their mental mathematics skills whereas the control group used more habitual classroom methods. The students were evaluated with standardized examinations at the start as well as the end of the term and the results indicated those who used the HCGs showed considerable improvements in both the accuracy and speed of their self-concept and calculation compared to those in the control group. Pareto, Haake and Lindstrom et al. (2012) study also revealed that educational game in mathematics cause the math comprehension skills to increase significantly. The researchers presented an education game in mathematic founded on apprentice model applying the teachable agent and an assessment study of how the game influences the student conceptual comprehension as well as their attitude towards Maths. A game playing group consisting of 19 students and a control group consisting of students following the regular curriculum was used. The researchers noted that there was not considerable variation in attitude alteration between the control group and game playing group, however their post hoc analysis revealed that game-playing mostly affects the confidence of students in teaching mathematics to a peer, however not their delight to do so. They also discovered that competitive and collaborative activities usually have a strong motivational impact for the learners to play mathematical games. Pareto, Haake and Lindstrom (2012) call for a potential interaction impact of performance, motivation, and social factors when playing mathematical games. They note that a two-fold approach is required to study cognitive and motivation factors as they are intricately related and hence should not be studied in isolation. Unlike other research studies discussed on the positive association between mathematical games and computational skills, Bragg (2012) research findings indicated that mathematical games did not assist students in demonstrating a mathematical comprehension of the concepts subjected to test conditions. Bragg used ten to twelve year old students in eight classrooms in three primary schools using different instructional methods to teach division and multiplication of decimals. Bragg used a quasi-experimental research design with delayed post-test, post-test, and pre-test and the impacts of the interventions were assessed using the written test performance of the children. The results from the tests showed lesser learning benefits in game playing contexts relative to non-game activities. Children learning did not also improve during and after the teacher-led discussions. Bragg argued that teachers should carefully consider the use and suitability of mathematical games before using them as a means of introducing mathematics concepts. Mathematical Games and Numeracy Skills Yen-Hua, Chee-Kit and Chiu-Pin et al. (2012) study revealed that mathematical game, “cross number puzzle” are very beneficial in learning addition as well as subtraction. Schiro (2009) argued that most mathematics games usually put children in charge of generating the numbers they use and hence the problems they solve-frequently by giving children control of number generating devices, such as dice. In doing so, the mathematical games help children to see mathematics as a human endeavor in which they can take part in. This is critical for children to learn if they are to be autonomous users and creators of mathematics according to Schiro (2009). In addition, the games help in memorizing number facts. Schiro (2009) noted that number facts are mostly best memorized in situations that create a need for them to be memorized, offer for adequate repetitive recall of the things that were memorized, supply both desirable and immediate rewards for facts memorization, and also enable children to meaningfully understand facts while memorizing them. Mathematical games usually provide this context. According to Wiest (2006), playing digits and dice help in fostering number sense; place value, number relationships, number representation and counting. Playing dice and digits with computation problems can improve the student understanding of while-number operations. As an example, Wiest noted that the students might be asked to find the largest or smallest positive products, quotient, different and sum of two numbers through plugging numbers into boxes in calculation problems. The games number sense enables students to understand computation procedures. Liedtke (2010) argued that number sense is the key to numeracy and this can be illustrated and reinforced with discussions about the operations with decimals. Wiest (2006) noted that digits and dice could be used in various ways to suit classroom objectives and student capacities. The games may be tailored to many concepts such as whole-number operations, even-odd numbers and divisibility, fractions and decimals and negative numbers. Wiest further argued that number skills can be practiced together with digits and dice, such a reading decimals, fractions and whole numbers correctly and estimating the variation between two numbers or the solution to calculation problems. Mathematical Games and Mathematics Attitudes Some studies have pointed to the positive impact of mathematical games on mathematics attitude (Ke & Grabowski, 2007; Ke, 2008). Both studies used pre and post Tapia’s attitudes towards mathematics inventory in measuring mathematics attitudes after and before their studies in mathematics games. Ke (2008) used a mixed-method case study of fifth and fourth grade students, 4 boys and 10 girls took part in a summer computer mathematics gaming class for five weeks. On the other hand, Ke and Grabowski (2007) investigated 125 5th grade students who were randomly assigned to three diverse mathematics gaming groups undertaken in two forty minute sessions for 4 weeks. The length and timing of the study did not change the results, which pointed to a positive mathematics attitude after playing mathematical games. Conclusion The main area of agreement was that mathematical games play a positive and important role in development of numeracy and computational skills in middle primary school aged students. Most of the reviewed research studies general conclusion indicated that mathematical games lead to increased computation skills, student engagement, motivation, accuracy, and speed of calculation. Nonetheless, Bragg (2012) research findings contradicted these results as they indicated that mathematical games do not assist students in demonstrating a mathematical comprehension. While most of the evidence pointed towards a positive association between mathematical games and numeracy and computation skills, it must also be considered that the studies did not extensively focus on the development, extent and type of computational and numeracy strategies and skills that students use while playing mathematical games. They did not also focus on, whether they transferred the learning to their general mathematics performance. The study of Pareto, Haake and Lindstrom (2012) is a good starting point as it encourages researcher to pay close attention to the potential effects of performance, motivational and social aspects in the context of playing mathematical games. References Ashman, A., & Elkins, J. (2009). Education for inclusion and diversity. (3ed.).Sydney: Prentice Hall Asplin, P., Frid, S., & Sparrow, L. (2006). Game playing to develop mental computation: A case study. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures, and learning spaces, Proceedings of the 29th conference of the Mathematics Education Research Group of Australasia 29, Canberra, 46-53. Bragg, L. (2012). The effect of mathematical games on on-task behaviors in the primary classroom. Math Ed Res J., 24, 385-401 Bragg, L. (2007). Students’ Conflicting Attitudes Towards Games as a Vehicle for Learning mathematics: A Methodological Dilemma. Mathematics Education Research Journal. 19(1), 29-44 Bragg, L. (2012). Testing the effectiveness of mathematical games as a pedagogical tool for children’s learning. International Journal of Science and Mathematics education, 10, 1445-1467 Commonwealth of Australia (2008). National numeracy review report. Commissioned by the Human capital working group. Council of Australian Governments. Garcia, A., Jimenez, J., & Hess, S. (2006). Solving arithmetic word problems: An analysis of classification as a function of difficulty in children with and without arithmetic LD. Journal of Learning Disabilities, 39 (3), 270-281. Ke, F. (2008). A case study of computer gaming for math: Engaged learning from game play? Computers & Education, 51(4), 1609-1620. Ke, F., & Grabowski, B. (2007). Gameplaying for maths learning: Cooperative or not? British Journal of Educational Technology, 38 (2), 249-259. Liedtke, W. (2010). Making mathematics meaningful for students in the intermediate grades. Trafford Publishing. Main, S., & O’Rourke, J. (2011). New Directions for traditional lessons: Can handheld game consoles enhance mental mathematics skills. Australian Journal of Teacher Education, 36(2), 42-55 Miller, S., Stringfellow, J., Kaffar, B., Ferreira, D., & Mancl, D. (2011). Developing computational competence among students who struggle with mathematics. Teaching Exceptional Children, 44(2), 38-46 Pareto, L., Haake, M., Lindstrom, P., Sjoden, B. & Gulz, A. (2012). A teachable-agent-based game affording collaboration and competition: evaluating math comprehension and motivation. Education Tech Research Dev., 60, 723-751 Ryan, A., & Patrick, H. (2001). The classroom social environment and changes in adolescents’ motivation and engagement during middle school.American Educational Research Journal, 38(2), 437-460. Schiro, M. (2009). Mega-Fun Math Games and Puzzles for the Elementary Grades: 125 ready to use activities that teach math facts, concepts and thinking skills. San Francisco, CA: Jossey-Bass Wiest, L. (2006). Fostering number sense through digits & dice. APMC, 11(4), 10-14 Yeh, C., Cheng, H., Chen, Z., Liao, C., & Chan, T. (2010). A Tetris Game to support students mental computation: Design and Evaluation. Proceedings of the 18th International Conference on Computers in Education. Putrajaya, Malaysia. Yen-Hua, C., Chee-Kit, L., Chiu-Pin, L., Yin-Juan, S., & Tak-Wai, C. (2012). Utilizing a Collaborative Cross Number Puzzle Game to Develop the Computing Ability of Addition and Subtraction. Educational Technology & Society, 15 (1), 354–366. Read More