EXPERIMENTAL MATH PROGRAM IN SUMMER CAMP Aikaterini Stamou1, Charalambos Lemonidis2 1
MA Student, Department of Primary Education, University of Western Macedonia
[email protected] 2
Professor, Department of Primary Education, University of Western Macedonia
[email protected]
Abstract The current study explores children’s attitudes and emotions towards mathematics at middle grade levels (ages 8-12). The main purpose of the study is to examine how summer math activities and games in a camp could influence and improve students’ attitude and participation in mathematical education. The central questions of the research are: 1) Can a mathematical program for primary school children be applied in a camp as an educational activity? 2) How does the math program affect students’ emotions and attitudes towards mathematics? and 3) Is there a link between emotions and attitudes of children towards mathematics and participation in the program? To answer the aforementioned questions, a number of relevant activities were selected and developed according to the principles of the teaching of mathematics. The activities were playful, avoided the didactic and tried to keep up with the participants’ psychology in a joyful summer environment. The research sample consisted of 41 students/campers in EuroCamp on the Greek island of Thassos who answered attitudes and feelings towards math pre-test and post-test questionnaires and participated in the camp math activities. The results show that mathematics could be integrated in a camp program and children could come into contact with the subject in an out-ofclassroom environment in an interesting and productive way. The findings also indicate that children find math camp activities attractive and consider them pleasant summer activities. Finally, the majority of children in the experiment demonstrated positive emotions and feelings of love for mathematics. Keywords: math camp, attitudes, out of school mathematics, activities. Introduction Bibliography on Math camp concerns both primary and secondary education. It involves mathematical programs aiming to improve mathematical
education and its effects. The findings of the research focus mainly on children’s mathematical knowledge and skills before and after the programs, but also on their emotions and attitudes towards the subject. The basic finding is that Math camp was acknowledged by educational communities as a successful academic intervention which helps students to improve their performance in Mathematics and boosts their self confidence in solving mathematical problems (Wiest, 2008). The present research is part of the same hopeful framework. It is an effort to make mathematics meaningful for children through an interesting and appealing mathematical program in a summer camp. The goal of this research is to pave the way for the study of leisure time mathematics in Greece and to apply out-of-school programs that relate mathematics to real life, knowledge to creative pastime, thought to pleasure and fun. The field of the research was a typical summer camp with a mainly athletic program. Theoretical background As mentioned before, math camp is considered a successful educational intervention aimed at improving mathematical education in terms of research. However, not a lot of math camp programs have been developed. On the contrary, they cover long time periods and they appear improved and adjusted to curriculums. Two such programs – Ling Siew-Eng’s, Lai KimLeong’s, Ling Siew-Ching’s (2010) in Malaysia for primary education and Lydia Wiest’s (2008) in North Nevada for middle school girls – provide important research findings. According to the first research in Malaysia most students had a positive attitude towards mathematics before participating in the camp, and participation showed that this attitude had improved by the end of math camps (Ling et al., 2009). Positive results also appeared in the second research, where students and their parents reported greater knowledge and skills, better marks, increased participation in program issues and better social skills as benefits of the children’s participation in the program (Wiest, 2008). As far as the activities are concerned, they had been influenced by the philosophy of math camps according to Edward et al. (2001), and most of them involved team building, interesting, entertaining mathematics and mathematics related to students’ everyday lives. Cognitively they were related to the areas of problem solving and logic and their types were entertainment and social skills, games and stages. According to Cooper et al. (2006) these activities help students believe in their abilities, reinforcing
their self confidence and self-esteem and motivate them to meet challenges successfully (Ling et al., 2009). An important factor in math camp was, apart from the participating students, the accompanying teachers. Through the programs they realized that math camp provides students with opportunities to take on different challenges. They noted that their students enjoy the activities, they are motivated to learn and they feel excited about learning mathematics. The teachers agreed that math camp is beneficial for all students, providing them with the chance to participate in different challenging and interesting activities (Ling et al., 2009). Moreover, parental involvement played a successful and essential role in the camp. Feeling like family was a basic principle in the organization of math camp by Edward et al. (2001) along with students’ interaction and teambuilding learning. Students felt like being in the family environment, they were motivated by their families to learn mathematics and found support in developing their mathematical skills. Parents expressed the hope of continuing math camps in the future, so that more students would have the opportunity to attend the math camp program (Ling et al., 2009; Wiest, 2008). Based on the literature review and the findings of relevant studies we can assume that a mathematical program is applicable in a summer camp and it can become a creative part of its curriculum. Moreover, we assume that its application affects students’ attitudes towards mathematics positively and it is considered an enjoyable summer activity and a creative pastime. Finally, we assume that children’s attitude and feelings towards mathematics are directly related to their participation in the mathematical program of the camp. The aforementioned assumptions constitute the basic lines of the present research, whose method is going to be presented below. Method Tools. Ten (10) activities with precise mathematical content and specific teaching goals were designed for the research. In particular, the activities were: 1) “Mental race”, 2) “Tell me a number” and 3) “Abstract lost his hat” involved natural numbers and engaged students in mental calculation and applied strategies. They helped children to practice in the analysis of natural numbers to their sum and in the quick verbal recognition of natural numbers. 4) “Dishes with dots” involved the recognition of numerical quantities through schematical standards (subitizing). In this way students practiced
quick and correct reproduction or from memory pronunciation of the number that each model represented. 5) “Counting with shadow” and 6) “The giant’s paw” involved the mathematical concepts of ratio and proportion in measurements. In the first activity students found the ratios of accessible objects for their shade and calculated the inaccessible height point (tree or building) through ratio. In the second activity students used the proportions of the human body to calculate the height of a giant based on the length of his paw. 7) “Odd - Even ... with jokes!’’ involved even and odd natural numbers. Students distinguished between them and understood that an even number is of the form 2n, while an odd number is of the form 2n + 1. 8) “Animate tangram” involved the mathematical concepts of geometric shape and measurement and intertwined mathematics with literature. Students listened to a story and at selected points made shapes with 7 pieces of tangram, recognizing geometric figures and comparing them. 9) “Travel in fractions country” connected mathematics to literature. Students dealt with fractions, transported into the magical space of the story, and solved problems in ways that contain conceptual understanding. This gradually led to the procedural and purely mathematical solution. 10) “3D card - surprise for my friend” concerned geometric shapes and especially transformations. Students formed geometric shapes by folding paper, constructed both two-dimensional and three-dimensional shapes, named them and discussed the forms and their properties. Participants. Forty one (41) students/campers (27 males and 14 females), aged from 8 to 12 participated in the program. All of them come from north east Greece. They are all primary school students in grades 2-5. The researcher. The researcher applied the mathematical program. She was a member of the camping staff and attended all daily activities in order to become familiar with students/campers and encourage their participation in the mathematical program. Data sources. Methods used to collect data: pre-tests and post-tests, questionnaires, observation and researcher’s notes. A questionnaire with 45 items on a five-point Likert-type scale (1 = totally disagree, …, 5 = totally agree) was used to measure students’ attitudes towards mathematics. Reverse scoring was also used for statements in negative terms. The items focused on four aspects of attitudes towards mathematics: 1. Value (e.g. Mathematics is important and useful),
2. Joy / pleasure (e.g. I enjoy studying mathematics at school), 3. Confident (e.g. Studying mathematics makes me feel nervous). 4. Motivations (e.g. I like the challenge of mathematics) The questions 1-40 come from Attitude Towards Mathematics Inventory (ATMI) questionnaire (Tapia & Marsh, 2004), which was slightly adapted for our research. Five questions (41-45) were added relevant to the connection between mathematics, camp and games (e.g. I like playing mathematic games in camp). Supplementarily, an open question questionnaire was also used. The questions in the pre-test concerned the children’s attitude towards mathematics, the reason for this attitude and their attitude towards the camp. The ones in the post-test concerned their views and thoughts after their participation in the program. The questions concerning the usefulness and the applications of mathematics in everyday life were the same in both tests. Procedure. The researcher visited the students/campers in their cabins on the second day of their arrival at the camp. She discussed with them their attitude towards mathematics and informed them about the research. The children decided to participate in the mathematical program freely and filled in the pre-test questionnaires in one hour (60’) without the researcher being present (1st day). The application of the mathematical program started in the afternoon of the same day. The activities took place on the beach in the morning (10:3012:30) or during noon at rest time (3:00-5:00) or during the afternoon activities (5:30-7:30). They were relevant to a range of mathematical areas (Arithmetic, Geometry, Stochastic Mathematics, Problem Solving, Mental Calculations) and they were designed as a game. The program lasted eleven (11) days. On the last day it was evaluated by the students through the post-test questionnaires immediately after it was completed and while the experience of attending it was still vivid. The posttests were filled in again the same way as the pre-tests were. The researcher discussed with the students/campers and wrote down what they thought about participating in the program. Results Quantitative analysis Children’s attitudes towards mathematics in pre-tests and post-tests are categorized as shown in table 1.
Table1: Frequency and mean score of attitudes by type per test attitudes strong negative negative neutral positive strong positive total
pre-test post-test frequency mean (%) frequency mean (%) 1 2.4 0 0.0 0 0.0 1 2.4 7 17.1 6 14.7 10 24.4 11 26.8 23 56.1 23 56.1 41 100.0 41 100.0
In pre-tests attitudes range from neutral to strong positive. The great majority of children appear to show a strong positive attitude and children with a positive attitude follow. Next are the children with a neutral attitude, while there are no children with a negative attitude. There is only one (1) child showing a strong negative attitude. In post-tests the percentage of 80.5% where both the strong positive and positive attitudes had gathered together during the pre-test research rose to 82.9%. The one (1) strong negative attitude turned into negative and the neutral one turned into positive. Generally, both before and after the application of the program most children had a positive attitude towards mathematics. This finding leads us to the assumption that there is a strong relation between children’s emotions and attitudes towards mathematics and their participation in the mathematical program. Qualitative analysis Children’s emotions towards mathematics. In the open sentence of the pre-test “Describe your emotions generally towards mathematics” most students expressed positive emotions, three (3) neutral and three (3) negative ones. Some typical children’s answers were “Mathematics is a great subject and I„d like to do maths all day. I feel wonderful when I have this lesson” (positive emotions), “I have no emotions towards maths” (neutral emotions), “Maths is a torture to me” (negative emotions). In the question of the pre-test “Why do you have the emotions that you described in the previous question towards mathematics?” children with positive emotions mentioned as reasons the pleasure and aesthetic enjoyment that the subject offers, the fact that mathematics is an easy subject and their ability to cope with it, the stimulation of interest during the lesson of mathematics, the usefulness of the subject, the good teacher and the opportunity for cooperation that mathematics has to offer.
Mathematics in children’s everyday lives. The question “Do you believe that Mathematics appear in everyday life? Yes/No and Why?” was set in both tests. In the pre-test 92.7% (38 children) seemed to consider that mathematics appear in life, while only 7.3% (3 children) mentioned the opposite. In the post-test all children (100%) answered positively. In the sentence “If you answered “Yes” to the previous question, write as many cases as you can think of where Mathematics appear in everyday life” the children answered in the pre-test that mathematics is used in trades, in banking transactions, in professions, in school and in problem solving. They also mentioned measurements, cooking, vacations and games, studies, quick calculations and the development of logical thinking. The answers were similar in the post-test, too. Children’s emotions towards camping and game. In the question of the pre-test “Describe your emotions towards camping and game generally” all children noted positive emotions towards camping and associated the activities there with game and entertainment. The reasons for their positive emotions were the feelings of joy, pleasure and entertainment that camping offers, the game as dominant in camping, the development of friendship/feeling of warmth, the variety of the activities, the athletic activities and gaining new knowledge. More specifically, the children mentioned “When I come to the camp, I feel excited”, “Camping is holidays and you have fun”, “I like camping, because I have a lot of fun”, “I enjoy being at the camp very much, because we play a lot of games”, “Camping is great, because I have good friends and play very good games”, “I met new friends. I liked Mrs [the camp leader]”, “I like it and it feels like a big family”, “I like camping, because it has a lot of activities”, “I like camping, because you work out and you can do sports”, “I like it a lot, because I learn new things”. The questions of the post-test gave significant answers regarding the impact of the mathematical program on students/campers. So, to the question “What did you and what didn‟t you like about the mathematical activities of the camp? Comment on your emotions and your impressions after participating in them” the children answered all activities or specific activities, like mental calculations, origami creations, the giant’s paw, tangram, the joy and satisfaction they felt, the spirit of cooperation and helping each other, the game and the fun, first place in problem solving and new knowledge. In the question “How did mathematical activities affect the way you see mathematics?” twenty three (23) students/campers (56.1%) mentioned that the program changed their attitude towards mathematics for the better.
Thirteen (13) students (31.7%) stated that the program did not affect the way they see mathematics, because their attitude was already positive and they loved it. Four (4) students (9.8%) stated that they were not affected by the program and their attitude remained neutral. Finally, one (1) student (2.4%) who expressed a strong negative attitude in the pre-test and a negative attitude in the post-test, did not change his attitude towards mathematics and replied “[I see maths] the same”. However, it is evident that the way of expression had become moderate compared to the one in the pre-test, where he confessed that mathematics is a torture to him. In the question “What is your opinion about the activities at the camp that combine Mathematics with game?” thirty-nine (39) students (95.1%) described the activities of the mathematical program positively. Specifically, they mentioned that the activities were pleasant and enjoyable, they related mathematics to game, they were interesting, they made mathematics more popular with children and they were educational. Finally, in the question “What did you learn from your participation in the mathematical activities at the camp?” thirty-nine (39) students (95.1%) stated that they benefited a lot from the program. There were general answers, like “A lot of new things”, “A lot of great things”, and answers on specific subjects, like “I learned how to do shapes in tangram”, “How to construct things”, “[I learned ] How to calculate a giant‟s height by looking at his paw”. Also, answers on specific skills, like “[I learned] How to combine game with mathematics”, “[I learned] how to think more quickly and easily”. Answers on personal skills, like “[I learned] That I can do better at mathematics”, “[I learned] to cooperate”. Answers regarding the usefulness of mathematics, like “[I learned] That I can use maths in many useful ways”, “That [with mathematics] you can do a lot of cool stuff” and, finally, answers regarding the nature of mathematics, like “I learned that there is more in maths than just operations”. Conclusion The results of the research lead to the following conclusions. Regarding the question of whether a mathematical program for primary school children can be applied in a camp, the results showed that the students enriched their experience and felt that they had become better at mathematics. One (1) student stated that she had gained a bigger confidence in school mathematics after the math camp program, while most students confirmed that they learned several interesting things. The same finding is confirmed through the international research, according to which students improve their knowledge, skills and performance in math camp (Branch, 1999; Wiest, 2008).
Regarding the second question of the research, that is, the way the mathematical program affected students’/campers’ attitudes towards mathematics, more than half of the students stated that the mathematical program led them to express a more positive attitude towards the subject. The number is impressive, if we take into account that 80.5% of the students participated in the program having a positive attitude towards the subject. This is also respective to previous studies, according to which Math Camps improved students’ attitude towards Mathematics (Ling et al., 2009; Wiest, 2008; Tichebir & Plavchan, 2010), introduced the idea of fun while learning Mathematics (Edward et al., 2001; Hall, 2006; Ling et al., 2009), prolonged the joy of learning (Beer et al., 2008; Hall, 2006; Ling et al., 2009) and motivated participants to learn (Beer et al., 2008; Ling et al., 2009). A very big percentage of children (80.5%) who participated in the program expressed emotions of love for mathematics when answering the third question of the research on the relation between children’s emotions and attitudes towards mathematics and their participation in the program. This finding matches the 53.2% of the Model of Mathematical Camp in Malaysia (Wiest, 2010) where a big percentage of children showed positive attitude towards Mathematics before the beginning of the camp. Consequently, most students that participate in math camp programs have a positive attitude towards mathematics, while this percentage increases after their participation. Other interesting parts of the research are the type of mathematical activities at the camp and parental involvement in their children’s mathematical program. The activities suggested in the bibliography on Math Camps are entertaining and designed as games. As for parental involvement, proposed for the camp, it was an informal incident in our case. Some parents that lived on the camp were interested in the mathematical program and asked for information. They were positive towards it and stated that it would be interesting to include it in the camp program on a regular basis. Lastly, they discussed their part in their children’s mathematical education and the assistance they could offer, while they also expressed their concern about their children’s progress in mathematics of upper cognitive levels. Finally, the mathematical program of the present research was evaluated as interesting and successful. It was included in the program of a typical summer camp with a curriculum of mainly athletic activities. The literal review has not studied it as a case. Respective mathematical programs were applied in specialized camps - Math Camps - exclusively orientated towards mathematical education and its didactic purposes. For this reason it could be
maintained that it is a unique, interesting and successful application, although certain teachers assumed that the combination of mathematics and holidays could pressure children psychologically. As an extension of this research, it would be useful for future study to investigate the application of the mathematical program to a purely training camp which will include it in the daily program. Also, it would be interesting to investigate the effect of a mathematical program on campers/students in a training camp, where many parents enroll their children in summer, as they work in large urban centers. Bibliography Lauer, P. A., Akiba, M., Wilkerson, S. B., Apthorp, H. S., Snow, D., & Martin-Glenn, M. (2004). The Effectiveness of Out-of-School-Time Strategies in Assisting Low-Achieving Students in Reading and Mathematics: A Research Synthesis. Updated. Lemonidis, Ch. (2013). Nature and Life Mathematics: Mental calculations. Thessaloniki: Zygos. [InGreek]. Siew-Eng, L., Kim-Leong, L., & Siew-Ching, L. (2010). Mathematics Camp Model for Primary School. Procedia-Social and Behavioral Sciences, 8, 248-255. Siew-Eng, L., Kim-Leong, L., & Siew-Ching, L. (2009). The Effect of Mathematics Camp: Stake Holders Perception and Pupils Attitude towards Mathematics. Paper presented at the International conference on educational research and practice (ICERP) 2009, Putrajaya, Malaysia. Tichenor, M., & Plavchan, J. (2010). Summer camps: A fun way to reinforce math skills. Journal of Instructional Psychology, 37(1), 71-76. Van de Walle, J. A. (1990). Elementary School Mathematics, Teaching Developmentally. Addison-Wesley/Longman, Route 128, Reading, MA 01867. Wiest, L. (2008). Conducting a Mathematics Camp for Girls & Other Mathematics Enthusiasts. Australian Mathematics Teacher, 64(4), 1724. Wiest, L. R. (2004). Impact of a summer mathematics and technology program for middle school girls. Journal of Women and Minorities in Science and Engineering, 10(4).
