Understandings:
“Young people learn a great deal about the world through play, and games are one source of play” (cited by Cavanagh, 2006, p. 46)
Student anxiety about math
Our country is facing an epidemic in many schools called math-phobia, an extreme fear of mathematics. Students who have had bad experiences learning math often develop this phobia and, in turn, struggle learning various concepts because they feel they are unable to do the math (Resek & Rupley, 1980). Many researchers have found that after fourth grade, students’ attitudes about math often change and they begin to dislike and avoid math. This fear and avoidance of math often gets carried with them throughout their schooling and can limit their career opportunities later in life. As math anxiety increases, their academic achievement and performance inevitably decreases (Fillier, 2005). Students who suffer from this anxiety are often afraid of making mistakes and of asking what they think are dumb questions (Johnson & Johnson, 1991). Teachers must work towards breaking this cycle of math-phobia in order to insure the success of all students.
There are several causes of math anxiety including parent and teacher attitudes, teaching methods, previous experiences and societal influences (Fillier, 2005). Both teachers’ and parents’ attitudes about math often get passed down to students. If they feel anxious about math, or do not value its importance and relevance, then often the students will pick up on that attitude as well. There are several teaching strategies that can also perpetuate this math anxiety, such as being taught directly from a textbook without differentiating for a variety of learning styles or abilities, or if students are made to feel there is only one way to solve a problem, inhibiting creativity. Certain societal stereotypes can also inhibit a student’s performance in math. The idea that men are better at math than women, math ability is inherited and you either have it or you don’t, and math problems only have one correct answer, all affect a student’s attitude towards math. It is essential for people to become aware of these causes of math anxiety in order to limit and prevent them (Fillier, 2005).
As teachers, we need to be sensitive to this anxiety towards math and continuously work towards building students’ self confidence. There are many ways that we can reduce or eliminate math anxiety in the classroom. Studies have found that allowing students to work on math in a less traditional environment often eases their fear about learning math. When referring to a less traditional classroom, I mean a classroom that does not follow the model of teacher lecture followed by students working independently on answering a set of math problems. A less traditional classroom might include more math projects and games where students explore various math concepts as opposed to just learn a procedure. When students are having fun and playing they are more relaxed, which will help them learn math concepts as well as increase their self confidence and the belief that they are capable (Resek & Rupley, 1980). When certain students of mine feel overwhelmed with a math concept we are learning, they will often shut down, therefore retaining minimal content. For these students especially, we need to boost their self-esteem and confidence by showing them difficult math concepts can be fun to learn, and they will be successful in doing so.
Creating a math curriculum that incorporates multiple opportunities to explore math through games will ease students’ fears about learning math (Cavaneigh, 2006; Allen & Main, 1976). Since children learn best through hands-on exploration, games are one strategy to increase student understanding in math. Published in the journal, Teaching Exceptional Children (2005), Shaftel, Pass, and Schnabel wrote:
Mathematic games allow the learner many opportunities to reinforce current knowledge and try out strategies or techniques without fear of getting the “wrong” answer… Games can provide an environment for experiencing incorrect solutions not as mistakes but as in steps in connecting pieces of mathematical knowledge. (2005, p. 26)
Math games also help spark interests in math within students that otherwise might not feel confident. This type of math community that sparks students’ interests, will also allow students to embrace the many mistakes from which mathematicians learn and grow.
Research has proven that math games help to close the achievement gap in minority schools. Studies have found that students’ performance in math is generally lower among ethnic minorities and lower income schools. The 2003 Trends in International Mathematics and Science Study (TIMMS) found eighth grade achievement was 57 points higher in schools with fewer students coming from low income households. Cavanagh (2006) refers to a study by Seigler, Geetha, and Ramani which introduced various math related board games into Head Start Preschools, a program that primarily serves children from low income areas. Students played these board games four times a week for a two week period of time. They found that students’ knowledge of number sense increased greatly by the end of the two week period. I hope that making math games an integral part of my math curriculum will help to close the achievement gap that I have observed within my own classroom. I also believe that if I can plan opportunities for students to play math games with their families at home, not only will this reinforce specific math concepts, but the cycle of math-phobia might come to a close. As I further research the effects of math games on student engagement and achievement, I will continue to uncover new and old games that can help transform students’ attitudes about math and aid in breaking down the math-phobia that exists today.
Traditional Math Education vs. Math Games
Although there has been much reform in the way math is taught, many math curriculums are still structured for the purpose of teaching students a plethora of isolated math concepts, often incorporating a “drill and kill” method of teaching. This does not encourage students to develop a strong conceptual foundation, making it very difficult for them to make relevant connections. It also does not teach students how to problem solve and reason mathematically (Johnson & Johnson, 1991). The 2003 TIMMS study found that the most commonly used instructional activities in math classrooms were teacher lecture, teacher-guided student practice and students working independently on a set of problems. Through numerous classroom observations and interviews, Stodolsky, Salk and Glaessner (1991) also found that in the typical math classroom, especially found in public school classes, the math teacher explains a concept or math algorithm to the whole class, followed by students working individually at their seats in their text books or on worksheets. There is little to no team work, and everyday often follows a similar pattern. Students frequently experience feelings of high anxiety and shame in these classes and tend to become extremely bored. Many students in turn adopt the attitude of either, “I can do it” or “I can’t do it.” This attitude, along with commonly accepted societal beliefs about math ability being inherited, cause students to give up and shut down, often following this pattern through their entire life (Stodolsky, et al, 1991).
Studies have found only nine percent of American 13-year olds could understand certain math concepts compared to forty percent of their Korean counterparts (Kadijevich, D., 2003). Johnson and Johnson state in Learning Mathematics in a Cooperative Classroom, “Children born today will enter a work force where knowledge about mathematics is crucial to their career opportunities, their participation in society, and their conduct in their private lives” (1994, p. 1). If we want our students to be successful members of society, we need to reform the way we teach math in order to close this math achievement gap. Teachers and curriculum developers must acknowledge that math is more than memorizing rules and procedures. These findings help me to understand the negative baggage that my students often bring to my math class. As a teacher, I need to break up the monotony of what many students have experienced in math class and show them that they will not only have fun in my class, but also feel successful learning math.
Research has shown that students are more likely to be actively engaged in learning math while playing games and doing hands-on projects rather than learning in the traditional math classroom. Educators have been researching the effects of math games verses traditional math instruction for many years. In 1976, Allen and Main conducted a research study in the inner city of Detroit, Michigan where high student absenteeism rates plagued the school. The essential question they sought to answer was whether or not a learning environment organized around games has a positive effect on students’ attitudes towards learning. In order to increase student learning in math, they felt it was essential for students to attend school in the first place. This led them to focus on ways they could minimize student absenteeism within their school. They studied two types of untracked traditional seventh grade math classes. One continued with their usual, more traditional math curriculum daily, while the other implemented an equations based math game and tournament two days a week. The math tournament, called Equations, allowed for students to compete against each other based on their own mathematical ability, while cooperating with teammates in order to create challenging questions for their opponents to answer. This study continued for two semesters and the ratio of student absences to the total number of days was compared among both groups of students. The teacher noticed that students were pushing themselves to create and answer challenging problems that were purely student generated, and many students playing this tournament developed an “I can do it” attitude. During cooperative team activities such as this game, students were working problems out together, explaining their ideas to each other and discussing their strategies for the Equations tournament with one another. Allen and Main found a dramatic decrease in the number of student absences within the classroom consistently playing the Equations Tournament. In fact, they found the non-absenteeism rate was over three times higher than that of students in the traditional math classrooms. They suspected that the main reason for student absenteeism rates decreasing in classrooms that involved math games was because these students developed more positive attitudes towards math.
Students are more apt to achieve and grapple with difficult math concepts if they are engaged in their learning. When students dislike school or a particular class, they are less likely to grasp concepts being taught. Stodolsky, Salk and Glaessner write, “As educators, we must seriously assess the presumed contribution schooling itself makes in the development of attitudes, beliefs, and conceptions that students hold toward different school subjects” (1991, p. 113). The strategies we use to teach different subjects greatly impact the students’ attitudes towards that class and that subject matter.
Implementing Math Games
Games are one form of math instruction and should be implemented along with other learning experiences. In a 1985 monograph, Bright, Harvey, and Wheeler write about the effects of learning through math games and categorize games into three categories; pre-instructional, post-instructional, and co-instructional. A pre-instructional game is played to introduce and launch a concept before it is explicitly taught. Post-instructional games are played in order to review concepts previously taught and co-constructional games are played to teach new concepts or accompany direct instruction. Most games involve a challenge against a task or opponent and require following a set of rules and structures. Bright and his colleagues stress that it is essential for the teacher to determine and state the instructional objectives clearly and explicitly to the students before playing the game. The rules and format of the game need to be clearly modeled and taught to the students as well, prior to playing the game. This helps to eliminate any student confusion about the game. As with all great teaching practices, it is vital to know exactly what students’ academic abilities are and group them together accordingly.
There are several variables that affect the quality of an instructional math game, such as the format of the game, the content of the game, the instructional level of the game and the level of peer interaction and competition. Many teachers use games to “…trick students into paying attention before the ‘real teaching’ starts, or as a reward for students who finish their work early” (Klawe & Phillips, 1995, p. 2). This does not allow for games to become an integral part of the curriculum. Instead, it sends the message to students that games are not important or worthwhile. In Math Games for Adolescents, Shaftel, Pass and Schnabel (2005) state specific cautions for using math games in the classroom. In order to continue to motivate students, they argue it is important for teachers to not over-use math games. Like anything in the classroom, students will get bored by having the same experiences over and over again. Teachers should also watch out for excessive competition and over stimulation among students. Games should be fun for students and not stressful. It is also imperative to consider the complexity of the rules and the math content covered in the game as well as the physical requirements and social skills needed for students to be successful while playing. One challenge I have come across is the difficulty of pin pointing exactly what my students are achieving while playing a math game. In order to hold them accountable for their learning, I have used multiple strategies for assessing student knowledge during math games. When discussing how to present challenging, yet accessible math problems, Resek and Rupley write:
A very delicate balance must be sought where students are pushed and challenged, yet do not become so frustrated that they give up. If they are not challenged, they will not gain the self confidence they need to survive future courses, and, more importantly, they will not feel the sense of mastery, which makes doing mathematics enjoyable. (1980, p. 428)
Through the implementation of my action research project, I worked towards creating this balance.
Benefits of Math Games
There are countless benefits of math games. According to research, math games can increase student engagement in the classroom, provide ample opportunities for cooperative learning, and help to increase student achievement levels. I discuss each of these below.
Engagement
A recent study on how teachers motivate and engage their students conducted by Dolezal, Welsh, Pressley, and Vincent (2003) explores a variety of strategies to increase student engagement in the classroom; they define engagement as, “…a high degree of on-task behavior with tasks that are appropriately academically demanding and worthwhile for students” (p. 243). They observed nine teachers over the course of the year, interviewing them and their students and tracking students’ engagement and achievement levels. Students were determined to be engaged if they were actively participating in the task at hand and doing what the teacher asked of them. Based on their findings and results, teachers were classified into three separate categories; low, moderately and highly engaging. Researchers observed negative classroom management, students not being challenged or interested in what they were learning and unenthusiastic teachers in the five less engaging classrooms. Creative thinking and problem solving were rarely encouraged and students were most often off task. The four moderately engaging teachers used many highly motivating teaching strategies, but they were assigned to low difficulty leveled tasks. However, the two highly engaging teachers used numerous motivating strategies and required students to accomplish cognitively challenging tasks. Students’ desks were arranged in table groups that promoted collaboration and cooperation, and within both of these classrooms teachers tried to make content interesting, challenging, and playful.
When referring to highly engaging activities, Dolezal, Welsh, Pressley, and Vincent state, “These activities often captured students’ attention by providing opportunities to use manipulatives, play a game, create a skit, or design art. As a result, students were enthusiastic as the teacher introduced lessons” (2003, p. 252). Projects were planned and games played that actively involved all students. When describing a highly engaging teacher, the authors also claim, “Ms. Irving’s lessons were not just hands-on but minds-on as well” (p. 254). Students in these extremely engaging classrooms were consistently focused on the task at hand (Dolezal et al., 2003). Although this study focused solely on student engagement, I looked at both student engagement and achievement. Throughout my action research project, I sought to prove in my classroom that higher levels of student engagement and on-task behaviors will lead to an increase in my students’ achievement levels. Students must be active, rather than passive, in the learning process.
I do not want my math classroom to be a boring and dry place for my students; instead, I want to show students that learning math can be fun and playful. I believe students are more likely to remember their colorful math experiences, such as playing games and doing projects rather than the more dull and dry “drill and kill” methods of teaching math. My 6th grade students are so active and playful with each other. Many of them are constantly tapping on the desks or moving around in their seat. Shouldn’t we make learning math more active and playful for them? Children’s brains and bodies are not wired to sit in their seats for long periods of time and listen to their teacher talk. This is not how they learn best. They learn through doing and talking and playing (Dolezal, et al., 2003). In order to increase student engagement in my classroom, I created more playful experiences that provide opportunities for my students to be “doing” math in a fun and energetic way.
Cooperative Learning
Teaching various math concepts through playing games will give students numerous opportunities to work cooperatively with each other. There is evidence that cooperative learning helps students learn math, while increasing student engagement. For the past 40 years, math classrooms have been structured for students to work primarily independently; competing against their peers for higher grades and test scores. This not only creates a negative community atmosphere, but is also detrimental to a student’s self esteem and helps to perpetuate anxiety about math (Johnson & Johnson, 1991).
According to Johnson and Johnson (1991), cooperative learning exists when students are working together to achieve a specific shared goal. The goal of the team is not only for each student to learn the math, but to ensure that all group members are successful as well. In an effectively structured cooperative learning math lesson, students have the opportunities to explain what they are learning to each other, hear other points of views, and observe a variety of ways to solve a problem and give and get support from their peers. Giving students opportunities to communicate about math is essential in helping them acquire meaning and leads to a deeper understanding about a concept. Evidence also suggests that cooperative learning helps to promote positive social relationships among students, increases students’ self esteem about math and creates more positive attitudes towards mathematics (Johnson, Johnson & Holubec, 1994). Students who might feel anxiety sharing their ideas with the entire class often feel more comfortable sharing in smaller groups. These are among many of the benefits of cooperative learning.
Implementing more cooperative learning opportunities through games in my math class helped to fight the anxiety many students feel about the subject. Research supports the notion that students gain more self confidence in their own math abilities while working cooperatively, rather than working independently in more competitive classroom environment (Johnson, Johnson & Holubec, 1994). Since students are receiving, as well as giving, each other immediate help and feedback, they are more likely to develop an “I can do it” attitude about themselves, increasing their confidence in their ability to learn math. In cooperative group settings, students are more comfortable making mistakes and taking risks. Risk-taking is extremely important for students to be successful in learning math, as it reaffirms the idea that mistakes make for valuable learning opportunities.
To further explore the effects of cooperative learning, the Electronic Games for Education in Math and Science (E-GEMS) conducted a study at an interactive science museum called Science World, in 1993. Whether in a classroom, or at a child’s home, they noticed that children naturally gather together in groups around video games and computers. This is what guided their research. They set up a computer exhibit that involved playing a game called The Incredible Machine (TIM), requiring players to build “Rube Goldberg” machines out of an assortment of parts to perform various challenges the computer would pose. An example of a challenge is building a machine to shoot a basketball in a hoop while trapping a mouse in a cage. Children could choose from various parts such as ropes, pulleys, trampolines, elastics and so forth. The exhibit was set up into three different sections; one solo play machine where a child could play by his or her self, another parallel play section where two children played on side-by-side machines and finally, an integrated play machine in which two children played together on one machine. Throughout this two month long exhibit, over ten thousand randomly chosen children participated and hundreds of children were interviewed. The partnerships formed were single gendered. Inkpen and colleagues (1993) found that both boy and girl partnerships playing on the one integrated machine solved considerably more puzzles than those individual children playing on the solo and parallel machines. They also noticed that girls solved fewer puzzles competing against each other on the parallel machine compared to the solo machine. They seemed to be most successful while working cooperatively, yet least successful when put in more competitive situations. They also observed that more children would play for the entire 30 minute session on the integrated machines. This led them to believe that the different stations affected the children’s motivation and engagement (Inkpen, K et al., 1993). If used effectively, cooperative learning, particularly while playing math games, can be used to increase motivation and engagement within the classroom.
Achievement
Andy Isaacs, the director of the third edition of Everyday Mathematics stated, “Not only do games engage students, they also present the opportunity to present “high level” math concepts in a colorful and simple way” (Isaacs as cited in Cavanagh, 2006 p. 46). Since student participation levels are higher while playing games, retention of math concepts overtime is also higher (Shaftel, Pass, & Schnabel, 2005). In order to present challenging math concepts in “colorful” ways that lead to increased math achievement, I feel it is essential to include math games throughout my curriculum.
Using technology is a very efficient way to incorporate math games throughout my curriculum. Although I do not have a class set of computers readily available within the construct of my classroom walls, I do have access to a computer lab. As it is evident that educational reform must occur within our country, there have been extensive studies on the impact of educational technology on student achievement. In 1998, Harold Wenglinsky assessed the effects of computer simulation and higher order thinking technologies on a sample of 6,227 fourth graders and 7,146 eighth graders throughout our country. He emphasized the importance of higher order thinking because he found that while many teachers use technology throughout their curriculum, they use computers for drill and practice methods that do not require students to apply higher order thinking skills. He sought out to verify that if computers were used effectively for learning games that require higher order thinking, then student achievement would inevitably increase. His report examined and interpreted the results of a national study conducted by the National Assessment of Educational Progress (NAEP). This is a national study that is given every two years to evaluate trends in student performance and achievement over time. The NAEP includes surveys and questionnaires that are given to students, teachers, and principles and encompass various subject areas. For the first time ever, the NAEP included in depth questions about technology.
Wenglinsky (1998) examined the relationship that technology played on both the academic achievement, measured by standardized tests as well as the social environment of the school, encompassing student tardiness, teacher and student absenteeism and student and teacher morale. He found that the use of computer learning games that required students to use higher order thinking skills positively affected academic achievement. He also found a positive relationship between teachers receiving professional development in the use of computer learning games to their students’ academic achievement. When both professional development and higher order computer learning games were utilized within fourth grade classrooms, students’ academic achievement level increased by about a tenth of a grade level, or a few weeks of instruction. This growth was far more substantial in eighth grade classrooms, with an increase in academic achievement of about one-third of a grade level. However, this study does not take into consideration the characteristics of the different teachers, therefore making it difficult to pinpoint the results solely on higher order thinking computer learning games. It is evident that computer learning games are one of many different teaching tools that can help increase student achievement in the classroom (Wenglingsky, 1998). If when used for higher order thinking skills, computer learning games help to increase student achievement, then it is vital to increase school funding for not only computer access in the classrooms, but professional development that will enable teachers to feel more confident using technology in an effective manner.
In the study described above, math achievement was measured by the use of standardized testing, however, achievement can be measured in a variety of other ways, including tests, quizzes, projects, and student observations. One example of measuring achievement is found in the 2003 TIMMS research study. Four benchmarks levels that described math achievement on an international level were created based on what students knew and could do mathematically. The categories developed were Advanced, High, Intermediate and Low. Eighth grade students in the advanced category demonstrated their knowledge of a variety of mathematic concepts in more complex problem solving situations. They could “organize information, make generalizations, solve non-routine problems and draw and justify conclusions from the data” (p.62). Students in the High benchmark “can apply their understanding and knowledge in a variety of relatively complex situations” (p.62). In the Intermediate Benchmark, students “can apply basic mathematical knowledge in straightforward situations” (p. 62). Lastly, students in the Low Benchmark “have some basic mathematical knowledge” (p.62). The results of the study demonstrate the idea that successful problem solving is a result of mastering the math concepts and skills needed. Results of the study show that in both the fourth and eighth grades, Singapore was the top performing country with their average achievement levels considerably higher than any other country. So what does a typical math lesson look like in Singapore? What math instructional strategies do they implement in order to increase their student achievement levels? These are crucial questions for me to further explore in order to learn and grow from other countries’ successes in teaching math. Through my journey into researching the effects of math games on student achievement, I have found a significant gap in the research. This gap has inspired me to design my action research around specifically games and achievement in order to provide educators with concrete data that can help fill this void I have observed.
Why examine students’ attitudes towards math?
Within most facets of life, personal attitudes are often what drive us towards success or failure. Math is a subject that evokes very strong feelings that greatly influence a student’s ability to learn and develop a deep conceptual understanding. The TIMS study mentioned above examined the relationship between three dimensions of mathematics attitude to math achievement. This study included 137,346 eighth graders from thirty three countries. An instrument was developed to measure how students’ attitudes towards math affected their academic achievement in math. There were numerous statements in which students scaled their answers from 1-4. Mathematics attitudes were categorized into three separate groups: students’ perception on learning math or self-confidence; whether the students liked or disliked math; and lastly, how useful the students felt math was for them. Although results from this study varied from country to country due to the varying mathematics instruction practiced in the classrooms, there were important findings which remained consistent across the study (Kadijevich, 2003). Self confidence in learning math was directly related to math achievement in thirty one countries studied. Students in countries with higher levels of math achievement demonstrated higher self confidence and were more likely to believe they were capable and successful when learning math. Researchers also found a positive correlation between students who liked math and math achievement. Because self confidence is so directly related to students’ academic performance and achievement, it is vital for teachers to design curriculum around building students’ self confidence. We need to arrange our classrooms in a way that allow students to experience success and not failure when investigating math.
As my students leave their elementary schools and enter my sixth grade classroom, I can usually pick out the majority of students that feel negatively, or anxious, towards math. As they write me a “get to know you” letter about themselves, these students are the first to express their concerns and apprehensions about math. Identifying a student’s initial attitude towards math was essential to helping them break the math-phobia they may have developed throughout their previous years of schooling. Math-phobia creates a wall that needs to be broken down in order for students to be successful learning math. Their attitudes about math seem to be directly linked to their academic successes or failures in the classroom. Because of this, I examined student attitudes about math along with their achievement and engagement levels in various learning contexts. Since students’ attitudes are strong predictors of levels of engagement and achievement, it was essential for me to explore their attitudes towards mathematics over time and use my findings to drive my action research project. When students are exposed to a curriculum that is centered on various math games, my hopes was that there would be a shift in students’ attitude and an increase in student achievement.
Student anxiety about math
Our country is facing an epidemic in many schools called math-phobia, an extreme fear of mathematics. Students who have had bad experiences learning math often develop this phobia and, in turn, struggle learning various concepts because they feel they are unable to do the math (Resek & Rupley, 1980). Many researchers have found that after fourth grade, students’ attitudes about math often change and they begin to dislike and avoid math. This fear and avoidance of math often gets carried with them throughout their schooling and can limit their career opportunities later in life. As math anxiety increases, their academic achievement and performance inevitably decreases (Fillier, 2005). Students who suffer from this anxiety are often afraid of making mistakes and of asking what they think are dumb questions (Johnson & Johnson, 1991). Teachers must work towards breaking this cycle of math-phobia in order to insure the success of all students.
There are several causes of math anxiety including parent and teacher attitudes, teaching methods, previous experiences and societal influences (Fillier, 2005). Both teachers’ and parents’ attitudes about math often get passed down to students. If they feel anxious about math, or do not value its importance and relevance, then often the students will pick up on that attitude as well. There are several teaching strategies that can also perpetuate this math anxiety, such as being taught directly from a textbook without differentiating for a variety of learning styles or abilities, or if students are made to feel there is only one way to solve a problem, inhibiting creativity. Certain societal stereotypes can also inhibit a student’s performance in math. The idea that men are better at math than women, math ability is inherited and you either have it or you don’t, and math problems only have one correct answer, all affect a student’s attitude towards math. It is essential for people to become aware of these causes of math anxiety in order to limit and prevent them (Fillier, 2005).
As teachers, we need to be sensitive to this anxiety towards math and continuously work towards building students’ self confidence. There are many ways that we can reduce or eliminate math anxiety in the classroom. Studies have found that allowing students to work on math in a less traditional environment often eases their fear about learning math. When referring to a less traditional classroom, I mean a classroom that does not follow the model of teacher lecture followed by students working independently on answering a set of math problems. A less traditional classroom might include more math projects and games where students explore various math concepts as opposed to just learn a procedure. When students are having fun and playing they are more relaxed, which will help them learn math concepts as well as increase their self confidence and the belief that they are capable (Resek & Rupley, 1980). When certain students of mine feel overwhelmed with a math concept we are learning, they will often shut down, therefore retaining minimal content. For these students especially, we need to boost their self-esteem and confidence by showing them difficult math concepts can be fun to learn, and they will be successful in doing so.
Creating a math curriculum that incorporates multiple opportunities to explore math through games will ease students’ fears about learning math (Cavaneigh, 2006; Allen & Main, 1976). Since children learn best through hands-on exploration, games are one strategy to increase student understanding in math. Published in the journal, Teaching Exceptional Children (2005), Shaftel, Pass, and Schnabel wrote:
Mathematic games allow the learner many opportunities to reinforce current knowledge and try out strategies or techniques without fear of getting the “wrong” answer… Games can provide an environment for experiencing incorrect solutions not as mistakes but as in steps in connecting pieces of mathematical knowledge. (2005, p. 26)
Math games also help spark interests in math within students that otherwise might not feel confident. This type of math community that sparks students’ interests, will also allow students to embrace the many mistakes from which mathematicians learn and grow.
Research has proven that math games help to close the achievement gap in minority schools. Studies have found that students’ performance in math is generally lower among ethnic minorities and lower income schools. The 2003 Trends in International Mathematics and Science Study (TIMMS) found eighth grade achievement was 57 points higher in schools with fewer students coming from low income households. Cavanagh (2006) refers to a study by Seigler, Geetha, and Ramani which introduced various math related board games into Head Start Preschools, a program that primarily serves children from low income areas. Students played these board games four times a week for a two week period of time. They found that students’ knowledge of number sense increased greatly by the end of the two week period. I hope that making math games an integral part of my math curriculum will help to close the achievement gap that I have observed within my own classroom. I also believe that if I can plan opportunities for students to play math games with their families at home, not only will this reinforce specific math concepts, but the cycle of math-phobia might come to a close. As I further research the effects of math games on student engagement and achievement, I will continue to uncover new and old games that can help transform students’ attitudes about math and aid in breaking down the math-phobia that exists today.
Traditional Math Education vs. Math Games
Although there has been much reform in the way math is taught, many math curriculums are still structured for the purpose of teaching students a plethora of isolated math concepts, often incorporating a “drill and kill” method of teaching. This does not encourage students to develop a strong conceptual foundation, making it very difficult for them to make relevant connections. It also does not teach students how to problem solve and reason mathematically (Johnson & Johnson, 1991). The 2003 TIMMS study found that the most commonly used instructional activities in math classrooms were teacher lecture, teacher-guided student practice and students working independently on a set of problems. Through numerous classroom observations and interviews, Stodolsky, Salk and Glaessner (1991) also found that in the typical math classroom, especially found in public school classes, the math teacher explains a concept or math algorithm to the whole class, followed by students working individually at their seats in their text books or on worksheets. There is little to no team work, and everyday often follows a similar pattern. Students frequently experience feelings of high anxiety and shame in these classes and tend to become extremely bored. Many students in turn adopt the attitude of either, “I can do it” or “I can’t do it.” This attitude, along with commonly accepted societal beliefs about math ability being inherited, cause students to give up and shut down, often following this pattern through their entire life (Stodolsky, et al, 1991).
Studies have found only nine percent of American 13-year olds could understand certain math concepts compared to forty percent of their Korean counterparts (Kadijevich, D., 2003). Johnson and Johnson state in Learning Mathematics in a Cooperative Classroom, “Children born today will enter a work force where knowledge about mathematics is crucial to their career opportunities, their participation in society, and their conduct in their private lives” (1994, p. 1). If we want our students to be successful members of society, we need to reform the way we teach math in order to close this math achievement gap. Teachers and curriculum developers must acknowledge that math is more than memorizing rules and procedures. These findings help me to understand the negative baggage that my students often bring to my math class. As a teacher, I need to break up the monotony of what many students have experienced in math class and show them that they will not only have fun in my class, but also feel successful learning math.
Research has shown that students are more likely to be actively engaged in learning math while playing games and doing hands-on projects rather than learning in the traditional math classroom. Educators have been researching the effects of math games verses traditional math instruction for many years. In 1976, Allen and Main conducted a research study in the inner city of Detroit, Michigan where high student absenteeism rates plagued the school. The essential question they sought to answer was whether or not a learning environment organized around games has a positive effect on students’ attitudes towards learning. In order to increase student learning in math, they felt it was essential for students to attend school in the first place. This led them to focus on ways they could minimize student absenteeism within their school. They studied two types of untracked traditional seventh grade math classes. One continued with their usual, more traditional math curriculum daily, while the other implemented an equations based math game and tournament two days a week. The math tournament, called Equations, allowed for students to compete against each other based on their own mathematical ability, while cooperating with teammates in order to create challenging questions for their opponents to answer. This study continued for two semesters and the ratio of student absences to the total number of days was compared among both groups of students. The teacher noticed that students were pushing themselves to create and answer challenging problems that were purely student generated, and many students playing this tournament developed an “I can do it” attitude. During cooperative team activities such as this game, students were working problems out together, explaining their ideas to each other and discussing their strategies for the Equations tournament with one another. Allen and Main found a dramatic decrease in the number of student absences within the classroom consistently playing the Equations Tournament. In fact, they found the non-absenteeism rate was over three times higher than that of students in the traditional math classrooms. They suspected that the main reason for student absenteeism rates decreasing in classrooms that involved math games was because these students developed more positive attitudes towards math.
Students are more apt to achieve and grapple with difficult math concepts if they are engaged in their learning. When students dislike school or a particular class, they are less likely to grasp concepts being taught. Stodolsky, Salk and Glaessner write, “As educators, we must seriously assess the presumed contribution schooling itself makes in the development of attitudes, beliefs, and conceptions that students hold toward different school subjects” (1991, p. 113). The strategies we use to teach different subjects greatly impact the students’ attitudes towards that class and that subject matter.
Implementing Math Games
Games are one form of math instruction and should be implemented along with other learning experiences. In a 1985 monograph, Bright, Harvey, and Wheeler write about the effects of learning through math games and categorize games into three categories; pre-instructional, post-instructional, and co-instructional. A pre-instructional game is played to introduce and launch a concept before it is explicitly taught. Post-instructional games are played in order to review concepts previously taught and co-constructional games are played to teach new concepts or accompany direct instruction. Most games involve a challenge against a task or opponent and require following a set of rules and structures. Bright and his colleagues stress that it is essential for the teacher to determine and state the instructional objectives clearly and explicitly to the students before playing the game. The rules and format of the game need to be clearly modeled and taught to the students as well, prior to playing the game. This helps to eliminate any student confusion about the game. As with all great teaching practices, it is vital to know exactly what students’ academic abilities are and group them together accordingly.
There are several variables that affect the quality of an instructional math game, such as the format of the game, the content of the game, the instructional level of the game and the level of peer interaction and competition. Many teachers use games to “…trick students into paying attention before the ‘real teaching’ starts, or as a reward for students who finish their work early” (Klawe & Phillips, 1995, p. 2). This does not allow for games to become an integral part of the curriculum. Instead, it sends the message to students that games are not important or worthwhile. In Math Games for Adolescents, Shaftel, Pass and Schnabel (2005) state specific cautions for using math games in the classroom. In order to continue to motivate students, they argue it is important for teachers to not over-use math games. Like anything in the classroom, students will get bored by having the same experiences over and over again. Teachers should also watch out for excessive competition and over stimulation among students. Games should be fun for students and not stressful. It is also imperative to consider the complexity of the rules and the math content covered in the game as well as the physical requirements and social skills needed for students to be successful while playing. One challenge I have come across is the difficulty of pin pointing exactly what my students are achieving while playing a math game. In order to hold them accountable for their learning, I have used multiple strategies for assessing student knowledge during math games. When discussing how to present challenging, yet accessible math problems, Resek and Rupley write:
A very delicate balance must be sought where students are pushed and challenged, yet do not become so frustrated that they give up. If they are not challenged, they will not gain the self confidence they need to survive future courses, and, more importantly, they will not feel the sense of mastery, which makes doing mathematics enjoyable. (1980, p. 428)
Through the implementation of my action research project, I worked towards creating this balance.
Benefits of Math Games
There are countless benefits of math games. According to research, math games can increase student engagement in the classroom, provide ample opportunities for cooperative learning, and help to increase student achievement levels. I discuss each of these below.
Engagement
A recent study on how teachers motivate and engage their students conducted by Dolezal, Welsh, Pressley, and Vincent (2003) explores a variety of strategies to increase student engagement in the classroom; they define engagement as, “…a high degree of on-task behavior with tasks that are appropriately academically demanding and worthwhile for students” (p. 243). They observed nine teachers over the course of the year, interviewing them and their students and tracking students’ engagement and achievement levels. Students were determined to be engaged if they were actively participating in the task at hand and doing what the teacher asked of them. Based on their findings and results, teachers were classified into three separate categories; low, moderately and highly engaging. Researchers observed negative classroom management, students not being challenged or interested in what they were learning and unenthusiastic teachers in the five less engaging classrooms. Creative thinking and problem solving were rarely encouraged and students were most often off task. The four moderately engaging teachers used many highly motivating teaching strategies, but they were assigned to low difficulty leveled tasks. However, the two highly engaging teachers used numerous motivating strategies and required students to accomplish cognitively challenging tasks. Students’ desks were arranged in table groups that promoted collaboration and cooperation, and within both of these classrooms teachers tried to make content interesting, challenging, and playful.
When referring to highly engaging activities, Dolezal, Welsh, Pressley, and Vincent state, “These activities often captured students’ attention by providing opportunities to use manipulatives, play a game, create a skit, or design art. As a result, students were enthusiastic as the teacher introduced lessons” (2003, p. 252). Projects were planned and games played that actively involved all students. When describing a highly engaging teacher, the authors also claim, “Ms. Irving’s lessons were not just hands-on but minds-on as well” (p. 254). Students in these extremely engaging classrooms were consistently focused on the task at hand (Dolezal et al., 2003). Although this study focused solely on student engagement, I looked at both student engagement and achievement. Throughout my action research project, I sought to prove in my classroom that higher levels of student engagement and on-task behaviors will lead to an increase in my students’ achievement levels. Students must be active, rather than passive, in the learning process.
I do not want my math classroom to be a boring and dry place for my students; instead, I want to show students that learning math can be fun and playful. I believe students are more likely to remember their colorful math experiences, such as playing games and doing projects rather than the more dull and dry “drill and kill” methods of teaching math. My 6th grade students are so active and playful with each other. Many of them are constantly tapping on the desks or moving around in their seat. Shouldn’t we make learning math more active and playful for them? Children’s brains and bodies are not wired to sit in their seats for long periods of time and listen to their teacher talk. This is not how they learn best. They learn through doing and talking and playing (Dolezal, et al., 2003). In order to increase student engagement in my classroom, I created more playful experiences that provide opportunities for my students to be “doing” math in a fun and energetic way.
Cooperative Learning
Teaching various math concepts through playing games will give students numerous opportunities to work cooperatively with each other. There is evidence that cooperative learning helps students learn math, while increasing student engagement. For the past 40 years, math classrooms have been structured for students to work primarily independently; competing against their peers for higher grades and test scores. This not only creates a negative community atmosphere, but is also detrimental to a student’s self esteem and helps to perpetuate anxiety about math (Johnson & Johnson, 1991).
According to Johnson and Johnson (1991), cooperative learning exists when students are working together to achieve a specific shared goal. The goal of the team is not only for each student to learn the math, but to ensure that all group members are successful as well. In an effectively structured cooperative learning math lesson, students have the opportunities to explain what they are learning to each other, hear other points of views, and observe a variety of ways to solve a problem and give and get support from their peers. Giving students opportunities to communicate about math is essential in helping them acquire meaning and leads to a deeper understanding about a concept. Evidence also suggests that cooperative learning helps to promote positive social relationships among students, increases students’ self esteem about math and creates more positive attitudes towards mathematics (Johnson, Johnson & Holubec, 1994). Students who might feel anxiety sharing their ideas with the entire class often feel more comfortable sharing in smaller groups. These are among many of the benefits of cooperative learning.
Implementing more cooperative learning opportunities through games in my math class helped to fight the anxiety many students feel about the subject. Research supports the notion that students gain more self confidence in their own math abilities while working cooperatively, rather than working independently in more competitive classroom environment (Johnson, Johnson & Holubec, 1994). Since students are receiving, as well as giving, each other immediate help and feedback, they are more likely to develop an “I can do it” attitude about themselves, increasing their confidence in their ability to learn math. In cooperative group settings, students are more comfortable making mistakes and taking risks. Risk-taking is extremely important for students to be successful in learning math, as it reaffirms the idea that mistakes make for valuable learning opportunities.
To further explore the effects of cooperative learning, the Electronic Games for Education in Math and Science (E-GEMS) conducted a study at an interactive science museum called Science World, in 1993. Whether in a classroom, or at a child’s home, they noticed that children naturally gather together in groups around video games and computers. This is what guided their research. They set up a computer exhibit that involved playing a game called The Incredible Machine (TIM), requiring players to build “Rube Goldberg” machines out of an assortment of parts to perform various challenges the computer would pose. An example of a challenge is building a machine to shoot a basketball in a hoop while trapping a mouse in a cage. Children could choose from various parts such as ropes, pulleys, trampolines, elastics and so forth. The exhibit was set up into three different sections; one solo play machine where a child could play by his or her self, another parallel play section where two children played on side-by-side machines and finally, an integrated play machine in which two children played together on one machine. Throughout this two month long exhibit, over ten thousand randomly chosen children participated and hundreds of children were interviewed. The partnerships formed were single gendered. Inkpen and colleagues (1993) found that both boy and girl partnerships playing on the one integrated machine solved considerably more puzzles than those individual children playing on the solo and parallel machines. They also noticed that girls solved fewer puzzles competing against each other on the parallel machine compared to the solo machine. They seemed to be most successful while working cooperatively, yet least successful when put in more competitive situations. They also observed that more children would play for the entire 30 minute session on the integrated machines. This led them to believe that the different stations affected the children’s motivation and engagement (Inkpen, K et al., 1993). If used effectively, cooperative learning, particularly while playing math games, can be used to increase motivation and engagement within the classroom.
Achievement
Andy Isaacs, the director of the third edition of Everyday Mathematics stated, “Not only do games engage students, they also present the opportunity to present “high level” math concepts in a colorful and simple way” (Isaacs as cited in Cavanagh, 2006 p. 46). Since student participation levels are higher while playing games, retention of math concepts overtime is also higher (Shaftel, Pass, & Schnabel, 2005). In order to present challenging math concepts in “colorful” ways that lead to increased math achievement, I feel it is essential to include math games throughout my curriculum.
Using technology is a very efficient way to incorporate math games throughout my curriculum. Although I do not have a class set of computers readily available within the construct of my classroom walls, I do have access to a computer lab. As it is evident that educational reform must occur within our country, there have been extensive studies on the impact of educational technology on student achievement. In 1998, Harold Wenglinsky assessed the effects of computer simulation and higher order thinking technologies on a sample of 6,227 fourth graders and 7,146 eighth graders throughout our country. He emphasized the importance of higher order thinking because he found that while many teachers use technology throughout their curriculum, they use computers for drill and practice methods that do not require students to apply higher order thinking skills. He sought out to verify that if computers were used effectively for learning games that require higher order thinking, then student achievement would inevitably increase. His report examined and interpreted the results of a national study conducted by the National Assessment of Educational Progress (NAEP). This is a national study that is given every two years to evaluate trends in student performance and achievement over time. The NAEP includes surveys and questionnaires that are given to students, teachers, and principles and encompass various subject areas. For the first time ever, the NAEP included in depth questions about technology.
Wenglinsky (1998) examined the relationship that technology played on both the academic achievement, measured by standardized tests as well as the social environment of the school, encompassing student tardiness, teacher and student absenteeism and student and teacher morale. He found that the use of computer learning games that required students to use higher order thinking skills positively affected academic achievement. He also found a positive relationship between teachers receiving professional development in the use of computer learning games to their students’ academic achievement. When both professional development and higher order computer learning games were utilized within fourth grade classrooms, students’ academic achievement level increased by about a tenth of a grade level, or a few weeks of instruction. This growth was far more substantial in eighth grade classrooms, with an increase in academic achievement of about one-third of a grade level. However, this study does not take into consideration the characteristics of the different teachers, therefore making it difficult to pinpoint the results solely on higher order thinking computer learning games. It is evident that computer learning games are one of many different teaching tools that can help increase student achievement in the classroom (Wenglingsky, 1998). If when used for higher order thinking skills, computer learning games help to increase student achievement, then it is vital to increase school funding for not only computer access in the classrooms, but professional development that will enable teachers to feel more confident using technology in an effective manner.
In the study described above, math achievement was measured by the use of standardized testing, however, achievement can be measured in a variety of other ways, including tests, quizzes, projects, and student observations. One example of measuring achievement is found in the 2003 TIMMS research study. Four benchmarks levels that described math achievement on an international level were created based on what students knew and could do mathematically. The categories developed were Advanced, High, Intermediate and Low. Eighth grade students in the advanced category demonstrated their knowledge of a variety of mathematic concepts in more complex problem solving situations. They could “organize information, make generalizations, solve non-routine problems and draw and justify conclusions from the data” (p.62). Students in the High benchmark “can apply their understanding and knowledge in a variety of relatively complex situations” (p.62). In the Intermediate Benchmark, students “can apply basic mathematical knowledge in straightforward situations” (p. 62). Lastly, students in the Low Benchmark “have some basic mathematical knowledge” (p.62). The results of the study demonstrate the idea that successful problem solving is a result of mastering the math concepts and skills needed. Results of the study show that in both the fourth and eighth grades, Singapore was the top performing country with their average achievement levels considerably higher than any other country. So what does a typical math lesson look like in Singapore? What math instructional strategies do they implement in order to increase their student achievement levels? These are crucial questions for me to further explore in order to learn and grow from other countries’ successes in teaching math. Through my journey into researching the effects of math games on student achievement, I have found a significant gap in the research. This gap has inspired me to design my action research around specifically games and achievement in order to provide educators with concrete data that can help fill this void I have observed.
Why examine students’ attitudes towards math?
Within most facets of life, personal attitudes are often what drive us towards success or failure. Math is a subject that evokes very strong feelings that greatly influence a student’s ability to learn and develop a deep conceptual understanding. The TIMS study mentioned above examined the relationship between three dimensions of mathematics attitude to math achievement. This study included 137,346 eighth graders from thirty three countries. An instrument was developed to measure how students’ attitudes towards math affected their academic achievement in math. There were numerous statements in which students scaled their answers from 1-4. Mathematics attitudes were categorized into three separate groups: students’ perception on learning math or self-confidence; whether the students liked or disliked math; and lastly, how useful the students felt math was for them. Although results from this study varied from country to country due to the varying mathematics instruction practiced in the classrooms, there were important findings which remained consistent across the study (Kadijevich, 2003). Self confidence in learning math was directly related to math achievement in thirty one countries studied. Students in countries with higher levels of math achievement demonstrated higher self confidence and were more likely to believe they were capable and successful when learning math. Researchers also found a positive correlation between students who liked math and math achievement. Because self confidence is so directly related to students’ academic performance and achievement, it is vital for teachers to design curriculum around building students’ self confidence. We need to arrange our classrooms in a way that allow students to experience success and not failure when investigating math.
As my students leave their elementary schools and enter my sixth grade classroom, I can usually pick out the majority of students that feel negatively, or anxious, towards math. As they write me a “get to know you” letter about themselves, these students are the first to express their concerns and apprehensions about math. Identifying a student’s initial attitude towards math was essential to helping them break the math-phobia they may have developed throughout their previous years of schooling. Math-phobia creates a wall that needs to be broken down in order for students to be successful learning math. Their attitudes about math seem to be directly linked to their academic successes or failures in the classroom. Because of this, I examined student attitudes about math along with their achievement and engagement levels in various learning contexts. Since students’ attitudes are strong predictors of levels of engagement and achievement, it was essential for me to explore their attitudes towards mathematics over time and use my findings to drive my action research project. When students are exposed to a curriculum that is centered on various math games, my hopes was that there would be a shift in students’ attitude and an increase in student achievement.
References:
Allen, L., & Main, D. (1976). The Effects of Instructional Gaming on Absenteeism: The First
Step. Journal for Research in Mathematics Education. 7 (2), 113-128.
Bright, G., Harvey, J., & Wheeler, M. (1985). Learning and Mathematic Games. Journal for Research in Mathematics Education. Monograph. (1), 1-189.
Cavanagh, Sean (2006) “Playing Games in Class Helps Students Grasp Math.” Education Week, Nov 2008, 43-46.
Dolezal, S., Welsh, M., Pressley, M., & Vincent, M. (2003). How Nine Third-Grade Teachers
Motivate Student Academic Engagement. The Elementary School Journal. 103 (3), 239- 267.
Fillier, K. (2005) Math Anxiety: Strategies for Preventing, Reducing, and Overcoming the Problem.Faculty of Ed. Submitted to Professor Robert Kelly of Memorial University of Newfoundland.
Inkpen, K., Booth, K., Klawe, M., & Upitis, R. (1993) Playing Together Beats Playing Apart, Especially for Girls. Department of Computer Science, University of British Columbia.
Johnson, David W. & Johnson, Roger, T & Holubec, Edith J. (1994) Cooperative Learning in the Classroom, Alexandria, Virginia: Association for Supervision and Curriculum Development.
Johnson, David W. & Johnson, Roger, T. (1991) Learning Mathematics and Cooperative Learning Lesson Plans for Teachers, Edina, Minnesota: Interactive Book Company.
Kadijevich, D., TIMMS 2003: Relating Dimensions of Mathematics Attitude to Mathematics Achievement. Mathematical Institute of the Serbian Academy of Sciences and Arts, and Megatrend University, Belgrade, Serbia.
Klawe, M. & Phillips, E. (1995) A Classroom Study: Electronic Games Engage Children As Researchers. Department of Computer Science, University of British Columbia.
Kysh, J. & Sallee, T. & Hoey B. (2002) College Preparatory Mathematics (CPM) Foundations for Algebra, Sacramento, California: CPM Educational Program.
McGraw Hill &Wright Group. Teacher’s Guide to Games, An Everyday Mathematics Games. (2003). Chicago, Illinois.
Resek, D., & Rupley, W. (1980). Combating ‘Math-phobia’ with a Conceptual Approach towards Mathematics. Education Studies in Mathematics, 11 (4) 423-441.
Stodolsky, S., Salk, S., & Glaessner, B. (1991). Student Views about Learning Math and Social Studies. American Educational Research Journal. 28 (1), 89-116.
Shaftel, J., Pass, L., & Schnabel. (2005). Math Games for Adolescents. Teaching Exceptional Children. 37 (3), 25-30.
Boston College, TIMMS & PIRLS International Study Center, Lynch School of Education. (2004). TIMMS 2003 International Mathematics Report. Retrieved May 10, 2009, from timss.bc.edu
Wenglingsky, H. (1998). Does it Compute? The Relationship Between Educational Technology and Student Achievement in Mathematics. Educational Testing Service Policy Information Center. Princeton, New Jersey.
