Conclusions and Implications
In my action research project, students explored various math concepts through a curriculum that was centered on playing different math games. Some of the games were used to introduce new concepts, some were used to practice a math concept following a short mini-lesson, while others were meant to help students review math content they previously learned. In a 1985 monograph, Bright, Harvey, and Wheeler categorized these games into three groups; pre-instructional, co-instructional, and post-instructional. Many of the math games involved cooperative learning, either working in teams of three or four students or in partnerships. My primary goals of implementing a curriculum centered on math games were as follows:
· to provide students with fun and playful, yet rigorous experiences in math that would
help to improve their attitudes towards math.
· to present learning opportunities that reached a variety of readiness levels.
· to engage students in more cooperative learning.
· to increase student comprehension in math.
As I analyzed various data collected throughout my project, and observed how students responded to different math games, some common themes surfaced. I used various tools such as surveys, exit slips, student work samples, interviews, and anecdotal observations to gather data about how students felt about math and how they viewed themselves as mathematicians. From my initial data, it was clear that there was a high level of what Fillier calls “Math Phobia,” or a complete fear of mathematics (2005). From within the first week of school, I noticed many of my students initially did not like math and experienced extremely low self confidence in math. When asked in a survey which learning experience students preferred to learn through, the majority of students chose games as their response. This led me to believe that when students were learning math through more playful experiences, they would begin to enjoy the subject more, rather than fear it.
Indeed, this is exactly what I found happened as my study progressed. Students’ attitudes began to shift from strongly disliking math, or even feeling fearful towards math, to actually enjoying it and looking forward to coming to my math class. Through various exit cards, interviews and surveys, students responded extremely positively about the math games we played and said they wanted to play more games. As students entered the classroom and saw a game planned on the agenda, I would hear hoots and hollers of excitement. Many students expressed a strong desire to play math games and have stated that until this year, they did not like math. Students were having fun and their confidence in their own math abilities grew. The feelings of fear and hatred towards math shifted in a positive direction towards enjoyment. When I asked students for feedback about how math was going for them, often students would state that they would like to play even more math games. I used their feedback to help guide and direct my action research project. This gain in student’s self confidence within their own math abilities carried over to a variety of learning experiences in math. Hopefully, they take this new found self confidence though their future years of schooling.
After analyzing various exit cards students wrote after playing different games, I realized that games provide a great tool for differentiating for students’ various readiness level. However, I learned through this process and by reading student feedback that some games did not differentiate as much as others. This had a direct correlation with how students felt about a specific game. Students tended to enjoy the games that offered more differentiation; one student wrote, “The problems were just right for me and I could solve them. It was a fun game.” I noticed that with games that allowed for students to work at their own pace and were differentiated to match their readiness level, such as the Subtraction Football game, students exemplified more self confidence and seemed to feel more comfortable while playing the game. Whereas other games that were timed and more competitive, that usually involved students answering identical problems, seemed to rush students and cause more student anxiety. As a whole, students tended to not enjoy these games as much as others. Prior to planning a math game, it is essential to plan ways to differentiate for a variety of learning styles and abilities in order to address a wide spectrum of readiness levels found within one classroom of students. Since one of my primary goals was to increase students’ self confidence, differentiating for my various students was a necessity. I began to lean towards games that focused more on cooperation, rather than competition.
In life, it is essential for people to learn how to work cooperatively with one another. Few careers or jobs do not require this skill. Many students begin my class having little to no experience with working in a team setting within math. The majority of math games I planned required students to work cooperatively in either teams of three or four, or in partnerships. I found many connections between student engagement levels and cooperative learning. I observed and documented the amount of “on task” comments verses “off task” comments spoken within the following two contexts: firstly while students were playing a math game with a partner and secondly while students were working with a team of four to solve a problem set out of our textbook. According to Dotzel, Welsh, Pressley, and Vincent, engagement is defined as, “… a high degree of on-task behavior with tasks that are appropriately academically demanding and worthwhile for students” (2003, p.243). The amount of students’ “on task” comments were considerably higher while playing a math game compared to working on a set of problems out of our text book. Therefore, one can conclude that student engagement is considerably higher while playing math games verses working out of a text book. On another instance, I had my principal come in to observe my teaching. I had planned a math game show for that day. He wrote me a letter raving about the high levels of student engagement during the lesson and how nearly every student seemed focused and determined to solve the math problems presented in the game show. I have found that math games not only increase cooperative learning, but also raise student engagement levels within a cooperative learning setting.
One of the biggest challenges for me throughout this project was finding a way to pinpoint the affects of math games on student achievement. I measured student achievement while focusing on two different aspects of student learning; the students’ ability to articulate their math thinking and the students’ ability to accurately solve problems. Since math games provide an abundance of opportunities for students to teach their problem solving strategies and discuss their solutions with one another, students became comfortable sharing their math thinking with the class as a whole. They transitioned from saying something like, “I got ___ as my answer” to “I got ____ as my answer because I know that…” As students began to feel more comfortable explaining and writing about their thinking, their confidence grew and they began to comprehend various math concepts at a much deeper level.
Another way I measured the affects of games on student comprehension was through quick pre and post math problems. After answering the pre math problem, students would play a math game and then answer a similar math problem directly after playing the game. I found that most students that answered the problem incorrectly before playing the game would no longer make the same mistake during the post game math problem. I think this increase in accuracy for problem solving was due to a combination of things. First, students were working closely with their partner or teams and often times, the game required them to teach their partner how they came to their solution. I also contribute this gain in student comprehension to a higher level of student engagement. Dozel described a teacher as “…lessons were not just hands-on, but minds on as well” (2003, p.254). When students are involved in their learning, they are far more likely to understand.
Tips for Teachers: What are some essentials when planning a math game?
My journey through creating a classroom culture of collaboration where math games were an integral part of our learning was not always a smooth journey. There were many road blocks and bumps along the way. Below, are some pointers to help set up a classroom culture built on collaboration where kids are doing math together, sharing their learning and relying on each other for success. These pointers will also hopefully help you avoid the bumps and road blocks I encountered along my journey. In addition to my own pointers, I also met with a small group of students to cooperatively create a list of aspects about various math games they have played that they really enjoyed and found useful. Some ideas are more student generated than others. Here is what we have come up with.
It is important to play a variety of games. Some students like games that involve a component of competition, while others respond better to games more geared to cooperation and collaboration. A healthy balance seemed to work for my students. There are so many different types of games, see what your students respond best to and be sure to mix the type of games up for them.
While planning for a math game, think about your students’ readiness levels. I found it helpful to group students heterogeneously, or with mixed learning abilities. However, if the gap between each students’ comprehension level was too wide, I observed that often one of more students would either get bored, frustrated, or discouraged. You know your students best. As you observe your students actually playing the game, don’t be afraid to modify a game on the spot for students that seem to be struggling, or need more of a challenge. Some ways to do this include, giving students more challenging or easier numbers to work with, changing student groupings, encouraging students to work together in order to problem solve, and creating various leveled problems according to your students current readiness levels. At times, if I noticed a group of students struggling with a game, I would join their group and play with them. This would help provide students with a model on how to play the game effectively and how to communicate and behave while playing the game.
Be sure to “close the loop” with your students after playing a math game. With every math lesson I teach, including playing math games, I always save a few minutes at the end of the class to summarize what we have learned that day. This helps students reflect on and solidify their understanding about a particular concept. I find often students can summarize what they have learned in more effective ways than I can. By having students share one “take away” from that class, or something they learned that they will take with them, students not only begin to look at math concepts from different perspectives, but also become more proficient in articulating their math thinking. When students listen to how their classmates think about a particular concept, hmany will gain a deeper level of comprehension, or have an “ah ha” moment where things begin to click for them and make sense. I know that often times, we are pressed for time. We look at the clock and think, “Ah, class is almost over!” For these occasions, I would often have my students partner up with another group and do a quick “take away” pair share. This allows them to still share their thinking while hearing another group’s perspective on what they learned for the day. Other times when time permitted, students shared what they learned with the class as a whole.
Building a Culture of Teamwork: You may encounter certain groups that are not working effectively together. I know at times, I did. Here are some helpful ways to either prevent this, or help remedy these types of teamwork problems. Remember, building a respectful classroom culture of collaboration begins on day one of the school year and is a process that happens over time.
Be flexible with your grouping: Experiment with ways that students are grouped together. At times, I would choose my students’ teams, while other times, I would let students pick their partners. See what works best for your students. When students join together in new teams, I try to plan some sort of ice breaker, or get to know your teammates activity. Often, we assume that students in our class all know each other well, which is in fact not always the case. Brainstorm with your class what an effective and supportive team looks like and sounds like. I also have students give non examples as well. Be sure to acknowledge respectful behaviors that you observe while students are working with their teams. Point these examples out to the entire class.
When I notice students are having disagreements while working together, I first observe them to see if they can come to an agreement. If not, I might intervene by joining their group to help diffuse, or mediate the situation. There have been occasions where two students are just not getting along with one another and my interventions do not seem to help. As a last resort, I have switched groups around according to who I believe will work well together.
Games that involve “cool new things” are more fun: When you introduce new materials, such as the double sided dice, or a new spinner, students become more excited and involved. However, you want to be sure to not overuse these novelties, or students might become bored.
A teacher’s enthusiasm and excitement about playing a math game in contagious. This will spread like wild fire to the students. Pump it up, teachers!
I have found that games not only help students enjoy math, but they also make teaching math more fun. Who doesn’t like to play? It is easy for teachers to become comfortable in their ways of teaching and fall into the patterns of repeating the same curriculum year after year. However, as I had previously experienced, this can become very boring and monotonous for both the students and the teacher. Making games an integral part of my math curriculum has totally rejuvenated me as a teacher and also refreshed many of my students who did not yet realize that math can be fun. Many teachers think that math games are frivolous or just “time fillers.” While some are, many are not. Playing math games can provide invaluable learning experiences for our students, while making them fun as well. We need to challenge the notion that “rigorous” equals working from a text book If more schools began to see the value in not only a curriculum that included various games, but also a culture of collaboration and teamwork, then less of our students would enter our classes fearing math and not seeing the importance of it. We live in a world run by technology and math. Johnson and Johnson stated, “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). Having the skills and knowledge mathematics nurtures can help our kids to become successful, contributing members of our society.
· to provide students with fun and playful, yet rigorous experiences in math that would
help to improve their attitudes towards math.
· to present learning opportunities that reached a variety of readiness levels.
· to engage students in more cooperative learning.
· to increase student comprehension in math.
As I analyzed various data collected throughout my project, and observed how students responded to different math games, some common themes surfaced. I used various tools such as surveys, exit slips, student work samples, interviews, and anecdotal observations to gather data about how students felt about math and how they viewed themselves as mathematicians. From my initial data, it was clear that there was a high level of what Fillier calls “Math Phobia,” or a complete fear of mathematics (2005). From within the first week of school, I noticed many of my students initially did not like math and experienced extremely low self confidence in math. When asked in a survey which learning experience students preferred to learn through, the majority of students chose games as their response. This led me to believe that when students were learning math through more playful experiences, they would begin to enjoy the subject more, rather than fear it.
Indeed, this is exactly what I found happened as my study progressed. Students’ attitudes began to shift from strongly disliking math, or even feeling fearful towards math, to actually enjoying it and looking forward to coming to my math class. Through various exit cards, interviews and surveys, students responded extremely positively about the math games we played and said they wanted to play more games. As students entered the classroom and saw a game planned on the agenda, I would hear hoots and hollers of excitement. Many students expressed a strong desire to play math games and have stated that until this year, they did not like math. Students were having fun and their confidence in their own math abilities grew. The feelings of fear and hatred towards math shifted in a positive direction towards enjoyment. When I asked students for feedback about how math was going for them, often students would state that they would like to play even more math games. I used their feedback to help guide and direct my action research project. This gain in student’s self confidence within their own math abilities carried over to a variety of learning experiences in math. Hopefully, they take this new found self confidence though their future years of schooling.
After analyzing various exit cards students wrote after playing different games, I realized that games provide a great tool for differentiating for students’ various readiness level. However, I learned through this process and by reading student feedback that some games did not differentiate as much as others. This had a direct correlation with how students felt about a specific game. Students tended to enjoy the games that offered more differentiation; one student wrote, “The problems were just right for me and I could solve them. It was a fun game.” I noticed that with games that allowed for students to work at their own pace and were differentiated to match their readiness level, such as the Subtraction Football game, students exemplified more self confidence and seemed to feel more comfortable while playing the game. Whereas other games that were timed and more competitive, that usually involved students answering identical problems, seemed to rush students and cause more student anxiety. As a whole, students tended to not enjoy these games as much as others. Prior to planning a math game, it is essential to plan ways to differentiate for a variety of learning styles and abilities in order to address a wide spectrum of readiness levels found within one classroom of students. Since one of my primary goals was to increase students’ self confidence, differentiating for my various students was a necessity. I began to lean towards games that focused more on cooperation, rather than competition.
In life, it is essential for people to learn how to work cooperatively with one another. Few careers or jobs do not require this skill. Many students begin my class having little to no experience with working in a team setting within math. The majority of math games I planned required students to work cooperatively in either teams of three or four, or in partnerships. I found many connections between student engagement levels and cooperative learning. I observed and documented the amount of “on task” comments verses “off task” comments spoken within the following two contexts: firstly while students were playing a math game with a partner and secondly while students were working with a team of four to solve a problem set out of our textbook. According to Dotzel, Welsh, Pressley, and Vincent, engagement is defined as, “… a high degree of on-task behavior with tasks that are appropriately academically demanding and worthwhile for students” (2003, p.243). The amount of students’ “on task” comments were considerably higher while playing a math game compared to working on a set of problems out of our text book. Therefore, one can conclude that student engagement is considerably higher while playing math games verses working out of a text book. On another instance, I had my principal come in to observe my teaching. I had planned a math game show for that day. He wrote me a letter raving about the high levels of student engagement during the lesson and how nearly every student seemed focused and determined to solve the math problems presented in the game show. I have found that math games not only increase cooperative learning, but also raise student engagement levels within a cooperative learning setting.
One of the biggest challenges for me throughout this project was finding a way to pinpoint the affects of math games on student achievement. I measured student achievement while focusing on two different aspects of student learning; the students’ ability to articulate their math thinking and the students’ ability to accurately solve problems. Since math games provide an abundance of opportunities for students to teach their problem solving strategies and discuss their solutions with one another, students became comfortable sharing their math thinking with the class as a whole. They transitioned from saying something like, “I got ___ as my answer” to “I got ____ as my answer because I know that…” As students began to feel more comfortable explaining and writing about their thinking, their confidence grew and they began to comprehend various math concepts at a much deeper level.
Another way I measured the affects of games on student comprehension was through quick pre and post math problems. After answering the pre math problem, students would play a math game and then answer a similar math problem directly after playing the game. I found that most students that answered the problem incorrectly before playing the game would no longer make the same mistake during the post game math problem. I think this increase in accuracy for problem solving was due to a combination of things. First, students were working closely with their partner or teams and often times, the game required them to teach their partner how they came to their solution. I also contribute this gain in student comprehension to a higher level of student engagement. Dozel described a teacher as “…lessons were not just hands-on, but minds on as well” (2003, p.254). When students are involved in their learning, they are far more likely to understand.
Tips for Teachers: What are some essentials when planning a math game?
My journey through creating a classroom culture of collaboration where math games were an integral part of our learning was not always a smooth journey. There were many road blocks and bumps along the way. Below, are some pointers to help set up a classroom culture built on collaboration where kids are doing math together, sharing their learning and relying on each other for success. These pointers will also hopefully help you avoid the bumps and road blocks I encountered along my journey. In addition to my own pointers, I also met with a small group of students to cooperatively create a list of aspects about various math games they have played that they really enjoyed and found useful. Some ideas are more student generated than others. Here is what we have come up with.
It is important to play a variety of games. Some students like games that involve a component of competition, while others respond better to games more geared to cooperation and collaboration. A healthy balance seemed to work for my students. There are so many different types of games, see what your students respond best to and be sure to mix the type of games up for them.
While planning for a math game, think about your students’ readiness levels. I found it helpful to group students heterogeneously, or with mixed learning abilities. However, if the gap between each students’ comprehension level was too wide, I observed that often one of more students would either get bored, frustrated, or discouraged. You know your students best. As you observe your students actually playing the game, don’t be afraid to modify a game on the spot for students that seem to be struggling, or need more of a challenge. Some ways to do this include, giving students more challenging or easier numbers to work with, changing student groupings, encouraging students to work together in order to problem solve, and creating various leveled problems according to your students current readiness levels. At times, if I noticed a group of students struggling with a game, I would join their group and play with them. This would help provide students with a model on how to play the game effectively and how to communicate and behave while playing the game.
Be sure to “close the loop” with your students after playing a math game. With every math lesson I teach, including playing math games, I always save a few minutes at the end of the class to summarize what we have learned that day. This helps students reflect on and solidify their understanding about a particular concept. I find often students can summarize what they have learned in more effective ways than I can. By having students share one “take away” from that class, or something they learned that they will take with them, students not only begin to look at math concepts from different perspectives, but also become more proficient in articulating their math thinking. When students listen to how their classmates think about a particular concept, hmany will gain a deeper level of comprehension, or have an “ah ha” moment where things begin to click for them and make sense. I know that often times, we are pressed for time. We look at the clock and think, “Ah, class is almost over!” For these occasions, I would often have my students partner up with another group and do a quick “take away” pair share. This allows them to still share their thinking while hearing another group’s perspective on what they learned for the day. Other times when time permitted, students shared what they learned with the class as a whole.
Building a Culture of Teamwork: You may encounter certain groups that are not working effectively together. I know at times, I did. Here are some helpful ways to either prevent this, or help remedy these types of teamwork problems. Remember, building a respectful classroom culture of collaboration begins on day one of the school year and is a process that happens over time.
Be flexible with your grouping: Experiment with ways that students are grouped together. At times, I would choose my students’ teams, while other times, I would let students pick their partners. See what works best for your students. When students join together in new teams, I try to plan some sort of ice breaker, or get to know your teammates activity. Often, we assume that students in our class all know each other well, which is in fact not always the case. Brainstorm with your class what an effective and supportive team looks like and sounds like. I also have students give non examples as well. Be sure to acknowledge respectful behaviors that you observe while students are working with their teams. Point these examples out to the entire class.
When I notice students are having disagreements while working together, I first observe them to see if they can come to an agreement. If not, I might intervene by joining their group to help diffuse, or mediate the situation. There have been occasions where two students are just not getting along with one another and my interventions do not seem to help. As a last resort, I have switched groups around according to who I believe will work well together.
Games that involve “cool new things” are more fun: When you introduce new materials, such as the double sided dice, or a new spinner, students become more excited and involved. However, you want to be sure to not overuse these novelties, or students might become bored.
A teacher’s enthusiasm and excitement about playing a math game in contagious. This will spread like wild fire to the students. Pump it up, teachers!
I have found that games not only help students enjoy math, but they also make teaching math more fun. Who doesn’t like to play? It is easy for teachers to become comfortable in their ways of teaching and fall into the patterns of repeating the same curriculum year after year. However, as I had previously experienced, this can become very boring and monotonous for both the students and the teacher. Making games an integral part of my math curriculum has totally rejuvenated me as a teacher and also refreshed many of my students who did not yet realize that math can be fun. Many teachers think that math games are frivolous or just “time fillers.” While some are, many are not. Playing math games can provide invaluable learning experiences for our students, while making them fun as well. We need to challenge the notion that “rigorous” equals working from a text book If more schools began to see the value in not only a curriculum that included various games, but also a culture of collaboration and teamwork, then less of our students would enter our classes fearing math and not seeing the importance of it. We live in a world run by technology and math. Johnson and Johnson stated, “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). Having the skills and knowledge mathematics nurtures can help our kids to become successful, contributing members of our society.
